The Fundamentals of Thermal Analysis 9798886977592, 9798886978759

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Renewable Energy: Research, Development and Policies The Fundamentals of Thermal Analysis Mamdouh El Haj Assad, PhD, Ali Khosravi, PhD and Mehran Hashemian, PhD (Editors) 2023. ISBN: 979-8-88697-759-2 (Hardcover) 2023. ISBN: 979-8-88697-875-9 (eBook) Solar Collectors and Systems Mamdouh El Haj Assad, DSc and Mohammad Alhuyi Nazari, PhD (Editors) 2023. ISBN: 979-8-88697-774-5 (Softcover) 2023. ISBN: 979-8-88697-860-5 (eBook) The Future of Solar Power Hussain H. Al-Kayiem (Editor) 2023. ISBN: 979-8-88697-709-7 (eBook) Power Electronic Converters and Induction Motor Drives Jorge Rodas, PhD (Editor) 2022. ISBN: 978-1-68507-950-5 (Hardcover) 2022. ISBN: 979-8-88697-271-9 (eBook) The Future of Wind Energy M. Dhurgadevi, PhD, P. Sakthivel, PhD and K. Gunasekaran, PhD (Editors) 2022. ISBN: 979-8-88697-232-0 (Softcover) 2022. ISBN: 979-8-88697-344-0 (eBook)

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Mamdouh El Haj Assad Ali Khosravi and Mehran Hashemian Editors

The Fundamentals of Thermal Analysis

Copyright © 2023 by Nova Science Publishers, Inc. DOI: https://doi.org/10.52305/VVVP3207 All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. We have partnered with Copyright Clearance Center to make it easy for you to obtain permissions to reuse content from this publication. Please visit copyright.com and search by Title, ISBN, or ISSN. For further questions about using the service on copyright.com, please contact:

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Library of Congress Cataloging-in-Publication Data Names: Assad, Mamdouh El Haj, editor. | Khosravi, Ali, editor. | Hashemian, Mehran, editor. Title: The fundamentals of thermal analysis / Mamdouh El Haj Assad, PhD (editor), Professor, Department of Sustainable and Renewable Energy Engineering, University of Sharjah, Sharjah, UAE, Ali Khosravi, PhD (editor), Associate Professor, Department of Mechanical and Electrical Engineering, University of Southern Denmark (SDU), Denmark, Mehran Hashemian, PhD (editor), Department of Mechanical Engineering, Urmia University, Iran. Description: New York : Nova Science Publishers, 2023. | Series: Renewable energy: research, development and policies | Includes bibliographical references and index. | Identifiers: LCCN 2023021199 (print) | LCCN 2023021200 (ebook) | ISBN 9798886977592 (hardcover) | ISBN 9798886978759 (adobe pdf) Subjects: LCSH: Thermal analysis. | Thermogravimetry. | Thermal analysis--Industrial applications. Classification: LCC QD117.T4 F86 2023 (print) | LCC QD117.T4 (ebook) | DDC 543/.26--dc23/eng20230708 LC record available at https://lccn.loc.gov/2023021199 LC ebook record available at https://lccn.loc.gov/2023021200

Published by Nova Science Publishers, Inc. † New York

This book is dedicated to our families, friends and universities.

Contents

Preface

........................................................................................... ix

Acknowledgment......................................................................................... xi Chapter 1

Applications of Thermogravimetric Analysis (TGA) for Biomass Thermal Characterization ...............1 Bojan Ž. Janković, Nebojša G. Manić and Miloš B. Radojević

Chapter 2

The Use of Thermogravimetric Analysis in the Production of Catalytic Support Formed by CaO and Nb2O5 ............................................53 Paulo Sergio Theodoro, Pedro Augusto Arroyo, Edson Antonio da Silva and Joseane Debora Peruço Theodoro

Chapter 3

Thermoelectric Generators (TEGs) ...............................63 Behnam Talebjedi, Ali Khosravi and Mamdouh El Haj Assad

Chapter 4

Thermal Analysis of Thermoelectric Devices................89 Farzad Tohidi, Mehran Hashemian and Mamdouh El Haj Assad

Chapter 5

Bubble Dynamics Analysis in Subcooled Flow Boiling ...................................................................113 Shahriyar Ghazanfari Holagh and Mohammad Ali Abdous

Chapter 6

Entropy Generation in Flow Boiling and Condensation ..........................................................139 Mohammad Ali Abdous and Shahriyar Ghazanfari Holagh

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Contents

Chapter 7

An Energy Model of Heat Pump Systems for Hot Water Assisted by PV/T Solar Energy in Climates above 15°C .................................................165 Juan Garcia Pabon, Ali Khosravi and Mamdouh El Haj Assad

Chapter 8

3D Numerical Modeling to Evaluate the Thermal Performance of Single and Double U-Tube Ground-Coupled Heat Pumps ...........185 Ali H. Tarrad

Chapter 9

Solid Oxide Fuel Cells ...................................................211 Ali Khosravi, Behnam Talebjedi, Juan Garcia Pabon and Mamdouh El Haj Assad

Index

.........................................................................................239

Editors’ Contact Information ..................................................................243

Preface

Thermal analysis is an important approach to determine the performance of thermal systems for wide range of industrial applications. This book presents a thermal analysis of different systems. Thermal analysis in Chapter 1, emphasized the description of the operation of thermogravimetric (TG) analyser and the influence of various experimental parameters on the quality of measurements in different reaction atmospheres. The study of the measurement accuracy, together with the reproducibility and repeatability required for the accurate thermal characterization of biomass samples by TG were implemented. Chapter 2 presents the evaluation of the mass loss in the production of CaO/Nb2O5 catalysts and obtaining the temperature of interaction between the active phase and the support using thermogravimetric analysis (TGA). Chapter 3 explained thermoelectric generator (TEG) technology along with its different applications on a small and large scale for the energy efficiency improvement of the industrial and domestic sectors. In addition, the TEGs performance mechanism, parameters affecting their performance and efficiency, and the relevant equations have been provided. Moreover, TEG examples for industrial applications is presented. Chapter 4 presents an overview of the analytical modeling of thermoelectric devices, where the basic concepts of thermoelectricity. The chapter provides a comprehensive understanding of the analytical modeling of thermoelectric devices, with the hope of advancing the development and widespread use of these attractive energy conversion devices. Bubbles dynamic behavior is presented in Chapter 5 where a force balance analysis has been proven to be an effective way for analyzing bubbles behavior and predicting their departure and lift off diameters. In this chapter, different forces exerting on bubbles are expounded the relations proposed for calculating such forces are explained, and the impact of flow conditions on bubbles dynamic behavior is discussed. Chapter 6 presents a mathematical model to determine the entropy generation in flow boiling and condensation. Based on the simulation results, the impacts of important geometrical

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parameters and flow conditions on thermos-hydraulic losses are also analyzed. Chapter 7 presents a mathematical model to obtain the energy efficiency of a heat pump powered by solar energy via photovoltaic cells. The system in this chapter is simulated using MATLAB software. The mathematical model of the photovoltaic-thermal system (PV/T) includes a set of 4 unknown variables that must be solved simultaneously: temperature of the PV panel, evaporator, condenser, and water in the tank. Chapter 8 demonstrated a steady-state numerical study for the ground thermal conductivity and temperature distribution effects on the double U-tube heat exchanger heat duty for single and multi-layer soil domains. Finally, Chapter 9 focuses on solid oxide fuel cell’s (SOFC) components, modeling, and its applications for heat and power generation. Additionally, it offers the key design variables needed to model SOFC's behavior. This book can be a reference book for researchers, universities’ instructors and engineers in the fields considered in its chapters. Mamdouh El Haj Assad, Editor

Acknowledgment

We would like to thank our universities for giving us the time to come out with this book. Editors

Chapter 1

Applications of Thermogravimetric Analysis (TGA) for Biomass Thermal Characterization Bojan Ž. Janković1,* Nebojša G. Manić2 and Miloš B. Radojević2 1University

of Belgrade, Department of Physical Chemistry, “Vinča” Institute of Nuclear Sciences - National Institute of the Republic of Serbia, Mike Petrovića Alasa, Belgrade, Serbia 2University of Belgrade, Laboratory for Thermal Analysis, Faculty of Mechanical Engineering, Kraljice Marije, Belgrade, Serbia

Abstract Thermal analysis represents a group of techniques that analyse various physical and/or chemical properties of a sample as a function of temperature, during heating or cooling according to a certain temperature program. In order to obtain accurate results, the precise measurement of sample mass and temperatures are crucial. For that reason, the development of thermo-analytical (TA) techniques was conditioned by development of sufficiently precise instruments for measuring temperature and other characteristics of substances, such as changes in mass, enthalpy (heat), deformation, dimensions, electrical and magnetic properties. In this chapter, emphasis was placed on the description of the operation of thermogravimetric (TG) analyser and the influence of various experimental parameters on the quality of measurements in different reaction atmospheres. In regard to diversity of biomass sample properties, special attention is given to the adaption of experimental procedures for biomass thermal characterization by non-isothermal TG*

Corresponding Author’s Email: [email protected].

In: The Fundamentals of Thermal Analysis Editors: Mamdouh El Haj Assad, Ali Khosravi and Mehran Hashemian ISBN: 979-8-88697-759-2 © 2023 Nova Science Publishers, Inc.

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Bojan Ž. Janković, Nebojša G. Manić and Miloš B. Radojević runs. It was considered the impact of sample homogeneity determined by proper mechanical preparation. Additionally, the application of the calibration procedures and baseline correction measurements for obtaining more precise output data was shown. The study of the measurement accuracy, together with the reproducibility and repeatability required for the accurate thermal characterization of biomass samples by TG were implemented.

Keywords: thermogravimetric analysis (TGA), heating rate, baseline correction, granulometry, biomass sample

1. Introduction Thermal analysis represents the group of techniques which measure the physical properties and/or reaction products as a function of temperature, while the material is exposed to a controlled temperature program. Thermogravimetric analysis (TGA) is the technique through which the sample mass change is recorded as a function of time or temperature, using highly sensitive microbalance. A small quantity of powdered sample is heated inside a furnace within given atmosphere either in an isothermal mode (constant temperature) or in a non-isothermal mode with a pre-set heating rate. Meanwhile, within dedicated software, mass change curve, displayed in either mg or %, is recorded, as a function of furnace temperature (non-isothermal mode) or time (isothermal mode). The goal of such measurement is evaluation of structure of examined material, based on thermal degradation. That means that change in sample temperature is followed by decrease of sample mass, which further points to the change of certain physical or chemical characteristics of the sample. Those changes can be determined by evaluation and analysis of obtained curves and could be utilized for different biomass or waste materials [1]. The enormous need to develop a technique, which could accurately control the temperature and also provide a temperature versus time programed within a specific requirement, was the genesis of thermogravimetry (TG). The TGA is a frequently used technique in the analysis of kinetic data [2]. Additionally, in a thermochemical process such as pyrolysis, an exhaustive knowledge of a biomass feedstock is important to the process design, feasibility, the evaluation and scaling for industrial processes. The kinetic methods for the analysis of biomass and their relative advantages and disadvantages were discussed [2]. They also establish from their search of the Web of Science that there is a growing trend in research on the TGA of

Applications of Thermogravimetric Analysis (TGA) …

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biomass. Their research highlighted the significance of TG in the study of biomass to energy conversion processes. It should be noted that TGA can be used as an effective tool to carry out the proximate analysis of solid fuels. The main components of a TG analyzer are: sample pan or crucible and furnace, balance, the temperature measurement and control unit, environmental control unit, and recording system. A precision balance supports the crucible. The crucible is placed in a furnace under a controlled heating condition and temperature. This implies that the physical and chemical properties of biomass, in this case, are continuously recorded. During TG measurement, only one crucible, which is connected to the microbalance, is used, which allows only the recording of direct mass change [3, 4].

Figure 1. Different crucible types: (a) ceramic crucible; (b) Platinum crucibles with lids for DSC (differential scanning calorimetry) analysis; (c) Alumina crucibles for TG-DSC analysis; (d) lids for TG-DSC alumina crucibles; (e) beaker and plate shaped crucibles for TG and TG-DTA (DTA: differential thermal analysis) analysis.

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Crucibles are containers, used to hold the sample while it is heated up to a certain temperature. For example, for determining proximate analysis data using standard method, ceramic crucibles are used. On the other hand, for the needs of thermal analysis, they can be made of alumina, platinum-rhodium (Pt/Rh), aluminum, chrome-nickel, titanium, etc. For biomass experiments, alumina (Al2O3) is mostly used. Crucibles exist in various shapes, where some of them are displayed in Figure 1. Derivative thermal analysis (DTG) is a derivative function of TG, where obtained curve represents the first derivative of the mass change curve in a function of time, whereas it defines mass change rate. Therefore, a moment of time, along with related temperature, at which mass change rate reaches its peak, can be obtained, which is essential from the aspect of mass loss due to thermal degradation (thermochemical conversion – pyrolysis, gasification, combustion, etc.) or mass gain, due to oxidation. Mass change rate curve is displayed in mg·min-1, g·min-1 or %·min-1 as a function of time or furnace temperature [5]. The advance in thermal analysis derives when the thermocouple was added to a sample carrier. Moreover, an additional crucible was added, besides existing one containing the sample, which was, mostly, empty, and it was named a reference crucible. Measuring the temperatures within the crucibles, and measuring temperature differences, a new curve is obtained, through a method named differential thermal analysis (DTA). Sample and reference crucibles are heated at the same time, under same temperature program, inside the small electric furnace. The existence of thermocouples allowed continuous measurement of temperature difference between crucibles, which is recorded as a function of sample temperature or time [3, 5]. When an endothermic reaction takes place, a delay of sample temperature (Ts) rise is recorded, compared to a reference temperature (Tr). Therefore, the following equation is valid [6]: ΔT = Tu - Tr

(1)

which was characterized with a first peak in Figure 2. DTA uses only one thermocouple per crucible. On the other hand, measuring crucible temperature in more different spots using special sensors and by implementing the thermal bridge, signal exchange takes place between sample and a reference, while the temperature field is formed. Afterwards, using proper calibration file, heat transfer, or the heat flux, can be determined. This analysis type is named differential scanning calorimetry (DSC), where

Applications of Thermogravimetric Analysis (TGA) …

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calorimetry stands for heat transfer determination [4]. The signal obtained through this method represents the amount of energy that the sample has absorbed or released, measured in mW·mg-1. This allows the detection of exothermic and endothermic processes that take place while the sample is heated and therefore the determination of latent heat, specific heat capacity and other material characteristics that are of interest. Namely, the same way as DTA, when, for example, an exothermic reaction takes place, samples enthalpy is rising compared to a reference, which is recorded as an exothermic peak (second peak in Figure 2).

Figure 2. Typical DTA or DSC curve; according to convention, endothermal (endothermic) peak is pointed downwards; Δ – represent the differential signal.

All positive aspects of previously mentioned methods are combined into a method named Simultaneous Thermal Analysis (STA). It represents the merge of TG and DSC (or DTA), and therefore, simultaneous measurement and analysis of mass change and heat transfer is enabled, while changes in physical and chemical characteristics of examined sample are recorded (in other words, STA generally refers to the simultaneous application of thermogravimetry (TG) and differential scanning calorimetry (DSC) to one and the same sample in the single instrument). The main advantage of such analysis, compared to separate measurements, is that measurement errors are minimized because test conditions are absolutely identical for TG and DSC measurements – same atmosphere, gas flow, thermic contact between the crucibles and thermocouples, the influence of radiation, etc. while the time needed for conducting the experiments is halved. The analyzability of the signals is improved, since two or more sets of information concerning sample behavior are always simultaneously available (differentiation between phase

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Bojan Ž. Janković, Nebojša G. Manić and Miloš B. Radojević

transformation and decomposition, between addition and condensation reactions, recognition of pyrolysis, oxidation, and combustion reactions, etc.). Improved simultaneous thermal analysis (STA; TG-DTA or TG-DSC devices) since 1972 (coupling with tools for analysis of evolved gases (EG), e.g., the mass spectrometer) renders this a powerful tool to distinguish between natural materials and activated organic/inorganic materials. Although, the main disadvantage of STA is reflected in the reduced sensitivity of one or more signals, as a result of compromises that had to be made due to instruments complexity [7, 8]. For the need of STA, various sample carriers can be used, where some of the most used ones are displayed in Figure 3.

Figure 3. Sample carrier measurement heads: (a) – TG with beaker type crucibles, (b) – TG-DTA with beaker type crucibles, (c) – TG-DTA with plates, (d) – TG-DSC, (e) – TG-DSC-cp [9].

Presented sample carrier measurement heads are for top loading TG type, although it can also be horizontal. The construction of sample carrier in modern top-loading TG instruments is displayed in Figure 4. Sample carrier consists of the plug, which is in direct contact with highly sensitive microbalance, the capillary, radiation shield and the measuring head. While the base of the sample carrier is similar for every sample carrier type, measuring head is always different and it defines the measurement type. For the TG, only the measurement head from Figure 3a is sufficient. To obtain the DTG curve, the second crucible is not necessary, since it represents first derivative in the function of time, and in case of TG, only time and mass are variables. For TG-DTA, measuring heads from Figure 3b and 3c are used, while the sample plates are better than beaker shaped crucibles from the aspect of determining kinetic parameters, because the sample is placed directly on

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the plate, so the sample is more exposed to the direct carrier gas flow. Therefore, better sample transformation is achieved. Figure 3d and 3e shows measurement heads to TG-DSC analysis, while the first one is for more rough measurements, and it can be used to determine heat flux. On the other hand, the latter is for fine measurements, allowing specific heat capacity to be determined. Since the TG-DTA and TG-DSC both perform TG measurements, and yet at the same time record if the process is exothermic and endothermic, the usage of TG-DTA sample measurement head becomes questionable, because unlike TG-DSC, it cannot be used to determine heat flux. TG-DSC measurement head is made of platinum (which makes it more sensitive and more expensive), while TG-DTA is mostly consisted of Al2O3. Basically, TG-DTA is used for more rough measurements, containing dirty samples with unknown behavior at high temperatures. Accordingly, TG-DTA is used to characterize the sample and obtain the basic data regarding mass change and chemical characteristics. When sample behavior becomes known and when temperature program is defined, TG-DSC sample carrier can be used to determine additional characteristics, such as the latent heat, heat flux, etc. For example, if the sample is very reactive, and if the measurement atmosphere is reductive (> 3% of H2), the atmosphere could contaminate TG-DSC measurement head, while in such case TG-DTA measurement head could be additionally heated to burnout at high temperatures and it would be ready for reuse. Regarding the DSC, it is important to emphasize that there are several different instrument types for this kind of analysis: Heat flow DSC, heat flux DSC, high pressure DSC, fast scan DSC, etc. Most of STA devices use heat flux DSC, displayed in Figure 5, and it was found as the most suitable for biomass testing. In this case, heat flow between the sample and the reference is measured based on temperature difference and the later adapting those results using dedicated calibration file. Since the sample and the reference are heated up inside the same furnace, and some parts of the sensors are connected to a thermocouple (in which they could be integrated as well), this approach is less sensitive to small fluctuations and changes, which affects obtained results precision, while using some other DSC types could achieve a lot higher sensitivity [11]. Heat flux DSC can be explained using diagrams displayed in Figure 6. At the beginning, both sample and the reference will have the same temperature rise. But, due to the difference in heat capacity between the sample and reference, reference will continue to heat up and it will achieve continuous temperature rise, while the sample temperature will stop rising for

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Bojan Ž. Janković, Nebojša G. Manić and Miloš B. Radojević

some time, but when it continues, it will continue to rise the same was as reference does. Temperature rising delay is recorded as a gap between the red and the green line in Figure 6, which represent samples (Ts) and references (Tr) temperature rise, respectively.

Figure 4. Construction of sample carrier and radiation shield [9, 10].

Figure 5. Schematic display of TG-DSC instrument [12].

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Figure 6. Forming the DSC peak [12].

Sample and the reference, represented by respective signals, have similar behavior at the beginning of the process while they are heated at a continuous heating rate, until the chemical reaction – melting, within the sample, begins, at the moment of t1. Sample temperature does not change during the phase change, while the reference temperature continues to rise undisturbed. After the melting process is done, the sample temperature continues to rise at a linear rate, and it continues to follow the course of the reference from the moment of t2, like it did at the beginning of the process. Differential signal (ΔT) of two independent curves is displayed in the lower part of Figure 6. In the middle part of the differential signal, while temperature differences are recalculated, and blue area is obtained, which depicts that endothermic process – melting took place. Depending on if the reference temperature is added or subtracted from the sample temperature, the obtained peak can be the positive or the negative, which corresponds to exothermic or endothermic reaction. The peak area, depicted in blue in Figure 6, presents the latent heat, which is presented in J·g-1 using sensitivity calibration.

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Bojan Ž. Janković, Nebojša G. Manić and Miloš B. Radojević

2. Improving TGA Results When using TGA for biomass experiments, there are several influencing factors that need to be considered such as: sample preparation, purge and protective gas flow, instrument calibration, sample temperature control (STC), buoyancy effect and correction measurements, as well as crucibles lid usage.

2.1. Sample Preparation and Instrument Compatibility In order to obtain the best results from TGA measurements using biomass samples, the instrument has to be optimized for such usage. It is necessary to use tube furnaces that can reach temperatures above 1000°C, such as siliconcarbide [13]. The amount of sample that is used for measurements is limited by crucible volume. Crucibles are pan or beaker shaped, while the volume varies from couple of dozen µl up to several ml, depending on the sample carrier requirements. For the best results, less than half of crucible must be filled with prepared sample [14], while the alumina (Al2O3) crucibles are established as the most suitable for the research of biomass thermochemical conversion processes. On the other hand, in case when latent heat or specific heat capacity (using specialized sample carrier for such need) are to be measured, platinum or aluminum crucibles should be used because of higher sensitivity. Moreover, aluminum crucibles have several times higher sensitivity than platinum ones, but they are not of much use because aluminum melting temperature is 660°C, which does not cover the temperature range needed for biomass testing, so the platinum crucibles are found as more suitable. Research has proved [15, 16], that in order to minimize the heat and mass transfer effect, as small sample mass as possible should be used, which is established to be 10 ± 0.5 mg. Therefore, ~ 85 µl pan shaped crucibles are used or 0.3 ml beaker shaped ones, while the initial sample mass should be measured on the external balance with the sensitivity of 0.01 mg. Besides, in order to homogenize the sample as much as possible, sample should be grinded and particle size under 250 µm should be used. This is particularly important for non-homogenous samples such as raw biomass, in order to obtain more accurate results for the further analysis on multiple heating rates [17].

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2.2. Purge and Protective Gas Flow Since TGA devices have highly sensitive balances (such as 0.1 µg), they need protective gas to fill the atmosphere around them in order to maintain stationary working conditions. Protective gas is usually an inert gas, such as argon (Ar), CO2, helium or nitrogen, but might as well be synthetic air.

Figure 7. TGA schematic view [10].

During measurement preparation, when the tube furnace, in which the sample thermochemical conversion takes place, is opened to place the sample, the area filled with the protective gas is exposed to atmospheric air. In order to prevent air from mixing with protective gas, overpressure is needed to be established in the area around the balance. Therefore, before the furnace is opened, protective gas flow is increased by the order of ten. After the sample is placed onto the sample carrier and the furnace is closed, high protective gas

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Bojan Ž. Janković, Nebojša G. Manić and Miloš B. Radojević

flow should be maintained for at least two more minutes to refill the tube furnace volume. Purge and protective gas flows are then adjusted to match the measurement definition, and they are left like that for two additional minutes, while the balance is stabilized. This procedure allows the stationary measurement conditions to be established before the measurement starts. It is important to start the measurement right after those two additional minutes have passed, because continuous exposure to purge and protective gas before the measurements might over dry the sample and therefore remove surface moisture from the sample, which will not be shown in measurement data, so the final result would not be valid. The look of the contemporary TGA device with important cross-section segments is shown in Figure 7.

2.3. Instrument Calibration In order to obtain the precise measurement results, the instrument needs proper calibration. In fact, due to thermo-physical characteristics of materials that the instrument is made of, instrument performance is not uniform, whilst certain errors might occur. Calibration represents software correction which eliminates those errors. Therefore, six reference materials, with known melting temperatures and latent heat are heated and cooled through predefined temperature programs. Those programs are formed so that the sample is heated right above melting point, then cooled beneath it and heated once again, so that obtained values can be considered to match characteristic temperature values from stationary working conditions. Obtained temperature values differ from nominal values, so they are entered into the software, through which calibration file is formed, which is later used during measurements to eliminate those errors. Usually, the manufacturer provides those reference materials, but in order to cover the temperature range used for biomass testing, the following materials are used: Indium, tin, bismuth, zinc, aluminum and gold. Besides, silver and nickel can be used as well, but it has been proven that they do not figure for this cause.

2.4. Forming the Calibration File The mass of reference material used for calibration measurement should be as close as possible to the sample mass that is mostly used when performing

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measurements. In the case of biomass, the most common sample mass is 10 ± 0.5 mg. Since reference materials come in the shape of foil or wire, it is usually possible to cut the sample to the desired mass, except for bismuth which easily breaks into small pieces, so the mass in the range of 10 ± 2 mg is considered acceptable. Temperature programs used for calibration with reference materials are as follows: In: 260 – 50 – 260, Sn: 340 – 130 – 240, Bi: 380 – 170 – 340, Zn: 480 – 350 – 480, Al: 760 – 560 – 760, Au: 1150 – 950 – 1150, where numbered values are in Celsius degrees (°C). Figure 8 presents the example of calibration temperature program for In. Even though calibration should be adjusted to the heating rate, sample carrier, experimental atmosphere, purge and protective gas flow and expected sample mass, it would be vastly time consuming (making a calibration file for one measurement type takes about three work days), and expensive (each calibration requires new piece of expensive reference material), to form the calibration file which would match each and exact measurement conditions. Therefore, calibration is formed for the conditions that closely match the majority of experimental conditions. For instance, if the TGA can vary the heating rate from 1 to 50 K/min, the calibration should be made for 10 K/min. On the other hand, separate calibration files have to be made for different sample carriers and experimental atmospheres. It is important to emphasize that defined final heating and cooling temperatures should be used when STC is turned off. This is especially important when defining temperature program for zinc, because zinc might slightly evaporate on high temperatures and at temperatures around 500°C, vapors formed from zinc can damage sample carrier. The usage of STC will be explained later.

2.5. Calibration Data Evaluation At first, it can be seen that sample mass is not constant during calibration measurement, even though it is clear that mass of reference materials cannot

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Bojan Ž. Janković, Nebojša G. Manić and Miloš B. Radojević

be changed. That happens because of balance sensitivity – due to phase transfer, from solid to liquid and vice versa, balance recognizes those changes as mass loss or gain. This error can be eliminated using the correction measurement, which will be later spoken of, but it is not relevant at this point, since only onset points that correspond to melting temperature, are relevant in this situation.

Figure 8. The example of the calibration temperature program for indium (In).

As melting points are known characteristics of reference materials, it is important to compare them with measurement data in order to make the calibration file. Melting points correspond to onset points that can be found of DSC or DTA curves obtained from the measurement, according to DIN EN ISO 11357-1:2010-03. Only data from the second heating interval is taken into account since it is considered that by that point stationary measurement conditions are reached.

Figure 9. Determining the onset temperature for indium (In).

Applications of Thermogravimetric Analysis (TGA) …

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Figure 10. Determining the peak area for indium (In).

When desired curve is selected, the onset function is chosen. At this point, a new curve (blue curve in Figure 9) is displayed, which represents the first derivative function of selected curve and it is used to define the boundaries for determining onset point more precisely. The left boundary should be positioned right before the beginning of peak formation at the first derivative curve, while at the main curve that point should correspond to the point where curve linearity ends. The right boundary is placed after peak formation for both curves is ended, so the linearity is reached. In Figure 9, it can be seen that determined onset temperature is 155.6°C which depicts the difference from nominal melting temperature for indium – 156.6°C. In the case when the sample carrier supports simultaneous thermal analysis (TGA combined with differential thermal analysis (DTA) or differential scanning calorimetry (DSC)), besides temperature calibration, sensitivity calibration file has to be made in order to convert obtained raw signal to mW·mg-1. For that cause, instead of the onset temperature, the peak area is determined (for the same peak used for onset point determination) (Figure 10). Obtained value is later compared in software with predefined nominal value for each reference material, therefore obtaining the sensitivity calibration curve.

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2.6. Calibration File Definition Both temperature and sensitivity calibration files require defining measurement conditions (Figure 11). Furnace and crucible type are defined in this step. Later, the gas atmosphere is defined along with heating rate used (Figure 12):

Figure 11. Defining furnace and crucible type for calibration file.

Figure 12. Defining gas atmosphere and heating rate for calibration file.

Figure 13. Entering obtained experimental values of onset temperatures for temperature calibration.

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Then, used reference materials are chosen from the list, and the obtained experimental values of onset temperatures (Figure 13) or peak areas (Figure 14), are entered next to predefined nominal values.

Figure 14. Entering obtained experimental values of peak areas for sensitivity calibration.

Figure 15. Temperature calibration curve.

By calculating quadratic approximation, calibration curves are obtained (Figure 15 and Figure 16). They are saved into separate calibration files, which are later imported when setting up the measurement definition. It can be noticed though that the mathematical weighting of indium is ten, compared to one for all other reference materials. That is because indium is considered as

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the most stable and important material, and it is used to cover lower temperature range, in which high temperature furnaces lack sensitivity. Calibration file should be updated – the procedure has to be repeated once a year.

Figure 16. Sensitivity calibration curve.

Figure 17. Comparison of control calibration measurements using new and reused indium (In) sample.

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Figure 18. Obtained temperature profile difference for the same temperature program, with, and without using the STC.

2.7. Control Measurement After the calibration files have been formed, it should be checked if they are formed properly so that they perform the proper correction. For that cause, new piece of indium is put up to test using newly formed calibration file, under same temperature program. If the calibration is right, obtained experimental onset temperature for indium should match nominal value of 156.6°C. The slight deviation of 0.1°C is considered as acceptable (even 0.2°C for high temperature furnaces such as silicon-carbide). Moreover, after one year, when it is suggested to form new calibration file, control measurement can be performed to check if the onset temperature deviation for indium is more than 0.1°C. If it is, the new calibration should definitely be made. In the case of sensitivity calibration, acceptable peak area deviation is considered to be up to 3% from the nominal value. If the deviation is 3 – 5%, it should be considered to perform new calibration, depending on the acceptable final measurement results error, but if it is over 5%, the calibration file cannot be considered as valid.

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Even though reference materials are the pure metals and they do not change their mass by the heating and cooling the sample, it was proved that the sample used for calibration measurement cannot be reused, which is shown in the Figure 17, where the comparison for two control calibration measurements, using the same piece of indium, has been made. Using the calibration file made for the heating rate of 10 K/min for the measurements with higher or lower heating rates, surely increases measurement error. For example, using calibration file made for 10 K/min for the heating rate of 50 K/min can increase onset temperature error up to 2 K. But if such an error is not of high importance for the needed results, it can be neglected. Some manufacturers have proved using the sample carriers and furnaces that provide high sensitivity, that when the temperature calibration for 10 K/min is used for 1 K/min, obtained the onset temperature is 156.58°C, while for 50 K/min it can be up to 158°C.

2.8. Sample Temperature Controller In Figure 18, the column showing STC checkbox can be noticed, where the STC stands for sample temperature control. In Figure 7, it can be noticed that there is a thermocouple on the furnace itself, while the sample carrier has its own thermocouple. During the measurement, the obtained temperature profile displays the sample temperature, measured with a thermocouple on the sample carrier. When defining temperature program during measurement setup, it can be chosen to turn the STC on or off. When the STC is on, the reference temperature used to lead the process is obtained from the thermocouple from the sample carrier. On the other hand, when the STC is off, the process is led by the temperature obtained from the furnaces thermocouple. Without STC, obtained sample temperature will always be slightly less than the defined temperature. In Figure 18, the difference between obtained temperature profiles is shown for the same temperature program, while STC was turned on and off. The final temperature that was set for the measurements displayed in Figure 18 was 950°C. When the STC was turned on, the final temperature that was reached was very close to the set temperature, while the gap between set and reached final temperature was somewhat larger when the STC was not used. Even though that, according to temperature program, linear heating rate is defined, and thus linear sample temperature rise should be obtained, until

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200°C was reached, due to the specific heat capacity of the sample and inability to establish stationary working conditions, temperature profile manifests significant non-linearity when the STC is on. On the other hand, when the STC is off and the process is led by the temperature from within the furnace, obtained temperature profile is more linear for the temperature region up to 200°C, while after that, established linearity is maintained for both types of measurements.

2.9. Correction Measurements and Buoyancy Effect During a measurement, purge and protective gas are mixed into a carrier gas which streams around the sample that is placed into a crucible. Regardless of the TGA system structure – whether it is top-loading, horizontal or superposition system, while the carrier gas streams around the sample, buoyancy effect is manifested on the sample carrier, and thereby it affects the mass change curve, causing fictional mass loss and gain which are recorded in the software [18, 19]. For example, during the calibration measurement of reference material, sample mass does not change. Nevertheless, the mass loss and gain are recorded due to buoyancy effect, which is presented in the Figure 19.

Figure 19. Calibration measurement for indium (In).

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Figure 20. Buoyancy effect on mass change for different carrier gases.

Figure 21. Gas flow change defined in measurement setup triggers the buoyancy effect.

The buoyancy effect is influenced by four factors: gas atmosphere, sample carrier type, heating rate and the crucible size. For instance, when using argon (Ar) to form the measurement atmosphere, the buoyancy effect is vastly emphasized, while helium, due to its lightweight, causes almost no buoyancy at all. In Figure 20, buoyancy effect on mass change for different carrier gases is compared, during an “empty” measurement – both crucibles are empty, only the linear heating rate is defined.

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The higher the heating rate is, the buoyancy effect is more emphasized, while it decreases on higher temperatures. Basically, any change that occurs during a measurement and therefore disturbs stationary working conditions triggers the buoyancy effect. This is especially important, because it might cause mass gain and loss peaks at the beginning of the measurement if the measurement is not set up properly (Figure 21). As calibrations are used to correct obtained temperature and heat transfer results, measurement correction is used to improve obtained mass change data by neutralizing buoyancy effect. Therefore, more precise and reliable measurement results are obtained. There are four ways to perform measurement correction. First, and the most common way, is to use software integrated mathematical correction, provided by the manufacturer, such as TG BeFlat provided by [12]. This particular tool works best for heating rates in the range of 5 to 20 K/min, and especially if the sample is heated up to temperatures higher than 300°C. Therefore, it is not recommended to use this tool for low temperature measurements, such as those where 100°C is not exceeded. The second way is the most reliable, but the most time consuming. It implies defining the temperature program, and running an empty measurement, without the sample, at least two times. Thereby, reference crucible is left empty as well. On the other hand, the third type implies using a reference sample, such as sapphire, alumina or similar, that is placed into a reference crucible, but the sample crucible is still left empty, in order to calibrate the correction file. This type of correction is used only when very small mass changes are expected, as such when testing glass, ceramics and similar materials. The fourth type is used when there is not enough time for the correction files to be made first. In that case, a measurement is performed without using any type of correction, and after that a correction is made by running a measurement with empty sample and reference crucibles. The differences in mentioned correction types are that for the first and fourth type, measurement error cannot be determined, because those corrections are formed on mathematical basis. The second correction type, which is the most precise needs at least two correction measurements in order to obtain valid correction baseline. There is a clear difference between first and second correction run, while in most cases, third correction run matches the second one (Figure 22).

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Figure 22. Differences between correction runs.

Figure 23. Effect of different corrections on neutralizing buoyancy effect.

It is important to follow the procedure for the correction runs in the very same manner as when the sample is tested. That implies adjusting protective gas flow to form overpressure in the balance, opening the furnace, and even

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taking off and bringing back the crucible, even though it is empty, and no sample will be used. If this is not done and two consecutive correction runs are performed without opening the furnace, different conditions might be formed in the system, so the measurement run will not be simulated properly, and that would affect the reliability of the correction file. Unlike the calibration files that can be used over again, correction runs have to be made for each specific measurement definition. That means that the main measurement (sample run), has to match the correction measurement in every detail, while it can be reused as long as measurement conditions are not changed. Should the heating rate, the gas flow, or any other parameter need to be changed, new correction measurements would have to be performed. Moreover, even if the parameters are changed back to the setup which would match previously formed correction measurement; it is not recommended to reuse the old correction measurement because stationary conditions that were established are disturbed when the measurement conditions were changed. Therefore, it is best to perform correction measurements for the series of tests. For example, if three samples were to be tested at three different heating rates, two correction runs would be made for one particular heating rate, where the second run would be adopted. All the samples would be tested using the same correction measurement, and after that new correction would be made for second heating rate. Should there be a need for repetition of measurement at the first heating rate, two new correction runs should have been performed again. Mathematical correction can be performed simultaneously with correction measurement, but, when the obtained results are analyzed, only one correction type can be chosen for the final output. During calibration measurements, mass change does not occur, because reference materials are metals, and during those measurements only phase change takes place. Nevertheless, the mass change is not represented as a straight line. This defect is removed by using the measurement corrections, which is presented in Figure 23, where three mass change curves are displayed, while each corresponds to the very same measurement file, but with different corrections. Red curve depicts the case where no correction of any kind is used, so the influences of temperature, phase change, etc. on the highly sensitive balance are mostly emphasized. Using a mathematical correction, those influences are reduced, but a straight line still cannot be obtained. This case is presented with a green curve. Only when the calibration is performed after a correction measurement run, a straight line (blue line in the Figure 23) can be obtained. Although calibration measurements do not need correction runs, since the mass change curve does

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not figure in the onset temperature determination. In this case, it was just used for demonstration purpose. In Figure 24, an example of a biomass test run is displayed, with different corrections in use. Rose curve represents the correction measurement. It is usually not displayed on graphs, but it is subtracted from sample mass change curve (blue curve) within the software. Green curve represents the mass change curve with mathematical correction while the red curve represents the mass change curve with correction, and it is obtained by subtracting rose curve from the blue one. This proves that for high temperature measurements, where the mass change over 30% takes place, there is no need invest time into the correction measurements, because mathematical correction is sufficient. Even though measurement error cannot be determined while mathematical correction is used, it is not necessary when biomass samples are investigated, because most of measurement uncertainties are related to sample homogeneity which mostly affects the result quality and repeatability.

Figure 24. TGA curves for biomass sample with different corrections.

In addition to mass change curves match when using correction measurement and mathematical correction, in Figure 25 is displayed the match of DTG curves (first derivative of mass change curve) when using those two correction types. It can be seen that at lower temperatures there is a certain

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noise at DTG curve when using mathematical correction, which is an additional proof that mathematical correction should not be used for low temperature ranges. Nevertheless, the match of curves is unambiguous, which justifies the usage of mathematical correction.

Figure 25. DTG curves for biomass sample with different corrections.

2.10. Using Lids for Crucibles The usage of crucibles lid can be found for almost any purpose and crucible type. At first, it might reduce the effect of the moisture removal from the sample right before the measurement starts, when the sample is exposed to carrier gas flow, while it is waited for the balance to stabilize and stationary conditions to be established, which was previously explained. Besides, using the lid enhances the formation of uniform temperature field within the crucible, giving better results in terms of the heat transfer, which is of great importance when performing TG-DSC measurements (Figure 26). Considering that flat plate should be used as sample holder in order to obtain best results for kinetic analysis, lids do not contribute to this cause. Also, when performing TG-FTIR analysis, due to the continuous gas analysis, lid usage disturbs the sampling dynamics resulting in delay in gas detection

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[20]. On the other hand, lid usage during TG-DSC-MS (MS: mass spectrometry) is mandatory, because it enhances DSC results quality and it does not disturb gas sampling in the MS [21]. Besides, lids might cause problems during diffusion control. If such a problem might occur, it would be seen as linear mass loss, but such case is not usual during biomass investigation. It can be concluded that lids contribute do TG-DSC measurements and prevent the prematurely moisture removal but can be a downgrade to a diffusion control or disturb the FTIR gas analysis. Anyhow, their usage should be always carefully considered in order to achieve best possible results.

Figure 26. TG-DSC (a) and TG-DTA (b) crucibles with lids.

Figure 27. Building block of an MS [25].

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Although complicated setup and calibration procedures for using the STA as an analytical experimental technique the application of STA is highly important with the non-uniform raw samples (such as biomass samples) which require more pretreatment and demanding sample preparation procedure in order to obtain a representative sample [22]. Also, simultaneous obtaining mass loss (TG-DTG) and energy effects (DTA-DSC) during the thermal decomposition of the tested material could improve the accuracy of the obtained results due to the elimination of the influence of possible tested sample non-homogeneity, which could lead to non-acceptable results deviations. This issue could be further improved by direct coupling STA and TG with a mass spectrometer in order to obtain a more comprehensive evolved gas analysis during the thermal decomposition process, which is extremely important for the possible analysis of biomass for further utilization as an energy source or for producing biofuels or other value-added products (such as key platform chemicals).

3. Coupling of TG Analyzer with Mass Spectrometer (TG-MS Coupling) – in Depth Gas Analysis 3.1. Introduction to Mass Spectrometry Thermal analysis is used to obtain useful information which is used to describe different physical and chemical characteristics of examined sample. However, these results can be enhanced with the information about structural characteristics of components that are decomposed during the thermal analysis. For this cause, thermal analyzers are coupled with instruments for gas analysis, such as gas chromatographer, FTIR or the mass spectrometer. This became quite common, because such coupling can provide in depth gas analysis along with TG measurements. All of those instrumental methods have their limitations, regarding gas release profiles. It was found that TG-MS coupling is the most common instrumental setup when examining biomass samples [23, 24]. Mass spectrometer (‘MS’) is an analytical instrument in which an ion beam is formed from the gaseous phase of examined sample. Ions are therefore sorted by mass to charge ratio (m/z) using electrical and/or magnetic field. As a result, analogue or digital signal is obtained in the form of curve peaks, from which m/z ratio, as well as relative abundance, of each detected ion can be

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determined. MS is consisted (see Figure 27) of ion source (Figure 28) – where ions are formed from the gaseous sample, the mass analyzer (Figure 29) – which acts as a mass filter and it defines which m/z ratio of ions or going to reach the detector, and the detector itself (Figure 30) – where ion detection takes place by determining ions relative abundance and converting it into the electrical signal.

Figure 28. Electron ionization source [26].

Figure 29. Schematic of linear quadrupole mass analyzer [27].

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Figure 30. Schematic of linear channel electron multiplier (a) and curved channel electron multiplier (b) [28].

Figure 31. The example of total ion current profile for the sawdust (wood biomass) sample using argon as a carrier gas.

Unit used to describe the ion detection is the ion current measured in amperes. First, a diagram which shows the profile of total ion current used for ion detection during the measurement is obtained (Figure 31). Afterwards, it is converted to a diagram on which all of the detected m/z ratios are displayed, as a function of time. It should be noted that for biomass samples, only m/z ratios up to 50 are considered relevant because all molecules of interest fit within that scanning range [29]. Even though the MS detects higher values of m/z ratio, it was proved that molecules that could be detected with those masses do not significantly affect composition of released gas during biomass thermochemical conversion processes, which is why they should not be considered.

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Moreover, it was found that m/z signal with the intensity lower than 1e12 A, should not be taken into consideration, because it is mostly consisted of signal noise. Even if it would manifest a peak, such small ion current reflects the very small amount of detected gas, which is why it is not taken into account. Also, during biomass thermochemical conversion processes, such gases are released so that when they are detected by the MS, m/z ratio corresponds to molecular mass. Detected molecules ion current is not directly related to the quantity of corresponding gas release, but it is a fact that the higher is ion current, the higher is the quantity of corresponding molecule released/detected. Gases that could be detected with the MS have their unique specter, represented by the 2D graph, in which the distribution and relative abundance of corresponding ions is displayed. Each gas is represented by two or more ion fragments in the mass specter. Those specters can be found in the base of National Institute of Standards and Technology – NIST [30] (Figure 32). Displayed peaks are actually signals of detected ions which were formed in the ion source, and they are manifested by different intensities that are shown on y-axis. Presenting peak intensities using absolute values of ion current used for their detection is not relevant, because obtained values could be characteristic for each individual instrument, while the overlap of range of absolute values, at different ion quantities due to differences in the atomic masses, can take place as well. Therefore, all peaks are normalized according to a base peak for which is adopted the relative abundance of 100%, while values of all other detected peaks are smaller, making obtained mass specters comparable to each other. Base peak represents the most stable ion which remains after ionization process, resulting with the highest abundance in the mass specter. Molecular ion is followed by smaller peaks, always characterized with smaller m/z ration than the molecular ion, thereby forming ion fragment peaks. That proves that the energy that is brought to molecules during the ionization process can lead to decomposition of molecular ion, but also to further fragmentation of newly formed fragments. Since that molecular ion is not always the base ion, which means that base ion can also be a fragment (Figure 33). Isotope peaks are the only ones that can have higher m/z ratio values than the molecular ion, and they appear when the examined material contains the elements which have their isotopes in their natural form. Most common isotope peaks are related to a carbon isotope C13. In Figure 32, molecular ion peak corresponds to methane molar mass of M (CH4) = 16 g·mol-1, and it is also a base peak. The only peak with detected higher m/z ratio

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is number 17 which corresponds to the ion containing carbon isotope C13. The other detected ions are fragment peaks.

Figure 32. An example of a mass specter – Methane mass specter.

Displayed peaks are actually signals of detected ions which were formed in the ion source, and they are manifested by different intensities that are shown on y-axis. Presenting peak intensities using absolute values of ion current used for their detection is not relevant, because obtained values could be characteristic for each individual instrument, while the overlap of range of absolute values, at different ion quantities due to differences in the atomic masses, can take place as well. Therefore, all peaks are normalized according to a base peak for which is adopted the relative abundance of 100%, while values of all other detected peaks are smaller, making obtained mass specters comparable to each other. Base peak represents the most stable ion which remains after ionization process, resulting with the highest abundance in the mass specter. Molecular ion is followed by smaller peaks, always characterized with smaller m/z ration than the molecular ion, thereby forming ion fragment peaks. That proves that the energy that is brought to molecules during the ionization process can lead to decomposition of molecular ion, but also to further fragmentation of newly formed fragments. Since that molecular ion is not always the base ion, which means that base ion can also be a

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fragment (Figure 33). Isotope peaks are the only ones that can have higher m/z ratio values than the molecular ion, and they appear when the examined material contains the elements which have their isotopes in their natural form. Most common isotope peaks are related to a carbon isotope C13. In Figure 32, molecular ion peak corresponds to methane molar mass of M (CH4) = 16 g·mol-1, and it is also a base peak. The only peak with detected higher m/z ratio is number 17 which corresponds to the ion containing carbon isotope C13. The other detected ions are fragment peaks.

Figure 33. An example of a mass specter – Ethane mass specter.

Table 1. Proximate analysis, ultimate analysis and calorific value of studied samples

Proximate analysis [wt. %]

Moisture Volatile matter Fixed carbonc Ash Calorific value [MJ kg-1] HHV LHVa Ultimate analysisb [wt. %] C H O N a Calculated according to EN ISO 18125:2017. b on dry basis. c by the difference.

SCG 10.33 70.30 16.35 3.02 19.12 17.3 52.75 6.95 34.68 2.25

SD 7.16 74.01 17.02 1.81 17.78 16.21 49.46 6.82 41.74 0.03

WS 9.63 67.32 15.17 7.88 15.29 13.91 45.16 6.34 39.15 0.63

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3.2. Qualitative Gas Analysis The identification of released gases during biomass thermochemical conversion processes can be determined using MS which detects mass-tocharge (m/z) ratio. Meanwhile, every molecule that passes through the MS decomposes on the smaller fragments due to electron ionization, according to the following equations [31, 32]: А + е- → А+ + 2е-

(2)

АВ + е- → АВ+ + 2е-

(3)

АВ + е- → А+ + В + 2е-

(4)

АВ + е- → А + В+ + 2е-

(5)

АВ + е- → АВ2+ + 3е-

(6)

АВ + е- → АВ3+ + 4е-

(7)

where for every molecule entity, a separate mass specter is formed of several different m/z ratios. For the purpose of explanation of procedures how the data that is obtained through a mass spectrometer is evaluated, three biomass samples are used – spent coffee grounds (SCG), sawdust (SD) and wheat straw (WS). Main characteristics of these samples, as proximate and ultimate analysis data, are presented in Table 1. For example, the mass specter of a water molecule (Figure 34) consists of atomic mass units (amu) from 16 to 20, where amu 18, the molecular ion, is the one with the highest relative abundance. Numbers depicted in green in figures that display mass specters of certain molecules, do not necessarily represent precise percentage of certain fragment in the respective gas, because that the percentage is specific for each individual instrument. During obtained data evaluation, curve represented by amu 18, which is related to the m/z =18, can be used as an indicator for the identification of water molecule. This can be viewed in Figure 35 for the pyrolysis of sawdust, using the argon as a carrier gas.

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Figure 34. Mass specter of the water molecule.

Figure 35. Ion current absolute intensity for amu 17 and amu 18 as a function of temperature, for the pyrolysis process of sawdust, while using argon as a carrier gas.

During this type of qualitative analysis, released molecules are identified by the amu values. A problem occurs when several molecules with the same molar mass, and so with the same molecular ion, are released during the

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process. Moreover, the molecular ion value of some lighter molecule can match with the fragment value of some heavier molecule, making identification process more complicated. For example, molecular ion of CO2 has the value of amu 44, while fragments that are contained in CO2 specter are a mu 28, 16 and 12 and some other, minor ones (Figure 36). Likewise, molecular ion of CO corresponds to amu 28, where detected fragments are amu 16 and 12 (Figure 37). When CO and CO2 molecules are found in the same atmosphere, their identification using the MS is not unambiguous, because an overlap of molecular ions and fragments with the same m/z takes place. Such phenomenon is vastly emphasized when testing biomass samples, because they consist of huge number of organic and inorganic molecules that decompose to a huge number of fragments, causing difficulties in identification of released molecules.

Figure 36. Mass specter of the carbon-dioxide molecule.

Because of presented problems, it was found that gas identification solely by molecular ion is not reliable, unless proven differently, which is achieved by simultaneous analysis of molecular ions and fragments and comparing obtained m/z ratios and molecular molar masses with NIST database. Analysis of desired curves using absolute values of ion current on y-axis is not sufficient for detailed analysis, because obtained ion current values for different masses can differ by several orders of magnitude. Thus, it is needed to individually scale compared curves in order to display their relative intensity, making obtained results comparable to each other. It was found that when results are

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displayed with individual scaling, if molecular ion and fragment curves of the same molecule match, they can be identified as the same molecule. Although, such a situation is possible only when materials with known degradation process and material structure are examined, such as calcium oxalate, sodium bicarbonate, etc. On the other hand, this phenomenon is recorded while water release process took place during biomass thermochemical conversion processes. That means that amu 17 and amu 18 from Figure 35 should have the same shape while they are individually scaled, which in fact, is the case, presented in Figure 38.

Figure 37. Mass specter of the carbon-monoxide molecule.

Since the match is almost absolute, this proves that amu 17 and amu 18 basically correspond only to a water molecule. Although those amu’s might have been influenced by fragments of some heavier molecules, their influence is negligible. As a result, amu 18 can be adopted as the curve that depicts water release profile. However, the identification of other gases of interest that are released during biomass thermochemical conversion process is not as transparent as water identification. In those cases, more fragments must be analyzed simultaneously in order to identify which mass curve, in which temperature range depicts certain gas. According to CO and CO2 mass specters, it is observed that those molecules contain the same fragments, which is why it is exceptionally hard to describe the release of carbon monoxide.

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Figure 38. Ion current relative intensity of amu 17 and amu 18 as a function of temperature, for the pyrolysis process of sawdust, while using argon as a carrier gas.

Figure 39. Ion current absolute intensity for amu 12, amu 28 and amu 44 as a function of temperature, for the pyrolysis process of spent coffee grounds, while using argon as a carrier gas.

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Figures 39 and 40 show that there is no perfect match between amu 28 and amu 44, as there is between amu 17 and amu 18 for water molecule; in fact, the match between amu 12 and amu 44 is much better, despite that amu 12 is the fragment with very small relative abundance in the CO and CO2 mass specters.

Figure 40. Ion current absolute intensity for amu 12, amu 28 and amu 44 as a function of temperature, for the pyrolysis process of spent coffee grounds, while using argon as a carrier gas.

Taking into consideration the mechanisms of carbon-monoxide release as well as temperature range in which this release takes place during pyrolysis process, it is found that shoulder that appears at amu 28 in the temperature range between 400 and 500°C does not originate from CO, but from various hydrocarbons [29]. Even though that fragment amu 28 is contained in CO2 in the range of 220 - 400°C it can be concluded that amu 28 corresponds to CO release profile. When using nitrogen as a carrier gas for the pyrolysis process, or during the combustion process, it is almost impossible to identify CO release profile, because nitrogen is also identified as amu 28 so its influence is dominant in amu 28. In the example of methane release profile, the situation is shown where molecule fragment is used to identify gas release profile, instead of molecular ion curve (Figure 41). In Figures 42 and 43, peak from amu 16 is found at about the temperature of 100°C. Methane release cannot be found at this temperature. Therefore, it

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is concluded that it represents the fragment from the oxygen molecule O2, which is confirmed by displaying amu 32 curves, which corresponds to molecular ion of oxygen. Besides, amu 16 is under the influence of fragments from CO and CO2, but also from various higher hydrocarbons which are released during pyrolysis process. Accordingly, amu 15, a highly abundant fragment in the methane mass specter, is used for the analysis of methane release profile.

Figure 41. Mass specter of the methane molecule.

Figure 42. Ion current absolute intensity for amu 15, amu 16 and amu 32 as a function of temperature, for the pyrolysis process of a wheat straw sample, while using argon as a carrier gas.

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Figure 43. Ion current relative intensity for amu 15, amu 16 and amu 32 as a function of temperature, for the pyrolysis process of a wheat straw, while using argon as a carrier gas.

This kind of analysis is extremely important in order to identify each of the fragments which influenced the particular amu’s peak within consider temperature range, due to the fact the MS could not separate the ion current from different chemical compounds. This approach is applied for thermochemical process analysis of different biomass samples where the evolved gas analysis is crucial for the entire process description and assessment of the gaseous products of interest for the particular thermochemical conversion processes of biomass, such as gasification and/or pyrolysis. In order to further improve the process of characterization, and due to the fact that MS delivers only qualitative and not a quantitive approach to evolved gas analysis, in the following, the newly proposed semi-quantitive approach will be presented.

3.3. Semi Quantitative Evolved Gas Analysis Previously described methodology is related to qualitative gas analysis. But, upgrading the existing methodology and by making few assumptions, a model for semi- quantitative analysis is formed, through which the quantity of released gases can be estimated by following equation:

Applications of Thermogravimetric Analysis (TGA) …

𝑣𝑖 =

1 𝑉̇𝐴𝑟 𝑇 𝐼𝐶 ∫ 2 𝑖 𝑑𝑇 𝛽 𝑚𝑠𝑎𝑚𝑝𝑙𝑒 𝑇1 𝐼𝐶𝐴𝑟

[𝑘𝑔

𝑚3 𝑠𝑎𝑚𝑝𝑙𝑒

]

43

(8)

where 𝑣𝑖 is the volumetric share of respective gas (defined by the amu with the highest relative abundance in the mass specter),

1

𝛽

is inversed value of

heating rate [min K-1], 𝐼𝐶𝑖 and 𝐼𝐶𝐴𝑟 are ion current intensities used for detection of respective carrier gas (argon in this particular case) respectively ̇ is volumetric flow of the carrier [mL·min-1], 𝑚𝑠𝑎𝑚𝑝𝑙𝑒 is the sample [A], 𝑉𝐴𝑟 mass [mg], while the upper and lower integral boundaries depict the temperature range used for released gas quantity estimation. The concept of semi quantification was found in previous works [33, 34] where the volumetric and molar share of detected gases is obtained. Dimension analysis of previous equation can be explained by the following equation: 𝑚3 𝑘𝑔𝑠𝑎𝑚𝑝𝑙𝑒

=

𝑚𝑖𝑛 𝐾

𝐴𝑖

∙𝐴

𝐴𝑟

∙

𝑚𝐿𝐴𝑟 𝑚𝑖𝑛

𝑚𝑔𝑠𝑎𝑚𝑝𝑙𝑒

∙𝐾

(9)

The flow of argon on the right side of previous equation can be referred to as a flow of i-th component (on the left side of the equation), because the ion current ratio of i-th gas and argon is used to obtain normalized signal, which represents the normalized release profile of the i-th gas. Normalization is necessary because amu 40, which characterizes argon, is not constant through the whole process, despite the constant flow of argon gas. Values such as heating rate and sample mass at the beginning of the experiment, are also constants, and after their input, peak area is determined for the within set temperature range, according to equation (8), which represents the volumetric share of respective gas. In order to complete this calculation, following assumption have to be made – amu used for curve normalization has to correspond to the highest relative abundance from the mass specter of the respective gas (molecular ion does not have to be the one with the highest relative abundance). But, before that, it is necessary to establish which amu corresponds mostly to which gas within considered temperature range. Since it is not possible to analyze all gases that are released during biomass thermochemical conversion process, the focus is on those gases that are primarily released (according to following equation), as well as on certain hydrocarbons that are found to have significant contribution to the process:

Bojan Ž. Janković, Nebojša G. Manić and Miloš B. Radojević

44

Biomass  H2(g) + CO(g) + CO2(g) + CH4(g) + H2O(g) + Tar(l) + Bio-char(l)

(10)

During pyrolysis process, for the samples that are presented in Figures 35, 38, 39, 40, 42 and 43, for the analysis of gases of interest, following molar amu’s are used within following temperature ranges presented in Table 2. Summing up all of the calculated volumetric shares, an estimation of syngas yield is obtained during the pyrolysis process using argon as a carrier gas, where in dry syngas the yield of water is subtracted. Afterwards, heat flux that corresponds to energy capacity of obtained syngas from respective biomass sample can be determined as: 𝐸 = (∑ 𝑣𝑖 − 𝑣𝐻2𝑂 ) ∙ 𝐵 ∙ 𝐻𝑑 𝑖 [MW]

(11)

Table 2. Temperature ranges and amu’s used for semi quantification of respective gases аmu 2 16 18 28 28 29 32 44

Gas H2 CH4 H2O CO C2H4 + C2H6 O2 C3H8 CO2

Temperature range [°C] 200-800 200-800 40-800 190-390 390-800 200-600 40-500 150-800

where B is the fuel consumption [g∙s-1] and 𝐻𝑑 𝑖 is lower calorific value of respective gas [MJ∙m3]. Low calorific value is calculated considering all combustible constituents of the syngas, according to following equation: 𝐻𝑑𝑖 = 𝑣 + ∑𝐶𝑂 𝑣𝑖

𝑣𝐻2 ∑ 𝑣𝑖

∙ 𝐻𝑑 𝐻 +

∙ 𝐻𝑑 𝐶𝑂 +

2

𝑣𝐶3 𝐻8 ∑ 𝑣𝑖

𝑣𝐶𝐻4 ∑ 𝑣𝑖

∙ 𝐻𝑑 𝐶𝐻 + 4

∙ 𝐻𝑑 𝐶

3 𝐻8

𝑣𝐶2 𝐻4 +𝐶2 𝐻6 ∑ 𝑣𝑖

[MJ m−3]

∙

𝐻𝑑 𝐶

2 𝐻4

+𝐻𝑑 𝐶

2 𝐻6

2

+ (12)

where index i corresponds to respective gases, such as H2, CH4, H2O, CO, C2H4 + C2H6, O2, C3H8 or CO2.

Applications of Thermogravimetric Analysis (TGA) …

45

Table 3. Analysis of released gases during pyrolysis process of examined biomass samples, using newly proposed method for semi-quantitative analysis Sample Spent coffee Sawdust Wheat straw grounds Released gaseous producta H2 [%] 9.10 11.85 9.63 CH4 [%] 5.70 5.28 5.06 H2O [%] 57.10 51.56 56.63 C2H4 + C2H6 [%] 2.62 3.04 2.45 CO [%] 6.95 8.17 7.02 O2 [%] 2.16 2.00 2.07 C3H8 [%] 1.55 4.48 2.45 CO2 [%] 14.82 13.62 14.69 Syngas yield [m3 · kg-1 feedstock] 648 624.5 612.7 x 103 Dry syngas yield [m3 · kg-1 278 302.5 265.7 feedstock] x 103 LHVsyngas [MJ m-3] 6.97 10.27 7.54 LHVsyngas [MJ m-3] -- literature 6.6 – 12.7b 6.8 – 14.39c 6.5 – 7.9d Esyngas [MW] 1.94 3.11 2.00 a For the analysis of released gases, the following amu values are used to identify them: 2 (H2), 15, 16 (CH4), 17, 18 (H2O), 28, 27, 26, 29 (C2H4), 30, 28, 27, 29 (C2H6), 28, 12, 29 (CO), 16, 32 (O2), 28, 28, 44 (C3H8), 44, 28 and 12 (CO2). b [36]. c [37-38]. d [40]

Values of lower calorific value of respective gases, needed for conducting the calculation according to equation (12), are obtained as tabular according to reference [35]. In Table 3, the results that are obtained by the proposed method are displayed. Except for the H2O vapor, the highest yield of hydrogen (H2) and carbon monoxide (CO) gases among considered biomasses was obtained for sawdust, while comparatively high yield of carbon dioxide (CO2) was obtained for both, spent coffee grounds and wheat straw (Table 3). Compared to other permanent gases, the yield of methane (CH4) is quite lower and more uniform to all biomasses. The yield of light hydrocarbons is significantly lower (in sizably lower amounts) compared to the permanent gases yield; only slightly higher yield of propane (C3H8) may be observed for sawdust biomass feedstock. The majority of these observations are directly related to the biochemical composition of examined biomass feedstock as well as the contents of watersoluble alkali. Specifically, cellulose, lignin and potassium (K) contents can

46

Bojan Ž. Janković, Nebojša G. Manić and Miloš B. Radojević

be associated with H2 as well as CO and CH4 formation. Positive correlation can be observed between H2 and CO yields and cellulose rich biomass, such as sawdust (Table 3). On the other hand, positive correlation is maintained between CH4 yield and lignin rich biomass samples, such as spent coffee grounds and sawdust. However, elevated content of K in wheat straw and sawdust [41] has a dual role in correlating with H2, CO and CH4 gas yields. First, it is a positive correlation between probably high content of K and H2 yield, and negative correlations between CO and CH4 yields and K content (compare yields of considered gases for sawdust and wheat straw biomass samples in Table 3). Probably negative relationships between K content and CO and CH4 arise from the fact that the mineral matter can influence pyrolysis reactions occurring inside the component’s particle and decrease the yield of aforementioned gases. However, these relationships can also be explained by the occurrence of the char gasification reactions, such as water-gas (WG) reaction and water-gas shift (WGS) reaction, which are likely to be a result of combination of lignin and alkali contents. Strong positive correlation between CO yield and cellulose rich biomass (sawdust biomass sample) is directly related to higher content of carbonyl groups in the cellulose. Significant difference in the yields of H2 and CO gases for sawdust and other biomasses may lead to gas mixtures with noticeable variability in H2/CO ratios. In accordance with established results, the LHV value of syngas derived from sawdust pyrolysis process is greater than LHV’s obtained from pyrolysis process by other two biomass feedstock (Table 3). The low heating value (LHV) of produced syngas obtained under the pyrolysis conditions used in the present study, which reaches a maximum value of 10.27 MJ·m-3, indicates the high content of combustible gases from the observed feedstock. This relatively elevated LHV of syngas can be valorized as an alternative source of heating for the pyrolysis reactor. It is interesting to note that the obtained heating values identified (Table 3) are slightly lower than obtained heating values of gases from conventional pyrolysis (13 – 14 MJ·m-3), but most of them are within the range of heating values for microwave method/approach (6.6 - 8.6 MJ m-3 (Table 3)). The maximum value of 10.27 MJ·m-3 is located between the values related to conventional and microwave pyrolysis pathways. This behavior is followed by calculated values of syngas energy capacity related to observed biomass feedstock in an order: sawdust > wheat straw > spent coffee grounds (Table 3). The heating rate (and other conditioned parameters) which was used in Table 3 proved to be very optimal for syngas production by labscale performed pyrolysis from various biomass feedstock, monitored via proposed TGA-MS semi-quantitative approach. To further improve the

Applications of Thermogravimetric Analysis (TGA) …

47

operational characteristics by applying the described approach, where bedding material such as sawdust is used, the sawdust addition to the composting process would be an efficient way to exploit this material for the waste-toenergy utilization.

Conclusion Based on presented results in this chapter, the following conclusions could be made: •

•

•

•

For the best performance of thermogravimetric analysis (TGA), whether it is coupled with a gas analyzer, it is important to fulfill all of the previously mentioned suggestions. Those improvements are closely related to each other and if any of the proposed suggestions are not met in full, obtained results cannot be considered reliable because the measurement error will progressively rise. Application of proposed techniques for improving the TGA for all analyzed heating rates provides more accurate results which could be used for further analysis, for an example, for the kinetic analysis of thermal decomposition process of considering biomass samples. While defining a temperature program for biomass testing, measurement conditions have to be carefully examined, so the parameters can be set properly. First, the instrument has to be properly calibrated, after which the sample carrier along with respective crucibles have to be chosen wisely in order to achieve desired results. Maintaining adequate gas flow in order to achieve the desired atmosphere along with protective gas, the need for protection of the highly sensitive microbalance is mandatory goal. Depending on the precision needed for the obtained results, proper correction should be used, whether it is a measurement or mathematical correction. This factor is highly influenced by the available time to conduct the series of measurements. The repeatability of the results for the organic samples such as biomass could be only achieved by following the presented procedure as well as applying suggestions made in this chapter. The main issues during these experimental runs are related to the homogeneity of the tested sample, due to the small amount of used sample during TGA.

Bojan Ž. Janković, Nebojša G. Manić and Miloš B. Radojević

48

•

•

Also, overlapping reaction mechanisms during thermal decomposition as well as different distribution of the volatiles and biochar residue produced from analyzed samples, could additionally complicate the obtaining the accurate results, especially in the case of multiple heating rates experiments. Coupling TG instrument with the MS provides in-depth gas analysis, which is used to obtain results needed for the explanation of structural changes that take place during thermal analysis, along with derivative thermal analysis. If the TG would be coupled simultaneously with FTIR (Fourier transform infrared) spectroscopy and MS, or GC-MS (gas chromatography – mass spectrometry), gases released during thermochemical conversion processes might have been more precisely estimated, but that could be a subject for further research studies. Furthermore, the simultaneous TG and MS coupling could reduce the time for the comprehensive characterization of the biomass samples, in order to identify the main decomposition steps, by determination of mass loss, energy effects, and evolved gasses at the defined temperature ranges. This kind of analysis could provide more information about the biomass characterization by the identification of characteristic temperatures, required and available energy yield during the process as well as the composition of the evolved gases (by application of the proposed semi-quantitive procedure) and could identify the possible pathway for analyzed sample utilization on the industrial-scale level. It was established that using the suggested procedure, the identified low heating value (LHV) of the produced syngas corresponds to heating values between conventional and microwave pyrolysis pathways, where high content of combustible gases is present, considering all tested biomass feedstock samples. The estimated LHV values for obtained syngas products track the real-calculated values of syngas energy capacities. For all three types of biomass (waste) samples, the strong correlation between the hydrogen (H2) yield and the yield of produced syngas (not on dry basis) is identified. Besides, the presented results in this chapter can notably contribute to a much better characterization and testing of different lignocellulose raw materials, with the aim to know their technical and economic feasibility for the syngas production, through different standard thermal analysis methods.

Applications of Thermogravimetric Analysis (TGA) …

49

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Chapter 2

The Use of Thermogravimetric Analysis in the Production of Catalytic Support Formed by CaO and Nb2O5 Paulo Sergio Theodoro1,*, PhD Pedro Augusto Arroyo2, PhD Edson Antonio da Silva1, PhD and Joseane Debora Peruço Theodoro3, PhD 1Department

of Chemical Engineering, State University of the West of Paraná, Toledo, Paraná, Brazil 2Department of Chemical Engineering, State University of Maringá, Maringá, Paraná, Brazil 3Department of Environmental Engineering, Federal Technological University of Paraná, Londrina, Paraná, Brazil

Abstract This study aims to evaluate the mass loss in the production of CaO/Nb2O5 catalysts and to obtain the temperature of interaction between the active phase and the support using thermogravimetric analysis (TGA). The catalysts were synthesized by means of the solid dispersion of calcium oxide (CaO) on niobium pentoxide hydrated. The percentage by mass of 5%, 10%, 20% and 30% of CaO was used as active phase, for an amount of niobium pentoxide (Nb2O5) as catalytic support. Thermogravimetric analysis was performed in the production of CaO/Nb2O5 catalysts. According to the TGA and DTG (derivative thermogravimetric) curves, it was observed that there was a mass variation of greater intensity at *

Corresponding Author’s Email: [email protected].

In: The Fundamentals of Thermal Analysis Editors: Mamdouh El Haj Assad, Ali Khosravi and Mehran Hashemian ISBN: 979-8-88697-759-2 © 2023 Nova Science Publishers, Inc.

54

P. Sergio Theodoro, P. Aaugusto Arroyo, E. Antonio da Silva et al. temperatures close to 100 oC. At this temperature, the mass gradient is possibly generated by the loss of water physically adsorbed on the surface of the solid and by the removal of water of crystallization through dehydroxylation of the (OH-) bound to the Nb2O5 structure. For the CaO/Nb2O5 catalysts, the percentages of mass reduction were in the range of 12 to 15%. According to the TGA and DTG curves, the mass gradients occurred with greater intensity at temperatures close to 100 °C, possibly these mass gradients at these temperatures close to 100 °C arose as a result of the removal of water molecules physisorbed on the surface of the solids. Other mass variations were observed at the temperature close to 375 °C, at this temperature there was a significant mass loss indicating an interaction of the active phase, calcium oxide (CaO) with the catalytic support, niobium pentoxide (Nb2O5). In this second event at 375 °C, the mass gradient was proportional to the percentage of CaO deposited on the support (Nb2O5). Thus, at the temperature of 375 °C, the formation of CaO/Nb2O5 catalysts occurred, according to the TGA analysis, the variation in the mass percentage of the calcium oxide (CaO) active phase did not cause a difference in the temperature of interaction with Niobium pentoxide (Nb2O5). Thus, with the use of thermogravimetric analysis (TGA), the values of the catalyst formation temperature were obtained, as well as the percentages of the mass gradients.

Keywords: TGA, DTG, niobium, calcium, thermobalance

1. Introduction 1.1. Use of Catalysts The importance of catalysis is due to the large number of applications in catalytic processes, in the chemical and petrochemical industry, in energy generation, in the preservation of the environment and in the development of new materials, since the use of catalysts allows chemical reactions to be performed under milder conditions, with reduced energy consumption. Although many important catalytic processes have mostly been solved, there is great room for the development of new processes and new more efficient catalysts in different industrial areas [1, 2].

The Use of Thermogravimetric Analysis …

55

1.2. Supported Catalysts Supported catalysts consist of an active phase dispersed on a porous support. An adequate support must present a set of properties, such as: thermal stability, mechanical resistance and high specific area, high porosity [3, 4]. In addition to the physical-chemical and mechanical properties, the support must have perfect interaction with the active phase. When the support has catalytic activity, the catalyst will be bifunctional, that is, both the active phase and the support have catalytic activity. Further to the above functions, other desirable effects of the support include: increasing the substrate's accessibility to active agents deposited on the porous support; protect active sites from poisons; dissipate heat in reactions [5]. Supported catalysts can be used in flow reactors, be easily separated from unconverted reactants and reaction product. Allows recovery and reuse of the catalyst. All these benefits can help to minimize the waste generated in a process [2].

1.3. Use of Niobium as a Support Due to its strength properties, niobium is widely used in materials technology. It is used as an additive in many metal alloys, which improves thermal shock resistance, hot ductility and tensile strength. Niobium is resistant to most aggressive compounds such as acids, including hydrochloric nitro (aqua regia), HCl, H2SO4, HNO3, and H3PO4 and many organic and inorganic compounds. It is attacked by concentrated (hot) inorganic acids, such as HF and HF/HNO3 mixtures, and resistant to molten alkali [6].

1.4. Structures of Niobium Oxide The main oxides formed by niobium are designated as: niobium pentoxide Nb2O5 (niobium oxide V); niobium dioxide NbO2 (niobium oxide IV) and niobium monoxide NbO (niobium oxide II). In the lower oxidation states, niobium forms a large number of lattices, with groups of metallic atoms bonded together [6, 7]. Niobium pentoxide (Nb2O5) has different forms. The presence of polymorphic forms and the phase transformations of niobium oxide strongly depend on the heat treatment. The amorphous niobium oxide after heat

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P. Sergio Theodoro, P. Aaugusto Arroyo, E. Antonio da Silva et al.

treatments with temperatures ranging from 300 oC to 1000 oC, undergoes an increase in the degree of crystallinity for more stable phases and forms. Amorphous niobium oxide (Nb2O5) has as structural units the NbO6 distorted octahedron, NbO7 pentahedron and NbO8 hexahedron [8].

1.5. Use of CaO as an Active Phase CaO is one of the alkaline earth metal oxides, which are formed from an ionic crystal and with low Lewis acidity, due to the low electronegativity of the metal cation. As the conjugated oxygen anion has a strong basic characteristic, it gives calcium oxide a strong basic property [9–11]. The high basic strength of the CaO surface sites is responsible for the excellent adsorbent property of this oxide. Thus, several studies were developed using CaO as an adsorbent, among them we have the destructive adsorption of chlorinated hydrocarbons [12], removal of SO2 at low temperature [13], removal of H2S [14], CO2 adsorption [15, 16], destructive adsorption of toxic chemicals, including chlorine carbon, organophosphorus compounds and acid gasses [17]. In the same way, this character of high basicity provides to the structural arrangement of CaO, the property of catalytic activity.

1.6. Thermogravimetric Analysis (TGA) Thermogravimetric analysis is one of the thermal analysis techniques, in which the mass loss of the sample is monitored as a function of temperature. With this technique, it is possible to evaluate the detailed path of the changes that heating can cause in substances, making it possible to establish the temperature ranges where decomposition, sintering, phase change and other changes in the structure occur according to the properties of each material, this profile of the mass variation as a function of temperature is represented by thermogravimetric curves [18, 19].

2. Objective The present study aims to evaluate the mass loss in the production of CaO/Nb2O5 catalysts and to obtain the temperature of interaction between the

The Use of Thermogravimetric Analysis …

57

active phase (CaO) and the support (Nb2O5) using thermogravimetric analysis (TGA).

3. Materials and Methods 3.1. Preparation of Niobium Oxide Support (Nb2O5) The support niobium pentoxide (Nb2O5) was prepared from hydrated niobium pentoxide, supplied by Brazilian Metallurgy and Mining Company (CBMM). First, the hydrated pentoxide was screened on a 100 mesh sieve, followed by heat treatment with a heating rate of 5 °C/min. up to 400 °C for 4 hours. The fraction of solids smaller than 100 mesh was used for the production of the catalysts.

4. CaO Preparation Calcium oxide (CaO) was dried at 120 °C for 12 hours followed by heat treatment at 600 °C for 3 hours. The fraction of solids smaller than 100 mesh was used for the production of catalysts by solid dispersion.

4.1. Synthesis of Catalysts (CaO/Nb2O5) The catalysts were prepared by solid dispersion of calcium oxide (CaO) on niobium pentoxide Nb2O5, in percentages of 5, 10, 15 and 20% of calcium oxide for Nb2O5.

4.2. Thermogravimetric Analysis (TGA) Thermogravimetric curves were determined on a Perkin Elmer model ST6000 thermobalance. The analyzes were performed under nitrogen flow, and the temperature range studied was from room temperature 30 °C to 400 °C, with a heating rate of 5 °C/min., using approximately 10 mg of sample.

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5. Results Figures 1 (a), (b), (c) and (d) show the thermogravimetric analysis curves (TGA) and the thermogravimetric derivative curves (DTG), for the respective CP71 catalysts (5% CaO), CP72 (10% CaO), CP73 (20% CaO) and CP74 (30% CaO).

Figure 1. TGA and DTG curves of catalysts, (a) CP71 (5%CaO/Nb2O5), (b) CP72 (10%CaO/Nb2O5), (c) CP73 (20%CaO/Nb2O5), (d) CP74 (30%CaO/Nb2O5).

In Figures 1 (a), (b), (c) and (d) it is observed that the TGA curves point to occurrences of mass loss events. These mass loss events presented intensities proportional to the concentration of calcium oxide (CaO) deposited on the Nb2O5 support. Which leads us to believe that at this temperature the active phase (CaO) interacted with the niobium pentoxide support (Nb2O5) forming the CaO/Nb2O5 catalyst. At the end of the heat treatment, the catalysts showed a reduction in mass percentage from 12 to 15%.

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According to the DTG curves in Figures 1(a), 1(b), 1(c) and 1(d) mass losses occur with greater intensity at the temperature close to 100 oC, this event possibly occurred due to the removal of the molecules of water physisorbed on the surface of solids, and by the reaction of water molecules with CaO so that the intensity of this event reduced as the percentage of mass CaO increased over Nb2O5. It is observed that another significant event of mass loss proportional to the levels of CaO deposited on the support, occurred at a temperature around 375 oC, possibly this event was caused by the removal of water molecules and the adsorption of the active phase CaO to the Nb2O5 support, occurring the formation of the CaO/Nb2O5 catalyst.

Conclusion Using thermogravimetric analysis (TGA), the behavior of mass loss in the production of catalysts formed by the active phase of calcium oxide and the niobium pentoxide support (CaO/Nb2O5) was obtained. Using the TGA and DTG curves, the percentages of mass gradients and temperatures where the events occurred were determined. At the end of the heat treatments, the catalysts showed a reduction in mass percentage from 12 to 15% and at the temperature of 375 oC, the formation of calcium oxide catalysts supported on niobium pentoxide (CaO/Nb2O5) occurred.

Acknowledgment Brazilian Metallurgy and Mining Company (CBMM).

References [1] [2]

[3]

Schmal M., Catálise Heterogênea [Heterogeneous Catalysis], Rio de Janeiro, 2011. Barbaro P., F. Liguori, Heterogenized Homogeneous Catalysts for Fine Chemicals Production: Materials and Processes, Springer Science & Business Media, Firenze Italy, 2010. https://doi.org/10.1007/978-90-481-3696-4. Campanati M., G. Fornasari, A. Vaccari, Fundamentals in the preparation of heterogeneous catalysts, Catalysis Today. 77 (2003) 299–314.

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P. Sergio Theodoro, P. Aaugusto Arroyo, E. Antonio da Silva et al. Xia W. S., H. L. Wan, Y. Chen, Cluster model study on the surface interactions of g -alumina-supported metal oxides, Journal Molecular Catalysis A: Chemical. 138 (1999) 185–195. Ciola R., Fundamentals of Catalysis, 1 th, Modern, São Paulo, SP, 1981. Nowak I., M. Ziolek, Niobium Compounds: Preparation, Characterization, and Application in Heterogeneous Catalysis., Chemical Reviews. 99 (1999) 3603–3624. http://www.ncbi.nlm.nih.gov/pubmed/11849031. Braga V. S., Preparation and characterization of catalysts based on niobium pentoxide and copper(ii) oxide applied in esterification and transesterification reactions, University of Brasilia-Brasilia, 2007. Jehng J. M., I. E. Wachs, The molecular structures and reactivity of supported niobium oxide catalysts, Catalysis Today. 8 (1990) 37–55. https://doi.org/10.1016/ 0920-5861(90)87006-O. Kouzu M., J. Hidaka, Transesterification of vegetable oil into biodiesel catalyzed by CaO: A review, Fuel. 93 (2012) 1–12. https://doi.org/10.1016/j.fuel.2011.09.015. Iizuka T., H. Hattori, Y. Ohno, J. Sohma, K. Tanabe, Basic sites and reducing sites of calcium oxide and their catalytic activities, Journal of Catalysis. 22 (1971) 130– 139. http://linkinghub.elsevier.com/retrieve/pii/0021951771902739. Witoon T., S. Bumrungsalee, P. Vathavanichkul, S. Palitsakun, M. Saisriyoot, K. Faungnawakij, Biodiesel production from transesterification of palm oil with methanol over CaO supported on bimodal meso-macroporous silica catalyst., Bioresource Technology. 156 (2014) 329–334. https://doi.org/10.1016/j.biortech. 2014.01.076. Koper O., Y. X. Li, K. J. Klabunde, Destructive adsorption of chlorinated hydrocarbons on ultrafine (nanoscale) particles of calcium oxide, Chemistry of Materials. 5 (1993) 500–505. https://doi.org/10.1021/cm00028a017. Renedo M. J., F. González, C. Pesquera, J. Fernández, Study of Sorbents Prepared from Clays and CaO or Ca(OH) 2 for SO 2 Removal at Low Temperature, Industrial & Engineering Chemistry Research. 45 (2006) 3752–3757. https://doi.org/10.1021/ ie060126q. Sotirchos S. V., A. R. Smith, Performance of Porous CaO Obtained from the Decomposition of Calcium-Enriched Bio-Oil as Sorbent for SO 2 and H 2 S Removal, Industrial & Engineering Chemistry Research. 43 (2004) 1340–1348. https://doi.org/10.1021/ie034176w. Reddy E. P., P. G. Smirniotis, High-Temperature Sorbents for CO 2 Made of Alkali Metals Doped on CaO Supports, The Journal of Physical Chemistry B. 108 (2004) 7794–7800. https://doi.org/10.1021/jp031245b. Liu W., H. An, C. Qin, J. Yin, G. Wang, B. Feng, M. Xu, Performance Enhancement of Calcium Oxide Sorbents for Cyclic CO 2 Capture—A Review, Energy & Fuels. 26 (2012) 2751–2767. https://doi.org/10.1021/ef300220x. Koper O. B., I. Lagadic, A. Volodin, K. J. Klabunde, Alkaline-Earth Oxide Nanoparticles Obtained by Aerogel Methods. Characterization and Rational for Unexpectedly High Surface Chemical Reactivities, Chemistry of Materials. 9 (1997) 2468–2480. https://doi.org/10.1021/cm970357a.

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Brown M. E., Introduction to the thermal analysis : techniques and applications, 2. ed., Publishers, ORDRECHT : Kluwer Academic, London, 2001. Ionashiro M., J. F. Caires, J. C. D. Gomes, Giolito - Fundamentals of Thermogravimetry, Differential Thermal Analysis and Differential Exploratory Calorimetry, 2nd ed., São Paulo ISBN 978-85-7855-222-0, 2014.

Chapter 3

Thermoelectric Generators (TEGs) Behnam Talebjedi1, Ali Khosravi2 and Mamdouh El Haj Assad3 1Department

of Mechanical Engineering, School of Engineering, Aalto University, Espoo, Finland 2SDU Mechatronics (CIM), Department of Mechanical and Electrical Engineering, University of Southern Denmark, Sønderborg, Denmark 3Department of Sustainable and Renewable Energy Engineering Department, University of Sharjah, United Arab Emirates

Abstract Restrictions on the use of fossil fuels, environmental concerns, and rising prices for energy carriers are issues facing the industry today. Therefore, energy-harvesting power generators are a viable option to increase energy efficiency in industrial plants. Thermoelectric generators (TEGs) have proven their power in straight converting thermal energy into electrical energy through the Seebeck effect. Furthermore, TEGs are considered green technology due to the absence of chemical materials production. In addition, they operate smoothly and silently since they have no moving parts. In this chapter, thermoelectric generator (TEG) technology is explained along with its various applications on a small and large scale for the energy efficiency improvement of the industrial and domestic sectors. In addition, the TEGs performance mechanism, parameters affecting their performance and efficiency, and the relevant equations have been provided. A discussion of some practical TEG examples for industrial applications is presented at the end of this chapter. 

Corresponding Author’s Email: [email protected].

In: The Fundamentals of Thermal Analysis Editors: Mamdouh El Haj Assad, Ali Khosravi and Mehran Hashemian ISBN: 979-8-88697-759-2 © 2023 Nova Science Publishers, Inc.

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Keywords: thermoelectric generators, clean energy, energy conversion, waste heat, power generation

1. Introduction One of the main daily issues is the availability of clean and non-polluting energy. Currently, fossil fuels contribute the most to the world’s energy production. Fossil-based energy sources are harmful, release greenhouse emissions, and there are limitations in their exploration and extraction [1]. On the other hand, energy efficiency improvement of sectors that produce or use energy has become crucial due to the growing usage of fossil fuels to supply the energy needed by industry and the residential sector as well as growing environmental concerns about the impact of burning fossil fuels [2, 3]. In this regard, heat recovery or the use of green energy sources is one of the most important issues in the field of energy today [4]. One of the latest developments in the electricity generation industry is the use of thermoelectric technology to generate electrical energy. Thermoelectric generators (TEGs) are suitable alternatives for heat recovery and direct conversion of heat into electricity. TEG technology has several advantages over conventional methods of generating electricity, such as high reliability, simplicity that does not have a moving part (which increases its reliability and longevity), as well environmentally friendly (not using any refrigerants or greenhouse gases). Several other substrates, including silicon, polymers, and ceramics, can be used to create them. TEGs are also position-independent, have a long operational lifespan, and may be included in bulky and flexible devices [5]. Straight conversion of the temperature differences among two irrelevant materials to electrical energy is introduced as the thermoelectric (TE) phenomenon. The Seebeck effect is the name given to the phenomenon that Thomas Seebeck identified in 1821. He demonstrated how two conductors' junction heating with different properties might generate an electromotive force. Figure 1 depicts the Seebeck effect in thermoelectric materials. The temperature gradient effect on the distribution of free charge pathways (electrons and holes) causes a voltage difference at the two open ends of the unicouple. Researchers have been attempting to comprehend and regulate thermoelectricity (TE) since Seebeck discovered it in 1821 [1]. Precise mathematical models are needed to simulate and design TEGs. Different

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mathematical models have been presented in previous research, where their simplifications and operating conditions are reported in [6–8]. Overall, the current chapter attempts to offer a realistic and clear perspective on the applications and characteristics of thermoelectric generators within the framework of the current energy market. In section 2 of this chapter, we introduce the principles of thermoelectric generators. Section 3 presents the TEGs design methodology and section 4 discusses TEG materials. The TEG applications are then thoroughly covered in section 6. In section 7, we give our conclusion.

Figure 1. Schematic diagram of Seebeck effect in thermoelectric unicouple [9].

2. Fundamentals of Thermoelectric Generators Thermoelectric generators (TEGs) are based on the Seebeck effect phenomenon, where the main use is the direct conversion of thermal energy into electrical energy. TEGs are composed of a large number of interconnected thermopiles, which increase their output power. Each thermopile consists of many thermocouples that have a series of electrical structures and a parallel thermal structure. The thermoelectric generator principle and the equivalent electrical circuit is shown in Figure 2. Thermocouples are assembled with two distinct materials with an opposite Seebeck coefficient and concatenated at their ends. Because of the Seebeck phenomenon, the temperature difference between the cold and hot ends causes a difference in potential and, ultimately, the electrical voltage. The energy harvesting thermoelectric generator output voltage is provided in Eq. 1 [5] as: 𝑉 𝑜𝑢𝑡 = 𝑁(∝1 −∝2 )(𝑇ℎ𝑜𝑡 − 𝑇𝑐𝑜𝑙𝑑 )

(1)

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Behnam Talebjedi, Ali Khosravi and Mamdouh El Haj Assad

where 𝑉𝑜𝑢𝑡 is the TEG output voltage; 𝑁 represents the number of thermocouples in series; ∝1 and ∝2 are the Seebeck coefficients of joint materials constructing the thermoelectric generator; 𝑇ℎ𝑜𝑡 and 𝑇𝑐𝑜𝑙𝑑 are the temperature of the cold and hot junctions in the thermocouple, respectively. The Seebeck coefficient (∝) shows the generated voltage difference for an applied temperature gradient, which is given as: ∝= ∆𝑉⁄∆𝑇

(2)

Total electrical internal resistance is proportional to the 𝑁 since thermocouples are electrically linked in a series arrangement. Accordingly, increasing the number of thermocouples will increase the output voltage while increasing the internal resistance, as shown in Figure 2b. The internal resistance of TEGs is expressed as: 𝑅𝑇𝐸𝐺 = 𝑁(

𝜌𝐴 𝐿𝐴 𝑆𝐴

+

𝜌𝐵 𝐿𝐵 𝑆𝐵

+2

𝜌𝐶 𝐿𝐶 𝑆𝐶

)

(3)

where 𝜌𝐴 , 𝜌𝐵 and 𝜌𝐶 are the electrical resistivity of the materials A, B, and metallic contact, respectively. 𝑆𝐴 , 𝑆𝐵 , and 𝑆𝐶 are cross-sectional areas of the materials A and B thermocouples and contacts, respectively. 𝐿𝐴 and 𝐿𝐵 are the arms lengths of the thermocouple crossed by the heat flow, and 𝐿𝐶 is the contact length. The generator output provided power is obtained as: 2 𝑃 = 𝑉𝑜𝑢𝑡

𝑅𝐿 (𝑅𝑇𝐸𝐺 +𝑅𝐿 )2

(4)

where 𝑅𝑇𝐸𝐺 and 𝑅𝐿 are the internal electrical resistance and external load resistance, respectively (Figure 2b).

Figure 2. Typical structure of thermoelectric generator. a) principle, b) electrical circuit [5].

Thermoelectric Generators (TEGs)

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3. TEGs Design Approach TEG design approaches differ according to the arrangement of the thermocouples on the substrate concerning the heat flow direction. The main design approaches based on the configuration of thermoelectric (TE) materials can be classified as planar (lateral TCs arrangement, lateral heat flow) and vertical (vertical heat flow, vertical TCs arrangement). Despite the fact that vertical TEGs generally contain more thermocouples (TCs) and provide a better density power production than the planar design, these types of TEGs are made of thick, expensive, and non-CMOS-compatible TE materials, such as 𝐵𝑖2 𝑇𝑒3 . In contrast, planar TEGs authorize a more straightforward execution of TCs with a high aspect ratio (thickness vs. length) and the option to utilize cheap, thin, and CMOS-compatible TE such as poly-Silicon (pSi) [10]. Planar TEGs (Figure 3a) utilize a lateral TCs set up to convert a lateral heat flow. The advantage of this method compared to other types is the possibility of manipulating the length and thickness of the thermocouple arm, and its compatibility with the placement of a thin film layer that allows making longer and thinner thermocouples. On the other hand, the use of long thermocouples arms increases the temperature gradient, thermal resistance, and ultimately the delivered voltage. The vertical TEG design (second design method) consists of vertically positioned thermocouples between the heat sink and heat sources (Figure 3b). Hence the heat flows vertically along the arms of the thermoelements. Due to the simplicity of the TEGs with the vertically arranged thermocouples, these types of TEGs are the most commercial types that deliver high output voltage.

Figure 3. Different TEGs designs: (a) Planar, (b) Vertical [5].

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Behnam Talebjedi, Ali Khosravi and Mamdouh El Haj Assad

3.1. Figure of Merit FOM and Conversion Efficiency Choosing the right semiconductor and conductive materials to achieve greater electrical efficiency, such as lower internal resistance, higher voltage, and output power, is essential. The figure of merit (𝑧) is the quality factor that evaluates the suitability of thermoelectric materials, which is expressed as: 𝑧=

𝛼2

(5)

𝜌𝜆

where 𝜌, 𝛼, and 𝜆 are the electrical resistance [𝛺 𝑚], the Seebeck coefficient [V/K], and the material thermal conductivity [W/(Km)], respectively. This metric shows the efficiency of thermoelectric materials in converting thermal energy to electricity. The higher value for the FOM metric shows the higher efficiency of the material. Therefore, the figure of merit (FOM) is temperature dependent, and each substance expresses its maximum figure of merit in its specific temperature range. The dimensionless figure of merit for one TE material is given as [11]: 𝑧𝑇 =

𝛼2 𝜌𝜆

𝑇

(6)

where 𝑇 is the absolute average temperature [K], the dimensionless figure of merit for a thermoelectric made of materials A and B is: (𝑧𝑇)𝐴𝐵 =

[(𝜌𝐴 𝜆𝐴

2 𝛼𝐴𝐵 0.5 ) +(𝜌

0.5 2 𝐴 𝜆𝐴 ) ]

𝑇

(7)

Since TEGs use the concept of the temperature difference between two samples to convert heat into electricity, their efficiency is calculated according to Eq. 8 as: 𝜂=

𝑁𝑒𝑡 𝑜𝑢𝑡𝑝𝑢𝑡 𝑝𝑜𝑤𝑒𝑟

(8)

𝐼𝑛𝑝𝑢𝑡 ℎ𝑒𝑎𝑡

Equation 9 gives the maximum energy conversion efficiency (Carnot efficiency) as a function of the dimensionless figure of merit of the used material, which is expressed as: 𝜂𝑚𝑎𝑥 =

𝑇ℎ −𝑇𝑐 √1+𝑧𝑇̅ −1 𝑇ℎ

𝑇 √1+𝑧𝑇̅ + 𝑐

𝑇ℎ

(9)

Thermoelectric Generators (TEGs)

69

where 𝑇̅ is the average temperature of the heat source (𝑇ℎ ) and sink (𝑇𝑐 ), and 𝑧𝑇̅ is the figure of merit. Equation 9 gives insight into selecting material for fabricating TEG, where higher 𝑧𝑇̅ gives higher efficiency for constant 𝑇ℎ 𝑎𝑛𝑑 𝑇𝑐 . Low thermal conductivity and electrical resistance with a high Seebeck coefficient for the thermoelectric materials improve the figure of merit and, consequently, conversion efficiency. 𝐵𝑖2 𝑇𝑒3 , 𝑃𝑏𝑇𝑒 and 𝐶𝑜𝑆𝑏3 are the most prominent and widely used materials for thermoelectric which deliver a 𝑧𝑇̅ of almost 1. [12]. FOM decreases with higher thermal conductivity because it causes unwanted heat transfer between the hot and cold sides of the thermoelectric device. Nowadays, new thermoelectric materials having a higher figure of merit are of interest to researchers to industrialize the use of thermoelectrics. However, a major problem limiting access to the larger figure of merit is the Seebeck factor dependency on electrical conductivity, where they are inversely related. Nevertheless, research shows that synthesizing some materials like 𝐶𝑢2−𝑥 𝑆𝑒, and 𝑃𝑏𝑇𝑒0.7 𝑆0.3, it is possible to achieve 𝑧𝑇̅ of bigger than 2 [13].

4. Thermoelectric Materials In the segmented TEGs construction, the TE materials are organized from high to low temperatures in accordance with their ideal working range. The compatibility of the segmented materials, however, may be impacted by heterogeneity between various stacked materials, with different mechanical properties, particularly chemical and thermal stability, mechanical stresses, and thermal expansion coefficients, which would then lower the maximum thermoelectric efficiency (𝜂𝑚𝑎𝑥 ). The field of thermoelectric materials, comprising composites, organics, oxides, Heusler, clathrates, Zintls, skutterudites, silicides, and chalcogenides, has seen significant advancements equipped with a variety of methodologies, including magnetic effects strategy, nano-engineering, phonon-glass electroncrystal (PGEC) strategy and electronic band engineering [9]. As a result, Figure 4 displays the figure of merit against temperature for a few modern n/ptype bulk TE materials that have been reported during the previous 20 years.

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3

a) n-type

2.5

zT(-)

2 1.5 1 0.5 (Sr,Ba,Yb)y

0

300

400

600 700 500 Temperature (K)

800

400

500 600 700 Temperature (K)

800

900

b) p-type 3.5 3

zT(-)

2.5 2 1.5 1 0.5 0

300

900

Figure 4. A brief summary of some of the best temperature-dependent zT for bulk thermoelectric materials [9].

This graph makes it clear that even the best thermoelectric materials are only useful and effective for a limited range of temperatures. One of the key problems of device-level design is combining these materials to get the best

Thermoelectric Generators (TEGs)

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performance. Furthermore, raising zT value and enhancing TE materials' thermoelectric capabilities are just the beginning. The materials' toxicity, chemical stability, thermal stability, machinability, mechanical stability, availability of raw materials, and other issues make it difficult to bring these materials to practical application levels.

5. TEGs Applications The working conditions of TEGs, as well as their heat source, are two important parameters in the classification of their applications [14]. TEGs are used in different applications based on their size and supply power. Therefore, TEGs can be divided into micro and large TEGs (or bulk). The first type operates with small wasted heat and provides electrical power from μW to a few mW [15]. The second class is small with a millimetric size and delivers output power from several to hundreds of Watts, mainly used for industrial purposes where there is a high heat level. Five important applications of TEGs are provided as follows:

5.1. Electricity Production in Harsh Environments Electricity generation in harsh conditions necessitates fulfilling a set of very stringent features. These sorts of applications are primarily critical and require a highly consistent energy source for a long period. Maintenance must be as low as possible since, in many circumstances, they are hard to access. For instance, these systems should be able to function in space (that is hard to access) in a vacuity and resist high vibrations [16]. Another example is industrial applications in remote areas.

5.1.1. Space Industry TEGs have been used in space exploration based on nuclear technology: radioisotope thermoelectric generators (RTGs). Nuclear fission or fusion does not happen in Radioisotope generators, whereas heat is generated by the natural radioactive decay of plutonium-238. The initial use of TEG (Pb-Te) belongs to the US Navy’s Transit navigation satellite (1961). The satellite was equipped with a space Nuclear Auxiliary Power (SNAP-3) where the generated power was only 2.7 𝑊 operating for over fifteen years. RTGs were

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prominent because of their small mass and high reliability. RTGs are able to operate for several decades after installation. RTGs can be used to deliver electricity for distant missions where sunlight is inadequate to provide solar panels. Solar radiation on the Earth is about 1375 𝑊/𝑚2 where the radiation drops to 1 𝑊/𝑚2 near Pluto. RTGs have also been utilized in the Voyager I and II spacecraft because of their outstanding reliability in powering the onboard devices and communication systems.

5.1.2. Industrial Applications TEGs in Remote Areas TEGs can create power in remote locations with high reliability and little maintenance. Today, Gentherm [17] is the industry leader in the manufacture of power generation for isolated locations. In its 30 years of operation, the business has created around 22,000 installations. These TEGs utilized the heat generated by combusting propane, butane, or natural gas.

5.2. Waste Heat Recovery Waste heat that is rejected from a thermal process is referred to as waste heat. Equipment inefficiencies and process-related thermodynamic constraints are the two primary causes of waste heat. Although heat losses resulting from inefficiencies must be minimized, those resulting from thermodynamic constraints must be recovered and used again in another process. TEGs are promising technology to contribute to the heat recovery of thermal energy. The two major energy-consuming sectors in the world are transportation and industry, both of which primarily rely on fossil fuels and release enormous amounts of heat into the atmosphere. The automotive sector is also interesting because of the competition in the green transportation industry. So far, various attempts have been made to recover the lost heat of the engine exhaust. For example, it is important to recover heat from the hot gas in the exhaust of the choppers and airplanes in the aeronautics industry.

5.2.1. Industrial Waste Heat Various industrial waste heat sources are available, and the thermoelectricity integration with diverse heat sources is beneficial to improving industrial energy efficiency. In this regard, TEGs have been utilized in a variety of waste heat recovery (WHR) applications. These applications can be categorized as flue gas waste heat recovery (an example is shown in Figure 5), waste heat

Thermoelectric Generators (TEGs)

73

recovery from industrial process products, and other unconventional heat sources for TEGs in the industry (such as glass melting process).

Figure 5. Waste heat recovery setup recovering heat from flue gas: schematic of the heat pipe thermoelectric generator (HP-TEG) [18].

5.2.2. Automotive Industry Increasing the efficiency of engines in the automotive industry is very important because reducing fuel consumption due to high prices and

74

Behnam Talebjedi, Ali Khosravi and Mamdouh El Haj Assad

greenhouse gases due to environmental issues is a necessity. Several studies [19-21] investigate the possibility of recovering heat generated by internal combustion engines and converting it directly into electrical energy. About 40% of the energy from fuel combustion inside the engine is wasted as exhaust gas in passenger cars, which is a good heat source for thermoelectrics [22]. Two appropriate locations for using TEGs in an automobile are the radiator (used for cooling the engine) and waste exhaust heat. Due to the exhaust outlet’s high temperature, the thermoelectrics placement at the exhaust heat exchanger is the most mentioned in the literature articles [19], [23]. The TE modules are affixed to the exhaust system shell in a matrix arrangement. The heating flow from the exhaust inlet to the exhaust outlet delivers the TEGs' hot sides thermal energy. Figure 6 shows the arrangement of 32 TEG modules, consisting of 24 TCs each, on flat exhaust gas [24]. Mainly liquid is utilized to keep the cold side temperature of the TEG module. Saved fuel costs result of using TEGs can be analytically calculated by combining different efficiency factors. Equation 10 presents the expression for the fuel cost saving: 𝑆𝑎𝑣𝑒𝑑 𝐹𝑢𝑒𝑙 𝐶𝑜𝑠𝑡 =

𝜂𝑇𝐸𝐺 ×𝜂𝐸𝑋 ×𝜂𝐻𝐸 𝜂𝐴𝐿 ×𝜂𝐸𝑁𝐺

(10)

where 𝜂 𝑇𝐸𝐺 is thermoelectric generator efficiency, 𝜂𝐸𝑋 is the exhaust gas efficiency, 𝜂𝐻𝐸 is the heat exchanger efficiency, 𝜂𝐴𝐿 is the alternator efficiency, and 𝜂𝐸𝑁𝐺 is the engine's thermal efficiency. Considering an energy efficiency of 10% and diesel price of 0.794 $/𝑙, the saving in the fuel cost would be 0.1588 $/𝑙 which is equal to almost 20% fuel cost saving.

Figure 6. TEG setup on a flat heat exchanger [24].

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Figure 7. Rectangular exhaust heat exchanger [26].

Large, international automakers have shown an interest in exhaust heat recovery by creating TEG-based systems, including BMW, Ford, Renault, and Honda [25]. They all have rather similar designs. The TEGs are often mounted on the surface of the exhaust pipe (which may be rectangular, hexagonal, etc.) and cooled with cold blocks utilizing engine coolant.

Figure 8. Hexagonal exhaust heat exchanger [26].

Figure 7 and Figure 8, respectively, show examples of heat exchangers with rectangular and hexagonal shapes [26]. This technology is currently in the idea phases and has not yet been incorporated into current production vehicles. Shell and tube heat exchangers are utilized in the BMW setup. The

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Behnam Talebjedi, Ali Khosravi and Mamdouh El Haj Assad

system is capable of producing 750 W from a number of 20 W rated TEGs when high-temperature TEGs are employed. There are several tiny parallel passages coated with thermoelectric material for the exhaust gases to travel through the Ford system heat exchanger. In this instance, liquid cooling is applied. A maximum of 400 W may be generated by this setup using 4.6 kg of thermoelectric material. Additional TEGs waste heat recovery uses include the ship, locomotive, aviation, and helicopter sectors.

5.3. Combined Heat and Power (CHP) Generation Systems Most electricity is generated by large central units that are delivered to the energy consumer by transmission lines. Nevertheless, considerable areas, particularly in developing countries, are not still electrified. In addition, connecting to the natural grid in some remote areas in developed countries is not economical and environmentally friendly because of the energy loss in transmission lines. Therefore, an independent energy production system (Energy Hubs) is a reliable option for power production for developed and developing countries [27]. TEGs are applicable for both electricity production and combined heat and power systems. Micro-combined heat and power (micro-CHP) technologies provide encouraging solutions to improve power production efficiency. Integrating domestic gas-fired boilers and high-temperature thermoelectric generators (TEGs) as an innovative micro-CHP system without moving components permits various applications [28]. The ultra high power density of 2.1W/cm2 and 5.3% electrical efficiency are produced by TEGs made with high-efficiency nanostructured bulk half-Heusler alloys under temperature variations of 500°C between the hot and cool sides. Depending on the TEG's total heat input, the TEG system turns thermal energy into electrical energy with an energy efficiency of 4% by making use of the untapped exergy between the water and combustion gas. Numerous potentials exist to revolutionize power-generating methods and increase energy efficiency thanks to high-performance TEGs. Figure 9 illustrates a layout of a micro-CHP system utilizing bulk TEGs that have been nanostructured for the greatest temperature differential between the boiler water tubes and combustion gas heat exchanger.

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Figure 9. Micro-CHP system employing nanostructured bulk TEGs sandwiched for maximal temperature gradient between the boiler water tubes and combustion gas heat exchanger [28].

Due to the affordable fuel cost for space heating, solid-fuel stoves are more widely utilized in impoverished nations, rural areas, and generally. An additional advantage is a potential for producing energy and heating water with a stove. Figure 10 presents thermoelectric generators used for a solid-fuel stove to simultaneously heat water and charge a lead-acid battery for heating and domestic consumption. The suggested CHP system’s viability is shown for a typical solid-fuel stove. During a 2-hour trial, this system generated an average of 600 Wth and 27 Wel (42 Wel peak), where the TEG energy efficiency is almost 5% [29]. Micro combined heat and power (µCHP) system based on a stovepowered thermoelectric generator (SPTEG) was created and tested for the Coproduction of electricity and heat in off-grid regions and the countryside, especially in case of emergency circumstances [30]. They presented a method for simultaneously increasing heating power to over 9.8 kW and electric power to over 200 W. This method combines heat collecting, temperature management, electricity conditioning, and storing, and thermoelectric (TE) module wiring. In-depth research and discussion were conducted on material cost analyses, power load characteristics, temperature distributions, battery charging curves, and heat collecting. According to their findings, the SPTEGbased µCHP (SPTEG-µCHP) system can significantly improve living conditions in rural and urban regions, particularly in times of emergency. The proposed SPTEG-µCHP system is shown in Figure 11.

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Figure 10. Schematic diagram of the connections and measurements for the CHP system for the stove [29].

Figure 11. Representation of the SPTEG-mCHP system (a) configuration, (b) electric circuit and energy flow [30].

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5.4. Domestic TEG in Developed Countries High-performance wood stove utilization is increasing in developed countries to minimize the cost and environmental impact. These types of stove combustion are required to be controlled accurately for the minimum emission. Electronic elements such as actuators, fans, sensors, microcontrollers, and valves are essential components. Electricity availability is crucial for these systems’ operation. The electricity grid connection can be costly for houses not being used regularly. Renewable energies such as solar power are also limited because of their dependency on weather conditions, time of day, and massive batteries to store electricity, while stove heat can be used for electricity generation. Power cuts often happen during the cold season in the homes connected to the grid in Europe, which causes dissatisfied residents because of cutting their access to the heat. Therefore, developing a system to guarantee stove independence is valuable. Codecasa [31] investigated TEG integration with a gas heater. The first TEG was examined on an autonomous heat-radiating gas heater for commercial outdoor environments, where a power of 8W was received. Another prototype has been developed for gas combustion heat radiating units utilized in industrial and residential settings. These heaters work autonomously with a regional gas supply. The heating efficiency can be increased by using a fan to force air through the heat exchanger. The TEG enables the local electricity production to supply the fan without the necessity of the electricity grid.

5.5. Micro-Generation for Sensors and Microelectronics Sensors are essential devices to control industrial processes. Manufacturers can improve the quality of their products by online monitoring of the system and processes through installed sensors in the production line. However, recent smart sensors need only a few mW to function. Therefore, long cables are required to provide electricity for the online sensors from the electricity grid, which costs considerably to supply little electricity. The lifespan of the sensor must match the power supply. Wireless sensors are able to operate for over ten years; however, batteries are limited to functioning for a few years in the best case. Battery replacement in industrial processes is hard, costly, and causes an interruption in the production line. Manufactories are interested in using micro-generators to deliver self-sufficient electricity for their sensors.

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There are different heat sources in industrial mills, such as hot steam, hot fluids, motors, etc. TEGs are an ideal option to overcome this problem. Reliable operation and satisfactory performance in challenging environments are furthermore significant benefits for TEGs [32]. Five subsystems make up a comprehensive thermoelectric energy harvesting-powered wireless sensor network (WSN) system, as depicted in Figure 12 [33]. It includes the TEG module, the WSN mote, the output power regulation, the energy storage unit, and the ultra-low voltage step-up DC/DC converter.

Figure 12. Block diagram of a wireless sensor network driven by thermoelectric energy [33].

5.6. A Solar Thermoelectric Generator (STEG) There is a strong desire to create technology that can supply dependable and autonomous conversion of sunshine into power because many of the finest solar resources in the world are inversely connected with urban areas. Due to their lack of moving parts and ability to operate in distant areas, thermoelectric generators are gradually making progress in this field. A solar thermoelectric generator (STEG) is a promising new technology that uses the sun’s heat to produce electricity similar to photovoltaic systems. It uses the Seebeck effect for heat-to-electricity conversion. This system is similar to photovoltaics for the direct conversion of heat to electricity without a mechanical process. Due to the low efficiency of TEG systems, their application in industry and other applications has been limited, but with recent improvements, this technology can be very reassuring. In order to compute the efficiency of Solar TEGs, the efficiency of converting sunlight energy into heat, as well as thermoelectric efficiency, are influential.

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Both concentrated and non-concentrated systems are becoming more interested in STEG systems, which have also been used in hybrid configurations with solar thermal and photovoltaic systems. Figure 13 shows the use of thermoelectric generators in various solar thermal systems. Liu et al. [35] developed a sandwich-like shape model for a flat-plate solar thermoelectric generator (STEG), as presented in Figure 14. Numerical simulations were used to examine the effects of the length of the thermoelectric legs, the heat concentration ratio, and other geometrical parameters on the performance of the STEG. According to their findings, 𝐵𝑖2 𝑇𝑒3 -based STEGs operating in the Earth’s orbit has an output power per unit mass and maximum conversion efficiency of 6.5 W/kg and 5.5%, respectively.

Figure 13. Thermoelectric generator deployed in different solar thermal systems [34].

Figure 14. Schematic of the unit cell of a sandwich-like STEG, which is made up of a heat sink, a pair of p-type and n-type thermoelectric legs, and a flat-plate thermal absorber [35].

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5.7. Other Applications 5.7.1. Photovoltaic System TEGs can also be used on the rear side of photovoltaic panels to gather waste heat. The performance analysis of solar photovoltaics integrated with the TEG system has been done by Bjork et al. [36]. They used an analytical model for four diverse types of commercial photovoltaic panels and a commercial 𝐵𝑖2 𝑇𝑒3 TEG. It has been proved that because of the low efficiency of TEG, the reduction in photovoltaic performance due to higher temperature is more than TEG power production. Lately, Attivissimo et al. [37] did the same analysis and reached more favorable results, while Makki et al. [38] studied a more comprehensive system consisting of a heat pipe removing the heat from the cold side of the photovoltaic TEG system. Results indicated a 1–2% increase in efficiency in the conventional photovoltaic panel. 5.7.2. Geothermal Energy Geothermal energy is one of the renewable energy sources. TEG is one of the systems that transform geothermal energy into electrical energy. They are ecologically benign since they don’t emit greenhouse gases when producing electrical energy. In order to convert geothermal energy directly into electrical energy, Ahiska et al. [39] developed a microcontroller-controlled TEG. After testing the system, the performance analysis of the TEG was reviewed. Their system offered energy transformation through the Seebeck effect in the thermoelectric modules. The thermoelectric modules were able to provide a variable DC voltage in response to temperature differences. 5.7.3. Medical Domain In the past, TEGs have been widely employed for temperature control of medical equipment and patients, where dependability and noiseless operation are more crucial than the coefficient of performance (COP). TEGs are positioned as key micro energy harvesters due to the Medical Internet of Things (MIoT) development, next-generation wearable devices, and Ultrasmall sensors. Figure 15 illustrates a general classification of TEGs used in medical applications.

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Medical applications of TED

Patient cooling

Medical devices temperature management

Thermoelectric generators

Implantable

Wearable

Figure 15. Classification of TED in medical applications [40].

Conclusion Thermoelectric devices can be used for heating/cooling or electricity generation. They are promising devices with the potential technology for heat recovery in various industrial applications. This chapter comprehensively analyzed thermoelectric generators for waste heat recovery in different sectors. Energy efficiency is the main challenge of using thermoelectrics, so the correct choice of materials used is one of the most important parameters in their design. Thermoelectric generators have proven their ability to produce high and low power as well as small and large scale, based on the utilized materials and the manufacturing process. Many of their applications and design parameters, performance, and related physics phenomena have been described in this book chapter.

Acknowledgments Aalto University’s Department of Mechanical Engineering is acknowledged by the first author. SDU Mechatronics (CIM), Department of Mechanical and Electrical Engineering, University of Southern Denmark is acknowledged by the second author.

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Chapter 4

Thermal Analysis of Thermoelectric Devices Farzad Tohidi1 Mehran Hashemian1, and Mamdouh El Haj Assad2 1Department

of Mechanical Engineering, Faculty of Engineering, Urmia University, Urmia, Iran 2Department of Sustainable and Renewable Energy Engineering, University of Sharjah, United Arab Emirates

Abstract In this chapter, an overview of the analytical modeling of thermoelectric devices is presented. The basic concepts of thermoelectricity are first introduced, followed by the derivation of the CPM model for three operation modes of thermoelectric unicouples. The limitations of the CPM model are discussed and methods for determining the constant value for the CPM model are introduced. Additionally, a brief examination of the parasitic losses in thermoelectric devices and their impact on thermal and electrical modeling is provided. The aim of this chapter is to provide a comprehensive understanding of the analytical modeling of thermoelectric devices, with the hope of advancing the development and widespread use of these attractive energy conversion devices.

Keywords: thermoelectricity, analytical modelling, power generation, heat transfer, heating/cooling



Corresponding Author’s Email: [email protected].

In: The Fundamentals of Thermal Analysis Editors: Mamdouh El Haj Assad, Ali Khosravi and Mehran Hashemian ISBN: 979-8-88697-759-2 © 2023 Nova Science Publishers, Inc.

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1. Introduction Thermoelectric converters are solid state devices capable of directly converting heat to electricity and vice versa. Outstanding characteristics of this green technology include high reliability, long lifespan, high scalability, compactness, noiseless operation, and so on. Although these characteristics have kept thermoelectric devices in the market for some niche applications, their low efficiency has prevented them from flourishing in the true sense [1]. Nevertheless, with the new advances in thermoelectric materials, thermoelectric devices are regaining some interest for a broad variety of potential applications [2]. However, to put such potential to practice is another matter and at the moment the newly found materials and practical applications seem far apart. Accurate thermal, electrical, and mechanical analysis of these materials can facilitate the development of new thermoelectric devices from newly introduced thermoelectric materials. However, finding an accurate and fast tool to analyze and optimize the thermal and electrical performance of thermoelectric devices is not straightforward. Since the discovery of thermoelectric effects, the theoretical analysis and accurate modeling of these phenomena have been a place of debate and discussion. Generally speaking, the coupling between thermal and electric fluxes along with the interdependency of transport coefficients (including thermal and electrical conductivities and Seebeck coefficient) and local temperature make the theoretical analysis of thermoelectric devices somewhat difficult. Also, other factors including the heat leakage from thermoelectric legs, contact resistances, and heat transfer to/from heat exchangers add to the complexity of the theoretical analysis of thermoelectric devices. Nevertheless, a variety of methods have emerged and evolved throughout the past decades including numerical and approximating analytical methods. Numerical methods can provide high accuracy at the expanse of long processing times while the approximate analytical methods, if used carelessly, can be misleading and highly inaccurate. The present chapter aims to show the challenges and advantages of using an approximate analytical model to simulate thermoelectric devices’ performance.

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2. Basic Concepts As shown in Figure 1 a typical thermoelectric device is made up of a number of pn unicouples sandwiched between two ceramic plates [3]. A pn unicouple is the smallest functioning unit of a thermoelectric device and is made of pand n-type thermoelectric materials electrically connected in series while thermally arranged in parallel. To appropriately understand the conversion of electricity and temperature gradient in a thermoelectric device, one should be familiar with the three basic thermoelectric effects including Seebeck, Peltier and Thomson effects.

Figure 1. A typical thermoelectric module reprinted from ref [3].

The Seebeck effect is the production of an electromotive force due to a temperature gradient between two junctions of a thermocouple. The so-called

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Seebeck coefficient (𝛼) equals the ratio of the electric potential difference (𝑉 ) between the two junctions to their temperature deference (∆𝑇). 𝑉

𝛼 = ∆𝑇

(1)

The Peltier effect is a heating or cooling effect due to the passing of an electric current through the junction of two dissimilar conductors connected in an electric circuit. Peltier coefficient (𝜋) of a thermocouple is defined as the ratio of the absorbed/released heat (𝑄 ) in the junction to the current (𝐼) passing through, 𝜋=

𝑄

(2)

𝐼

The Thomson effect is a heating or cooling effect due to the coexistence of a temperature gradient and an electrical current inside a homogeneous conductor. Thomson coefficient (𝜏) is defined as the heating/cooling rate (𝑄 ) caused by the transition of current (𝐼) through a conductor in which there is a temperature gradient (∆𝑇), 𝜏=

𝑄

(3)

𝐼∆𝑇

W. Thomson (later Lord Kelvin) was the first to provide a theoretical description of the thermoelectric effects. He discovered the Thomson effect by analyzing the relationship between Seebeck and Peltier effects. Also, he was able to draw the relations between the thermoelectric effects as follows (first and second Kelvin relations), 𝑑𝛼

𝜋 = 𝛼. 𝑇; 𝜏 = 𝑇 𝑑𝑇

(4)

Looking at Eq. (4), one can argue that the thermoelectric effects are essentially different manifestations of the same underlaying phenomenon. Thomson’s work showed that a thermoelectric device is a type of heat engine that can be utilized for purposes of power generation, cooling, or heating. However, utilizing thermoelectric effects for the mentioned purposes is not as straightforward as one may assume. In an operating thermoelectric device, the three above mentioned effects are accompanied by two other irreversible

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phenomena. Fourier heat conduction and Joule heating effect are inevitable when a conductor is subject to a temperature gradient and an electrical current, 𝑞𝐹 = −𝜆𝛻𝑇; 𝑞𝑗 = 𝜌𝑗 2

(5)

where 𝑞𝐹 and 𝑞𝑗 represent the differential forms of Fourier and Joule heat, respectively; 𝜆 is the thermal conductivity, 𝜌 is the electrical resistivity and 𝑗 is the current density. Looking at equations (1)-(5) one may deduce that the performance of a thermoelectric device depends on the struggle between the abovementioned reversible and irreversible forces. In the early 20th century it was Altenkirch who recognized such a pattern. He showed, with evidence, that a good thermoelectric material must have low thermal conductivity 𝜆, and low electrical resistivity 𝜌, to minimize the Fourier heat conduction and Joule heating, respectively and a high Seebeck coefficient 𝛼, to reversibly convert heat to electricity and vice versa. Based on this concept, Ioffe [4] defined the thermoelectric figure of merit, 𝑧 = 𝛼 2 /𝜌𝜆, as a reference parameter to compare different materials’ merit for thermoelectric energy conversion. Nowadays, the dimensionless form of the figure of merit, 𝑧𝑇, is commonly used to compare different thermoelectric materials. As for thermoelectric devices, the extrinsic form of figure of merit introduced by Goldsmid [5] is more common, 2

𝑍 = (𝐾

(𝛼𝑝 −𝛼𝑛 )

𝑝 +𝐾𝑛 )(𝑅𝑝 +𝑅𝑛 )

(6)

where subscripts p and n denote p-type and n-type leg properties, 𝑅 = 𝜌𝐿/𝐴, and 𝐾 = 𝜆𝐴/𝐿, are the electrical resistance and thermal conductance of a typical thermoelectric leg, respectively. It is not pointless to mention that at the present time commercial thermoelectric devices possess a 𝑍𝑇 value around unity but new advancements are able to push 𝑍𝑇 to values just over 3. Through a comparison with state of art heat engines, Vining [6] showed that thermoelectric devices need a minimum 𝑍𝑇 value of 4 to be competitive with existing engines. More information on the state of art thermoelectric materials and engineering techniques for improvement of thermoelectric materials can be found elsewhere [2, 7]. Having introduced the basic concepts of thermoelectricity, the next sections of this chapter will attempt to review the challenges and solutions in modeling of thermoelectric devices.

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3. Governing Equations For a homogeneous thermoelectric material under steady state conditions the heat balance equation reads as 𝛻 ∙ (𝜆𝛻𝑇) = 𝜌𝑗 2 + 𝜏𝑗 ∙ 𝛻𝑇

(7)

In a one-dimensional setup and assuming that the electrical current and heat flux are parallel Eq. (7) becomes a second-order non-linear partial deferential equation in the form of, 𝜕 𝜕𝑥

𝜕𝑇

𝑑𝛼 𝜕𝑇

[𝜆(𝑇) 𝜕𝑥 ] − 𝑗𝑇 𝑑𝑇 𝜕𝑥 = −𝜌(𝑇)𝑗 2

(8)

where first term corresponds to the local change of Fourier heat, the second term shows the local Thomson heat absorption, and the last term includes the locale Joule heat release. Eq. (8) can be solved using numerical methods; however, the numerical methods are expensive and time-consuming which does not suit parametrical analysis and design optimization. On the other hand, developing an analytical model to analyze the performance of thermoelectric devices is a challenging task because the temperature dependent coefficients result in strong non-linearity of Eq. (8). Accordingly, several simplified methods have been proposed to achieve approximate analytical solutions. Next sections will be devoted to the introduction of some of these approximated methods.

4. Constant Properties Model Among the analytical approximations the so-called constant properties model (CPM) developed by Ioffe is the most popular and frequently used. As the name gives away, the constant properties model assumes constant values for temperature dependent coefficients in Eq. (8). With this assumption the second term in Eq. (8) vanishes and the heat balance equation in a thermoelectric element reduces to, 𝑑2 𝑇 𝑑𝑥 2

=−

𝜌𝑗 2 𝜆

(9)

Thermal Analysis of Thermoelectric Devices

95

which balances only the Fourier heat and Joule heat. Eq. (9) can be solved analytically using a set of boundary conditions i.e., the absolute temperatures at boundaries of a thermoelectric element. Integrating Eq. (9) over 𝑥 of a thermoelectric element gives the temperature distribution, 𝑇=−

𝜌𝑗 2 2𝜆

𝑥 2 + 𝐶1 𝑥 + 𝐶2

(10)

with constant length (𝐿) and cross-sectional area (𝐴) and boundary conditions 𝑥 = 0 → 𝑇 = 𝑇0 {

𝑥 = 𝐿 → 𝑇 = 𝑇𝐿

𝑇=−

𝜌𝑗 2 2𝜆

it is evident that,

𝑇𝐿 −𝑇0

𝑥2 + [

𝐿

+

𝜌𝑗 2 2𝜆

𝐿 ] 𝑥 + 𝑇0

(11)

Eq. (11) reveals that the temperature distribution along a thermoelectric element is a parabolic function of position. However, considering that for a typical thermoelectric material 𝜆 would be several orders of magnitude bigger than 𝜌, the temperature distribution would be fairly close to a linear function of position. Note that although the internal Thomson heat vanishes by assuming a constant Seebeck coefficient, the Peltier heat at the boundaries must be considered separately because in contrast with element’s body, Seebeck coefficient would experience a drastic change at the physical boundaries (either between two dissimilar thermoelectric materials or a thermoelectric element and a conductor). Thus, one can express the heat power density entering and leaving an element as, 𝑑𝑇

𝑑𝑇

𝑞𝑥=0 = −𝜆 𝑑𝑥 |𝑥=0 + 𝛼𝑗𝑇0 ; 𝑞𝑥=𝐿 = −𝜆 𝑑𝑥 |𝑥=𝐿 + 𝛼𝑗𝑇𝐿

(12)

After a couple of simple algebra steps one can write the global form of Eq. (12) for a thermoelectric leg, 1

𝑄𝑥=0 = −𝐾(𝑇𝐿 − 𝑇0 ) − 2 𝑅𝐼 2 + 𝛼𝐼𝑇0 ; 1

𝑄𝑥=𝐿 = −𝐾(𝑇𝐿 − 𝑇0 ) + 2 𝑅𝐼 2 + 𝛼𝐼𝑇𝐿

(13)

where 𝐼 = 𝐴𝑗, is the electrical current, 𝑅 = 𝜌𝐿/𝐴, is the electrical resistance and 𝐾 = 𝜆𝐴/𝐿, is the thermal conductance for a thermoelectric leg with

96

Farzad Tohidi, Mehran Hashemian and Mamdouh El Haj Assad

constant length 𝐿, and cross-sectional area 𝐴. It is notable from Eq. (13) that considering constant value for electrical resistivity leads to a symmetric distribution of Joule heat. Now, based on CPM, performance parameters for thermoelectric devices including thermoelectric generator (TEG), cooler (TEC), and heat pump (TEH) can be derived with ease. As mentioned before a unicouple is the smallest functioning unit of a typical thermoelectric device and it will be used as a reference point to derive the expressions of performance for thermoelectric devices. Different setups for a thermoelectric unicouple are depicted in Figure 2. The following subsections would be devoted to CPM-based expressions for these three operating modes. a)

b)

c)

Tc

Th

Th

x

x P

x

P

N

Tc

Tc

N

Th

RL

Th VL

P

N

Tc

Tc VL

Figure 2. A thermoelectric unicouple operating in a) power generation, b) cooling, and c) heating modes.

4.1. Thermoelectric Generator A TEG is basically a direct conversion engine that absorbs heat from the hot side, converts a fraction of it to electrical power based on the Seebeck effect and rejects the remaining fraction to the cold side. A thermoelectric unicouple in power generation mode is schematically shown in Figure 2-a. Specifying Eq. (13) for such a setup will give the input and output heat powers as follows, 𝑄𝑖𝑛 = 𝛼𝑝𝑛 𝐼𝑇ℎ + 𝐾𝑝𝑛 ( 𝑇ℎ − 𝑇𝑐 ) −

𝑅𝑝𝑛 2 𝐼 2

𝑄𝑜𝑢𝑡 = 𝛼𝑝𝑛 𝐼𝑇𝑐 + 𝐾𝑝𝑛 ( 𝑇ℎ − 𝑇𝑐 ) +

𝑅𝑝𝑛 2 𝐼 2

(14) (15)

where 𝑅𝑝𝑛 = 𝑅𝑝 + 𝑅𝑛 , 𝐾𝑝𝑛 = 𝐾𝑝 + 𝐾𝑛 , and 𝛼𝑝𝑛 = 𝛼𝑝 − 𝛼𝑛 are the material properties of the unicouple. Moreover, in both equations the first term on the right-hand side is the absorbed and released Peltier heat at the hot and cold pn

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97

junctions, the second term represents the sum of Fourier heat conduction through both legs and the third term is the symmetric distribution of Joule heat to hot and cold sides. Now, assuming that there are no other sources of energy waste, one can find the output power of the unicouple based on the energy conservation principal, 𝑃𝑜𝑢𝑡 = 𝑄𝑖𝑛 − 𝑄𝑜𝑢𝑡 = 𝛼𝑝𝑛 𝐼(𝑇ℎ − 𝑇𝑐 ) − 𝑅𝑝𝑛 𝐼 2

(16)

And the conversion efficiency can follow as, 𝜂 𝑇𝐸𝐺 =

𝑃𝑜𝑢𝑡

=

𝑄𝑖𝑛

𝛼𝑝𝑛 𝐼(𝑇ℎ −𝑇𝑐 )−𝑅𝑝𝑛 𝐼2 𝛼𝑝𝑛 𝐼𝑇ℎ +𝐾𝑝𝑛 ( 𝑇ℎ −𝑇𝑐 )−

𝑅𝑝𝑛 𝐼2 2

(17)

On the other hand, the power consumed in the external load must be equal to the output power of the unicouple, 𝑃𝑜𝑢𝑡 = 𝑅𝐿 𝐼 2

(18)

In order to calculate equations (14)-(18), we must have the electric current as a known parameter, applying the Ohm’s law to the circuit of a thermoelectric generator gives, 𝐼=

𝑉𝑜𝑐 𝑅𝐿 + 𝑅𝑝𝑛

=

𝑉𝑒𝑓𝑓

(19)

𝑅𝐿

where 𝑉𝑜𝑐 and 𝑉𝑒𝑓𝑓 are the open circuit voltage and effective voltage output of the unicouple. The open circuit voltage can be calculated based on the definition of Seebeck coefficient and the effective voltage is the open circuit voltage minus the ohmic loss inside the thermoelectric unicouple, 𝑉𝑜𝑐 = 𝛼𝑝𝑛 (𝑇ℎ − 𝑇𝑐 )

(20) 𝑉𝑜𝑐 𝑅𝐿

𝑉𝑒𝑓𝑓 = 𝑉𝑜𝑐 − 𝑅𝑝𝑛 𝐼 = 𝑅

𝐿 + 𝑅𝑝𝑛

(21)

Having the set of equations (14)-(21), one can study and optimize the performance of thermoelectric generators. Looking at this set of equations, one can see that the performance parameters are expressed with respect to the electrical current 𝐼. However, an important parameter in a power generation

98

Farzad Tohidi, Mehran Hashemian and Mamdouh El Haj Assad

setup is the load resistance because the load resistance is the tool for controlling the current and therefore other performance parameters. Accordingly, it is common to derive performance parameters based on the ratio of the load resistance to internal resistance of a TEG, 𝑚 = 𝑅𝐿 /𝑅𝑝𝑛 , as follows, 𝑚

𝑉𝑒𝑓𝑓 = 𝑉𝑜𝑐 1+𝑚 𝐼=𝑅

(22)

𝑉𝑜𝑐

(23)

𝑝𝑛 (1+𝑚)

𝑃𝑜𝑢𝑡 =

2 𝑉𝑜𝑐

𝑚

(24)

𝑅𝑝𝑛 (1+𝑚)2

𝜂 𝑇𝐸𝐺 =

𝑇ℎ −𝑇𝑐 𝑇ℎ

𝑚 𝑇ℎ −𝑇𝑐 (1+𝑚)2 + 2𝑇ℎ 𝑍𝑇ℎ

(1+𝑚)−

(25)

where 𝑍 is the device figure of merit (see Eq. (6)). Now, maximum output power and efficiency can be optimized based on 𝑚; setting 𝜕𝑃𝑜𝑢𝑡 /𝜕𝑚 = 0, and 𝜕𝜂/𝜕𝑚 = 0, we get the optimum resistance ratio for maximum output power and efficiency of a TEG as, 𝑚𝑝 = 1

(26)

𝑚𝜂 = (1 + 𝑍𝑇𝑚 )0.5

(27)

where 𝑇𝑚 = (𝑇ℎ + 𝑇𝑐 )/2, is the mean operation temperature. This couple of equations shows that optimum operating point for maximum output power and efficiency are different. Substituting Eq. (26) and (27) respectively into Eq. (24) and (25) gives the maximum output power and efficiency, 𝑃𝑜𝑢𝑡,𝑚𝑎𝑥 = 𝜂 𝑇𝐸𝐺,𝑚𝑎𝑥 =

2 𝑉𝑜𝑐

4𝑅𝑝𝑛

=

2 (𝑇 −𝑇 )2 𝛼𝑝𝑛 ℎ 𝑐

4 𝑅𝑝𝑛

𝑇ℎ −𝑇𝑐 √1+𝑍𝑇𝑚 −1 𝑇ℎ

𝑇𝑐 ℎ

√1+𝑍𝑇𝑚 +𝑇

(28)

(29)

Thermal Analysis of Thermoelectric Devices

99

Eq. (28) reveals that the output power of a TEG is a parabolic function of the temperature difference. Obviously, the thermoelectric figure of merit is not directly involved in the maximum power production, but another material 2 influence called power factor, 𝑃𝐹 = 𝛼𝑝𝑛 /𝑅𝑝𝑛 , exists in this equation and better be considered as a deciding factor when choosing thermoelectric materials for power generation. Eq. (29) shows once again the importance of 𝑍𝑇 for the performance of a thermoelectric generator. It is obvious from this equation that with 𝑍 approaching infinity the maximum efficiency of a thermoelectric generator approaches the Carnot efficiency. Moreover, this equation shows that there are two main roots to improve a TEG’s efficiency, namely the temperature difference across the TEG and the device figure of merit.

4.2. Thermoelectric Cooler Thermoelectric coolers (TECs, also known as thermoelectric refrigerators or Peltier devices) are active cooling devices that consume direct electrical power to draw heat from a colder environment and release it to a hotter environment based on the Peltier effect. Figure 2-b shows a thermoelectric unicouple under cooling/refrigeration setup. We can drive expressions of absorbed and released heat at the cold and hot sides of a TEC by specifying Eq. (13) to the setup shown in Figure 2-b, as follows, 𝑄𝑐 = 𝛼𝑝𝑛 𝐼𝑇𝑐 − 𝐾𝑝𝑛 ( 𝑇ℎ − 𝑇𝑐 ) −

𝑅𝑝𝑛 2 𝐼 2

(30)

𝑄ℎ = 𝛼𝑝𝑛 𝐼𝑇ℎ − 𝐾𝑝𝑛 ( 𝑇ℎ − 𝑇𝑐 ) +

𝑅𝑝𝑛 2 𝐼 2

(31)

Then, one can get the consumed power in a TEC based on the energy conservation principal as, 𝑃𝑖𝑛 = 𝑄ℎ − 𝑄𝑐 = 𝛼𝑝𝑛 𝐼(𝑇ℎ − 𝑇𝑐 ) + 𝑅𝑝𝑛 𝐼 2

(32)

which should be equal to the power applied from the battery 𝑃𝑖𝑛 = 𝑉𝑖𝑛 𝐼. Moreover, the coefficient of performance for a thermoelectric cooler, 𝐶𝑂𝑃𝑐 , reads,

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Farzad Tohidi, Mehran Hashemian and Mamdouh El Haj Assad

𝐶𝑂𝑃𝑐 =

𝑅𝑝𝑛 2 𝐼 2 𝐼2

𝛼𝑝𝑛 𝐼𝑇𝑐 −𝐾𝑝𝑛 ( 𝑇ℎ −𝑇𝑐 )− 𝛼𝑝𝑛 𝐼(𝑇ℎ −𝑇𝑐 )+𝑅𝑝𝑛

(33)

Also, the resulting temperature difference across the unicouple can be calculated based on the cooling capacity (see Eq. (30)), 𝛥𝑇 =

𝑅𝑝𝑛 2 𝐼 −𝑄𝑐 2

𝛼𝑝𝑛 𝐼𝑇𝑐 −

𝐾𝑝𝑛

(34)

Similar to the TEG performance parameters the TEC performance parameters are expressed with respect to the electrical current flowing in the circuit which is balanced with the applied voltage to the circuit, 𝑉𝑖𝑛 , which should overcome the sum of ohmic voltage drop inside the unicouple and Seebeck voltage that is produced in the unicouple due to the temperature difference, 𝑉𝑖𝑛 = 𝑉𝑆 + 𝑉𝑅 = 𝛼𝑝𝑛 (𝑇ℎ − 𝑇𝑐 ) + 𝑅𝑝𝑛 𝐼

(35)

Having the equations (30)-(35) one can study and optimize a thermoelectric cooler based on CPM and Dirichlet boundary conditions. Based on these equations we can derive optimum operating conditions for a TEC. Setting 𝜕𝑄𝑐 /𝜕𝐼 = 0, 𝜕𝐶𝑂𝑃𝑐 /𝜕𝐼 = 0, and 𝜕𝑄𝑐 /𝜕𝐼 = 0, one can find the optimum operating condition for maximum cooling power, maximum coefficient of performance, and maximum temperature difference as follows, 𝐼𝑄 =

𝛼𝑝𝑛 𝑇𝑐 𝑅𝑝𝑛

𝐼𝐶𝑂𝑃 = 𝑅

𝛼𝑝𝑛 (𝑇ℎ −𝑇𝑐 )

𝑝𝑛 (√1+𝑍𝑇𝑚 −1)

𝐼𝛥𝑇 =

𝛼𝑝𝑛 𝑇𝑐 𝑅𝑝𝑛

(36)

(37) (38)

By substituting these values to the corresponding equations and after a few algebra steps maximum cooling power, maximum coefficient of performance, and maximum temperature difference read,

Thermal Analysis of Thermoelectric Devices

𝑄𝑐,𝑚𝑎𝑥 = 𝑤𝑖𝑡ℎ 𝑇ℎ −𝑇𝑐 =0

⇒

2 𝑇2 𝛼𝑝𝑛 𝑐

2𝑅𝑝𝑛

− 𝐾𝑝𝑛 (𝑇ℎ − 𝑇𝑐 ) = 𝐾𝑝𝑛 (

𝑄𝑐,𝑚𝑎𝑥 =

𝐶𝑂𝑃𝑐,𝑚𝑎𝑥 =

𝛥𝑇𝑚𝑎𝑥 =

(39)

√1+𝑍𝑇𝑚 −𝑇ℎ /𝑇𝑐 √1+𝑍𝑇𝑚 +1

−𝑄𝑐

𝐾𝑝𝑛

− (𝑇ℎ − 𝑇𝑐 ))

2𝑅𝑝𝑛

𝑇𝑐

2𝑅𝑝𝑛

2

2 𝑇2 𝛼𝑝𝑛 𝑐

𝑇ℎ −𝑇𝑐

2 𝛼2 𝑝𝑛 𝑇𝑐

𝑍𝑇𝑐2

=

𝑍𝑇𝑐2 2

101

𝑄

(40)

𝑤𝑖𝑡ℎ 𝑄𝑐 =0

−𝐾𝑐 ⇒ 𝑝𝑛

𝛥𝑇𝑚𝑎𝑥 =

𝑍𝑇𝑐2 2

(41)

Equations (39) and (41) are very similar because both have been derived from the same equation (Eq. (30)). It is obvious from these couple of equations that maximum temperature difference and maximum cooling capacity are achieved at the same operating current. However, the maximum cooling capacity and temperature difference are balanced with each other and have a linear relationship; at the extremes and for fixed material properties, the maximum cooling capacity is achieved when the temperature difference is equal to zero and the maximum temperature difference is achievable when the cold side of the TEC is adiabatic. Moreover, Eq. (40) shows that the maximum coefficient of performance for a TEC is a function of operation temperatures and unicouple figure of merit. Similar to the maximum efficiency of the TEG, the maximum COP for a TEC approaches the reverse Carnot cycles COP with 𝑍 approaching infinity.

4.3. Thermoelectric Heat Pump Thermoelectric heat pump (TEH, also known as thermoelectric heater) is a device that operates very similar to a TEC. The main difference between a TEH and a TEC is the purpose of operation which is the heating power for a TEH. Specifying Eq. (13) for the TEH setup shown in Figure 2-c gives the absorbed and released heat at the cold and hot sides as follows, 𝑄𝑐 = 𝛼𝑝𝑛 𝐼𝑇𝑐 − 𝐾𝑝𝑛 ( 𝑇ℎ − 𝑇𝑐 ) −

𝑅𝑝𝑛 2 𝐼 2

(42)

𝑄ℎ = 𝛼𝑝𝑛 𝐼𝑇ℎ − 𝐾𝑝𝑛 ( 𝑇ℎ − 𝑇𝑐 ) +

𝑅𝑝𝑛 2 𝐼 2

(43)

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Farzad Tohidi, Mehran Hashemian and Mamdouh El Haj Assad

Similar to the TEC, the power input for the TEH and heating coefficient of performance read, 𝑃𝑖𝑛 = 𝑄ℎ − 𝑄𝑐 = 𝛼𝑝𝑛 𝐼(𝑇ℎ − 𝑇𝑐 ) + 𝑅𝑝𝑛 𝐼 2 𝐶𝑂𝑃ℎ = 1 + 𝐶𝑂𝑃𝑐 =

𝑅𝑝𝑛 2 𝐼 2 𝐼2

𝛼𝑝𝑛 𝐼𝑇ℎ −𝐾𝑝𝑛 ( 𝑇ℎ −𝑇𝑐 )+ 𝛼𝑝𝑛 𝐼(𝑇ℎ −𝑇𝑐 )+𝑅𝑝𝑛

(44)

(45)

Moreover, in contrast to a TEC, the heating power for a TEH always increases with respect to the operating current but there is a maximum value for heating coefficient of performance, 𝐶𝑂𝑃ℎ,𝑚𝑎𝑥 =

𝑇ℎ 𝑇ℎ −𝑇𝑐

(1 − 2

√1+𝑍𝑇𝑚 −1 𝑍𝑇ℎ

)

(46)

which indicates that the maximum coefficient of performance will approach the Carnot coefficient of performance for a heating cycle with 𝑍 approaching infinity. Now that we have successfully derived the performance expressions for all three operating conditions of a thermoelectric unicouple, the performance parameters for a thermoelectric module comprising a number, 𝑁𝑇𝐸 , of these unicouples (connected electrically in series and thermally in parallel) can be easily calculated. 𝑅𝑇𝐸𝑀 = 𝑁𝑇𝐸 𝑅𝑝𝑛 ; 𝐾𝑇𝐸𝑀 = 𝑁𝑇𝐸 𝐾𝑝𝑛

(47)

𝐼𝑇𝐸𝑀 = 𝐼𝑝𝑛 ; 𝑉𝑇𝐸𝑀 = 𝑁𝑇𝐸 𝑉𝑝𝑛

(48)

𝑄𝑇𝐸𝑀 = 𝑁𝑇𝐸 𝑄𝑝𝑛 ; 𝑃𝑇𝐸𝑀 = 𝑁𝑇𝐸 𝑃𝑝𝑛 ; 𝜂 𝑇𝐸𝑀 = 𝜂𝑝𝑛 ; 𝐶𝑂𝑃𝑇𝐸𝑀 = 𝐶𝑂𝑃𝑝𝑛 (49) It is worth noting again that the expressions derived up to this point are all based on the assumption of constant properties and Dirichlet boundary conditions and can be far from accurate if used carelessly. These expressions will be accurate enough for cases with small temperature differences between the two junctions and small operating current (so that the variation in temperature dependent transport coefficients is insignificant and the Thomson heat is ignorable). Even for such cases these expressions are still pretty ideal because in a real thermoelectric device there are several other sources of

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irreversibility including heat leakage from the devices’ structure, electrical and thermal contact resistances, and heat transfer between thermoelectric devices and heat exchangers. Nevertheless, there are a lot of cases that the CPM has been used successfully; with appropriate choices for material properties and considering the significant irreversibility’s in thermoelectric devices, CPM can be almost as accurate as numerical solutions. At the next part we will discuss different ways of assigning a constant value for the properties of thermoelectric materials.

4.4. Choice of Constant Values for CPM As mentioned before, the constant properties model assumes constant values for transport coefficients in Eq. (8). Nevertheless, these coefficients are temperature dependent (and space dependent for inhomogeneous thermoelectric materials); therefore, assigning a single constant value for these properties is an important task and can lead to significant differences in the accuracy of a CPM analysis. In order to have an accurate estimation of the performance of a thermoelectric device, appropriate values should be chosen for these coefficients. In the earlier studies, two main approaches have been used to assign a single value for these coefficients namely the value of the temperature dependent coefficient at the mean operation temperature and the average of two temperature dependent coefficients at the boundary temperatures as shown below, 𝐶𝑚 = 𝐶𝑇𝑚 = 𝐶(𝑇𝑚 ) 𝐶𝑚 =

𝐶𝑇𝑐 +𝐶𝑇ℎ 2

=

(50)

𝐶(𝑇𝑐 )+𝐶(𝑇ℎ ) 2

(51)

where Cm is the constant value of coefficients 𝛼, 𝜆, and 𝜌. As one can imagine this method of choosing a constant value for transport coefficients can be very inconsistent and misleading because the temperature profiles for transport coefficients are not always monotonous and may have one or more extremums in-between the two boundary temperatures. Therefore, these methods are only suggested for small temperature differences and qualitative studies. A very straightforward method is to use integral averaging over the operation temperature of the device,

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𝐶̅ = 𝑇

1

𝑇

ℎ −𝑇𝑐

ℎ ∫𝑇 𝐶(𝑇)𝑑𝑇 𝑐

(52)

This method assigns a carefully averaged value for the transport coefficients based on the temperature dependence of these coefficients. Although it is still far from perfect, this method gives much better results compared to the previously mentioned ones. Sandoz et al. [8] showed in their study that the integral averaging over the operation temperature predicts the exact output power of a thermoelectric generator. A generalized version of their argument which could be used for any thermoelectric device follows next. Let’s reconsider the generalized form of heat balance equation in a thermoelectric element, 𝑑2 𝑇

𝑑𝛼 𝑑𝑇

𝜆 𝑑𝑥 2 − 𝑗𝑇 𝑑𝑇 𝑑𝑥 + 𝜌𝑗 2 = 0

(53)

Now we can integrate this equation over the length 𝐿 of the thermoelectric leg which gives, 𝐿

∫ 𝜆 0

= (𝜆

𝑑𝑇

𝐿 𝑑𝑇 | ) − 𝑗 [𝑇𝛼|𝑥=𝐿 − 𝑇𝛼|𝑥=0 − ∫0 𝛼 𝑑𝑥 ] + 𝑑𝑥 𝑥=0 𝑑𝑥 𝑑𝑇 𝑑𝑇 (−𝜆 𝑑𝑥 |𝑥=𝐿 + 𝑗𝑇𝛼|𝑥=𝐿 ) − (−𝜆 𝑑𝑥 |𝑥=0 + 𝑗𝑇𝛼|𝑥=0 ) =

|𝑥=𝐿 − 𝜆

𝑑𝑥 𝑅𝑒𝑎𝑟𝑒𝑛𝑔𝑖𝑛𝑔

→

𝐿 𝐿 𝑑2𝑇 𝑑𝛼 𝑑𝑇 𝑑𝑥 − ∫ 𝑗𝑇 𝑑𝑥 + ∫ 𝜌𝑗 2 𝑑𝑥 = 0 2 𝑑𝑥 𝑑𝑇 𝑑𝑥 0 0 𝑑𝑇

𝑇

𝜌𝑗 2 𝐿 + 𝑗 ∫𝑇 𝐿 𝛼𝑑𝑇

𝜌𝑗 2 𝐿

(54)

0

Interestingly, the first and second terms of the above equation indicate the heat power density at the boundaries of the element (see Eq. (12)). Thus, based on energy conservation principal, the left-hand side of this equation is exactly equal to the output power density in case of thermoelectric generator and input power density for thermoelectric cooler and heat pump, 𝑇

𝑝 = 𝜌𝑗 2 𝐿 + 𝑗 ∫𝑇 𝐿 𝛼𝑑𝑇 0

(55)

On the other hand, for the temperature averaged Seebeck coefficient we have,

Thermal Analysis of Thermoelectric Devices 1

𝑇

𝛼̅ = 𝑇 −𝑇 ∫𝑇 𝐿 𝛼(𝑇)𝑑𝑇 𝐿

0

0

105

(56)

Combining equations (55) and (56) we get, 𝑝 = 𝜌𝑗 2 𝐿 + 𝛼̅𝑗(𝑇𝐿 − 𝑇0 )

(57)

which is exactly equal to the CPM expression for output/input power for thermoelectric devices. This means that integral averaging of Seebeck coefficient over the operation temperature automatically considers the effect of Thomson heat in the calculation of output/input power. Although this is a great achievement for such a simple method, it does not apply to the calculation of heat flows in and out of the thermoelectric elements. Temperature averaging of the Seebeck coefficient means that the absorbed/released Thomson heat is equally distributed between the hot and cold boundaries of the thermoelectric element which in most cases leads to the underestimation of heat input and overestimation of efficiency. In fact, Sandoz et al. [8] found, for certain cases, that the error in calculating efficiency of thermoelectric generators based on integral averaging over operation temperature can be as high as 25%. Nevertheless, the authors concluded that this method of averaging can be sufficiently accurate (with errors under 2% for typical thermoelectric materials) for engineering purposes. On the other hand, integral averaging over the operation temperature does not provide an exact average value because the temperature distribution over a thermoelectric leg deviates from a linear one. Even for a CPM case we showed that there exists a slight bow in the temperature profile (see Eq. (11)) due to the Joule heating effect. However, as Ponnusamy et al. [9] showed, thermal conductivity’s temperature dependence has a much greater effect on temperature distribution compared to Thomson and Joule effects; which is sensible considering that thermal conductivity is typically several orders of magnitude larger than the other two coefficients in Eq. (8). Accordingly, for thermoelectric materials with strongly temperature dependent thermal conductivity, the assumption of linear temperature distribution can lead to large errors in performance estimation. To consider the contribution of temperature distribution on the average value of these coefficients, Ponnusamy et al. [9] proposed spatial averaging, 1

𝐿

𝐶𝑎𝑣 = ∫0 𝐶(𝑇(𝑥))𝑑𝑥 𝐿

(58)

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Obviously, to have the spatial average of a coefficient using Eq. (58) one must have the exact temperature distribution function, 𝑇(𝑥), for which the authors proposed a fast numerical method. Using spatial averaging method for thermal conductivity and electrical resistivity, they calculated efficiency of six different thermoelectric materials under large temperature differences and compared them to the exact efficiency; results indicate that the error in efficiency estimation for these materials lies between 0.5-1.5% which is a great achievement. Moreover, the authors concluded that the remaining marginal error is due to asymmetric generation and transportation of heat inside the element. The asymmetric distribution of Thomson and Joule heat can become important in certain cases; Garrido et al. reconsidered the distribution of Thomson heat inside a TEC and showed that assuming a symmetric distribution can lead to grossly inaccurate performance estimations using CPM. Also, they proposed a solution that corrects the Thomson heat distribution in the thermoelectric cooler. In a similar study, Ponnusamy et al. [10] introduced correction methods for the distribution of Thomson heat and improved the CPM model. All in all, it is obvious from these studies that using appropriate averaging methods can increase the accuracy of CPM while providing straightforward and high-speed analysis. However, CPM is not the only analytical approximation model for thermoelectric devices. At the early stages, the absence of Thomson heat in CPM was deemed as one of the main reasons for failure of this model in certain cases. Accordingly, researchers tried to introduce the effect of Thomson heat to the CPM model. Chen et al. [11] derived performance expressions for the TEG by considering constant values for thermal conductivity, electrical resistivity, and Thomson coefficient. Assuming a constant Thomson coefficient, they were able to consider the effect of Thomson heat in the temperature distribution (CPM considers only the effect of joule heat) and derive performance expressions including the effect of Thomson heat. However, considering a constant Thomson coefficient, much like constant electrical resistivity, leads to a symmetric distribution of Thomson heat. Although this was a great achievement at the time, now we know that these expressions will give exactly the same results as a standard CPM with temperature averaged Seebeck coefficient. The main difference between the two models is a slight difference in temperature profile. There are also more sophisticated analytical approximations for simulation of thermoelectric devices’ performance. Ju et al. derived analytical expressions for performance of TEG [12] and TEC [13] assuming parabolic functions for temperature dependent coefficients. They showed that the temperature dependency of thermal conductivity plays the

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determining role for temperature distribution in thermoelectric generator; while for the thermoelectric cooler it was deduced that temperature dependency of Seebeck coefficient and thermal conductivity can have a significant impact on the heat flow and coefficient of performance. Furthermore, the realistic modeling of a thermoelectric device goes beyond the raw thermoelectric materials that have been considered up to this point. Next section will introduce the additional aspects of a comprehensive and realistic modeling case.

5. Device Level Considerations Up to this point we have only considered the raw thermoelectric elements in the attempt to modeling their performance. However, there are several other factors that can significantly affect the performance of a thermoelectric device and the design optimization of it. This section will briefly introduce the challenges in the device level design and analysis of a thermoelectric converter.

5.1. Geometry Thermoelectric devices can adapt different shapes with respect to their applications; however, no specific shape for a thermoelectric element shows superior characteristics [14]. Also, the effect of different geometrical shapes can be applied to the modeling of thermoelectric devices with some algebra steps and without much complication. Nevertheless, after choosing the shape and materials for the thermoelectric device, one must optimize the length and cross-sectional area of the legs. For a typical thermoelectric device with rectangular legs and a pair of thermoelectric materials, the device figure of 2 merit, 𝑍 = 𝛼𝑝𝑛 ⁄𝑅𝑝𝑛 𝐾𝑝𝑛 , can be optimized by minimizing the product R pn K pn , 𝑅𝑝𝑛 𝐾𝑝𝑛 = (𝑅𝑝 + 𝑅𝑛 )(𝐾𝑝 + 𝐾𝑛 ) = ( 𝐴 𝐿

𝜌𝑝 𝐿𝑝 𝜌𝑛 𝐿𝑛 𝜆𝑝 𝐴𝑝 𝜆𝑛 𝐴𝑛 + )( + ) 𝐴𝑝 𝐴𝑛 𝐿𝑝 𝐿𝑛

𝐴 𝐿

= 𝜌𝑝 𝜆𝑝 + 𝜌𝑛 𝜆𝑛 + 𝜌𝑝 𝜆𝑛 𝐴𝑛𝐿𝑝 + 𝜌𝑛 𝜆𝑝 𝐴𝑝 𝐿𝑛 𝑝 𝑛

𝑛 𝑝

(59)

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Since the materials for the n- and p-type legs possess different properties, the product, R pn K pn , can be minimized through geometric manipulation. Differentiating the above with respect to

An Lp Ap Ln

and setting the result equal to

zero we get, 𝐴𝑛 𝐿𝑝

(𝐴

𝑝 𝐿𝑛

2

𝜌𝑛 𝜆𝑝

) =𝜌

(60)

𝑝 𝜆𝑛

Which is called the form factor for a thermoelectric unicouple and gives the optimum value of 𝑍 as, 𝑍𝑜𝑝𝑡 =

2 𝛼𝑝𝑛 2

(√𝜌𝑝 𝜆𝑝 +√𝜌𝑛 𝜆𝑛)

(61)

Moreover, for practical thermoelectric devices the n and p-type legs are usually of equal length and therefore the geometric optimization takes place through optimization of the cross-sectional area ratio of the legs. Note that this is only a relative optimization between the aspect ratio of the two legs and although there is an optimum ratio for the geometrical parameters of a thermoelectric unicouple, it does not set any limit on the length or crosssectional area of the legs. Accordingly, the cross-sectional area and leg length still should be optimized. For example, for a thermoelectric generator with Dirichlet boundary conditions the higher output powers are achieved in lower leg lengths while the higher lengths are associated with higher efficiencies [15]. Moreover, cross sectional area of the legs and fill factor of modules (the ratio of thermoelectric legs cross sectional area to the area of ceramic plate) gain importance when considering the heat source quality and cost of thermoelectric materials [16]. Therefore, the length and cross-sectional area of a thermoelectric device must be optimized based on the requirements of every application. Furthermore, parasitic losses should also be considered for the geometrical optimization and overall improvement of thermoelectric devices.

5.2. Parasitic Losses In general, a thermoelectric device comprises a number of p- and n-type thermoelectric elements connected to each other using metal connectors and

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then these series of interconnected elements are sandwiched between two ceramic plates to electrically insulate them from their surroundings. Obvious consequence of such configuration is several thermal and electrical contact resistances that can deteriorate the performance of a thermoelectric device. Moreover, empty spaces will exist in-between the thermoelectric elements that are subject to convective and radiative heat losses and if the fill factor of the thermoelectric modules get much lower than 50% then the effect of thermal spreading and concentration must also be considered. Furthermore, other thermal losses occur outside a thermoelectric module’s structure due to the thermal resistance added by the heat exchangers and thermal contact resistance between the thermoelectric module and the heat exchanger surface at both hot and cold sides. Any realistic analysis of a thermoelectric system should consider such parasitic losses in their estimation. A very efficient way to study the effect of these parasitic losses is using a thermal resistance network. a)

b)

Figure 3. Thermal resistance network of a TEG reprinted from a) [17] and b) [18].

Barry et al. [17] introduced a one-dimensional thermal resistance network model (see Figure 3-a) based on the constant properties model with integral averaged coefficients over the operation temperature. Using such a model they were able to comprehensively study the effect of different contacts on the performance of a thermoelectric generator and optimize its geometry. Qing et al. [18] used a similar approach to study the effect of heat exchangers on both sides of a thermoelectric generator on its performance. Their results highlight

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the importance of heat transfer coefficient on performance of thermoelectric generator and the load resistance ratio for optimum output power and efficiency. Wu et al. [19] derived device level performance expressions for a thermoelectric generator. Their model is based on the assumption of constant Thomson coefficient and includes the effect of thermal contact resistances, ceramic covers thermal conductance, and heat transfer through the gap between thermoelectric elements. Altogether, to have a realistic estimation of the performance of a thermoelectric device, it is of vital importance to consider the effect of these parasitic losses.

Conclusion In this chapter, it has been demonstrated that the derivation of the constant properties model (CPM) from the governing equations can be achieved easily; moreover, this model can be applied to different operational modes of thermoelectric devices without difficulty. However, it has also been shown that the limitations of CPM, such as its inability to account for the Thomson effect and predict the effect of temperature on material transport properties, result in potentially inaccurate modeling in cases of broad temperature differences or materials with strongly temperature-dependent properties. Nevertheless, the utilization of suitable averaging methods has been shown to enable the introduction of an accurate model for many thermoelectric devices based on CPM. It has also been emphasized that a comprehensive analysis of thermoelectric devices requires consideration of the effects of geometrical parameters and parasitic losses in each specific case. All in all, this chapter provides an overview of analytical modelling of thermoelectric devices.

References [1]

[2]

[3]

Tohidi, Farzad, Shahriyar Ghazanfari Holagh, Ata Chitsaz, Thermoelectric Generators: A comprehensive review of characteristics and applications, Applied Thermal Engineering, Volume 201, Part A, 2022, 117793. Shi, X. L., J. Zou, and Z. G. Chen, “Advanced thermoelectric design: From materials and structures to devices,” Chem. Rev., vol. 120, no. 15, pp. 7399–7515, 2020, doi: 10.1021/acs.chemrev.0c00026. Snyder, G. J. and E. S. Toberer, “Complex thermoelectric materials,” Mater. Sustain. Energy A Collect. Peer-Reviewed Res. Rev. Artic. from Nat. Publ. Gr., vol. 7, no. February, pp. 101–110, 2010, doi: 10.1142/9789814317665_0016.

Thermal Analysis of Thermoelectric Devices [4]

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Ioffe, A. F., L. S. Stil’bans, E. K. Iordanishvili, T. S. Stavitskaya, A. Gelbtuch, and G. Vineyard, “Semiconductor Thermoelements and Thermoelectric Cooling,” Phys. Today, vol. 12, no. 5, pp. 42–42, May 1959, doi: 10.1063/1.3060810. Goldsmid, H. J., Introduction to thermoelectricity/H. Julian Goldsmid. 2016. Vining, C. B., “An inconvenient truth about thermoelectrics,” Nat. Mater., vol. 8, no. 2, pp. 83–85, 2009, doi: 10.1038/nmat2361. Li, G., Q. An, B. Duan, L. Borgsmiller, M. Al Malki, M. Agne, U. Aydemir, P. Zhai, Q. Zhang, S. I. Morozov, W. A. Goddard nad G. J. Snyder, “Fracture toughness of thermoelectric materials,” Mater. Sci. Eng. R Reports, vol. 144, no. February, pp. 1– 12, 2021, doi: 10.1016/j.mser.2021.100607. Sandoz-Rosado, E. J., S. J. Weinstein, and R. J. Stevens, “On the Thomson effect in thermoelectric power devices,” Int. J. Therm. Sci., vol. 66, pp. 1–7, 2013, doi: 10.1016/j.ijthermalsci.2012.10.018. Ponnusamy, P., J. de Boor, and E. Müller, “Using the constant properties model for accurate performance estimation of thermoelectric generator elements,” Appl. Energy, vol. 262, no. January, p. 114587, 2020, doi: 10.1016/j.apenergy.2020.114 587. Ponnusamy, P., J. de Boor, and E. Müller, “Discrepancy between constant properties model and temperature-dependent material properties for performance estimation of thermoelectric generators,” Entropy, vol. 22, no. 10, pp. 1–18, 2020, doi: 10.3390/ e22101128. Chen, J., Z. Yan, and L. Wu, “The influence of Thomson effect on the maximum power output and maximum efficiency of a thermoelectric generator,” J. Appl. Phys., vol. 79, no. 11, pp. 8823–8828, 1996, doi: 10.1063/1.362507. Ju, C., G. Dui, H. H. Zheng, and L. Xin, “Revisiting the temperature dependence in material properties and performance of thermoelectric materials,” Energy, vol. 124, pp. 249–257, Apr. 2017, doi: 10.1016/j.energy.2017.02.020. Ju, C., X. Wang, G. Dui, C. G. Uhl, and L. Xin, “Theoretical Analysis of the Cooling Performance of a Thermoelectric Element with Temperature-Dependent Material Properties,” J. Electron. Mater., vol. 48, no. 7, pp. 4627–4636, Jul. 2019, doi: 10.1007/s11664-019-07217-3. Shittu, S., G. Li, X. Zhao, and X. Ma, “Review of thermoelectric geometry and structure optimization for performance enhancement,” Appl. Energy, vol. 268, no. April, p. 115075, Jun. 2020, doi: 10.1016/j.apenergy.2020.115075. Rowe, D. M. and G. Min, “Design theory of thermoelectric modules for electrical power generation,” IEE Proc. Sci. Meas. Technol., vol. 143, no. 6, pp. 351–356, 1996, doi: 10.1049/ip-smt:19960714. Yazawa, K. and A. Shakouri, “Cost-efficiency trade-off and the design of thermoelectric power generators,” Environ. Sci. Technol., vol. 45, no. 17, pp. 7548– 7553, 2011, doi: 10.1021/es2005418. Barry, M. M., K. A. Agbim, P. Rao, C. E. Clifford, B. V. K. Reddy, and M. K. Chyu, “Geometric optimization of thermoelectric elements for maximum ef fi ciency and power output,” Energy, vol. 112, pp. 388–407, 2016, doi: 10.1016/j.energy.2016. 05.048.

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Farzad Tohidi, Mehran Hashemian and Mamdouh El Haj Assad Qing, S., A. Rezania, L. A. Rosendahl, and X. Gou, “An Analytical Model for Performance Optimization of Thermoelectric Generator with Temperature Dependent Materials,” IEEE Access, vol. 6, pp. 60852–60861, 2018, doi: 10.1109/ ACCESS.2018.2874947. Wu, Y., L. Zuo, J. Chen, and J. A. Klein, “A model to analyze the device level performance of thermoelectric generator,” Energy, vol. 115, pp. 591–603, 2016, doi: 10.1016/j.energy.2016.09.044.

Chapter 5

Bubble Dynamics Analysis in Subcooled Flow Boiling Shahriyar Ghazanfari Holagh and Mohammad Ali Abdous† School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran

Abstract Bubbles dynamic behavior plays a crucial role in boiling heat transfer; essentially, boiling heat transfer coefficient is controlled by the density, generation frequency, and diameter of bubbles appearing on hot walls. Different factors including flow conditions, surface topographical conditions, and the geometry of the flow channel influence bubbles behavior and relevant characteristics. Force balance analysis has been proven to be an effective way for analyzing bubbles behavior and predicting their departure and lift off diameters. In this chapter, different forces exerting on bubbles are expounded, and the relations proposed for calculating such forces are explained. Also, previous studies from literature are briefly reviewed, and the impact of flow conditions on bubbles dynamic behavior is discussed.

Keywords: bubbles dynamic behavior, heat transfer coefficient, force balance analysis, departure and lift off diameters

 †

Corresponding Author’s Email: [email protected]. Corresponding Author’s Email: [email protected].

In: The Fundamentals of Thermal Analysis Editors: Mamdouh El Haj Assad, Ali Khosravi and Mehran Hashemian ISBN: 979-8-88697-759-2 © 2023 Nova Science Publishers, Inc.

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1. Introduction Since boiling phenomenon gives a high heat transfer rate and is complicated in nature, flow boiling has been introduced as a stimulating field of study over the past years [1]. Based on the liquid phase bulk temperature, flow boiling takes place at either the subcooled region, where liquid’s bulk temperature is less than saturation temperature at the system pressure, or the saturated region, where the bulk temperature of liquid equals the saturation one. Simultaneous occurrence of evaporation and condensation makes the subcooled flow boiling a more complex process. In such systems, coolant flow has a low temperature in comparison with the saturation one at system pressure; heat flux which is applied to the wall can form a thermal layer, where bubble nucleation and growth happens. However, as the bubble travels to the region of bulk liquid, which has a lower temperature in comparison with the saturated liquid/mixture, condensation occurs [2]. This kind of flow boiling is detected in a wide range of industrial applications, and it enhances the heat transfer coefficient to a greatly larger value than that of single-phase flows [3–5]. Heat transfer coefficient in the subcooled flow boiling region is highly influenced by the bubbles’ dynamic behavior, from their onset on the heated wall to their condensation in the bulk flow. In general, bubbles bear the responsibility of transferring the thermal energy of the heated wall to the bulk flow. Because bubbles’ dynamic behavior changes depending on the flow conditions or channel geometrical configuration, a thorough investigation of bubbles dynamic behavior is crucial for a better comprehension of the boiling process [4]. Overall, several characteristics are used to characterize the bubbles' dynamic behavior including but not limited to departure and lift-off diameters, growth (or departure), waiting, and lift-off times, and nucleation frequency and density. Specifically speaking, as shown in Figure 1, during flow boiling bubbles generate on nucleation sites and expand while the heated wall delivers heat to them. Once the size of bubbles reaches a certain value (i.e., departure diameter), they leave the nucleation sites and begin to slide on the hot surface. While sliding on the hoot surface, the bubbles grow more as they receive more heat from the wall; once their size reaches a certain value (i.e., lift-off diameter), bubbles detach from the hot surface. The times between the formation of a bubble and its departure/lift-off moments and that between the bubble formation and departure of the previous one are called growth/liftoff time and waiting time, respectively. The nucleation frequency is explained as the number of bubbles that leave a nucleation site (departure moment) per second.

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Figure 1. Bubbles creation, expansion, departure, sliding, and lift-off on a hot horizontal surface.

A precise estimation of bubble departure and lift-off diameters helps one to well understand the boiling process and define the interfacial transport terms [6, 7]. Furthermore, the above-stated characteristics strongly influence the precision of numerical models developed for simulating boiling phenomenon [8, 9]. As an illustrative example, in Wall Heat Flux Partitioning model, which is one of the common models applied to model boiling phenomenon, three parts constitutes the wall heat flux; they are called singlephase heat flux, evaporating heat flux, and quenching heat flux [10]. It is required to have appropriate relations for calculating the departure diameter and nucleation frequency to predict the quenching and evaporating heat fluxes by the sub-models [8]. Furthermore, the calculation of Interfacial Area Concentration (IAC) highly depends on bubble departure diameter and nucleation frequency [7]. Hence, it is important to select such bubble characteristics appropriately to reduce the deviation of numerical models [9]. Meanwhile, it has been shown that heat transfer mechanisms around bubbles and bubble-liquid interactions induce strong impacts on bubbles' characteristics [11, 12]. Figure 2 shows the schematics of a bubble and liquid layers around it in subcooled flow boiling. As it can be seen, a bubble is surrounded by three liquid layers. The first thin layer, called the evaporative micro-layer, with the shape of a wedge is confined to the heating wall and the bubble’s lower parts, and it begins to evaporate as bubbles nucleus are formed, which enhances the fluctuation of wall temperature [12–15]. As the bubble enlarges, a slight reduction occurs in the liquid region’s temperature close to the heating wall; the second layer is referred to as the superheated layer [13, 14]. In the next liquid layer (the third one) around the top of the bubble, named the subcooled region, the liquid’s bulk temperature is less than the saturation one. Basically, increasing the diameter of the bubble is due to vapor and heat transfer from the evaporative and superheated liquid layers to the bubble, though bubble diameter decreases because of condensation that happens in the

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subcooled region [13, 16]. In addition, bubbles' behavior and relevant characteristics are affected by the liquid and bubble interactions and forces acting on the bubbles [9, 17]. Accordingly, any element that affects mechanisms of heat transfer and interactions like flow conditions, turbulence of liquid flow near the bubble and geometrical parameters influence the bubbles departure/lift-off characteristics, considerably [3].

Figure 2. Schematics of three different liquid layers surrounding a bubble in subcooled boiling flow, redrawn with permission from Ref. [5] (Copyright 2021 Elsevier).

In this chapter, the dynamic behavior of bubbles and relevant characteristics in subcooled flow boiling within horizontal/vertical and curved channels are discussed. Different forces imposed on bubbles are introduced and force balance models are applied at departure and lift-off moments to determine bubbles diameter at these moments. Additionally, the empirical coefficients used in the force balance models are explained and different values suggested by different studies for these parameters are reviewed. Eventually, a brief review of the most important studies within the field is presented.

2. Forces Acting on Bubbles During a bubble’s lifetime in flow boiling, from its onset to lift-off and condensation, different forces are exerted on it. Different thorough studies

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117

have been carried out to develop models and relationships for precise estimation of bubble departure and lift-off diameters. These forces are categorized according to their direction with respect to the flow direction. When the balance between forces in the flow direction is disrupted, bubbles leave the nucleation sites [18]. This characterizes the departure instant as the moment that the bubble begins to slide on the hot surface. Likewise, an instance of the occurrence of an imbalance in the forces perpendicular to the flow direction is defined as the lift-off moment [19]. As shown in Figure 3, these forces are exerted in two directions, one in the direction of flow and the other in the perpendicular direction. Schematics of several forces acting on a bubble in a nucleation site located on horizontal, vertical, and curved walls are illustrated in Figures 3a, 3b, and 3c, respectively. Moreover, the angle between the bubble symmetry line and the wall normal line, i.e., the inclination angle, 𝜃𝑖 , angles formed between contact line of bubble and upstream and downstream flows which are called advancing and receding contact angles, 𝛼 and 𝛽 , respectively, and the bubble contact diameter, 𝑑𝑤 , which is the diameter of the area of the bubble in contact with the hot surface, at different wall geometrical shapes and positions are illustrated in Figure 3.

(a) Figure 3. (Continued).

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(b)

(c) Figure 3. Forces acting on a bubble in a nucleation site on (a) horizontal straight wall, (b) vertical straight wall, and (c) curved inclined wall (redrawn with permission from [4], Copyright 2019 Elsevier).

Bubble Dynamics Analysis in Subcooled Flow Boiling

119

As demonstrated in Figure 3, the same forces act on bubbles at different geometries; however, in the curved geometry due to the curvature of flow path, in addition to the others, two forces act on bubbles in the radial direction, that are radial pressure gradient force 𝐹⃗𝑅𝑃 , and centrifugal force 𝐹⃗𝑐 [4]. Hence, in this chapter, the forces are described in the curved geometry. According to Figure 3c, accounting for wall curvature, forces are projected in these two directions using the polar coordinate system. The forces can be categorized according to their direction. Forces exerted in the flow direction are quasisteady drag force 𝐹⃗𝑞𝑠 , surface tension force 𝐹⃗𝑠𝜃 , the tangential components of unsteady drag force 𝐹⃗𝑑𝑢𝜃 , and tangential component of buoyancy force 𝐹⃗𝑏𝜃 . Departure radius of the bubble can be determined using force balance analysis in this force group. The second category consists of forces in the perpendicular direction. Contact pressure force 𝐹⃗𝑐𝑝 , Shear lift force 𝐹⃗𝑠𝑙 , radial pressure gradient force 𝐹⃗𝑅𝑃 , hydrodynamic pressure force 𝐹⃗ℎ , centrifugal force 𝐹⃗𝑐 , and radial components of unsteady drag force 𝐹⃗𝑑𝑢𝑟 , radial component of buoyancy force 𝐹⃗𝑏𝑟 , and surface tension force 𝐹⃗𝑠𝑟 are in this category. Bubble lift-off radius can be calculated via force balance analysis in the second force group. Note that the expressions for 𝐹⃗𝑅𝑃 and 𝐹⃗𝑐 were developed for the first time in the study conducted by Abdous et al. [4]. In the following, each of these forces is explained briefly. It is to point out that in the definition of these forces, empirical coefficients are employed to match the force balance models to the experimental data.

2.1. Surface Tension Force Basically, the bubble contact with the surface leads to the surface tension force [18]. The components of the surface tension force in tangential and radial directions are defined as in Equations (1) and (2). 𝐹⃗𝑠𝜃 = −𝑑𝑤 𝜎

𝜋(𝛼−𝛽) 𝜋2 −(𝛼−𝛽)2

[𝑠𝑖𝑛 𝛼 + 𝑠𝑖𝑛 𝛽]𝑒⃗𝜃

𝜋 𝐹⃗𝑠𝑟 = −𝑑𝑤 𝜎 (𝛼−𝛽) [𝑐𝑜𝑠 𝛼 − 𝑐𝑜𝑠 𝛽]𝑒⃗𝑟

(1) (2)

where σ refers to the surface tension and 𝛼 and 𝛽 respectively represent advancing and receding angles. To determine these angles, images taken in

120

Shahriyar Ghazanfari Holagh and Mohammad Ali Abdous

experimental tests are processed. 𝑑𝑤 denotes the bubble contact diameter, which is described as 𝑑𝑤 /𝑟𝑑 = 𝐾 . In this equation, 𝑟𝑑 is the departure radius and 𝐾 is a constant.

2.2. Quasi-Steady Drag Force Summation of the frictional and pressure drag forces results in the quasisteady drag force. Equation (3) can be used to calculate this force and 𝐶𝐷 in this equation is obtained from Equation (4) [18]. 𝐹⃗𝑞𝑠 = 6𝜋𝐶𝐷 𝜇𝑙 𝑢𝑟 𝑟𝑏 𝑒⃗𝜃 2

𝐶𝐷 = + [( 3

12 𝑛 ) 𝑅𝑒𝑏

(3) −1 𝑛

+ 0.796𝑛 ]

𝑛 = 0.65

(4)

In Equation (4), 𝑅𝑒𝑏 is the Reynolds number of bubble, which is calculated by Equation (5). 𝑅𝑒𝑏 =

2𝑟𝑏 𝑢𝑟

(5)

𝜈𝑙

where 𝑢𝑟 denotes the bubble velocity relative to liquid phase at the bubble’s center of mass. The velocity of bubble up to the departure instant is zero, therefore, 𝑢𝑟 has the same value as the liquid phase velocity 𝑢𝑙 [18]. Liquid phase velocity, 𝑢𝑙 , is calculated at the center of mass of the bubble using the wall function. 𝑢

𝑢+ = 𝑢∗𝑙 =

+

𝑟 =

𝑟𝑢∗ 𝜈𝑙

𝑢𝑙

(6)

𝜏𝑤 𝑙

√𝜌

𝜏𝑤 𝜌𝑙

𝑟√

=

𝜈𝑙

|

(7) 𝑟=𝑟𝑏

1

𝑢+ = 𝑘 + 𝑙𝑛𝑟 + + 𝐶 +

(8a)

Bubble Dynamics Analysis in Subcooled Flow Boiling

𝑟+ 𝑟+ ≤ 5 𝑢 = {5𝑙𝑛𝑟 − 3.05 5 < 𝑟 + < 30 2.5𝑙𝑛𝑟 + + 5.5 𝑟 + ≥ 30 +

+

121

(8b)

Generally, Equation (8a) represents the relation of the velocity profile, and 𝑘 and 𝐶 + in this equation are obtained from Equation (8b). Results of this study demonstrated that the quantity of 𝑟 + in different cases ranges between 5 and 30, and in few other cases takes a value larger than 30. Wall shear tension, 𝜏𝑤 , is determined by Equation (9), in which 𝑣𝑙 denotes the areaaveraged velocity of liquid, 𝐶𝑓 is the friction coefficient and 𝑓𝑐 denotes the friction factor. +

1

𝜏𝑤 = 𝐶𝑓 𝜌𝑙 𝑣𝑙2

(9)

2

𝐶𝑓 =

𝑓𝑐

(10)

4

The equation presented by Ito [20] is employed to calculate the 𝑓𝑐 , and it is used to determine the friction coefficient of a fully developed single-phase turbulent flow inside inclined channels. This relation may be utilized in the present formulations (Equation (11)).

𝑓𝑐 =

𝐷𝐻 2 −0.25 ) ] 𝐷𝑐

0.029+0.304[𝑅𝑒( 2 𝐷𝑐 𝐷𝐻

(11)

4√

In Equation (11), 𝐷𝐻 and 𝐷𝑐 represent hydraulic and curvature diameters (𝐷𝑐 = 2𝑅𝑐 ), respectively. 𝑅𝑒 = 𝜌𝑙 𝑣𝑙 𝐷𝐻 /𝜇𝑙 is used to calculate the flow Reynolds number (𝑅𝑒). Almost all force balance models developed in the literature have applied above equations to estimate liquid phase velocity. This model gives accurate results for liquid phase velocity profile prediction in single phase flows; however, the presence of bubbles can affect the velocity field, which is not considered in this model. Hence, Particle Image Analysis (PIV) technique is highly recommended to be applied to achieve accurate experimental results for the liquid phase velocity around bubbles.

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Shahriyar Ghazanfari Holagh and Mohammad Ali Abdous

2.3. Unsteady Drag Force Bubble growth originates the unsteady drag force, which is determined using Equation (12) according to the hypothesis of spherical bubble growth in a viscous liquid [18]. 3

𝐹𝑑𝑢 = −𝜌𝑙 𝜋𝑟𝑏2 [𝑟𝑏 𝑟̈𝑏 + 𝐶𝑠 𝑟̇𝑏2 ]

(12)

2

In Equation (12), the empirical constant 𝐶𝑠 is obtained by analyzing the force balance of experimental data. As Figure 3 exhibits, the radial and tangential components of this force are determined by Equations (13) and (14). 3 𝐹⃗𝑑𝑢𝑟 = 𝐹⃗𝑑𝑢 𝑐𝑜𝑠 𝜃𝑖 = −𝜌𝑙 𝜋𝑟𝑏2 [𝑟𝑏 𝑟̈𝑏 + 2 𝐶𝑠 𝑟̇𝑏2 ] 𝑐𝑜𝑠 𝜃𝑖 𝑒⃗𝑟

(13)

3 𝐹⃗𝑑𝑢𝜃 = 𝐹⃗𝑑𝑢 𝑠𝑖𝑛 𝜃𝑖 = −𝜌𝑙 𝜋𝑟𝑏2 [𝑟𝑏 𝑟̈𝑏 + 𝐶𝑠 𝑟̇𝑏2 ] 𝑠𝑖𝑛 𝜃𝑖 𝑒⃗𝜃

(14)

2

Zuber bubble growth model [21] is employed to calculate the rate of bubble growth, in which the effects of flow subcooling are considered by using a suppression factor according to Equation (17) [19, 22]. 𝑟𝑏 (𝑡) = 𝑆=

2𝑏 √𝜋

1

𝐽𝑎𝑒𝑓𝑓 √𝛼𝑙 𝑡 = 𝐺𝑏 𝑡 2 1

1.17 1+2.53×10−6 𝑅𝑒𝑡𝑝

∆𝑇𝑠𝑎𝑡,𝑒𝑓𝑓 = 𝑆(𝑇𝑤 − 𝑇𝑠𝑎𝑡 )

𝐽𝑎𝑒𝑓𝑓 =

𝜌𝑙 𝐶𝑝𝑙 ∆𝑇𝑠𝑎𝑡,𝑒𝑓𝑓 𝜌𝑙 ℎ𝑙𝑣

(15) (16) (17) (18)

In Equation (16), 𝑅𝑒𝑡𝑝 which indicates the two −phase Reynolds number, is obtained considering the vapor quality equal to zero. Also, ‘𝑏’ in Equation (15), is called bubble growth constant; it is an empirical coefficient. This coefficient is called departure growth constant at the departure point and is shown as ‘𝑏𝑑 ’ in this chapter. Lift-off growth constant ‘𝑏𝑙𝑜 ’, which differs from departure growth constant 𝑏𝑑 , is determined by representing Equation (15) at the lift-off point [23].

Bubble Dynamics Analysis in Subcooled Flow Boiling

123

2.4. Buoyancy Force Bubble experience the buoyancy force in the opposite direction of acceleration of gravity and it can be written as Equation (19) [18]. Components of buoyancy force in the tangential and radial directions are written as Equations (20) and (21), based on the nucleation site location on the inclined wall (i.e., considering the angle of γ in Figure 3). 4 𝐹⃗𝑏 = 3 𝜋𝑟𝑏3 (𝜌𝑙 − 𝜌𝑣 )𝑔⃗

(19)

4 𝐹⃗𝑏𝜃 = 3 𝜋𝑟𝑏3 (𝜌𝑙 − 𝜌𝑣 )𝑔 𝑠𝑖𝑛 𝛾 𝑒⃗𝜃

(20)

4 𝐹⃗𝑏𝑟 = 3 𝜋𝑟𝑏3 (𝜌𝑙 − 𝜌𝑣 )𝑔 𝑐𝑜𝑠 𝛾 𝑒⃗𝑟

(21)

2.5. Shear Lift Force Shear lift force, denoted by 𝐹⃗𝑠𝐿 , acts in the perpendicular direction and tries to separate the bubble from the wall. Mei and Kluasner [24] proposed a relation to determine the shear lift force, which is derived assuming the bubble is a sphere surrounded by an infinite flow field having a low Reynolds number. This equation along with Auton relation [25], offers Equation (22) to calculate 𝐹⃗𝑠𝐿 in an extensive range of Reynolds numbers. Auton relation is related to 𝐹⃗𝑠𝐿 that acts on the bubble in a viscous flow with low tension rates. 1 𝐹⃗𝑠𝐿 = 2 𝐶𝐿 𝜌𝑙 𝑢𝑟2 𝜋𝑟𝑏2 𝑒⃗𝑟

(22)

where 𝐶𝐿 represents the lift-off coefficient that can be obtained from Equation (23). 1 2

−𝑚 2

1 2

1 𝑚

𝐶𝐿 = 3.877𝐺𝑠 [𝑅𝑒𝑏 + (0.344𝐺𝑠 )𝑚 ] , 𝑚 = 4

(23)

To determine the dimensionless shear rate, 𝐺𝑠 , in Equation (23), one can use Equation (24) [18].

124

Shahriyar Ghazanfari Holagh and Mohammad Ali Abdous 𝑑𝑢

𝑟𝑏

𝐺𝑠 = | 𝑑𝑟𝑙 |

𝑟=𝑟𝑏 𝑢𝑟

𝑢∗

𝑟

= |𝑘 + 𝑟| 𝑢𝑏 = 𝐶 𝑟

1

𝑟𝑘

(24)

+ 𝑢+

In Equation (24), the magnitude of

𝑑𝑢𝑙 𝑑𝑟

is calculated based on the velocity

distribution of wall function. The relative velocity coefficient is defined as 𝑢 𝐶𝑟 = 𝑢𝑟. Since the bubble location is fixed before the departure instant, 𝐶𝑟 is 𝑙

unit. When the bubble begins to slide on the surface and before it lifts off, the relative velocity coefficient takes a value between zero and one.

2.6. Contact and Hydrodynamic Pressure Forces Equations (25) and (26) were presented by Klausner et al. [18] for calculating the contact and hydrodynamic pressure forces, individually. The contact pressure forces are exerted because of the difference between pressures in the bubble’s inner and outer parts, and the hydrodynamic pressure generates the hydrodynamic force [18]. 2

𝜋𝑑 2𝜎 𝐹⃗𝑐𝑝 = 4𝑤 5𝑟 𝑒⃗𝑟 𝑏

(25)

2

9 𝜋𝑑 𝐹⃗ℎ ~ 𝜌𝑙 𝑢𝑟2 𝑤 𝑒⃗𝑟 8

4

(26)

2.7. Radial Pressure Gradient Force Passing through an inclined path always establishes a pressure gradient in the radial direction on the flow. This radial pressure gradient adds another force to the ones acting on bubbles in the radial direction. In essence, the pressure gradient is the reason for the difference between pressures at the contact point and tip of the bubble. This gradient shows that pressure of the bubble tip is lower than the pressure at the bubble contact point [4]. Hence, a radial force is exerted on the bubble pointing to the center of the curved path. In straight channels, this force does not exist due to the movement of the flow in straight paths and fairly uniform pressure distribution in the cross section [4]. Based on Fluid Mechanics principles, the radial pressure gradient in a flow passing through a curved path is determined according to Equation (27), in which ‘𝑟’ is the position in the radial direction [4].

Bubble Dynamics Analysis in Subcooled Flow Boiling 𝑑𝑃 𝑑𝑟

= 𝜌𝑙

𝑢𝑙2

125

(27)

𝑟

By integrating Equation (27) from 𝑟𝑡 (the radius up to bubble tip) to 𝑟𝑜 (outer wall radius) over 𝑟, Equation (28) is derived for the difference between pressures at the bubble’s top and bottom. 𝑟

∆𝑃 = 𝑃𝑜 − 𝑃𝑡 = 𝜌𝑙 𝑢𝑙2 𝑙𝑛 𝑟𝑜

(28)

𝑡

At the lift-off moment, it is assumed that bubbles are perfect spheres. Bearing in mind that 𝑟𝑜 = 𝑅𝑐 and 𝑟𝑡 = 𝑅𝑐 − 2𝑟𝑏 , Equation (28) is revised as Equation (29), ∆𝑃 = 𝑃𝑜 − 𝑃𝑡 = 𝜌𝑙 𝑢𝑙2 𝑙𝑛

1 (1−

(29)

2𝑟𝑏 ) 𝑅𝑐

Hence, to determine the force caused by the pressure gradient in the radial direction, one can multiply Equation (29) by the bubble cross sectional area as below [4]; 𝐹⃗𝑅𝑃 = ∆𝑃. 𝐴𝑏 = (𝜌𝑙 𝑢𝑙2 𝑙𝑛

1 (1−

2𝑟𝑏 ) 𝑅𝑐

) (𝜋𝑟𝑏2 )𝑒⃗𝑟

(30)

To achieve a simple final expression, natural logarithm is replaced by its Taylor series, and Equation (30) is rewritten as Equation (31) [4]; 2

2𝜋𝜌𝑙 𝑢𝑙 3 𝐹⃗𝑅𝑃 = ∆𝑃. 𝐴𝑏 = 𝑟𝑏 𝑒⃗𝑟 𝑅𝑐

(31)

Therefore, Equation (31) can be employed to estimate the force achieved by the radial pressure gradient. The 𝐹⃗𝑅𝑃 , is inversely related to 𝑅𝑐 [4]. So, smaller the curvature radius is, larger the amount of this force becomes [4].

2.8. Centrifugal Force As can be seen in Figure 3c, bubble motion on the hot wall of a curved channel results in a centrifugal force. According to principles of Mechanic, bubble is

126

Shahriyar Ghazanfari Holagh and Mohammad Ali Abdous

assumed as a body having a mass of 𝑚𝑏 , which moves with a velocity of 𝑢𝑣 on a curved route having a curvature radius of 𝑅𝑐 . In this case, Equation (32) can be used to calculate the applied centrifugal force and 𝑚𝑏 is determined by Equation (33) [4]. 2

𝑢 𝐹⃗𝑐 = 𝑚𝑏 𝑅𝑣 𝑒⃗𝑟 𝑐

4

𝑚𝑏 = 𝜌𝑣 ( 𝜋𝑟𝑏3 ) 3

(32) (33)

3. Forces Balance Analysis To calculate the departure and lift-off diameters, it is required to analyze the force balance at departure or lift-off moments of bubbles. A correct analysis of force balance is essential for calculating the departure and lift-off radii of bubbles accurately. The relations written in Equation (34) and Equation (35) separately show the forces balance at the moments of departure and lift-off in the general form [4]. ∑ 𝐹⃗𝜃 = 𝐹⃗𝑞𝑠 + 𝐹⃗𝑑𝑢𝜃 + 𝐹⃗𝑠𝜃 + 𝐹⃗𝑏𝜃 = 0

(34)

∑ 𝐹⃗𝑟 = 𝐹⃗𝑠𝑟 + 𝐹⃗𝑠𝑙 + 𝐹⃗𝑑𝑢𝑟 + 𝐹⃗𝑏𝑟 + 𝐹⃗𝑐𝑝 + 𝐹⃗ℎ + 𝐹⃗𝑅𝑃 + 𝐹⃗𝑐 = 0

(35)

3.1. Departure Moment It can be concluded from Equation (34) that at the point of departure, the summation of all forces in the tangential direction equals zero. Thus, Equation (36) can be obtained by rewriting Equation (34) [4]. 𝐹⃗𝑠𝜃 + 𝐹⃗𝑏𝜃 = 𝐹⃗𝑞𝑠 + 𝐹⃗𝑑𝑢𝜃

(36)

At the point of departure, where 𝑟𝑏 |@𝑑𝑒𝑝𝑎𝑟𝑡𝑢𝑟𝑒 = 𝑟𝑑 , the aforementioned relations for each force are inserted into Equation (36) to obtain Equation (37) [4].

Bubble Dynamics Analysis in Subcooled Flow Boiling 𝜋(𝛼−𝛽)

127

3

𝑑𝑤 𝜎 𝜋2 −(𝛼−𝛽)2 [𝑠𝑖𝑛 𝛼 + 𝑠𝑖𝑛 𝛽] + 𝜌𝑙 𝜋𝑟𝑑2 [𝑟𝑑 𝑟̈𝑑 + 2 𝐶𝑠𝑑 𝑟̇𝑑2 ] 𝑠𝑖𝑛 𝜃𝑖 = 4 3

𝜋𝑟𝑑3 (𝜌𝑙 − 𝜌𝑣 )𝑔 𝑠𝑖𝑛 𝛾 + 6𝜋𝐶𝐷 𝜇𝑙 𝑢𝑙 𝑟𝑑

(37) 3

In Equation (37), the term 𝑟𝑑2 [𝑟𝑑 𝑟̈𝑑 + 2 𝐶𝑠𝑑 𝑟̇𝑑2 ] can be written as Equation (39), based on the bubble growth model as in Equation (38). Therefore, considering the contact diameter as 𝑑𝑤 /𝑟𝑑 = 𝐾, Equation (37) is revised to obtain Equation (40). 2𝑏𝑑

𝑟𝑏 |@𝑑𝑒𝑝𝑎𝑟𝑡𝑢𝑟𝑒 = 𝑟𝑑 = ( 3

√𝜋

1/2

𝐽𝑎𝑒𝑓𝑓 √𝛼𝑙 ) 𝑡𝑑

1/2

= 𝐺𝑏𝑑 𝑡𝑑

(38)

3

4 𝑟𝑑2 [𝑟𝑑 𝑟̈𝑑 + 2 𝐶𝑠𝑑 𝑟̇𝑑2 ] = (8 𝐶𝑠𝑑 − 1)𝐺𝑏𝑑 (𝛼−𝛽)

(39)

3

1

4

4 𝐾𝑟𝑑 𝜎 𝜋2 −(𝛼−𝛽)2 [𝑠𝑖𝑛 𝛼 + 𝑠𝑖𝑛 𝛽] + (8 𝐶𝑠𝑑 − 4)𝐺𝑏𝑑 𝜌𝑙 𝑠𝑖𝑛 𝜃𝑖 = 3 𝑟𝑑3 (𝜌𝑙 −

𝜌𝑣 )𝑔 𝑠𝑖𝑛 𝛾 + 6𝐶𝐷 𝜇𝑙 𝑢𝑙 𝑟𝑑

(40)

Equation (40) can be formulated in a cubic form with real constants as follows [4]. 𝑟𝑑3 − 𝐴𝑟𝑑 − 𝐵 = 0 𝐴=

(41)

𝐾 𝜎(𝛼−𝛽)[𝑠𝑖𝑛 𝛼+𝑠𝑖𝑛 𝛽] −6𝐶𝐷 𝜇𝑙 𝑢𝑙 𝜋2 −(𝛼−𝛽)2 4 ∆𝜌𝑔 𝑠𝑖𝑛 𝛾 3

3 3

(42)

4 1 𝜌𝑙 𝐺𝑏𝑑 𝑠𝑖𝑛 𝜃𝑖

𝐵 = 4 (8 𝐶𝑠𝑑 − 4)

(43)

∆𝜌𝑔 𝑠𝑖𝑛 𝛾

Using Cardano’s method [26], Equation (41) can be solved to obtain the departure radius (Equation (44)) with constants defined by Equations (42) and (43) [4].

𝐵

𝐵 2

𝐴 3

1 3

𝐵

𝐵 2

𝐴 3

1 3

𝑟𝑑 = ( 2 + √( 2 ) − ( 3 ) ) + ( 2 − √( 2 ) − ( 3 ) )

(44)

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Shahriyar Ghazanfari Holagh and Mohammad Ali Abdous

3.2. Lift-off Moment Bubbles contact diameter approaches zero at the lift-off moment [18]. Therefore, at this point, contact pressure, surface tension, and hydrodynamic forces have null values. Moreover, from data analysis, it can be deduced that the centrifugal force in Equation (2) has an order of magnitude that is less than other forces by 5 to 7 times [4]. Therefore, it is possible to neglect the centrifugal force compared to other forces in Equation (35). Equation (35) can be rearranged as Equation (45) at the lift-off point [4]. 𝐹⃗𝑠𝑙 + 𝐹⃗𝑅𝑃 + 𝐹⃗𝑏𝑟 = 𝐹⃗𝑑𝑢𝑟

(45)

Because at the lift-off point, a bubble detaches from the hot surface, the angle of bubble inclination tends to zero (𝜃𝑖 → 0°). At this point, where 𝑟𝑏 |@𝑙𝑖𝑓𝑡−𝑜𝑓𝑓 = 𝑟𝑙𝑜 , by substituting each force in Equation (45) with the proper relations, Equation (46) is obtained [4]. 1 2

4

3 (𝜌 2 𝐶𝐿 𝜌𝑙 𝑢𝑟2 𝜋𝑟𝑙𝑜 + 𝜋𝑟𝑙𝑜 𝑙 − 𝜌𝑣 )𝑔 𝑐𝑜𝑠 𝛾 + 3

2𝜋𝜌𝑙 𝑢𝑙2 3 𝑟𝑙𝑜 𝑅𝑐

2 = 𝜌𝑙 𝜋𝑟𝑙𝑜 [𝑟𝑙𝑜 𝑟̈𝑙𝑜 +

3

𝐶 𝑟̇ 2 ] 2 𝑠𝑙 𝑙𝑜

(46) 3

2 2 Using Equation (48) to replace the term 𝑟𝑙𝑜 [𝑟𝑙𝑜 𝑟̈𝑙𝑜 + 𝐶𝑠𝑙 𝑟̇𝑙𝑜 ] in Equation 2

(46), Equation (49) can be derived from Equation (46) [4]. 2𝑏𝑙𝑜

𝑟𝑏 |@𝑙𝑖𝑓𝑡−𝑜𝑓𝑓 = 𝑟𝑙𝑜 = (

√𝜋

1/2

1/2

𝐽𝑎𝑒𝑓𝑓 √𝛼𝑙 ) 𝑡𝑙𝑜 = 𝐺𝑏𝑙𝑜 𝑡𝑙𝑜

3

3

1

2

8

4

(47)

2 2 4 𝑟𝑙𝑜 [𝑟𝑙𝑜 𝑟̈𝑙𝑜 + 𝐶𝑠𝑙 𝑟̇𝑙𝑜 ] = ( 𝐶𝑠𝑙 − )𝐺𝑏𝑙𝑜 4

(3 ∆𝜌𝑔 𝑐𝑜𝑠 𝛾 +

2𝜌𝑙 𝑢𝑙2 𝑅𝑐

1

(48) 3

1

3 2 4 + (2 𝐶𝐿 𝜌𝑙 𝑢𝑟2 ) 𝑟𝑙𝑜 = 𝜌𝑙 (8 𝐶𝑠𝑙 − 4)𝐺𝑏𝑙𝑜 ) 𝑟𝑙𝑜

(49)

Equation (49) can be arranged as a cubic polynomial as presented in Equation (50), where the constants are real [4]. 3 2 𝑟𝑙𝑜 + 𝐴𝑟𝑙𝑜 −𝐵 =0

(50)

Bubble Dynamics Analysis in Subcooled Flow Boiling

𝐴=

1 𝐶 𝜌 𝑢2 2 𝐿 𝑙 𝑟 2𝜌𝑙 𝑢2 𝑙

(51)

4 ∆𝜌𝑔 𝑐𝑜𝑠 𝛾+ 3 𝑅𝑐

𝐵=4 3

3 8

1 4

4 ( 𝐶𝑠𝑙 − )𝜌𝑙 𝐺𝑏𝑙𝑜

∆𝜌𝑔 𝑐𝑜𝑠 𝛾+

129

(52)

2𝜌𝑙 𝑢2 𝑙 𝑅𝑐

Cardano’s method is employed to solve Equation (52). Therefore, the liftoff radius of bubble is determined as Equation (53) [4]. 𝐴 3

𝐵

𝐵 2

𝐴 3

1 3

𝐵

𝐴 3

𝑟𝑙𝑜 = [( 2 ) − ( 3) + √( 2 ) − 𝐵 ( 3 ) ] + [( 2 ) − ( 3 ) − 𝐵 2

𝐴 3

1 3

√( ) − 𝐵 ( ) ] − 𝐴 2 3 3

(53)

4. Empirical Coefficients The precision of force models for predicting the bubble departure and lift-off radii is strongly influenced by empirical coefficients, which highly depend on the flow conditions and channel geometrical design [23]. Processing the images taken in experiments at the departure point gives the values of 𝛼 and 𝛽. Approximate values of α and 𝛽 are reported 45° and 36°, respectively by Klausner et al. [18]. Bibeau and Salkudean [27] investigated subcooled boiling of water in a straight passage at a pressure ranging between 2 bar to 3 bar. In their experiments, α and β angles were obtained in the range of 43° ≤ 𝛼 ≤ 53° and 40° ≤ 𝛽 ≤ 44°, respectively. Cho et al. [23] in their experiment found 𝛼 and 𝛽 in the ranges of 22.6° ≤ 𝛼 ≤ 84.3° and 21.9° ≤ 𝛽 ≤ 70.1°, respectively. Sugrue et al. [28] presented the rough quantities of α and β as 91° and 8°, respectively. Abdous et al. [4] carried out a study on bubbles behavior in curved channels and obtained α and β angles in the ranges of 42° ≤ 𝛼 ≤ 61° and 35° ≤ 𝛽 ≤ 52°, respectively. Klausner et al. [18] and Zeng et al. [29] stated that the bubble’s average inclination angle at the departure point is about 10°. The value of 10° for this angle was also reported by Cho et al. [23]. Abdous et al. [4] found that in curved channels, values of 𝜃𝑖 are in the range of 3.25° ≤ 𝜃𝑖 ≤ 4.6°, and using 𝜃𝑖 = 3.7° in the force balance model (Equation 44) produces the most accurate

130

Shahriyar Ghazanfari Holagh and Mohammad Ali Abdous

fit of departure radius to experimental data. Bubble inclination angle is smaller in curved channels compared with the straight channels, which is because of secondary flow formation in the curved passage owing to the pressure gradient in the radial direction [4]. This phenomenon causes the advancing and receding contact angles of bubbles to have close values, which results in a smaller inclination angle of bubble at the departure [4]. At the lift-off moment, since the bubble is close to separate from the hot surface, inclination angle vanishes [18]. Bubble contact diameter is not a measurable parameter and it should be set by user according to force balance in the flow direction [28]. Klausner et al. [18] suggested 𝑑𝑤 value equal to 0.09 mm. Yun et al. [30] recommended using the value of 𝑑𝑤 / 𝑟𝑑 = 0.134 and Hong et al. [31] proposed 0.9 for 𝑑𝑤 / 𝑟𝑑 . Cho et al. [23] proposed an equation as 𝑑𝑤 / 𝑟𝑑 = 2𝑠𝑖𝑛 𝜃𝑚 for contact diameter, in which 𝜃𝑚 is the mean of bubble advancing and receding contact angles. The value of 0.05 for 𝑑𝑤 / 𝑟𝑑 have been suggested by Sugrue et al. [28]. Abdous et al. [4] reported that the model developed by Sugrue et al. [28] can be utilized to calculate the bubble contact diameter in a curved channel. To determine the projections of unsteady drag force in the tangential and radial directions for calculating the departure and lift-off radii in the force balance model, empirical coefficients 𝐶𝑠𝑑 and 𝐶𝑠𝑙 are of paramount importance [4]. Value of 𝐶𝑠 = 1 used by Klausner et al. [18] and Sugrue et al. [28] for departure radius in force model. The value of 𝐶𝑠 = 20/3 used by Zeng et al. [29] is associated with data of pool boiling in the force models to calculate departure and lift-off radii in flow boiling. Abdous et al. [4] proposed values of 𝐶𝑠𝑑 = 0.77 and 𝐶𝑠𝑙 = 0.71 as the best ones to be employed in the analysis of forces balance for calculating the bubble radii of lift-off and departure. Zuber’s bubble growth model (Equation (17)) includes the important parameter ‘𝑏’ called the bubble growth constant. This parameter is influenced by the system pressure, working fluid, wall superheat, etc. [23]. In pool and flow boiling, Zeng et al. [29, 32] suggested values between 1 and √3 for ‘𝑏’ and stated that the value of 1 results in the best agreement between the model and experiments. The value of 𝑏 = 1.73 is used by Situ et al. [19] and Hong et al. [31], while Wu et al. [33] employed 𝑏 = 1.2, Yun et al. [30] applied 𝑏 = 1.56, and Yeoh et al. [34] suggested 𝑏 = 0.21. Recently, Sugrue et al. [28] used 1.56 for 𝑏 . Cho et al. [23] suggested various values between 0.1 and 0.5 for ‘𝑏’. They observed that rising the effective Jacob number of wall increases ‘𝑏’, since the growth rate of bubble is directly related to the wall

Bubble Dynamics Analysis in Subcooled Flow Boiling

131

superheat. Generally, based on the flow condition, ‘𝑏’ can take different values [4]. Nevertheless, researchers employ a fixed value that gives the finest agreement between departure and lift-off models and experimental data [23]. Abdous et al. [4] obtained different growth constants for lift-off and departure. They found out that bubbles’ departure growth constants in the curved channel, 𝑏𝑑 , ranges between 2.54 and 7.28, and bubble lift-off growth constants, 𝑏𝑙𝑜 , take values ranging between 2.51 and 5.27.

5. Previous Studies Tables 1 and 2 briefly summarize the most important studies conducted on the bubbles’ dynamic behavior in flow boiling available in open literature; as can be observed, bubbles characteristics have been experimentally studied under various flow conditions and geometrical parameters. The common measurement technique in these studies is high-speed photography. Also, these studies have investigated how bubbles characteristics are influenced by flow conditions and geometry. The majority of these studies are unanimous in the following statements about bubbles dynamic behavior. •

•

• •

Departure and lift-off diameters increase and waiting time decreases as wall heat flux and temperature of inlet flow increase (i.e., a reduction in inlet subcooling) and mass flux decrease, whereas increasing the temperature of inlet flow, surface heat flux, and mass flux lead to a reduction in bubbles growing time. Since waiting time is the governing parameter in the determination of bubble nucleation frequency, a decrease in the former causes a higher value of the latter. Therefore, increasing the surface heat flux, temperature of the inlet flow, and declining the mass flux results in a rise in the nucleation frequency. Bubbles departure and lift-off growth constants rise with the surface heat flux, mass flux, and temperature of flow at the inlet. Bubbles behavior versus variations in flow conditions in curved channels is similar to straight ones. However, in curved channels, bubbles have larger departure and lift-off diameters, shorter growth, lift-off, and waiting times, and higher nucleation frequencies than straight ones.

Rectangular Annular Annular

Water Water Water

Tolubinsky and Kostanchuk [36] Abdelmessih et al. [37] Ünal [6]

Annular Annular

Water Water Water Water Water Water R-134a Square

Situ et al. [40]

Cho et al. [23] Chu et al. [7] Euh et al. [41]

Zou and Jones [42]

Rectangular Annular Annular

Annular

Rectangular Square

R-113 FC-87

Klausner et al. [18] Thorncroft et al. [38] Prodanovic et al. [39] Situ et al. [19]

Rectangular

Water

Ghunther [35]

Geometry

fluid

Study

12.7

22.2 40.4

19.1

19.1

9.3

25 12.7

-

-

-

-

DH (mm)

Horizontal

Vertical Vertical Vertical

Vertical

Vertical

Vertical

Horizontal Vertical

Horizontal

Horizontal

Horizontal

Horizontal

Orientation

Stainless steel Stainless steel Stainless steel Copper NCF 600 Stainless steel Stainless steel and Copper

Heating surface Stainless steel Stainless steel Stainless steel Stainless steel Nichrome Nichrome

48

17 14 76

58

91

54

35 20

7

34

5

0-630

2.7-6.5 140-200 61-238

60.7-206

54-206

200-1000

11-26 1.3-14.6

380-550

187-460

470

63-378

20.7-47.2 300-700 214-1869

478-905

466-900

76-766

112-287 192-666

3100-3600

796-1274

192-198

kW kg Date q′′ ( 2 ) G ( 2 1) points m m s 38 4500-6140 77-6088

10-30

2.1-11.8 3.4-22.6 7.5-23.4

1.5-20

2-20

10-30

Saturated 1.9-5

3-6

1.85

5-60

20-86

∆Tsub (℃)

4.5-8

1 1.3-1.5 1.7-3.5

1

1

1-3

1 1

139-177

1

1

1-1.7

P (bar)

Table 1. Summary of some existing studies on bubbles dynamic behavior in in the literature (taken from [5], Copyright 2021 Elsevier)

●

●

●

● ●

●

● ●

●

●

● ●

●

●

●

●

●

Dlo fd

●

●

●

Dd

Square Rectangular Rectangular Rectangular

Water Water Water Water Water Water Water Water Water

Guan et al. [43]

Brooks et al. [44]

Goel et al. [45]

Ooi et al. [46] Vlachou and Karapantsios [17] Zhou et al. [47] Ren et al. [48]

Abdous et al. [4] Holagh et al. [3]

Rectangular Rectangular

Annular

Annular

Annular

Rectangular

Water

Sugrue et al. [9]

Geometry

fluid

Study

15.7 15.7

19.8 3.8

12.7 16

33

19.1

5.1

16.7

DH (mm)

U-shaped U-shaped and straight

Horizontal Vertical

Vertical 0° − 150°

Vertical

Vertical

Vertical

0° − 180°

Orientation

Aluminum Stainless steel Nichrome Nichrome

Heating surface Stainless steel Stainless steel Stainless steel Stainless steel Copper Copper

68 25

34 58

9 -

42

83

12

kg ) m2 s 1 250-400 G(

26.1-61.5 36.3-54.6

231-550 100-700

231-295 200-1000

52.6-95.5

100-492

114-255 129.3-260

949-1928 300-1700

260-422 330-830

6.6-13.3

235-986

68.2-101.4 87-319

kW Date q′′ ( 2 ) points m 64 50-100

1-8 1.7-5.7

7-14 20-50

12.1-24.3 70

10-30

5-40

8.5-10.5

10-20

∆Tsub (℃)

1 1

1.2-2.3 0.2-0.6

1.4-4.4 1

1

1.5-3

1

1-5

P (bar)

● ●

● ● ● ●

●

● ●

●

● ● ●

● ●

Dlo fd

●

●

●

Dd

Study Ghunther [35] Tolubinsky and Kostanchuk [36] Ünal [6] Klausner et al. [18] Thorncroft et al. [38] Prodanovic et al. [39] Situ et al. [19] Cho et al. [23] Chu et al. [7] Euh et al. [41] Zou and Jones [42] Sugrue et al. [9] Guan et al. [43] Brooks et al. [44] Goel et al. [45] Ooi et al. [46] Vlachou and Karapantsios [17] Zhou et al. [47] Ren et al. [48] Abdous et al. [4] Holagh et al. [3] (for straight channel) Holagh et al. [3] (for U-shaped channel) 0.15-0.45 0.22-0.66 0.62-1.85 0.05-0.3 0.31-0.58 0.2-0.5 0.02-0.66 0.21-0.31 0.01-0.78 0.53-1.67 0.21-0.78 0.38-1.75

0.46-0.56

Dd (mm) 0.32-1.02 0.47-1.24 0.11-0.18 0.1-0.65 0.09-0.25 0.3-2.68

3-7

0.35-0.95 0.15-0.65

0.82-2.4 0.35-1.25 0.52-1.98

1-1.8 0.41-9.5

0.12-45 0.37-2.86 0.145-0.6 0.55-0.9 0.51-1.71

0.31-0.96

t d (ms) 0.8-3 1.2

Dlo (mm)

1.6-3.45 0.45-1.65

0.81-18.6

t lo (ms)

2.3-8.5 1-6.1

22-90

17-30

t w (ms)

110-355 150-715

120-1450 10-41 10-600

77-300 20-900

fd (s −1 )

Table 2. Reported ranges for bubbles characteristics in the literature (taken from [5], Copyright 2021 Elsevier)

Bubble Dynamics Analysis in Subcooled Flow Boiling

135

Conclusion In this chapter, bubbles dynamic behavior was analyzed from a force balance analysis perspective; different forces acting on bubbles were introduced and explained. Using, the balance between the forces in both flow and perpendicular directions, the models predicting the departure and lift off diameters were achieved. Additionally, important studies from the literature were briefly reviewed and the influence of flow conditions on bubbles characteristics were discussed.

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Auton, T. The lift force on a spherical body in a rotational flow, J. Fluid Mech. 183 (1987) 199–218. doi:10.1017/S002211208700260X. Cardano, G., The great art: or, the rules of algebra, Mit Press, Chicago, 1968. Bibeau, E. L., M. Salcudean, A study of bubble ebullition in forced- convective subcooled nucleate boiling at low pressure, Int. J. Heat Mass Transf. 37 (1994) 2245–2259. Sugrue, R., J. Buongiorno, A modified force-balance model for prediction of bubble departure diameter in subcooled flow boiling, Nucl. Eng. Des. 305 (2016) 717–722. doi:10.1016/j.nucengdes.2016.04.017. Zeng, L. Z., J. F. Klausner, R. Mei, A unified model for the prediction of bubble detachment diameters in boiling systems—II. flow boiling, Int. J. Heat Mass Transf. 36 (1993) 2261–2270. doi:10.1016/S0017-9310(05)80112-7. Yun, B. J., A. Splawski, S. Lo, C. H. Song, Prediction of a subcooled boiling flow with advanced two-phase flow models, Nucl. Eng. Des. 253 (2012) 351–359. doi:10.1016/j.nucengdes.2011.08.067. Hong, G., X. Yan, Y. H. Yang, T. Z. Xie, J. J. Xu, Bubble departure size in forced convective subcooled boiling flow under static and heaving conditions, Nucl. Eng. Des. 247 (2012) 202–211. doi:10.1016/j.nucengdes.2012.03.008. Zeng, L. Z., J. F. Klausner, R. Mei, A unified model for the prediction of bubble detachment diameters in boiling systems—I. Pool boiling, Int. J. Heat Mass Transf. 36 (1993) 2261–2270. Wu, W., P. Chen, B. G. Jones, T. A. Newell, A study on bubble detachment and the impact of heated surface structure in subcooled nucleate boiling flows, Nucl. Eng. Des. 238 (2008) 2693–2698. doi:10.1016/j.nucengdes.2008.05.013. Yeoh, G. H., S. Vahaji, S. C. P. Cheung, J. Y. Tu, Modeling subcooled flow boiling in vertical channels at low pressures - Part 2: Evaluation of mechanistic approach, Int. J. Heat Mass Transf. 75 (2014) 754–768. doi:10.1016/j.ijheatmasstransfer. 2014.03.017. Ghunther, F., Photographic Study of Surface-Boiling Heat Transfer to Water Forced Convection, ASME J. Heat Transf. 73 (1951) 115–123. Tolubinsky, V., D. Kostanchuk, Vapour bubbles growth rate and heat transfer intensity at subcooled water boiling, In: Fourth Int. Heat Transf. Conf., Paris, 1970. Abdelmessih, A. H., F. C. Hooper, S. Nangia, Flow effects on bubble growth and collapse in surface boiling, Int. J. Heat Mass Transf. 15 (1972) 115–125. doi:10.1016/0017-9310(72)90170-6. Thorncroft, G. E., J. F. Klausner, R. Mei, An experimental investigation of bubble growth and detachment in vertical upflow and downflow boiling, Int. J. Heat Mass Transf. 41 (1998) 3857–3871. doi:10.1016/S0017-9310(98)00092-1. Prodanovic, V., D. Fraser, M. Salcudean, Bubble behavior in subcooled flow boiling of water at low pressures and low flow rates, Int. J. Multiph. Flow. 28 (2002) 1–19. doi:10.1016/S0301-9322(01)00058-1. Situ, R., M. Ishii, T. Hibiki, J. Y. Tu, G. H. Yeoh, M. Mori, Bubble departure frequency in forced convective subcooled boiling flow, Int. J. Heat Mass Transf. 51 (2008) 6268–6282. doi:10.1016/j.ijheatmasstransfer.2008.04.028.

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Chapter 6

Entropy Generation in Flow Boiling and Condensation Mohammad Ali Abdous* and Shahriyar Ghazanfari Holagh School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran

Abstract Heat transfer and pressure drop are the two main sources of entropy generation in flow boiling and condensation. If analyzed, the contributions made by heat transfer and pressure drop to entropy generation can lead to the identification and quantification of thermoshydraulic losses taking place in different industrial equipment operating under boiling/condensation conditions. Heat transfer enhancement techniques, on the other hand, impose considerable pressure drop while improving the heat transfer phenomenon. Therefore, an accurate entropy generation analysis can provide a valuable tool for the performance analysis of such techniques, which can extend to the detection of the optimized geometrical and flow conditions if operated under which entropy generation is minimized. Hence, in the present chapter, a mathematical model developed and widely applied in open literature for entropy generation analysis in flow boiling and condensation is first explained and then, utilized to simulate thermos-hydraulic losses of flow boiling and condensation in smooth straight tube and helically coiled and micro-fin tubes (as two common heat transfer enhancement techniques). Based on the simulation results, the impacts of important geometrical parameters and flow conditions on thermos-hydraulic losses are also analyzed. 

Corresponding Author’s Email: [email protected].

In: The Fundamentals of Thermal Analysis Editors: Mamdouh El Haj Assad, Ali Khosravi and Mehran Hashemian ISBN: 979-8-88697-759-2 © 2023 Nova Science Publishers, Inc.

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Mohammad Ali Abdous and Shahriyar Ghazanfari Holagh

Keywords: entropy generation; flow boiling; flow condensation; heat transfer enhancement; helical coils; micro-fin tubes

1. Introduction Numerous heat transfer enhancement methods (HTEM) have been extensively utilized over the past decades among engineers and scientists to increase heat transfer rate (HTR) [1] in different industrial processes. In a continuous search to find new methods to answer the growing demand for higher HTR, countless efforts have been made by researchers [2]. Basically, these methods are categorized into two common different classifications. In the first category, known as active methods, the researchers exploit external energy sources like electrical energy [3] or ultrasound [4] to enhance HTR. In the second one, known as passive methods, researchers mainly enhance the HTR via changing or manipulating the geometrical structure of the flow path to increase the flow turbulence intensity, and subsequently HTR. Take micro-fin tubes [5], helical coils [6], or using twisted tapes inside a tube [7, 8] as the most common examples of passive heat transfer techniques. Note that, generally, the HTEMs mentioned above can be applied for both single-phase [9] and two-phase flows (including boiling and condensation). The intensification in the flow turbulence plays a key role in different passive HTEMs. However, the rise in the unwanted pressure drop (PD) penalty together with the increase in heat transfer coefficient (HTC) is inevitable when using passive HTEMs. Therefore, although the HTC increases, the value of PD rises too. The entropy generation analysis (EGA) is one of the magnificent tools to simultaneously evaluate the weight of PD and heat transfer caused by different passive HTEMs. EGA also allows us to evaluate the potential thermal losses for an enhancement technique. That is, their capability to enhance heat transfer can be analyzed and the conditions within which such techniques are not performing optimally can be identified. PD and heat transfer in a two-phase flow system make hydraulic and thermal losses, respectively. These losses could be measured by EGA. Surprisingly, at some geometrical and flow conditions, a non-enhanced tube (i.e., smooth straight tube) can even outperform an enhancement technique from energy efficiency perspective. That is, the losses due to the PD will be so high that the energy demanded for pumping surpasses the energy saved due to the enhanced heat transfer. Therefore, the necessity of applying EGA to evaluate thermal-hydraulic losses

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for an enhancement technique is more pronounced as it can allow us to identify and avoid such conditions. To evaluate hydraulic and thermal losses by utilizing EGA in a two-phase saturated mixture system, researchers first need experimental correlations to calculate HTC and PD in their simulations. Then, using final numerical results of EGA, the influence of alterations in geometrical parameters (e.g., tube and coil diameters) and flow characteristics such as pressure, vapor quality, and mass flux on thermal-hydraulic losses could extensively examined. Revellin et al., [10] successfully calculated thermal and hydraulic losses in saturated two-phase mixture flowing in a pipe by computing their contributions to entropy generation (EG) using EGA. Later, the obtained expressions were suitably employed to different thermally enhanced geometries like helical coils in saturated two-phase fluid flow [11–13]. Also, the favorable range of geometrical and flow conditions within which the helical coil tube is preferred in performance to a straight tube was reported [11–13]. Researchers have utilized EGA to another thermally enhanced geometry namely micro-fin tube in flow boiling [14] and condensation [15]. Moreover, they compared the EGA’s numerical results for the micro-fin tube with the helical coil using EG number to detect the favorable regions within which applying smooth straight, helical coil, and micro-fin tubes is favorable. The idea of EGA has been also employed for another common HTEM called “twisted-tape” inserts. Inserting such a tape into a pipe results in higher flow turbulence, PD, and HTR. Holagh et al., Holagh et al., [16] applied EGA to analyze this enhancement method from thermal-hydraulic losses point of view.

2. Entropy Generation Model in Two-Phase Flow To better understand the passive enhancement methods, consider a straight tube shown in Figure1a with the inlet and outlet boundaries, through which two-phase saturated water passes. Imposing heat flux to its peripheral boundary causes the saturated water to evaporate. Now consider the same amount of saturated water flowing in a tube with different geometrical shape like a helical one as shown in Figure1b with the same length and boundary conditions indicated in Figure1a. The average HTC shows higher values for the helical coil tube [17]. This enhancement in HTC is achieved only by the change in the tube geometry from the straight structure to the helical one. In essence, the induced turbulence made by the secondary

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Mohammad Ali Abdous and Shahriyar Ghazanfari Holagh

flow due to the radial pressure gradient of the helical coil tube causes higher HTC and PD penalty in comparison to smooth straight tube [18].

(a)

(b) Figure 1. (a) A smooth straight tube and (b) a helical coil tube.

According to the second-law of thermodynamics, as a saturated two-phase flow enters the straight tube (Figure1a) or the helical coil tube (Figure1b), the ′ change in EG rate for unit length "dz" called (Ṡgen ) [11, 19] is achieved by: ′ Ṡgen =

d dz

[ṁv sv + ṁl sl ] −

dQ̇

(1a)

Tw dz

̇

d dQ ′ Ṡgen = ṁ dz [xsv + (1 − x)sl ] − T dz w

x = (ṁ

ṁv

v +ṁl )

(1b)

(2)

In above equations, ṁ is the mass flow rate, and x is the vapor quality. The specific entropy and wall temperature are denoted by s and TW, respectively. Eq. (1b) can be rewritten by considering slv = sv − sl :

Entropy Generation in Flow Boiling and Condensation

143

̇

dx ds dx ds dQ ′ Ṡgen = ṁ [sv dz + x dzv − sl dz + (1 − x) dzl ] − T dz

(3a)

w

dx ds ds ′ Ṡgen = ṁ [slv + x v + (1 − x) l ] − dz

dz

dhv −vv dpv

Using dsv =

Tv

dz

and dsl =

dQ̇

(3b)

Tw dz

dhl −vl dpl Tl

h

and defining 𝑠lv = T lv , Eq. sat

(4) is obtained. hlv dx (dhv − vv dpv ) (dhl − vl dpl ) dQ̇ ′ Ṡgen = ṁ [ +x + (1 − x) ]− Tsat dz Tv dz Tl dz Tw dz (4) Because of the nature of saturated two-phase flow, in Eq. (4), it could be assumed that Tsat = Tv = Tl and dp = dpv = dpl . Therefore, a more simplified form as shown in Eq. (5) can be obtained. ′ Ṡgen =

ṁ Tsat

[hlv

dx dz

+x

dhv

+ (1 − x)

dz

dhl dz

]−

ṁ[xvv +(1−x)vl ] dp Tsat

dz

−

dQ̇ Tw dz

(5) ′ Thus, Ṡgen can be written in the form of Eq. (6), where dhtp = hlv dx + xdhv + (1 − x)dhl and vtp = xvv + (1 − x)vl as follows: ṁ ′ Ṡgen =T

dhtp

sat

dz

−

ṁvtp dp Tsat dz

dQ̇

−T

(6)

w dz

In accordance with the first law of thermodynamics, Eq. (7) is achievable [20–22]. dQ̇ dz

= ṁ

dhtp

(7)

dz

Using Eq. (7) in Eq. (6), the rate of generation in entropy per unit length can be written as Eq. (8): dh v 1 1 ′ Ṡgen = ṁ [ dztp (T − T ) − T tp sat

w

sat

dp dz

Eq. (8) can be divided into two parts:

]

(8)

144

Mohammad Ali Abdous and Shahriyar Ghazanfari Holagh dhtp 1 1 ′ Ṡgen−ht = ṁ [ dz (T − T )] sat

w

ṁvtp dp ′ Ṡgen−pd = T (− dz ) sat

(9) (10)

where, Eq. (9), represents the thermal loss or heat transfer contribution to EG, whereas the hydraulic loss or the contribution of PD to EG is represented by Eq. (10). Bejan number (𝐵𝑒), irreversibility distribution ratio parameter (IDR), and entropy generation number (𝑁𝑠 ) can be obtained using Eq. (8), Eq. (9), and Eq. (10) as follows. 𝐵𝑒 =

Ṡ′gen−ht Ṡ′gen

𝐼𝐷𝑅 =

(11)

Ṡ′gen−pd Ṡ′

(12)

Ṡ′gen,EM Ṡ′gen

(13)

gen−ht

𝑁s,EM =

In Eq. (13), 𝑁s,EM is defined as the ratio of EG by different thermally enhanced heat transfer techniques to the smooth straight tube.

3. Entropy Generation in Smooth Straight, Micro-Fin and Helical Coil Tubes ′ ′ As mentioned in previous section, to evaluate the Ṡgen−ht (Eq.9) and Ṡgen−pd

(Eq.10), two empirical correlations are needed to calculate heat transfer (

dhtp dz

)

dp

and PD ( ) per unit length "dz". Based on two different two-phase heat dz

transfer mechanisms, namely boiling and condensation, these correlations were extracted by some researchers and are available in open literature.

3.1. Flow Boiling Assume that saturated refrigerant R-134a enters a tube at low vapor quality; heat flux is applied on the tube wall as exhibited in Figure 1. As the refrigerant

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flows inside the tube, thermal energy is absorbed, and boiling phenomenon occurs. Subsequently, the refrigerant leaves the tube with a higher vapor quality. The geometrical shape of the tube could be a smooth straight tube or a thermally enhanced tube such as micro-fin or helical coil one. For these three cases, the experimental correlations, extracted from the open literature, are explained in the following paragraphs. a) Smooth straight tube under flow boiling conditions Empirical correlations for heat transfer and frictional PD in smooth straight tube to compare its performance with thermally enhanced tubes using 𝑁𝑠 (Eq. (13)). In the present analysis, the ones developed by Wongsa-ngam et al., [23] are utilized. Table 1. HTC and frictional PD correlations of the smooth straight tube under flow boiling conditions

Boiling HTC correlations [23]

−0.17 ℎ𝑇𝑃 = 3.1737ℎ𝑙𝑜 (𝐵𝑜 × 104 )0.4 𝑋𝑡𝑡

𝑘𝑙 𝐺𝐷𝑖 0.8 𝑐𝑝,𝑙 𝜇𝑙 0.4 ℎ𝑙𝑜 = 0.023 ( ) ( ) 𝐷𝑖 𝜇𝑙 𝑘𝑙

Boiling frictional PD correlations [23]

S.1

S.2

d𝑃 2𝑓l 𝐺 2 (1 − 𝑥)2 | = 𝜑l2 ( ) d𝑧 f 𝐷i 𝜌l 2 −1.8042 𝜑𝑙 = 1 + 5.8750𝑋𝑡𝑡 1 − 𝑥 0.9 𝜌𝑣 0.5 𝜇𝑙 0.1 𝑋𝑡𝑡 = ( ) ( ) ( ) 𝑥 𝜌𝑙 𝜇𝑣

S.3 S.4 S.5

In Table 1, 𝑋tt depicts the Lockhart-Martinelli parameter and 𝐵𝑜 represents the boiling number. Also, ℎlo is the Dittus-Boelter correlation as indicated in in S.2. b) Micro-fin tube under flow boiling conditions The micro-fin tube is one of the enhanced heat transfer methods extensively utilize in industrial applications. Figure2 shows the schematic of micro-fin geometrical parameters [14]. The geometrical parameters of a micro-fin tube are defined in Table.2.

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Figure 2. The schematic of fins’ geometrical parameters, taken with permission from Ref. [14]. (Copyright 2021 Elsevier)

Table 2. The micro-fin tube’s geometrical parameters Symbols Do BW (Figure2) BT (Figure2) N Aw (Figure2) Sp (Eq.14) Ac (Eq.16) Dh (Eq.17)

Geometrical parameters Tube outer diameter Bottom width Bottom thickness Number of fins Cross sectional tube wall area Distance between the two successive fins’ tips Cross-sectional flow area Hydraulic diameter

Sp is the distance between the two successive fins’ tips; this parameter is achieved by: S p = Bw +

2ef cos (α)

(14)

Aw is the cross-sectional are of the tube wall defined per fin number, as formulated by Eq. (15), where Ac is defined by Eq. (16). Aw = e2f tan(α) + (2ef tan(α) + Bw )BT Ac =

πD2o 4

− NAw

(15) (16)

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147

Micro-fin tube’s hydraulic diameter is: Dh =

4Ac cos (β)

(17)

NSp

Alpha angle (α) shown in Figure2 is obtained by: α = tan−1 (

πDi −BW N

2ef

)

(18)

Finally, based on Eqs. (14-18) and utilizing experimental correlations for two-phase frictional PD and HTC [23], the EG, hydraulic and thermal losses could be calculated using the EGA model. Table 3 reports the HTC and frictional PD correlations suggested by Wongsa-ngam et al., [23] for R134-a flow boiling in micro-fin tubes. By assuming constant flow conditions in Table 4, the impact of variations in the fin height (ef ) is numerically investigated on the EG. It should be noted that, other geometrical parameters (BW , BT , N, D𝑜 ) are assumed to be constant as Table 5. As shown in Eq. (14), the increase in fin height (ef ) causes the values of Sp and Aw increase whereas the value of Ac decreases. At constant mass flow rate (ṁ = GAC), the reduction in Ac causes the increase in mass velocity (G = ρV). This leads to the increase in two-phase flow velocity leads to higher PD and better HTR. Therefore, the EG which ascribes to the PD increases and its thermal component decreases as shown in Figure3. Table 3. HTC and frictional PD correlations of micro-fin tube under flow boiling conditions Boiling HTC correlations [23]

Boiling frictional PD correlations [23] d𝑃

ℎ𝑇𝑃 = 5.5864ℎ𝑙𝑜 (𝐵𝑜 −0.14 × 104 )0.35 𝑋𝑡𝑡

ℎ𝑙𝑜 = 0.023

𝑘𝑙 𝑅𝑒 0.8 𝑃𝑟 0.4 𝐷ℎ 𝑙𝑜 𝑙

2 | = 𝜑𝑣𝑜 (

d𝑧 𝑓

S.6

2𝑓𝑣𝑜 𝐺 2 𝐷ℎ 𝜌𝑣

)

S.8

2 𝜑𝑣𝑜 = 2.3263 − 1.8043 {𝐺𝑋𝑡𝑡 / 0.5 0.0802

S.9

[𝑔𝐷ℎ 𝜌𝑔 (𝜌𝐿 − 𝜌𝑔 )] } S.7

4𝑓𝑣𝑜 =

1.325 𝑒 5.74 2 [ln (3.7𝐷 + 0.9 )] Revo

S.10

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Mohammad Ali Abdous and Shahriyar Ghazanfari Holagh

Table 4. Flow conditions used for flow boiling simulations in the micro-fin tube Symbols G q Tsat xin

Flow conditions Mass velocity Wall heat flux Saturation temperature Inlet vapor quality

Value 400 kg/m2 s1 10 kW/m2 15 °C 0.2

As the number of fins (N) increases, a decrease in the value of Ac appears (Eq.16). Although the value of Aw reduces due to the reduction of α (Eq. (18)), the multiplication of (NAw ) rises, leading to the reduction in the value of Ac. In this case, the flow conditions assumed to be as Table 4, while the geometrical parameters are constant according to Tables 5 and 6. Table 5. The micro-fin tube’s geometrical parameters when the change in 𝒆𝐟 is studied Symbols Do BW N

Geometrical parameters Outer diameter Bottom width Number of fins

Value 9.52 mm 0.27 mm 60

Table 6. The geometrical parameters of the micro-fin tube when the change in 𝐍 is investigated Symbols Do ef BW

Geometrical parameters Outer diameter Fin height Bottom width

Value 9.52 mm 0.2 mm 0.27 mm

Figures 3 and 4, demonstrate the impact of variations in fin height and number of fines on EG due to heat transfer and PD as well as total EG, correspondingly. Looking at Figure 3, one can see that the heat transfer contribution to EG reduces, while that of the frictional PD grows as the fin height increases. The same trends are observed when the number of fines increases. c) helical coil tube under flow boiling conditions As previously mentioned, helical coil tubes are highly energy-efficient heat exchangers. To evaluate the thermal and the hydraulic losses, the

Entropy Generation in Flow Boiling and Condensation

149

appropriate heat transfer and PD correlations should be extracted from literature. In the helical coil tube, the important geometrical parameters are tube diameter and coil diameter (Table.7). The ratio of coil diameter to tube diameter called diameter ratio. The geometrical parameters of the helical coil tube are illustrated in Figure 5. Table 7. The helical coil tube’s geometrical parameters Symbols di (Figure6) Dc (Figure6) H (Figure6) Acr (Eq.19) Ape (Eq.20)

Geometrical parameters Tube diameter Coil diameter Helical pitch Cross-sectional flow area Peripheral Area

Figure 3. Impact of fin height on total EG, and PD and heat transfer contributions to EG for the micro-fin tube under flow boiling conditions, taken with permission from Ref. [14]. (Copyright 2021 Elsevier).

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Mohammad Ali Abdous and Shahriyar Ghazanfari Holagh

The values of Acr and Ape are defined as below. Acr = 𝜋

d2i 4

Ape = 𝜋di L

(19) (20)

In Eq. (20), the value of L could be a differential length called dz in EG formulation mentioned above.

Figure 4. Impact of number of fins on total EG, and PD and heat transfer contributions to EG for the micro-fin tube under flow boiling conditions, taken with permission from Ref. [14]. (Copyright 2021 Elsevier)

To simulate EG for flow boiling in helical coils, HTC and PD correlations developed by [24] are applied; these correlations are shown in Table 8. Also, note that the EG simulations were done under constant flow conditions that are tabulated in Table 9.

Entropy Generation in Flow Boiling and Condensation

151

H

Figure 5. The schematic of helical coil geometrical parameters, redrawn with permission from Ref. [12]. (Copyright 2021 Elsevier)

Table 8. HTC and frictional PD correlations of helical coil tube under flow boiling conditions Boiling HTC correlations based on Nusselt number [24] Nutp −5.055 S.11 = 6895.98De0.432 (Bo Eq Prl 4 0.132 −0.0238 × 10 ) Xtt DeEq

Boiling frictional PD correlations [24]

𝜇𝑣 𝜌𝑙 0.5 di 0.5 = [𝑅𝑒𝑙 + 𝑅𝑒𝑣 ( ) ( ) ] ( ) 𝜇𝑙 𝜌𝑣 Dc

S.12

𝜑𝑙2 = 1 +

S.13

(

𝑅𝑒l =

𝑅𝑒v =

𝐺(1−𝑥)di 𝜇l

𝐺𝑥di 𝜇𝑣

S.14

𝑑𝑝𝐹 𝑑𝑝𝐹 ( ) = ∅2l ( ) 𝑑𝑧 tp 𝑑𝑧 l

𝑑𝑝𝐹 𝑑𝑧

) = l

13.37 1.492 𝑋𝑡𝑡

2𝑓l 𝜌l 𝑈l2 di

Dc 𝑓l ( )0.5 di = 0.00725 −0.25 Dc + 0.076 [𝑅𝑒l ( )−2 ] di

S.15

S.16 S.17

S.18

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Mohammad Ali Abdous and Shahriyar Ghazanfari Holagh

Table 9. Flow conditions used for flow boiling simulations in the helical coil tube Symbols G q Tsat xin

Flow conditions Mass velocity Wall heat flux Saturation temperature Inlet vapor quality

Value 400 kgm−2 s −1 10 kWm−2 15 °C 0.2

Figure 6. Effect of tube diameter on total EG, and PD and heat transfer contributions to EG for helical coil Dc = 305 mm under flow boiling conditions, taken from Ref. [11] (Copyright 2015 Elsevier).

The impact of tube diameter and coil diameter ratio on the generated entropies is shown in Figs. 6 and 7. Assuming a constant value of coil diameter (Dc ) and flow conditions (Table 9), an increase in the inner tube diameter (di) leads to a reduction in PD contribution to EG. This is due to the rise in the value of two-phase saturated flow density. The mass flow rate (ṁ = GAcr) is proportional to d2i , while the heat transfer (Q = qApe ) is proportional to di at

Entropy Generation in Flow Boiling and Condensation

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constant heat flux. Therefore, the value of vapor quality drops by gradual increase in tube diameter (di); this leads to the increase in two-phase mixture density at constant mass flux (G). Finally, the hydraulic loss decreases due to the fall in the mixture velocity. The thermal component of the EG shows an increasing trend by increasing the tube diameter due to the fall in the mixture velocity that causes a decline in the HTC [11].

Figure 7. Effect of coil diameter ratio on total EG, and PD and heat transfer contributions to EG for helical coil with Do = 9.52 mm under flow boiling conditions, taken from Ref. [11] (Copyright 2015 Elsevier).

An increase in the value of coil diameter (Dc ) at a constant inner tube diameter is proportional to a steady rise in diameter ratio as shown in Figure 7. As the value of coil diameter rises, the radial pressure gradient and the resultant secondary flow weaken [17, 18, 25], contributing to a degraded HTR and the rise in thermal loss known as heat transfer contribution to EG (see Figure 7). Moreover, the contribution of PD to EG or hydraulic loss decreases due to the lower two-phase frictional component of PD.

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The comparison of EG in the smooth straight and the helical coil tubes is plotted in Figure8. As mass velocity (𝐺) increases, the PD contribution to EG rises in contrast to thermal share for both tubes. The growth in the mixture velocity is mainly responsible for these trends. Briefly, the raise in the mixture velocity contributes to a better HTR and higher PD. Two EG lines intersect each other at the value of 380 kg/m2s1. At this point, the sum of thermal and hydraulic losses of the tubes become equal. Therefore, the application of the helical coil is recommended at mass velocities smaller than 380 kg/m2s1, where it exhibits lower EG compared to smooth straight tubes; at higher mass velocities, smooth straight tubes are recommended.

Figure 8. EG in the helical coil tube (Do = 9.52 mm, Dc = 305 mm) and the smooth straight one (Do = 9.52 mm) under flow boiling conditions, taken from Ref. [11] (Copyright 2015 Elsevier).

Figure (9) illustrates the variation in the EG and its thermal and hydraulic losses’ shares with mass flux (G) for the helical coil tube and smooth straight one. An increase in this parameter (G) results in a rise in the PD share in the

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EG and a reduction in the heat transfer one. There should be only a small difference in the EG lines crossing at the value of 490 kg/m2s1 for the microfin tube instead of 380 kg/m2s1 for the helical coil one (Figure8). Similar to the helical coil tube, for mass velocities less than 490 kg/m2s1, the application of the micro-fin tube is recommended, whilst at greater mass velocities, its usage is not advisable; that is, it is better to use smooth straight tubes.

Figure 9. EG in the micro-fin (Do = 9.52 mm, ef = 0.2 mm, BW = 0.27 mm, N = 60) and the smooth straight tubes (Do = 9.52 mm) under flow boiling conditions, taken with permission from Ref. [14]. (Copyright 2021 Elsevier).

Two critical values of 380 kg/m2s1 and 490 kg/m2s1 were introduced above. The first value represents the intersection point of total EG lines of the smooth straight tube and the helical coil one, whereas the second one is the intersection point of EG lines of the smooth straight and micro-fin tubes. Considering that flow conditions were assumed to be similar for both cases, one could easily compare the thermal performance of the helical coil tube and the micro-fin one under flow boiling conditions using 𝑁𝑠 as indicated in Figure10. It is obvious that increasing vapor quality results in wider the

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favorable ranges of mass velocity for using both HTEMs. In addition, at the same vapor quality value, using micro-fin tube is preferred to helical coil one.

Figure 10. Thermal performance comparison between helical coil and micro-fin tubes using 𝑁𝑠 at different inlet vapor qualities under flow boiling conditions (𝑇sat = 15 °C, 𝑞 = 10 kWm−2 ), taken with permission from Ref. [14]. (Copyright 2021 Elsevier).

3.2. Flow Condensation During condensation process, in contrast to boiling phenomenon, heat is transferred from saturated refrigerant R-134a to the environment. In other words, the saturated vapor entered the tube lose heat and condenses; as a result, it leaves the tube in form of a saturated mixture with a low vapor quality. EG during R134-a flow condensation in smooth straight and helical coil tubes is investigated in the following.

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a) Smooth straight tube under flow condensation As mentioned in Eq. (13), to define the 𝑁𝑠 for the helical coil tube as one of the enhanced heat transfer methods, the value of the EG in the smooth straight tube is necessary. Similar to flow boiling conditions, the HTC and frictional PD correlations are used from the literature, as reported in Table 10. Table 10. HTC and frictional PD correlations of the smooth straight tube under flow condensation conditions Condensation HTC correlations based on Nusselt number [26] 0.997 𝑁𝑢tp = 0.003𝑅𝑒𝐸𝑞 𝑃𝑟𝑙0.932

𝐶𝑝l 𝜇l 𝑘l 𝜇𝑣 𝜌𝑙 = 𝑅𝑒𝑙 + 𝑅𝑒𝑣 ( )( )0.5 𝜇𝑙 𝜌𝑣 𝐺(1 − 𝑥)di 𝑅𝑒l = 𝜇l 𝐺𝑥di 𝑅𝑒v = 𝜇𝑣 𝑃𝑟l =

𝑅𝑒𝐸𝑞

Condensation frictional PD correlations [27] S.19

𝑑𝑝𝐹 𝑑𝑝𝐹 ( ) = ∅2l ( ) 𝑑𝑧 tp 𝑑𝑧 l

S.20 S.21

𝜑𝑙2 = 1 + S.22

5.705 1.711 𝑋𝑡𝑡

𝑑𝑝𝐹 2𝑓l 𝜌l 𝑈l2 ( ) = 𝑑𝑧 l di

S.23

S.24

S.25

S.26

Table 11. HTC and frictional PD correlations of the helical coil tube under flow condensation conditions Condensation HTC correlations [28] 𝑁𝑢𝑡𝑝 = 0.1352𝐷𝑒Eq 0.7654 𝑃𝑟l 0.8144 𝑋𝑡𝑡 0.0432 𝑝r −0.3256 (𝐵𝑜 × 104 )0.112 𝜇v 𝜌l 0.5 di 0.5 𝐷𝑒Eq = [𝑅𝑒l + 𝑅𝑒v ( ) ( ) ] ( ) 𝜇l 𝜌v Dc

S.27 S.28

𝑃𝑟l =

𝐶𝑝l 𝜇l 𝑘l

S.29

𝑝r =

𝑃sat 𝑃crit

S.30

𝐵𝑜 =

𝑞′′ 𝐺ℎlv

S.31

𝐺(1 − 𝑥)di 𝑅𝑒l = 𝜇l

S.32

Condensation frictional PD correlations [28] 𝑑𝑝𝐹 𝑑𝑝𝐹 ( ) = ∅2l ( ) S.33 𝑑𝑧 tp 𝑑𝑧 l 5.569 1 ∅2l = 1 + 1.496 + 2 S.34 𝑋𝑡𝑡 𝑋𝑡𝑡 𝑑𝑝𝐹 2𝑓l 𝜌l 𝑈l2 ( ) = 𝑑𝑧 l di

Dc 𝑓l ( )0.5 di = 0.00725 −0.25 Dc + 0.076 [𝑅𝑒l ( )−2 ] di

S.35

S.36

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b) helical coil tube under flow condensation The empirical heat transfer and PD correlations for the helical coil tube used in the EG simulations are shown in Table 11. Also, flow conditions at which simulations have been conducted are listed in Table 12. Table 12. Flow conditions used for flow condensation simulations in the helical coil tube Symbols G q Tsat xin

Flow conditions Mass velocity Wall heat flux Saturation temperature Inlet vapor quality

Value 400 kgm−2 s −1 5 kWm−2 40 °C 0.8

Figure 11. Effect of tube diameter on total EG, and PD and heat transfer contributions to EG for the helical coil with Dc = 305 mm under flow condensation conditions, taken with permission from Ref. [13] (Copyright 2021 Elsevier).

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Figure 11 reveals the impact of tube diameter on EG for condensing flow in the helical coil tube. An increase in the tube diameter size (di) at constant flow conditions (Table 12) results in a gradual rise in the mass flow rate (ṁ). As mentioned before, the heat transfer and mass flow rate are proportionate to di and d2i , respectively. Consequently, the two-phase mixture density drops, and steady rises are observed in the two-phase mixture velocity and the PD when tube diameter increases. Therefore, the augmentation in hydraulic loss dp

share is observable as vtp, ṁ, and (− dz ) increase (Figure11). The growth in mass flow rate and vapor quality results in a reduction in HTC. Hence, the increase in the thermal loss share becomes inevitable (Figure11).

Figure 12. Effect of coil diameter ratio on total EG, and PD and heat transfer contributions to EG for the helical coil with Do = 9.52 mm under flow condensation conditions, taken with permission from Ref. [13]. (Copyright 2021 Elsevier).

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The impact of coil diameter ratio on the entropy generated within the helical coil during R134a flow condensation is exhibited in Figure 12. As the helical coil diameter (Dc ) becomes larger, a decrease in PD is expected due to the growing weakness in the radial pressure gradient and the resultant secondary flow [17]. Therefore, the PD contribution to EG falls slowly [12, 25]. Moreover, transferring heat to the two-phase flow decreases due to the decline in flow turbulence; consequently, the HTC decreases, leading to the rise in heat transfer contribution to the EG. The local minimum at Dr = 30 is propotional to Dc = 285.6 mm in coil diameter. Gradually, with increasing the thermal loss, the total EG rises as shown in Figure 12.

Figure 13. EG in the helical coil tube (Do = 9.52 mm, Dc = 305 mm) and smooth straight one (Do = 9.52 mm) under condensation, taken with permission from Ref. [12]. (Copyright 2021 Elsevier).

The variation in mass velocity from 200 kg/m2s1 to 500 kg/m2s1 leads to the rise in the value of the EG for both the helical coil and the smooth straight

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tube as shown in Figure 13. At 340 kg/m2s1, two EG lines intersect each other. At mass velocities lower than this value, the helical coil tube generates less entropy compared to the smooth straight tube. In contrast, at greater mass velocities, the helical coil generates more entropy because of higher values in hydraulic loss. Therefore, similar to boiling process, helical coils are recommended to be used at low mass velocities. In Figure14, at the inlet vapor quality and mass velocity equal to 0.8 and 340 kg/m2s1, respectively, the EG approaches unit value. Therefore, the application of helical coil tube is recommended for these ranges of mass velocity and vapor quality. As the inlet vapor quality reduces to 0.6, this favorable region in terms of mass velocity (G) becomes wider up to the value of G = 410 kg/m2s1.

Figure 14. Thermal performance comparison between helical coil (Do = 9.52 mm, Dc = 305 mm) and the smooth straight one (Do = 9.52 mm) using 𝑁𝑠 at different vapor qualities under flow condensation conditions (𝑇sat = 40 °C, 𝑞 = 5 kWm−2 ), taken with permission from Ref. [12]. (Copyright 2021 Elsevier).

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Conclusion In this chapter, a mathematical model was explained to calculate entropy generation caused by heat transfer and pressure drop during flow boiling and condensation; the model was then applied to simulate thermos-hydraulic losses taking place in smooth straight tubes as well as helical coils and microfin tubes when operating under flow boiling and condensation conditions. Moreover, the effects of crucial parameters like tube diameter and mass velocity on entropy generation were discussed. Entropy generation number was used to identify the conditions under which the mentioned heat transfer enhancement techniques give higher thermos-hydraulic performance from entropy generation perspective.

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R. B. C., K. P., S. Roy, R. Ganesan, A comprehensive review on compound heat transfer enhancement using passive techniques in a heat exchanger, Mater. Today Proc. 54 (2022) 428–436. https://doi.org/10.1016/J.MATPR.2021.09.541. Mousa M. H., C. M. Yang, K. Nawaz, N. Miljkovic, Review of heat transfer enhancement techniques in two-phase flows for highly efficient and sustainable cooling, Renew. Sustain. Energy Rev. 155 (2022) 111896. https://doi.org/10.1016/ J.RSER.2021.111896. Deylami H. M., Effects of EHD on the flow and heat transfer characteristics in a rectangular corrugated channel, Heat Mass Transf. 55 (2019) 3711–3720. https:// doi.org/10.1007/s00231-019-02693-z. Zhou J., X. Luo, C. Li, L. Liang, G. Wang, B. He, Z. Q. Tian, Flow boiling heat transfer enhancement under ultrasound field in minichannel heat sinks, Ultrason. Sonochem. 78 (2021) 105737. https://doi.org/10.1016/J.ULTSONCH.2021.105737. Lin Y., Y. Luo, E. N. Wang, W. Li, W. J. Minkowycz, Enhancement of flow boiling heat transfer in microchannel using micro-fin and micro-cavity surfaces, Int. J. Heat Mass Transf. 179 (2021) 121739. https://doi.org/10.1016/J.IJHEATMASS TRANS FER.2021.121739. Onal B. S., S. M. Kirkar, D. Akgul, A. Celen, O. Acikgoz, A.S. Dalkilic, S. N. Kazi, S. Wongwises, Heat transfer and pressure drop characteristics of two phase flow in helical coils, Therm. Sci. Eng. Prog. 27 (2022) 101143. https://doi.org/10.1016/ J.TSEP.2021.101143. Li W., Z. Yu, Y. Wang, Y. Li, Heat transfer enhancement of twisted tape inserts in supercritical carbon dioxide flow conditions based on CFD and vortex kinematics, Therm. Sci. Eng. Prog. 31 (2022) 101285. https://doi.org/10.1016/J.TSEP. 2022. 101285.

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Shelare S. D., K. R. Aglawe, P.N. Belkhode, A review on twisted tape inserts for enhancing the heat transfer, Mater. Today Proc. 54 (2022) 560–565. https://doi.org/ 10.1016/J.MATPR.2021.09.012. Mousa M. H., N. Miljkovic, K. Nawaz, Review of heat transfer enhancement techniques for single phase flows, Renew. Sustain. Energy Rev. 137 (2021) 110566. https://doi.org/10.1016/J.RSER.2020.110566. Revellin R., M. Padilla, A. Bensafi, P. Haberschill, J. Bonjour, Thermodynamic analysis of a diabatic two-phase flow for a pure refrigerant and a refrigerant/oil mixture under equilibrium conditions, Int. J. Refrig. 32 (2009) 1784–1790. https://doi.org/10.1016/j.ijrefrig.2009.07.004. Abdous M. A., H. Saffari, H. B. Avval, M. Khoshzat, Investigation of entropy generation in a helically coiled tube in flow boiling condition under a constant heat flux, Int. J. Refrig. 60 (2015) 217–233. https://doi.org/10.1016/J.IJREFRIG. 2015.07.026. Holagh S. G., M. A. Abdous, M. Shafiee, M. A. Rosen, Performance evaluation of helical coils as a passive heat transfer enhancement technique under flow condensation by use of entropy generation analysis, Therm. Sci. Eng. Prog. 23 (2021) 100914. https://doi.org/10.1016/J.TSEP.2021.100914. Cao Y., M. A. Abdous, S. Ghazanfari Holagh, M. Shafiee, M. Hashemian, Entropy generation and sensitivity analysis of R134a flow condensation inside a helically coiled tube-in-tube heat exchanger, Int. J. Refrig. 130 (2021) 104–116. https://doi.org/10.1016/J.IJREFRIG.2021.06.007. Abdous M. A., H. Saffari, H. Barzegar Avval, M. Khoshzat, The study of entropy generation during flow boiling in a micro-fin tube, Int. J. Refrig. 68 (2016). https://doi.org/10.1016/j.ijrefrig.2016.04.008. Holagh S. G., M. A. Abdous, H. Rastan, M. Shafiee, M. Hashemian, Performance analysis of micro-fin tubes compared to smooth tubes as a heat transfer enhancement technique for flow condensation, Energy Nexus. 8 (2022) 100154. https://doi.org/ 10.1016/j.nexus.2022.100154. Holagh S. G., M. A. Abdous, M. Shamsaiee, H. Saffari, Assessment of heat transfer enhancement technique in flow boiling conditions based on entropy generation analysis: twisted-tape tube, Heat Mass Transf. Und Stoffuebertragung. 56 (2020). https://doi.org/10.1007/s00231-019-02705-y. Abdous M. A., S. G. Holagh, H. Saffari, Numerical investigation of flow boiling heat transfer in helically coiled tube under constant heat flux, Therm. Sci. Eng. 1 (2018). https://doi.org/10.24294/tse.v1i2.375. Holagh S. G., M. A. Abdous, M. Shamsaiee, H. Saffari, An experimental study on the influence of radial pressure gradient on bubbles dynamic behavior in subcooled flow boiling, Therm. Sci. Eng. Prog. 16 (2020). https://doi.org/10.1016/j.tsep. 2019.100468. Revellin R., J. Bonjour, Entropy generation during flow boiling of pure refrigerant and refrigerant-oil mixture, Int. J. Refrig. 34 (2011) 1040–1047. https://doi.org/ 10.1016/j.ijrefrig.2011.01.010.

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Chapter 7

An Energy Model of Heat Pump Systems for Hot Water Assisted by PV/T Solar Energy in Climates above 15°C Juan Garcia Pabon1 Ali Khosravi2,* and Mamdouh El Haj Assad3 1Institute

of Mechanical Engineering, Federal University of Itajubá (UNIFEI), Itajubá, Brazil 2SDU Mechatronics (CIM), Department of Mechanical and Electrical Engineering, University of Southern Denmark, Sønderborg, Denmark 3Department of Sustainable and Renewable Energy Engineering, University of Sharjah, Sharjah, UAE

Abstract In this work, a mathematical model is used to calculate the energy efficiency of a heat pump that uses solar thermal energy from a aphotovoltaic panel. The city of Itajubá in the Brazilian state of Minas Gerais is the target of the case study. When compared to the performance of the equipment individually, the advantages of producing hot water and electricity simultaneously include maximizing the use of physical space and obtaining superior energy efficiency (photovoltaic panel and solar thermal collector). The system will be simulated using MATLAB software. The mathematical model of the photovoltaic-thermal system (PV/T) includes a set of 4 unknown variables that must be solved simultaneously: temperature of the PV panel, evaporator, condenser, and water in the tank. The compressor has a displacement volume of 1.2 m3/h *

Corresponding Author’s Email: [email protected].

In: The Fundamentals of Thermal Analysis Editors: Mamdouh El Haj Assad, Ali Khosravi and Mehran Hashemian ISBN: 979-8-88697-759-2 © 2023 Nova Science Publishers, Inc.

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Juan Garcia Pabon, Ali Khosravi and Mamdouh El Haj Assad and a volumetric and isentropic efficiency of 0.6 and 0.5, respectively. The condenser is a copper tube with a 10m length and 10mm diameter that is submerged in a water tank. The findings show that on a winter day, 300L of water could be heated from 16°C to 45°C using a 2.4m 2 PV panel while simultaneously producing 1.3 kWh of power. For comparison terms, a conventional solar collector would need more than twice the area to achieve the same level of water production.

Keywords: heat pump, PV/T system, solar energy, water heating

1. Introduction The usage of conventional fuels is beginning to decline, and their damaging effects on the environment are driving research into renewable energy sources [1, 2]. The utilization of solar energy resources for power generating and heating purposes is one of the available possibilities [3]. There are three things that need to be considered: (1) The photovoltaic panels directly transform solar energy into electrical power; however they have inefficient conversion rates that are between 10 and 15%, and the remaining 85 to 90% of the energy is wasted as heat to the environment [4]. The greatest detrimental factor affecting PV performance is the operation temperature. (2) Solar thermal collector has been widely used to produce domestic hot water owing to their simple structure, low cost, and stable operation. However, the daily and seasonal imbalance between energy supply and demand may make their use more constrained [5]. (3) However, by utilizing grid energy, a heat pump may deliver a consistent and reliable heat source to buildings and infrastructure [6]. Combining solar photovoltaic/thermal (PV/T) panels with heat pumps can help to overcome the drawbacks of the three concepts when used separately, allowing for the creation of heating systems for buildings and infrastructure that are energy-efficient, reliable, and affordable. In the next paragraphs, let us just go into more depth on this. One of the most popular solar energy technologies, photovoltaic cells (PV), transform a portion of solar radiation into electricity while a major portion is turned into thermal energy that may be used to heat water, lowering the amount of power needed for home water heating. The ideal operating temperature for the PV cells was identified to be 25 °C. However, in subtropical regions, during peak sunshine hours, the operating temperature of the PV panel varies between 60 and 80 °C [7]. For the above reason, over the

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past few decades, researchers have developed several passive and active thermal management techniques. Some examples of passive cooling techniques are fins, heat pipe, phase change material (PCM), etc. Regarding active cooling techniques it is possible to mention the use of air, water, or refrigerant fluid over the PV module for its thermal management [8]. Comparatively speaking, passive cooling offers less of an improvement in electrical efficiency than active cooling. An active cooling system is a smart choice when the heat collected from the PV panels is utilised for other practical uses. This concept led to the creation of the photovoltaic/thermal (PV/T) system. PV/T systems can be classed as air-, water-, or refrigerant-based systems based on the working fluid used. Due to its ability to concurrently produce heat and electricity, the PV/T system enables improved space usage. Additionally, a PV system may be used to attain a better conversion efficiency than individual solar thermal systems. Refrigerant-based PV/T system involves the integration of evaporator coils of the heat pump and PV module to form a cogeneration type system known as photovoltaic/thermal–solar assisted heat pump (PV/T-SAHP). The conversion efficiency of a PV cell reduces with an increase in operating temperature, and the high evaporator temperature is advantageous for heat pump operation. For this reason, a heat pump evaporator and a PV module can be favorably integrated as a single module to form a hybrid system. Numerous investigations and studies of refrigerant-based PV/T systems have been conducted. One of them that can be mentioned had an average electrical efficiency of 13.4% and COP of 5.4 [9, 10]. The refrigerant-based PV/T system described in Refs. [11, 12] used a glass vacuum tube PV/T collector, and the system’s COP ranged from 2.9 to 4.6, with a 1.9% improvement in electrical efficiency. Based on the PV/T-SAHP system’s overall performance, [13, 14] reported a COP of 7.09 and an overall efficiency of 86%. According to the Ref. [15], a heat pump assisted by a PV/T collector had a COP in the range of 2.80-4.10 under the climatic conditions of Coimbatore, India. It was also determined that the triangular tube PV/T collector had improved energy performance parameters when compared to the circular tube PV/T collector. In more recent work [16], a refrigeration system that may be utilized to satisfy the cooling needs of buildings was proposed. It is based on the conventional PVT solar heat pump. The system condenser uses PVT modules. The PVT modules primarily dissipate heat in two ways: convection with the surrounding air and radiation into the night sky (hybrid heat dissipation).

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In some cases, utilizing water to cool a PV/T collector and transfer heat to the evaporation of fluid might be an alternative; these systems are known as indirect expansion systems, and in recent years, research has become more and more interested in them. One such device with a composite collector that can absorb heat from both water and air was created by the Ref. [17]. Results showed that the average COP and COPsys for dual-heat-source operating mode were 2.49 and 2.24, respectively, and for single-heat-source operating mode were 1.40 and 1.31, respectively, which indicate that the system dual-heatsource had better system performance. Then, the actual PV/T collector was used in the system, the average COP and COPsys of the heat pump were 4.08 and 3.07, respectively. More recently, an optimization study was implemented for a water-based PV/T collector integrated with the heat pump system. From the study, R32 turned out to be the optimum working fluid, followed by R1234yf was reported by [18]. The system with 10m² of PV/T collector produced 4.33 kW of heat output and 0.53 kW of electricity output. The daily heat and electricity outputs were reported as 34.9 kWh and 5.13 kWh, respectively. The last option is a heat pump with “air-source” and “watersource” evaporators that are connected in series and are run alternately depending on the surrounding environment, system parameters, and operating modes. Additionally, the PVT panels are used to generate domestic hot water and act as a heat source for the “water-source” evaporator by using two storage tanks [19]. The above-mentioned research studies make it easy to see the enormous potential of this technology. Systems with PV/T assistance perform better than traditional systems. These systems are also more efficient, and the payback period is only 10 years [20]. In this chapter, a mathematical model of the PV/T-SAHP with direct expansion in steady state condition for electricity and hot water is described. The performance of the system is examined in relation to the impacts of compressor, water tank, and condenser size. The model is simulated for two refrigerant R134a and R1234yf. Brazil’s southeast, which is the country’s most populous area, is the focus of the case study. Residential water heating’s share of total power use decreased from 42% in 2005 to 35% in 2019 [21]. Despite the country’s growing usage of conventional solar collectors over the last year, a significant portion of customers still heat their houses’ water with electrical resistance. Investigating the performance under various climatic conditions is vital since PV/T performance is greatly influenced by climate factors. Therefore, it is assumed that the work suggested in this chapter will help with the comprehension of this technology in some manner.

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2. Methodology The schematic of the PV/T aided by heat pump that was selected for analysis and simulation using a mathematical model is shown in Figure 1. Following is how the schematic model operates: The solar panel’s extra heat is removed via an evaporator. The compressor then increases the pressure of the refrigerant fluid, which then passes through the condenser, which is a coil of copper tube submerged in the tank. The refrigerant exchange heat with water, and the fluid leaves at a lower temperature, but still at a high pressure. Then the refrigerant fluid passes through the expansion valve where its pressure is reduced and returns to the photovoltaic panel, evaporator and insulation set, closing the examined model’s cycle in the process. The mathematical model has the following considerations: − − − − − −

The pressure drop by refrigerant flow is neglected The isentropic efficiency of compressor is constant The heat transfer by conduction of copper or aluminum is negligible The thermostatic expansion valve guarantees a constant superheated degree in the evaporator The water in tank is unstratified effect of temperature The steady state is achieved in the first minutes of each hour.

Figure 1. Diagram of PV/T-SAHP system.

Figure 2 shows a refrigeration system works through a P-h diagram for the vapor compression cycle. The thermodynamic equations help in the

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analysis of the mass and energy balance from the internal point of view refrigerant fluid. 𝑄̇𝑒𝑣𝑎𝑝 = 𝑚̇𝑟𝑒𝑓 (ℎ𝑠𝑢𝑐 − ℎ𝑣𝑎𝑙𝑣 ) (𝑊)

(1)

in which 𝑄̇𝑒𝑣𝑎𝑝 is evaporator heat, 𝑚̇𝑟𝑒𝑓 is refrigerant mass, ℎ𝑠𝑢𝑐 is suction enthalpy in the compressor and ℎ𝑣𝑎𝑙𝑣 is inlet valve enthalpy. 𝑄̇𝑐𝑜𝑛𝑑 = 𝑚𝑟𝑒𝑓 (ℎ𝑑𝑒𝑠 − ℎ𝑣𝑎𝑙𝑣 ) (𝑊)

(2)

where 𝑄̇𝑐𝑜𝑛𝑑 , ℎ𝑑𝑒𝑠 are condenser heat transfer rate and compressor discharge enthalpy, respectively. 𝑊̇𝑐𝑜𝑚𝑝 = 𝑚𝑟𝑒𝑓 (ℎ𝑑𝑒𝑠 − ℎ𝑠𝑢𝑐 ) (𝑊)

(3)

where 𝑊̇𝑐𝑜𝑚𝑝 is compressor work. ℎ𝑑𝑒𝑠 =

(ℎ𝑖𝑠𝑒𝑛− ℎ𝑠𝑢𝑐 ) η𝑖𝑠𝑒𝑛

+ ℎ𝑠𝑢𝑐 (𝑘𝐽/𝑘𝑔)

(4)

in which ℎ𝑖𝑠𝑒𝑛 is isentropic enthalpy at the outlet of the compressor. 𝜂𝑖𝑠𝑒𝑛 is isentropic efficiency of compressor, which is constant.

Figure 2. Vapor compressor cycle model.

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2.1. Compressor Model The mass flow of compressor (𝑚̇𝑟𝑒𝑓 ) depends on evaporation and condensation pressures (𝑝𝑒𝑣𝑎𝑝 , 𝑝𝑐𝑜𝑛𝑑 ): 𝑚̇𝑟𝑒𝑓 = 𝜂𝑣𝑑 . 𝜌𝑠𝑢𝑐 . 𝑉𝑑 (𝑘𝑔/𝑠)

𝜂𝑣𝑑 = 1 − 𝑟𝑚,𝑒𝑓 ((

𝑝𝑐𝑜𝑛𝑑 𝑝𝑒𝑣𝑎𝑝

1 𝑘

) − 1) (-)

(5)

(6)

in which 𝑉𝑑 , and k are displacement volume of compressor, and isentropic coefficient of fluid, respectively. Especially attention to 𝑟𝑚,𝑒𝑓 , is an effective clearance ratio of compressor. Although Equation (6) is intended to take into account an isentropic compression process, this is not true in practice. A compressor’s effective clearance ratio is determined using the cooling capacity information provided by the compressor’s manufacturer in order to convert the theoretical volumetric efficiency (𝜂𝑣𝑑 ) into an actual number.

Figure 3. Evaporator model.

2.2. Evaporator Model Figure 3 shows the internal configuration inside the evaporator. A policrystalline silicon PV panel of 2 meters in length and 1.2 meters in width is installed on top of the evaporator. The exchanger is a multiport made for square mini-parallel channels of aluminum. Other configurations can be found in Refs. [22, 23]. The panel photovoltaic heat (𝑄̇𝑃𝑉 ) is the solar energy that cannot be converted into electricity. The PV panel can transfer heat with air

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and evaporator. Additionally, the evaporator can transfer heat with the bottom that we have isolation layer. The energy balance in the evaporator is: 𝑄̇𝑒𝑣𝑎𝑝 = 𝑄̇𝑝𝑣 − 𝑄̇𝑖𝑠𝑜𝑙 − 𝑄̇𝑝𝑣−𝑎𝑖𝑟 (𝑊)

(7)

𝑃̇𝑒𝑙𝑒 = 𝐼𝑇 . 𝜂𝑃𝑉 . 𝐴𝑃𝑉 (𝑊)

(8)

𝑄̇𝑝𝑣 = 𝐼𝑇 . (1 − 𝜂𝑃𝑉 ). 𝐴𝑝𝑣 (𝑊)

(9)

in which 𝐼𝑇 , 𝜂𝑃𝑉 , 𝐴𝑃𝑉 are irradiation, efficiency, and area of PV panel, respectively. 𝑄̇𝑖𝑠𝑜𝑙 = 𝑈𝑖𝑠𝑜𝑙 . 𝐴𝑒𝑣𝑎𝑝 (𝑇𝑎𝑖𝑟 − 𝑇𝑒𝑣𝑎𝑝 ) (𝑊)

(10)

where 𝑄̇𝑖𝑠𝑜𝑙 , 𝑈𝑖𝑠𝑜𝑙 , 𝐴𝑒𝑣𝑎𝑝 , 𝑇𝑎𝑖𝑟 , 𝑇𝑒𝑣𝑎𝑝 are isolation heat loss, heat transfer coefficient of isolation, evaporator area, air temperature and evaporation refrigerant temperature. ̅𝑒𝑣𝑎𝑝 . 𝐴𝑒𝑣𝑎𝑝 . (𝑇𝑝𝑣 − 𝑇𝑒𝑣𝑎𝑝 ) (𝑊) 𝑄̇𝑒𝑣𝑎𝑝 = 𝑈

(11)

̅𝑒𝑣𝑎𝑝 is the overall heat transfer in which 𝑇𝑝𝑣 is PV panel temperature. 𝑈 coefficient of refrigerant fluid inside the evaporator. For vapor flow, the Gnielinski [24] correlation is used, which is valid for flow with 2300 < 𝑅𝑒 < 10000. While for the two-phase flow, it is calculated using Shah [25] correlation which is valid for micro, mini and macro-channels. 𝑄̇𝑝𝑣−𝑎𝑖𝑟 = 𝑈𝑎𝑖𝑟 . 𝐴𝑝𝑣 . (𝑇𝑝𝑣 − 𝑇𝑎𝑖𝑟 ) (𝑊)

(12)

where 𝑄̇𝑝𝑣−𝑎𝑖𝑟 , is heat transfer rate between photovoltaic panel and the air, and 𝑈𝑎𝑖𝑟 is heat transfer coefficient of air. Finally, the efficiency of PV panel depends on the reference conditions given by manufacturer is: 𝜂𝑣𝑝 = 0.2(1 − 0.0035(𝑇𝑝𝑣 − 45)) (-)

(13)

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In the evaporator model, the input is the air temperature, solar radiation, and the refrigerant mass flow of compressor, Eqs. 1 and 7 should be solved simultaneously to find 𝑇𝑝𝑣 and 𝑇𝑒𝑣𝑎𝑝 .

2.3. Condenser Model The condenser is a round helical coiled tube submerged in the water tank, where the fluid refrigerant flows inside of it. The tank has heat losses 𝑄̇𝑖𝑠𝑜𝑙,𝑡𝑎𝑛𝑘 to the environment. The energy balance in the tank is: 𝑄̇𝑤𝑎𝑡𝑒𝑟 = 𝑄̇𝑐𝑜𝑛𝑑 − 𝑄𝑖𝑠𝑜𝑙,𝑡𝑎𝑛𝑘 (𝑊)

(14)

𝑄̇𝑖𝑠𝑜𝑙 = 𝑈𝑖𝑠𝑜,𝑡𝑎𝑛𝑘 . 𝐴𝑠,𝑡𝑎𝑛𝑘 . (𝑇𝑤 − 𝑇𝑎𝑖𝑟 ) (𝑊)

(15)

in which 𝑈𝑖𝑠𝑜,𝑡𝑎𝑛𝑘 , 𝐴𝑠,𝑡𝑎𝑛𝑘 are heat loss of the tank walls by conduction and superficial area of tank, respectively. (𝑇 −𝑇 ) 𝑄̇𝑤𝑎𝑡𝑒𝑟 = 𝑚𝑤 𝑐𝑝𝑤 . 𝑊 𝑤,𝑖 (𝑊)

(16)

∆𝑡

where 𝑄̇𝑤𝑎𝑡𝑒𝑟 , 𝑚𝑤 , 𝑐𝑝𝑤 , 𝑇𝑊 , 𝑇𝑤,𝑖 and ∆𝑡 are water heat, water mass in the tank, specific heat of water, water temperature, initial water temperature and time variation. ̅𝑐𝑜𝑛𝑑 . 𝐴𝑐𝑜𝑛𝑑 . (𝑇𝑐𝑜𝑛𝑑 − 𝑇𝑤 ) (𝑊) 𝑄̇𝑐𝑜𝑛𝑑 = 𝑈

(17)

̅𝑐𝑜𝑛𝑑 , 𝐴𝑐𝑜𝑛𝑑 , 𝑇𝑐𝑜𝑛𝑑 are condenser heat, overall heat transfer in which 𝑄̇𝑐𝑜𝑛𝑑 , 𝑈 coefficient of condenser, superficial area of coil, and condenser temperature, respectively. 𝐴𝑐𝑜𝑛𝑑 = 𝐿𝑠𝑒𝑝 . 𝐷𝑐𝑜𝑛𝑑 . 𝜋 (𝑚2)

(18)

where 𝐴𝑐𝑜𝑛𝑑 , 𝐿𝑠𝑒𝑝 , 𝐷𝑐𝑜𝑛𝑑 are condenser area, coil length, and diameter of coil tube, respectively. ̅𝑐𝑜𝑛𝑑 = ( 𝑈 𝐻𝑇𝐶

1

𝑐𝑜𝑛𝑑,𝑖𝑛𝑡

+ 𝐻𝑇𝐶

1

𝑐𝑜𝑛𝑑,𝑒𝑥𝑡

−1

)

(19)

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where ̅̅̅̅̅̅ 𝐻𝑇𝐶𝑐𝑜𝑛𝑑,𝑖𝑛𝑡 is the overall heat transfer coefficient of refrigerant. We used the Shah [26] correlation for two-phase flow and the Gnielinski [24] correlation for liquid and vapor phase. The ̅̅̅̅̅̅ 𝐻𝑇𝐶𝑐𝑜𝑛𝑑,𝑒𝑥𝑡 is the overall heat transfer coefficient of water side; Prabhanjan [27] correlation was chosen to calculate it, because it was developed for specific conditions like the tank in this model. In the condenser model, to compute the refrigerant mass flow of compressor and initial water temperature (respectively as 𝑇𝑐𝑜𝑛𝑑 and 𝑇𝑤 ), Eqs. 2 and 14 should be solved simultaneously.

Figure 4. Simulation procedure of the model.

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2.4. Simulation Procedure The procedure to solve the mathematical model is given in Figure 4. Initial values of 𝑇𝑐𝑜𝑛𝑑 , 𝑇𝑒𝑣𝑎𝑝 , 𝑇𝑃𝑉 and 𝑇𝑤 are used to calculate the evaporator heat in the refrigerant side and air side, and heat transfer rate of condenser of refrigerant and water side. If these heats are not equal in each side of exchanger device, the seeking algorithm should set new values for temperatures. The trust-region dogleg technique was the strategy used by MATLAB to solve the mathematical equations. The algorithm is a variant of the Powell dogleg method described in [28]. All this process is repeated for the next hour with different air temperature and solar radiation.

3. Results The mathematical model was applied for a case study, using the conditions of solar radiation and air temperature of Itajubá city, provided from the UNIFEI meteorological station. The day was selected in June 2022 during the winter season. The PV/T system was sized for a four-person family household in the study region. Thus, according to the NBR 15569 (ABNT, 2008) standard, a tank with a volume of 300L was selected. The initial temperature of water in the tank in the morning is 16°C. Other values adopted for the simulation are shown in table 1. The refrigerant used, R1234yf, is a fourth-generation fluid with a low global warming potential (GWP 1) that has just recently begun to be distributed in Brazil. Regarding water consumption, it was considered that the pick demand will be at night after 6:00 pm. Table 1. Design parameters of PV/T system Parameter 𝐿𝑃𝑉 = 2.0 𝑚 𝑤𝑃𝑉 = 1.2 𝑚 ℎ𝑐ℎ𝑎𝑛𝑛𝑒𝑙 = 0.015 𝑚 𝑤𝑐ℎ𝑎𝑛𝑛𝑒𝑙 = 0.015 𝑚 𝑉𝑡𝑎𝑛𝑘 = 0.3 𝑚³ 𝐷𝑡𝑎𝑛𝑘 = 0.55 𝑚 𝑈𝑖𝑠𝑜𝑙,𝑡𝑎𝑛𝑘 = 0.4 𝑊/𝑚²𝐾 𝑈𝑖𝑠𝑜 = 2.0 𝑊/𝑚²𝐾

Parameter ΔTsup = 5 𝐾 ΔTsub = 5 𝐾 𝑈𝑎𝑖𝑟 = 3.5 𝑊/𝑚²𝐾 𝑉𝑑 = 1.2 𝑚3 /ℎ 𝜂𝑖𝑠𝑒𝑛 = 0.52 𝑟𝑚,𝑒𝑓 = 0.29 𝐷𝑐𝑜𝑛𝑑 = 0.01 𝑚 𝐿𝑐𝑜𝑛𝑑 = 20 𝑚

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The simulation’s output for the equilibrium temperatures of the PV panel, evaporator, condenser, and tank’s water is shown in Figure 5. According to the manufacturer, the PV panel for an ambient temperature of 20°C and a solar radiation of 800W/m² has a panel operating temperature of 45°C, without any type of cooling system. Figure 5 shows that using the cooling system for simulated conditions (𝑇𝑎𝑖𝑟 = 26℃, 𝐼𝑇 = 707 𝑊/𝑚²) at 12:00h, the panel temperature is 25°C, a reduction of 20°C. This outcome improves the panel efficiency from 20% (@T_PV=45°C) to 35% (@T_PV=20°C). Nevertheless, the thermal energy absorbed from solar radiation and the surrounding environment allowed the water to reach a temperature of 44.5°C at the end of the day, which is very close to the Brazilian standard NBR 15569 recommendation of 50°C for the size of the tank and the selected number of people. The behavior of evaporation temperature, which is always lower than the ambient temperature and indicates that heat is transferred from air to a fluid refrigerant, is another factor that should be underlined. In the future, it may be required to investigate the possibility of removing the isolation layer from the evaporator’s bottom.

Figure 5. Temperatures and solar radiation profile for the day 06/22/2022 in Itajubá MG, Brazil.

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Figure 6 shows the results of electrical power produced by the PV panel, thermal energy stored in the water of tank and power consumed by the heat pump compressor. The PV panel reaches a peak power of 598 W at 12 pm. The compressor’s work varies between 83 and 164 W throughout the day. The heat stored in the tank varies between 366 and 1360W, including periods of very low solar radiation. According to Figure 6, the PV/T system converts solar energy from a surface area of 2.4 m2 into 3.5 kWh of electrical energy and 9,9 kWh of thermal energy, while the compressor uses 1.9 kWh of electrical energy. Thus, 1.7 kWh would be determined as the net electrical energy.

Figure 6. Electric Power produced by PV/T, work consumed by compressor, and heat stored in the tank.

3.1. Effect of Compressor Size One of the factors that has the most impact on system performance is compressor size. Larger compressors provide more heat for hot water and have better solar efficiency, but they also result in higher consumption. Table 2 presents the summary of results obtained when there was a variation in volumetric displacement of the compressor. The results of Table 2 show that net electricity generation (𝐸𝑒𝑙𝑒,𝑛𝑒𝑡,𝑑𝑎𝑦 ) declines as compressor size increases, however, transferred energy to heat

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water (𝐸𝑤𝑎𝑡𝑒𝑟,𝑑𝑎𝑦 ) increases. The work of the compressor was converted into heat for the condenser, and the amount of thermal energy received from the environment increased, resulting in a rise in the total energy generated (𝐸𝑇,𝑛𝑒𝑡,𝑑𝑎𝑦 ). From Figure 5, with solar radiation and PV area can be calculated that the available solar energy (𝐸𝑠𝑜𝑙𝑎𝑟,𝑑𝑎𝑦 ) is 9.35 kWh. Thus, with the values of Table 2, the global energy performance (𝐸𝑇,𝑛𝑒𝑡,𝑑𝑎𝑦 /𝐸𝑠𝑜𝑙𝑎𝑟,𝑑𝑎𝑦 ) of the system is increased from 120% to 127%, by increasing the size of compressor. This performance is >100% because the heat pump also extract energy from the environment. In the best cases, the heating efficiency of a conventional solar collector (𝐸𝑤𝑎𝑡𝑒𝑟,𝑑𝑎𝑦 /𝐸𝑠𝑜𝑙𝑎𝑟,𝑑𝑎𝑦 ) ranges from 60 to 80 percent. The PV/T-SAHP has a heating efficiency higher than 100%, also without electricity consumption. It is crucial to emphasize that when a compressor’s daily consumption (𝐸𝑐𝑜𝑚𝑝,𝑑𝑎𝑦 ) equals the energy generated by a PV panel (𝐸𝑒𝑙𝑒,𝑃𝑉,𝑑𝑎𝑦 ) and the net electricity (𝐸𝑒𝑙𝑒,𝑛𝑒𝑡,𝑑𝑎𝑦 ) falls to zero, the compressor’s displacement volume can no longer be increased. Table 2. Results for different sizes of the compressor

Final day 𝑇𝑤 (°C) Final day 𝑇𝑐𝑜𝑛𝑑 (°C) 𝑃𝑒𝑙𝑒,𝑚𝑎𝑥 (W) 𝐸𝑒𝑙𝑒,𝑃𝑉,𝑑𝑎𝑦 (kWh) 𝐸𝑐𝑜𝑚𝑝,𝑑𝑎𝑦 (kWh) 𝐸𝑒𝑙𝑒,𝑛𝑒𝑡,𝑑𝑎𝑦 (kWh) 𝐸𝑤𝑎𝑡𝑒𝑟,𝑑𝑎𝑦 (kWh) 𝐸𝑇,𝑛𝑒𝑡,𝑑𝑎𝑦 (kWh) 𝐶𝑂𝑃𝑚𝑎𝑥 (kWh) 𝐶𝑂𝑃𝑚𝑖𝑛 (kWh)

𝑉𝑑 = 1.0 𝑚3 /ℎ 42.8 47.9 580.0 3.5 1.5 1.9 9.3 11.2 8.4 3.7

𝑉𝑑 = 1.2 𝑚3 /ℎ 44.5 50.0 597.7 3.5 1.9 1.7 9.9 11.6 6.9 3.4

𝑉𝑑 = 1.4 𝑚3 /ℎ 46.0 51.8 611.6 3.6 2.2 1.4 10.4 11.9 6.0 3.2

Other information from the Table 2 is the coefficient of performance (𝐶𝑂𝑃 = 𝑄𝑐𝑜𝑛𝑑 /𝑊𝑐𝑜𝑚𝑝) of heat pump cycle. When the temperature differences between evaporation and condensation are less, the maximum COPmax occurs at the solar radiation maximum. Since the evaporation temperature falls and the condensation temperature rises as compressor size increases, the COP decreases. For the following simulations, we used the size of 𝑉𝑑 = 1.2 𝑚³/ℎ because it is advised not to reach condensation temperatures greater than 50°C.

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3.2. Effect of Refrigerant Fluid Table 3 shows a comparison between fluids R134a and R1234yf. The performance of both fluids is similar. When compared with R1234yf, the maximum electric power of R134a is somewhat greater. The fact that R1234yf, which has a lower GWP, may replace R134a in this application was thus proven. since the difference in energy performance is small, and with R1234yf we have the environmental benefits. Table 3. Comparative analysis for R134a and R1234yf refrigerants

𝑇𝑤 (°C) at end of day 𝑇𝑐𝑜𝑛𝑑 (°C) at end of day 𝑃𝑒𝑙𝑒,𝑚𝑎𝑥 (W) 𝐸𝑒𝑙𝑒,𝑃𝑉,𝑑𝑎𝑦 (kWh) 𝐸𝑐𝑜𝑚𝑝,𝑑𝑎𝑦 (kWh) 𝐸𝑒𝑙𝑒,𝑛𝑒𝑡,𝑑𝑎𝑦 (kWh) 𝐸𝑤𝑎𝑡𝑒𝑟,𝑑𝑎𝑦 (kWh) 𝐸𝑇,𝑛𝑒𝑡,𝑑𝑎𝑦 (kWh) 𝐶𝑂𝑃𝑚𝑎𝑥 (kWh) 𝐶𝑂𝑃𝑚𝑖𝑛 (kWh)

𝑅1234𝑦𝑓 44.5 50.0 597.7 3.5 1.9 1.7 9.9 11.6 6.9 3.4

𝑅134𝑎 45.1 50.5 604,3 3.6 1.9 1.8 9.9 11.7 6.9 3.4

Table 4. Results for different sizes of water tank

Final day 𝑇𝑤 (°C) Final day 𝑇𝑐𝑜𝑛𝑑 (°C) 𝑃𝑒𝑙𝑒,𝑚𝑎𝑥 (W) 𝐸𝑒𝑙𝑒,𝑃𝑉,𝑑𝑎𝑦 (kWh) 𝐸𝑐𝑜𝑚𝑝,𝑑𝑎𝑦 (kWh) 𝐸𝑒𝑙𝑒,𝑛𝑒𝑡,𝑑𝑎𝑦 (kWh) 𝐸𝑤𝑎𝑡𝑒𝑟,𝑑𝑎𝑦 (kWh) 𝐸𝑇,𝑛𝑒𝑡,𝑑𝑎𝑦 (kWh) 𝐶𝑂𝑃𝑚𝑎𝑥 (kWh) 𝐶𝑂𝑃𝑚𝑖𝑛 (kWh)

𝑉𝑡𝑎𝑛𝑘 = 300𝐿 44.5 50.0 597.7 3.5 1.9 1.7 9.9 11.6 6.9 3.4

𝑉𝑡𝑎𝑛𝑘 = 400𝐿 37.4 42.7 605.4 3.6 1.7 1.8 9.9 11.7 7.5 3.8

3.3. Effect of Volume of Water Tank The findings for two distinct tanks to storage water volume comparisons are shown in Table 4. It is expected that increase in water volume result in a slight

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temperature drop of water by day’s end because the same among of energy Is absorbed. The energy analysis shows similar performance for both cases, despite the condensation temperature is lower in the case of a 400L tank than it is in the case of a 300L tank, and the heat pump’s coefficient of performance (COP) is high. For residential application of hot water, the best temperature is more than 40°C, for this reason the tank of 300L is chosen.

3.4. Effect of Length of Condenser Table 5 present the simulations for PV/T-SHAP using R1234yf and compressor with 𝑉𝑑 = 1.2𝑚3 /ℎ with several length of condenser. Reduced condenser exchange area raises the condensation temperature required to reject the same amount of heat to water. Energy-wise, the effect is minimal, but a performance decline in the heat pump’s COP is well-known. Despite this, a short condenser might lower the heat pump’s initial cost. Table 5. Results for different sizes of the condenser length

Final day 𝑇𝑤 (°C) Final day 𝑇𝑐𝑜𝑛𝑑 (°C) 𝑃𝑒𝑙𝑒,𝑚𝑎𝑥 (W) 𝐸𝑒𝑙𝑒,𝑃𝑉,𝑑𝑎𝑦 (kWh) 𝐸𝑐𝑜𝑚𝑝,𝑑𝑎𝑦 (kWh) 𝐸𝑒𝑙𝑒,𝑛𝑒𝑡,𝑑𝑎𝑦 (kWh) 𝐸𝑤𝑎𝑡𝑒𝑟,𝑑𝑎𝑦 (kWh) 𝐸𝑇,𝑛𝑒𝑡,𝑑𝑎𝑦 (kWh) 𝐶𝑂𝑃𝑚𝑎𝑥 (kWh) 𝐶𝑂𝑃𝑚𝑖𝑛 (kWh)

𝐿𝑐𝑜𝑛𝑑 = 20𝑚 44.5 50.0 597.7 3.5 1.9 1.7 9.9 11.6 6.9 3.4

𝐿𝑐𝑜𝑛𝑑 = 15𝑚 44.5 51,5 591.1 3.5 2.0 1.5 9.9 11.5 6.4 3.3

𝐿𝑐𝑜𝑛𝑑 = 10𝑚 44.7 54.5 577.7 3.4 2.2 1.3 10.0 11.3 5.6 3.0

Conclusion Mathematical modeling was used to create a hybrid solar energy system that stores heat in a water tank utilizing a heat pump and solar panels as thermal energy collectors and electrical energy generators. Despite several simplification in the model, it remains with many nonlinearities and to solve it, we need a good computational method. For the case analyzed, the system showed several advantages such as: (1) cooling of the photovoltaic panel

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leading to an improvement in the efficiency of electrical energy conversion. (2) The net electrical energy is positive despite the consumption of the compressor. (3) The consumption of the compressor is justified by the increase in the capture of thermal energy. (4) When comparing the PV panel’s basic usage to the PV/T panel’s use of electrical and thermal energy, it is feasible to see that the area utilized has increased. (5) The system allows water heating even with low/without solar radiation. A benefit of PV panels with heat pumps is their efficient use of space. For example, under comparable circumstances, a family of four needs around 6 m2 of traditional solar collector to store 300 L of water at 50°C. In order to accomplish the same result, a heat pump and a PV panel need 2.5–2.8 m2, as the heat pump also uses ambient energy when solar radiation is low. The examination of impacts on PV/T-SAHP came to the conclusion that a solar area of 2.5m2 would be ideal for heating 300L of water to 45°C in 12 hours. The 1.2m3/h volume displacement of compressor corresponds to a cylinder of 5.5cm3 of compressor at 3600RPM. Condenser tubes can have less than 15m. The system’s major projected drawbacks are expected to be profit oriented; the PV/T system’s initial investment has to be researched, and the usage of a separate PV panel and a water heating system (electric, gas burner, or solar collector) needs to be contrasted.

Acknowlegments This work was supported by Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG), National Council for Scientific and Technological Development (CNPq) and Coordination for the Improvement of Higher Education Personnel (CAPES). Ali Khosravi expresses gratitude to the SDU Mechatronics (CIM) at Department of Mechanical and Electrical Engineering.

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Lu S, Zhang J, Liang R, Zhou C. Refrigeration characteristics of a hybrid heat dissipation photovoltaic-thermal heat pump under various ambient conditions on summer night. Renewable Energy 2020;146:2524–34. https://doi.org/10.1016/ j.renene.2019.06.179. Wang G, Quan Z, Zhao Y, Sun C, Deng Y, Tong J. Experimental study on a novel PV/T air dual-heat-source composite heat pump hot water system. Energy and Buildings 2015;108:175–84. https://doi.org/10.1016/j.enbuild.2015.08.016. Bellos E, Tzivanidis C. Multi-objective optimization of a solar assisted heat pumpdriven by hybrid PV. Applied Thermal Engineering 2019;149:528–35. https://doi.org/10.1016/j.applthermaleng.2018.12.059. Besagni G, Croci L, Nesa R, Molinaroli L. Field study of a novel solar-assisted dualsource multifunctional heat pump. Renewable Energy 2019;132:1185–215. https://doi.org/10.1016/j.renene.2018.08.076. del Amo A, Martínez-Gracia A, Bayod-Rújula A A, Cañada M. Performance analysis and experimental validation of a solar-assisted heat pump fed by photovoltaic-thermal collectors. Energy 2019;169:1214–23. https://doi.org/10. 1016/j.energy.2018.12.117. Abrahão K C F J. Evaluation of the regional weights of the RTQ-R from the analysis of the structure of residential electricity consumption by geografic region. Federal University of Minas Gerais, 2015. Herez A, el Hage H, Lemenand T, Ramadan M, Khaled M. Review on photovoltaic/thermal hybrid solar collectors: Classifications, applications and new systems. Solar Energy 2020;207:1321–47. https://doi.org/10.1016/j.solener.2020. 07.062. Kazem H A, Chaichan M T, Al-Waeli A H A, Sopian K. Comparison and evaluation of solar photovoltaic thermal system with hybrid collector: An experimental study. Thermal Science and Engineering Progress 2021;22:100845. https://doi.org/10. 1016/j.tsep.2021.100845. Gnielinski. New equations for heat and mass transfer in turbulent pipe and channel flow. Int. Chem. Eng. 1976;16:359–68. Shah M M. Unified correlation for heat transfer during boiling in plain mini/micro and conventional channels. International Journal of Refrigeration 2017;74:606–26. https://doi.org/10.1016/j.ijrefrig.2016.11.023. Shah M M. A correlation for heat transfer during condensation in horizontal mini/micro channels. International Journal of Refrigeration 2016;64:187–202. https://doi.org/10.1016/j.ijrefrig.2015.12.008. Prabhanjan D G, Rennie T J, Vijaya Raghavan G S. Natural convection heat transfer from helical coiled tubes. International Journal of Thermal Sciences 2004;43:359– 65. https://doi.org/10.1016/j.ijthermalsci.2003.08.005. Powell M J D. A Fortran subroutine for solving systems of nonlinear algebraic equations. 1968.

Chapter 8

3D Numerical Modeling to Evaluate the Thermal Performance of Single and Double U-Tube Ground-Coupled Heat Pumps Ali H. Tarrad*, PhD Mechanical Engineering, Université de Lorraine, CNRS, LEMTA, Nancy, France

Abstract The ground thermal properties play a vital role in the thermal performance and economic assessments of the ground-coupled heat pump. The present steady-state numerical study represents the ground thermal conductivity and temperature distribution effects on the double U-tube heat exchanger heat duty for single and multi-layer soil domains. A parallel fluid flow circuit in a parallel U-tube (PFPD) configuration was examined for water flow velocity of (0.1-0.5) m/s in a (150) mm borehole diameter and (35.2) m depth. Fifteen models were examined as single-layer and multi-layer soil in a thermal conductivity range of (1.02.4) W/m.K. Two and three hypothetical homogeneous soil layers were suggested for the ground surrounding the U-tube borehole with a grout thermal conductivity of (0.78) W/m.K. The COMSOL Multiphysics 5.4 software was implemented to build a 3-dimensional model for heat transfer in the borehole under a steady-state condition. The results revealed that the soil’s far distance undisturbed temperature, the soil geological structure, and the soil thermal conductivity play a vital role in the thermal performance assessment of the ground heat exchanger. Increasing the soil thermal conductivity from (1.0) W/m.K to (2.4) W/m.K for a single layer model has enhanced the heat transfer rate by the range of (38-43)% for fluid flow velocity range of (0.1-0.5) m/s. The 

Corresponding Author’s Email: [email protected].

In: The Fundamentals of Thermal Analysis Editors: Mamdouh El Haj Assad, Ali Khosravi and Mehran Hashemian ISBN: 979-8-88697-759-2 © 2023 Nova Science Publishers, Inc.

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Ali H. Tarrad corresponding borehole thermal resistance for the single layer of (2.4) W/m.K soil thermal conductivity was about (62)% and (53)% of that at the (1.0) W/m.K predicted at (0.5) m/s and (0.1) m/s respectively. At the higher examined flow rate, the heat load was higher than that of the lower mass flow rate by (23)% and (29)% at (2.4) W/m.K and (1.0) W/m.K, respectively. The equivalent single-layer models exhibited higher heat transfer rates than their multi-layer ones by (1-4)% for the examined condition ranges.

Keywords: numerical analysis, multi-layer soil, modeling, thermal performance, ground heat exchanger

Abbreviations Abbreviation GSHE GSHP HDPE PFCD PFPD SFPD

Definition Ground Source Heat Exchanger Ground Source Heat Pump High-Density Polyethylene Pipe Parallel Flow Crossed U-Tube Configuration Parallel Flow Parallel U-Tube Configuration Series Flow Parallel U-Tube Configuration

Greek Letters Parameter 𝛼 𝛽 𝜀 𝜉 𝜂 𝜅 𝜇 ρ Φ 𝜙 𝜓

Definition Thermal diffusivity, (m2/s) Equivalency coefficient, eq. (1) Dissipation rate of turbulent kinetic energy, m2/s3 Thermal parameter deviation percentage, (%) Heat load enhancement, (%) Turbulent kinetic energy, m2/s2 Fluid dynamic viscosity, (Pa.s) Fluid density, (kg/m3) Viscous dissipation rate, N/(m2 s) Model designation Thermal performance variable, eq. (7)

3D Numerical Modeling to Evaluate the Thermal Performance …

Nomenclature Parameter cp d g H k L 𝑚̇ n p 𝑞́ 𝑞𝑙 𝑄̇ 𝑟, 𝜃, 𝑧 R Sp t tp T ΔT u 𝑢𝑟 , 𝑢𝜃 , 𝑢𝑧

Definition Heat capacity at constant pressure, kJ/kg K Diameter, mm Gravitational acceleration, m/s2 Depth, m Thermal conductivity, W/m.K U-tube length, m Mass flow rate, kg/s Number of layers Pressure, kpa, or bar Heat generation per unit volume, W/m3 Specific heat transfer rate, W/m Heat transfer rate, kW Cylindrical-coordinate variables Specific thermal resistance, m.K/W Tube or pipe spacing, mm Time, sec Pipe thickness, mm Temperature, K Temperature difference, K Water flow velocity, m/s Cylindrical velocity components, m/s

Subscripts Subscript b c e g h H.E i in l

Definition Borehole Cooling Equivalent Grout Heating Heat exchanger Inside Inlet Layer

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m o out p ref s t w

mean Outside Outlet Pipe Reference Arrangement Soil or ground Total Water

1. Introduction The underground temperature is relatively constant over the year for a depth of (5) m to (10) m, and it is generally close to the mean annual temperature. The ground heat exchangers (GSHE) are utilized to take advantage of this criterion of the earth to be a part of the heat pump technology. Heat is extracted from the ground and transferred to the indoor area via (GSHPs) during the heating season; this phenomenon is reversed in the cooling season. A tremendous experimental and theoretical work has been conducted to investigate the thermal performance and economic issues for implementing the (GSHE), for example [1-7]. Consequently, accurate modeling of the ground-coupled systems is an inevitable factor for design and performance analyses. Therefore, scientists focused on the analytical investigations of the borehole models as a line source and cylinder source theories. Analytical models such as the infinite line source method were accomplished by [8, 9]. The finite line source model was utilized by [10, 11]. The finite cylinder source method was also analyzed by several investigators as [12, 13]. Empirical and semi-empirical correlations were also developed by several investigators [4, 14-17]. These models were mainly based on replacing the U-tube legs with a single equivalent tube with the same pipe thermal resistance as the original one. In these correlations, the equivalent tube size was assigned as: 𝑑𝑒 = 𝛽 𝑑𝑜

(1)

The equivalency coefficient (𝛽) is greater than unity. It corresponds to (√2) and (√3) as stated in [14, 15, 17], respectively, whereas [4] represented (𝛽) as a function of U-tube leg spacing (Sp). Tarrad (2019) [16] built a correlation that incorporated the borehole diameter (Db), U-tube leg spacing

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(Sp), and the tube outside diameter (do) for the equivalent diameter (de) prediction. Quantitative and Qualitative numerical analyses focused on the vertical U-tube borehole heat exchanger’s steady-state and time-dependent thermal performance [18-22]. The effect of ground geological composition was investigated [23]. They numerically studied the effect of fluid temperature variation with depth on the thermal performance of a vertical ground heat exchanger with multiple soil layers. The authors numerically investigated the (GHE) configuration and carrier fluid flow rate effects on the system’s thermal performance under transient conditions in [24]. They concluded that the system’s thermal performance was enhanced with a fluid flow rate increase inside the pipes for a given (GHE) length. The thermal performance of single and double U-tube configurations was studied numerically in a 3-dimensional model by the COMSOL Multiphysics 5.4 software by [7]. He concluded that the heat transfer rate enhancement for the double U-tube was in the range of (10-14)% when operating at the same total fluid flow rate and inlet temperature for a given borehole design as that of the single U-tube one. Tarrad (2021a) [25] numerically studied the grout and soil thermal conductivity influence the thermal performance of a double U-tube ground heat exchanger with (PFPD) configuration. He found that the heat load of the U-tube was doubled when the thermal conductivity of the grout was increased from (0.73) W/m.K to (2.0) W/m.K at a fixed ground thermal conductivity of (2.42) W/m.K. Increasing the soil thermal conductivity from (1.24) W/m.K to (2.8) W/m.K has doubled the borehole heat transfer rate and almost halved the total borehole thermal resistance. It has also been verified that increasing the borehole size has a negligible effect on the ground heat exchanger thermal performance when a grout with high thermal conductivity is utilized. More recently, Tarrad (2021b) [26] examined the effect of fluid flow circuit type and the double U-tube configuration on the thermal performance of the borehole, as illustrated in Figure 1. He emphasized that the (PFPD) U-tube configuration has achieved a higher heat load than other examined U-tube arrangements. The (PFPD), (PFCD), and (SFPD) heat exchangers have achieved a higher heat load and water temperature drop than those of the single U-tube ones by (16-19)%, (13-16)%, and (15-18)% respectively. The present work studied the effect of the carrier fluid flow rate, the undisturbed soil temperature, and soil geological composition on thermal performance for a double U-tube configuration borehole. The double U-tube was circuited in a parallel flow arrangement with a parallel orientation inside

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the borehole (PFPD) as the work in [25, 26] recommended. A multi-layer soil region was investigated in a 3-dimensional model by COMSOL Multiphysics 5.4 software [27]. In the present investigation, fifteen case studies were formulated to examine the influence of the above operating characteristics on the heat transfer rate in the cooling and heating processes under steady-state conditions.

(a)

(b) Figure 1. (Continued).

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(c)

(d) Figure 1. The various combinations of fluid flow and U-tube configurations in the borehole, Tarrad (2021b). (a) The (PFCD) configuration. (b) The (PFPD) configuration. (c) The (SFCD) configuration. (d) The (SFPD) configuration.

2. Model Methodology 2.1. Case Study Figure 2 illustrates the double U-tube ground heat exchanger structure. It mainly consists of a double U-tube of a parallel flow circuiting installed deep

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in the borehole and a grout filling. The soil surrounds this structure and extends to a specified distance from the center. In this study, the ground is suggested to possess three layers of different materials, as depicted in Figure 3.

(a)

(b) Figure 2. Double U-tube in parallel orientation (PFPD) [7]. (a) A schematic diagram of the borehole. (b) Tube layout in the borehole.

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Figure 3. A typical ground geological structure of three layers.

Table 1 illustrates the design characteristics of the U-tube, grout, and soil materials. Table 1. Physical dimensions of different zones for COMSOL modeling Zone Material *

(HDPE) High density polyethylene pipe

Borehole (Grout)

Soil

*

Parameter

Value

(do), (mm)

33.4

(di), (mm)

29.5

(tp), (mm)

2.0

(WF), (---)

17.0

(Sp), (mm)

66.8

(LU-tube), (m)

35.1

(db), (mm)

150

(Hb), (m)

35.2

(ds), (m)

5.0

(Hs) (m)

37.7

Dimensional data for the tube size were taken from references [7, 28].

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The model’s thermal properties and operating conditions are depicted in Table 2. Table 2a. Properties and operating conditions of the geothermal system utilized for the present COMSOL modeling Zone material +

Water

(HDPE)* High polyethylene pipe

Grout*

Soil**

density

Physical Parameter

Value

(Tin), (°C) Cooling Mode

33.0

(Tin), (°C) Heating Mode

6.0

(Pin), (bar)

1.013

(uin), (m/s)

0.1-0.5

(𝑚𝑤 ̇ ), (kg/s)

0.14-0.68

(kHDPE), (W/m K)

0.4

(ρHDPE), (kg/m3)

940

(cp,HDPE), (J/kg K)

2300

(kg), (W/m K)

0.78

(ρg), (kg/m3)

1000

(cp,g), (J/kg K)

1600

Soil (Ts), (°C)

16 10/16† 12.5/16‡ + The water flow velocity for each U-tube was assigned in the range of (0.1-0.5) m/s * Data were taken from references [7, 28]. ** Soil properties are listed in Table 2.b † Model (M.M-3B-T) in Table 2.b. ‡ Models (M.M-3B-TC) and (M.M-3B-TH) for cooling and heating modes in Table 2.b.

The multi-layer models were examined with the following soil materials and depths: •

•

The depths of clay, sandstone, and Calcium Carbonate were assigned as (10) m, (10) m, and (17.7) m, respectively, defined as (M.M-3A) model. The depths of clay, Calcium Carbonate, and rock were assigned as (10) m, (10) m, and (17.7) m, respectively, referred to as (M.M-3B) model.

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•

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For the two soil layers model, the depths of sandstone and Calcium Carbonate were assigned as (17.5) m and (20.2) m, respectively, (M.M-2) model.

Table 2b. Thermal properties of ground layers and the undisturbed temperature of soil boundary ks (W/m K) 1.0 1.2 1.5

𝝆𝒔 (kg/m3) 1500 2700 2800

cp, s (kJ/kg K) 0.8 0.91 0.92

Ts,m (°C) 16 16 16

Clay/Sandstone/Calcium Carbonate [29, 30] Clay/Sandstone/Calcium Carbonate [29, 30] Clay/Calcium Carbonate/Rock [28-30] Clay/Calcium Carbonate/Rock [28-30] Clay/Calcium Carbonate/Rock [28-30]

1.72

2455

0.862

16

1.0/1.5/2.25

----

-----

16

1.0/2.25/2.42

----

-----

16

1.0/2.25/2.42

----

-----

14.4

1.0/2.25/2.42

----

-----

15.1

Sandstone/Calcium Carbonate [29, 30] Sandstone/Calcium Carbonate [29, 30] Calcium Carbonate [30] Rock ground [7, 28]

1.5/2.25

----

----

16

1.90

2800

0.891

16

M.S-6 2.25 2800 0.865 M.S-7C 2.42 2800 0.84 M.S-7H + Mean physical properties of the multi-layer stated in column no. 3. * A model has a variable far-field undisturbed temperature with borehole depth.

16 16

Model

Ground

M.S-1 M.S-2 M.S-3C M.S-3H M.S-4+

Clay [29] Limestone [29] Sandstone [29]

M.M-3A M.M-3B M.M-3B-T M.M-3BTC* M.M-3BTH* M.M-2 M.S-5+

The soil far distance undisturbed temperature for the (M.M-3B) multilayer models was assigned as follow: •

•

The (M.M-3B) model was examined with a soil temperature distribution as (10) °C for the first (10) m depth and (16) °C for the rest of the borehole depth and bottom side; this model was designated as (M.M-3B-T). The (M.M-3B) model was also examined with variable far-field boundary temperature, assigned as (12.5) °C and 16 °C for regions of

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•

the clay and (Calcium Carbonate/Rock), respectively. This ground geological structure was studied for the cooling and heating processes defined as (M.M-3B-TC) and (M.M-3B-TH) respectively, Table (2.b). The bottom side of the soil was kept at a constant temperature of (16) °C.

2.2. Governing Equations The mathematical equations which control the heat transfer and fluid flow processes are presented in Appendix A. These relations represent energy, continuity, Navier-Stokes expressions, and Fourier’s law. Steady-state conditions were considered for all of these equations, and the time-dependent variables were dropped out of them. In the flow dynamics domain, the low Reynolds (𝜅 − 𝜀) turbulence module was implemented as described in COMSOL Multiphysics 5.4 [27].

2.2.1. Assumptions •

•

•

The groundwater advection is absent, and only the conduction heat transfer mode has existed between the heat exchanger and the surrounding soil of the borehole. A perfect contact existed between the boundaries of all material regions of the U-tube wall, the grouting fill, and the soil. Hence there is no contact resistance between their surfaces. The far-field boundary condition for the undisturbed temperature of (16) °C is considered at the bottom of the soil domain for all examined models.

2.2.2. Boundary Conditions The temperature at the far distance boundary and the bottom part of the borehole soil were fixed at (16) °C. This boundary condition didn’t include the (M.M-3B-T), (M.M-3B-TC), and (M.M-3B-TH) models. The latter three models were bounded at different soil temperatures with depth for the far side boundary and fixed soil bottom side of (16) °C. The ground surface that faces the ambient was assigned as an adiabatic boundary. Water was chosen as a carrier fluid; it enters the U-tube at (33) °C and (6) °C for cooling and heating

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objectives. A total mass flow rate of (0.14-0.68) kg/s corresponds to a flow velocity of (0.1-0.5) m/s through the borehole heat exchanger. A no-slip boundary condition is applied to the pipe walls for the fluid flow simulation inside the pipes.

2.2.3. Mesh Generation The mesh generation of the considered model has been performed by COMSOL Multiphysics 5.4 [27] in a tetrahedral element type. For example, the fluid and tube domains were discretized in a finer size than those of the backfilling and soil domains, as illustrated in Figure 4.

(a)

(b) Figure 4. Mesh generation for the examined double U-tube borehole configuration. (a) Mesh size of different zones. (b) Model mesh size distribution.

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3. Data Reduction The water temperature monitoring with borehole depth was accomplished as the solution of the steady-state heat transfer model. The rejected or absorbed heat load by the water was estimated from: 𝑄̇𝐻.𝐸 = 𝑚𝑤̇ 𝑐𝑝,𝑤 ∆𝑇𝑤

(2)

The water temperature drop across the heat exchanger for the cooling and heating processes was represented as: ∆𝑇𝑤,𝑐 = 𝑇𝑤,𝑖𝑛 − 𝑇𝑤,𝑜𝑢𝑡

(3a)

∆𝑇𝑤,ℎ = 𝑇𝑤,𝑜𝑢𝑡 − 𝑇𝑤,𝑖𝑛

(3b)

The heat loading of the heat exchanger per unit depth of the borehole corresponds to: 𝑄̇𝐻.𝐸

𝑞𝑙,𝐻.𝐸 =

(4)

𝐿

The total borehole thermal resistance was obtained from the general form of Fourier’s law as: 𝑅𝑡,𝑚 =

𝑇𝑤,𝑚 − 𝑇𝑠

(5)

𝑞𝑙

The mean water temperature (Tw,m) was estimated from: 𝑇𝑤,𝑚 =

𝑇𝑤,𝑖𝑛 + 𝑇𝑤,𝑜𝑢𝑡

(6)

2

The mean temperature of the soil boundary was used in eq. (5) when a variable far-field undisturbed soil temperature was considered. Finally, the deviation percentage of any thermal performance parameter was estimated by: 𝜉𝜓,𝐻.𝐸 =

𝜓𝐻.𝐸 −𝜓𝑟𝑒𝑓 𝜓𝐻.𝐸

× 100

(7)

3D Numerical Modeling to Evaluate the Thermal Performance …

199

In this expression, the parameter (𝜓) represents any thermal performance variable as (𝑄̇𝐻.𝐸 ), (∆𝑇𝑤 ), (𝑞𝑙,𝐻.𝐸 ) and (𝑅𝑡,𝑚 ).

4. Results and Discussion 4.1. Soil Single-Layer Model The variation of the borehole heat load dissipation to the ground domain with the flow velocity and soil thermal conductivity for the examined operating condition range is shown in Figure 5.

Figure 5a. Heat load dissipation variation with flow velocity for the single-layer ground model at (Ts) of 16 °C.

In this figure, a representative value of the soil thermal conductivity was utilized as the depth mean value of different layers in the multi-layer model as follows: 𝑘𝑠,𝑚 =

∑𝑛 1 𝐻𝑙 𝑘𝑙 𝐻𝑠

(8)

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Ali H. Tarrad

Figure 5b. The cooling heat load dissipation variation with soil thermal conductivity for the single-layer ground model at (Ts) of 16 °C.

The heat load dissipation exhibited an increase with the soil thermal conductivity and flow mass flow rate of water in the heat exchanger. These criteria were also confirmed by [7, 24-26]. Increasing the soil thermal conductivity from (1.0) W/m.K to (2.4) W/m.K has enhanced the heat load by the range of (38-43)% as predicted by eq. (7) for fluid flow velocity range of (0.1-0.5) m/s. In addition, this finding was also approved by the results produced for the (PFPD) as achieved by [25, 26]. At the higher examined flow rate, the heat load was higher than that of the lower mass flow rate by (23)% and (29)% at (2.4) W/m.K and (1.0) W/m.K, respectively. The other examined operating condition occupied the zone bounded by these value ranges. The corresponding values of heat load at (0.3) m/s as compared to (0.1) m/s was in the range of (18 -22)% predicted at (2.4)W/m.K and (1.0) W/m.K respectively. This result is mainly due to improved fluid heat transfer coefficient and minimized thermal resistance of the heat exchanger, Figure 6. The results indicated that soil thermal conductivity is an important factor in the thermal assessment of the ground heat exchanger. The borehole thermal resistance showed a declination as the soil thermal conductivity increased. Increasing the thermal conductivity to (2.4) W/m.K produced a borehole thermal resistance of about (62)% and (53)% of that of the (1.0) W/m.K predicted at (0.5) m/s and (0.1) m/s respectively. As the flow velocity increases, the numerical values of the thermal resistance are getting closer with thermal conductivity increase.

3D Numerical Modeling to Evaluate the Thermal Performance …

201

Figure 6a. Borehole thermal resistance variation with soil thermal conductivity for the single-layer ground model at (Ts) of 16 °C.

Figure 6b. Borehole thermal resistance variation with water flow velocity for the single-layer ground model at (Ts) of 16 °C.

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Figure 7. The cooling heat load dissipation variation with water flow velocity for the multi-layer ground model at different soil boundary temperatures.

4.2. Soil Multi-Layer Model Figure 7 illustrates the heat load dissipation to the ground for the multi-layer ground models performed in the cooling mode. The data reduction for these curves was deduced from a constant soil far distance undisturbed temperature of (16) °C for the (M.M-2), (M.M-3A), and (M.M.-3B) models. The effective mean soil temperatures of the (M.M-3B-T) and (M.M-3B-TC) models were (14.4) °C and (15.1) °C, respectively. Hence, the latter two models exhibited a higher load than fixed boundary temperature at (16) °C. This result is because they possess a higher potential temperature gradient between the soil and the carrier fluid, increasing the ability to augment the heat transfer rates. On the other hand, the (M.M-3A) model exhibited a lower heat load dissipation because it possesses a higher borehole thermal resistance when compared with other models, Figure 8. This behavior is because the (M.M-3A) model possesses the lower overall equivalent thermal conductivity of ground (1.72) W/m.K than other models. The (M.M-2) and the (M.M-3B) models have a close equivalent thermal conductivity of (1.9) W/m.K and (2.0) W/m.K, respectively. Therefore, they showed close heat load values for the examined range of fluid flow. The borehole thermal resistance decreased with water flow velocity for all examined models. The (M.M-3A) produced a higher thermal resistance than

3D Numerical Modeling to Evaluate the Thermal Performance …

203

the (M.M-3B) by (7.7)% and (9.7)% at a flow velocity of (0.5) m/s and (0.1) m/s, respectively.

Figure 8. The borehole thermal resistance variation with water flow velocity for the multi-layer ground model at different soil boundary temperatures.

A comparison of the heat load between the two and three layers models to the equivalent single layer is presented in Figure 9.

Figure 9. A comparison of the heat load of the multi-layer and the equivalent single soil layer models at (Ts) of 16 °C.

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Ali H. Tarrad

Figure 10. A comparison of the borehole’s achieved heat load between cooling and heating models.

The single-layer models exhibited higher heat transfer rates than the multi-layer ones by (1-2)% and (4)% for MS-5/M.M-2 and M.S-4/M.M.3A geometry configurations, respectively. As the soil equivalent thermal conductivity increases, then the deviation of the equivalent single layer from the multi-layer structure vanishes. The effect of heating and cooling modes on the thermal performance of the borehole for a variety of analyzed models is shown in Figure 10. The (M.S-7) models exhibited a higher heat transfer rate for cooling and heating manners than other soil geological structures. This scenario is mainly due to the lower borehole thermal resistance, as shown in Figure 6.a. The results showed differences in the potential temperature driving force between the cooling and heating modes. According to the imposed test conditions, the cooling mode has a higher temperature difference than heating. Therefore, the examined models produced higher cooling heat transfer rates than those in the cooling mode. 𝜂𝜙 =

𝑄̇𝑐,𝜙 − 𝑄̇ℎ,𝜙 𝑄̇𝑐,𝜙

(9)

3D Numerical Modeling to Evaluate the Thermal Performance …

205

In this expression, the variable (𝜙) refers to the model designation. Equation (9) indicated that the cooling load was higher than that of the heating mode for (M.S-7), (M.M-3B-T), and (M.S-3) models by (39-40)%, (44-46)%, and (38-41)% respectively. The results revealed that the borehole thermal resistance was independent of the heat transfer process, heating, or cooling modes.

Conclusion The present work has confirmed the following outcomes: 1. The steady-state 3-dimensional modeling for the borehole thermal performance provides an attractive tool for the preliminary groundcoupled heat pump design. 2. The soil’s far distance undisturbed temperature has a vital role in the thermal performance assessment of the ground heat exchanger. 3. The soil geological structure is a controlling parameter for the thermal design of the ground source heat exchanger. 4. The soil thermal conductivity plays a key role in the borehole thermal design. The higher examined soil thermal conductivity produced a higher heat transfer rate. 5. The heat transfer rate was ranged between (2.5) kW and (3.3) kW for the cooling mode of (M.S-7C) model; it declined to the range of (1.52.0) kW for the heating mode (M.S-7H). 6. The lower soil thermal conductivity (M.S-1) model exhibited the higher borehole thermal resistance. It fell in the range of (0.29-0.39) m.K/W. In contrast, the lower thermal resistance was experienced by the (M.S-7) model in the range of (0.18-0.21) m.K/W. 7. The multi-layer geological soil structures showed various thermal assessments according to the soil thermal conductivity and far distance temperature. For the cooling mode modeling, the (M.M-3A), (M.M-3B), and (M.M-3B-T) showed heat transfer rate ranges of (2.12.6) kW, (2.2-2.8) kW, and (2.3-3) kW, respectively. 8. The equivalent single-layer models exhibited higher heat transfer rates than the original multi-layer ones by (1-2)% and (4)% for MS5/M.M-2 and M.S-4/M.M.3A geometry configurations, respectively.

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Ali H. Tarrad

Appendix A Fluid Domain The fluid domain is described by the mathematical expressions of the conservation equations, continuity, Navier-Stokes, and energy in an incompressible flow as cited in [7, 31]:

Continuity Equation 1 𝜕 (𝑟 𝑢𝑟 ) 𝑟

𝜕𝑟

1 𝜕𝑢𝜃

+

𝑟 𝜕𝜃

+

𝜕𝑢𝑧 𝜕𝑧

=0

(A.1)

Navier-Stokes Equation 𝜕𝑢𝑟

𝜌(

1 𝜕

𝜇 [

𝑟 𝜕𝑟

𝜕𝑡

+ 𝑢𝑟

(𝑟

𝜕𝑢𝜃

𝜌(

1 𝜕

𝜇 [𝑟

𝜕𝑟

𝜕𝑡

𝜕𝑢𝑟 𝜕𝑟

𝜕𝑢𝜃 𝜕𝑟

𝜕𝑢

𝜇

(𝑟

𝜕𝑢𝑧

𝜕𝑢𝜃 𝜕𝑟

𝜕𝑢𝑧 𝜕𝑟

)+

𝑟 𝜕𝑟 𝜕𝑟 [ 1 𝜕2𝑢 𝜕 2 𝑢𝑧 𝑧 𝑟2

𝜕𝜃 2

+

𝜕𝑢 𝑢 2 + 𝑢𝑧 𝑟 − 𝜃 ) = 𝑟 𝜕𝜃 𝜕𝑧 𝑟 1 𝜕 2 𝑢𝑟 𝜕 2 𝑢𝑟 2 𝜕𝑢𝜃 𝑢𝑟

+

𝑢𝜃 𝜕𝑢𝑟

𝜕𝜃 2

+

𝜕𝑧 2

−

𝑟 2 𝜕𝜃

−

𝑟2

+

𝑢𝜃 𝜕𝑢𝜃

𝜕𝜃 2

+

𝑢𝜃 𝜕𝑢𝑧 𝑟

𝜕𝜃

𝜕𝑧 2

+

+ 𝑢𝑧

]

𝑟 2 𝜕𝜃 𝜕𝑢𝑧 𝜕𝑧

−

𝜌𝑔𝑟 −

𝜕𝑝 𝜕𝑟

+

]

𝜕𝑢 𝑢 𝑢 + 𝑢𝑧 𝜃 + 𝑟 𝜃) 𝑟 𝜕𝜃 𝜕𝑧 𝑟 1 𝜕 2 𝑢𝜃 𝜕 2 𝑢𝜃 2 𝜕𝑢𝑟 𝑢𝜃

+

) + 𝑟2

𝜌 ( 𝜕𝑡𝑧 + 𝑢𝑟 1 𝜕

𝜕𝑟

) + 𝑟2

+ 𝑢𝑟

(𝑟

𝜕𝑢𝑟

𝑟2

(A.2a) = 𝜌𝑔𝜃 −

]

) = 𝜌𝑔𝑧 −

1 𝜕𝑝 𝑟 𝜕𝜃

+ (A.2b)

𝜕𝑝 𝜕𝜃

+ (A.2c)

𝜕𝑧 2

Energy Equation 𝜕𝑇 𝜕𝑇 𝑢𝜃 𝜕𝑇 𝜕𝑇 𝑞́ 1 𝜕 𝜕𝑇 1 𝜕2𝑇 𝜕2𝑇 Φ + 𝑢𝑟 + + 𝑢𝑧 = +𝛼[ (𝑟 )+ 2 + ]+ 𝜕𝑡 𝜕𝑟 𝑟 𝜕𝜃 𝜕𝑧 𝑐𝑝 𝑟 𝜕𝑟 𝜕𝑟 𝑟 𝜕𝜃 2 𝜕𝑧 2 𝜌 𝑐𝑝

(A.3a) where the viscous dissipation rate is:

3D Numerical Modeling to Evaluate the Thermal Performance … 𝜕𝑢

2

1 𝜕𝑢𝜃

Φ = 2 𝜇 [( 𝜕𝑟𝑟) + (𝑟 𝑢𝜃 2

𝜕𝑢

) + ( 𝜕𝑧𝜃 + 𝑟

𝜕𝜃

1 𝜕𝑢𝑧 2 𝑟

𝜕𝑢

+

𝑢𝑟 2

2

𝜕𝑢

1 𝜕𝑢𝑟

) + ( 𝜕𝑧𝑧 ) ] + 𝜇 [(𝑟 𝑟

) + ( 𝜕𝑟𝑧 + 𝜕𝜃

𝜕𝑢𝑟 2 𝜕𝑧

) ]

𝜕𝜃

+

𝜕𝑢𝜃 𝜕𝑟

207

− (A.3b)

These equations represent the complete forms of the handled expressions in the fluid domain for the transient mode. In the present investigation, the heat generation (𝑞́ ) and gravity terms (ρg) were dropped out.

Solid Domains In the solid domains of the model, tube wall, grout, and soil, the general Fourier’s law is applicable: 1 𝜕 𝑟 𝜕𝑟

(𝑟

𝜕𝑇 𝜕𝑟

1

) + 𝑟2

𝜕 𝜕𝜃

(𝑟

𝜕𝑇 𝜕𝜃

𝜕

𝜕𝑇

𝑞́

1 𝜕𝑇

) + 𝜕𝑧 ( 𝜕𝑧 ) + 𝑘 = 𝛼

𝜕𝑡

(A.4)

́ . The reader is referred to [1, The energy generation per unit volume (𝑞) 2, 31] for the basic derivative of this equation.

References [1]

[2] [3] [4]

[5]

[6]

Ingersoll, L. R., Zobel, O. J., and Ingersoll, A.C. (1954). Heat conduction with engineering, geological and other applications, revised edition; University of Wisconsin Press, Madison, WI, USA. Carslaw, H. S., and Jaeger, J.C. (1959). Conduction of heat in solids, 2nd ed.; Oxford University Press, London, UK. Kavanaugh, S. P. (1985). Simulation and experimental verification of vertical ground-coupled heat pump systems. PhD thesis, Oklahoma State University, USA. Gu, Y., and O’Neal, D. L. (1998). Development of an equivalent diameter expression for vertical U-tubes used in ground-coupled heat pumps. ASHRAE Transactions, 104 (2), 1-9. Muttil, N., and Chau, K. W. (2006). Neural network and genetic programming for modeling coastal Algal blooms. Int. J. Environment and Pollution, 28(3-4), 223238. Tarrad, A. H. (2020a). Development of analytical model for a vertical single U-tube ground-coupled heat pump system. Global Journal of Researches in Engineering (J): General Engineering, 20(3), 1-14.

208 [7]

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[12] [13] [14]

[15]

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[18]

[19]

[20]

[21] [22]

Ali H. Tarrad Tarrad, A. H. (2020b). A 3-dimensional borehole numerical modeling for single and double U-tube ground-coupled heat pump. COMSOL 2020 conference, Grenoble, France. Molina-Giraldo, N., Blum, P., Zhu, K., Bayer, P., and Fang, Z. (2011). A moving finite line source model to simulate borehole heat exchangers with groundwater advection. Int. J. Therm Sci., 50(12), 2506–2513. Erol, S. and Francois, B. (2018). Multilayer analytical model for vertical ground heat exchanger with groundwater flow. Geothermics, 71, 294–305. Abdelaziz, S. L., Ozudogru, T. Y., Olgun, C. G., and Martin, J. R. (2014). Multilayer finite line source model for vertical heat exchangers. Geothermics. 51, 406–416. Bandos, T. V., Alvaro, M., Esther, F., Santander, J. L.G., José, M. I., and Jezabel, P. (2009). Finite line-source model for borehole heat exchangers: effect of vertical temperature variations. Geothermics. 38(2), 263–270. Eskilson P. (1987). Thermal analysis of heat extraction boreholes. Doctoral Thesis, Department of Mathematical Physics. University of Lund, Sweden. Diao, N. R. and Fang, Z. H. (2006). Ground-coupled heat pump technology. Beijing: Higher Education Press, 47–68. Claesson, J., and Dunand A. (1983). Heat extraction from the ground by horizontal pipes- a mathematical analysis. Document D1, Swedish Council for Building Research, Stockholm. Bose, J. E., Parker, J. D., and McQuiston, F. C. (1985). Design/data manual for closed-loop ground-coupled heat pump systems. American Society of Heating, Refrigeration, and Air Conditioning Engineers (ASHRAE). Atlanta, USA. Tarrad, A. H. (2019). A borehole thermal resistance correlation for a single vertical DX U-tube in geothermal energy application. American Journal of Environmental Science and Engineering, 3(4), 75-83. Tarrad, A. H. (2020c). A perspective model for borehole thermal resistance prediction of a vertical U-tube in geothermal heat source. Athens Journal of Technology and Engineering, 7(2), 73-92. Chiasson, A.D., Spitler, J.D., Rees, S.J., and Smith, M.D. (2000). A model for simulating the performance of a shallow pond as a supplemental heat rejecter with closed-loop ground-source heat pump systems. ASHRAE Transactions, 106(2), 107121. Fisher, D. E., and Rees, S. J. (2005). Modeling ground source heat pump systems in a building energy simulation program (ENERGYPLUS). Ninth International IBPSA Conference, 311-318, Montréal, Canada. Zanchini, E., Lazzari, S., Priarone, A. (2010a). Effects of flow direction and thermal short-circuiting on the performance of small coaxial ground heat exchangers. Renewable Energy, 35, 1255–1265. Zanchini, E., Lazzari, S., and Priarone, A. (2010b). Improving the thermal performance of coaxial borehole heat exchangers. Energy, 35, 657–666. Rees, S. J., and He, M. (2013). A three-dimensional numerical model of borehole heat exchanger heat transfer and fluid flow. Geothermics, 46, 1– 13.

3D Numerical Modeling to Evaluate the Thermal Performance … [23]

[24]

[25]

[26]

[27] [28]

[29]

[30]

[31]

209

Li, Z., and Zheng, M. (2009). Development of a numerical model for the simulation of vertical U-tube ground heat exchangers. Applied Thermal Engineering, 29(5), 920-924. Bidarmaghz, A., Narsilio, G., and Johnston, I. (2013). Numerical modelling of ground heat exchangers with different ground loop configurations for direct geothermal applications. Proceedings of the 18th International Conference on Soil Mechanics and Geotechnical Engineering, 3343-3346, Paris, France. Tarrad, A. H. (2021a). A 3-dimensional numerical thermal analysis for a vertical double U-tube ground-coupled heat pump. International Journal of Chemical Engineering and Applications, 12(2), 12-16. Tarrad, A. H. (2021b). A 3-dimensional numerical thermal analysis for the configuration effect of a single and double U-tube on the borehole performance. Proceedings of the ASME 2021 15th International Conference on Energy Sustainability ES2021, Paper No: ES2021-60659, 12 pages, on-line virtual, USA. COMSOL Multiphysics version 5.4. (2018). Heat Transfer Module User Guide. Sagia, Z., Stegou A., and Rakopoulos, C. (2012). Borehole resistance and heat conduction around vertical ground heat exchangers. The Open Chemical Engineering Journal, 6, 32-40. Florides, G. A., Christodoulides, P., and Pouloupatis, P., (2013). Single and double U-tube ground heat exchangers in multiple-layer substrates. Applied Energy, 102, 364-373. Vella, C., Borg, S. P., and Micallef, D. (2020). The effect of shank-space on the thermal performance of shallow vertical U-tube ground heat exchangers. Energies, 13, 602, 1-16. Bird, R. B., Stewart, W. E., and Lightfoot, E. N. (2002). Transport phenomena, 2nd ed., John Wiley, New York.

Chapter 9

Solid Oxide Fuel Cells Ali Khosravi1, Behnam Talebjedi2 Juan Garcia Pabon3 and Mamdouh El Haj Assad4 1SDU

Mechatronics (CIM), Department of Mechanical and Electrical Engineering, University of Southern Denmark, Sønderborg, Denmark 2Department of Mechanical Engineering, School of Engineering, Aalto University, Espoo, Finland 3Institute for Mechanical Engineering, Federal University of Itajubá (UNIFEI), Itajubá, Brazil 4Department of Sustainable and Renewable Energy Engineering, University of Sharjah, Sharjah, UAE

Abstract By producing direct electricity from oxidizing fuel, solid oxide fuel cells (SOFCs) are becoming more and more popular as a practical power production technique. This technology can be employed for large-scale power generation applications. Chemical energy in SOFCs is converted into electricity directly with an energy efficiency of more than 60%. These power generation technologies do not require a combustion process, making them environmentally friendly and green technology. Additionally, SOFCs are able to utilize electricity from industrial and domestic waste heat to increase energy conversion efficiency. This chapter focuses on SOFC's components, modeling, and its applications for heat and power generation. Additionally, it offers the key design variables needed to model SOFC's behavior. 

Corresponding Author’s Email: [email protected].

In: The Fundamentals of Thermal Analysis Editors: Mamdouh El Haj Assad, Ali Khosravi and Mehran Hashemian ISBN: 979-8-88697-759-2 © 2023 Nova Science Publishers, Inc.

212

Ali Khosravi, Behnam Talebjedi, Juan Garcia Pabon et al.

Keywords: hydrogen, solid oxide fuel cell, energy transition, thermal analysis, power generation, waste heat

1. Introduction Despite the fact that hydrocarbon burning and fossil fuel-based energy systems generate a considerable quantity of greenhouse gases, particularly carbon dioxide, which has a detrimental impact on the environment, fossil fuels remain the dominant resource that powers most of today's technology [1]. Over the past two decades, usage of alternative energy sources like solar and wind power has skyrocketed, but the fluctuating nature of these supplies poses several challenges for grid operators [2, 3]. One of the most promising options for assisting renewable energy sources in replacing conventional fossil fuels and reducing carbon emissions is hydrogen which mixes with oxygen in fuel cells to produce electricity, heat, and water [4]. As a consequence, compared to traditional systems like internal combustion engines, the chemical energy in the fuel is immediately transformed into electricity at higher efficiency and in a more ecologically friendly manner. The promise to deliver clean energy and long-term durability to customers has piqued the interest of all areas of research in fuel cell technologies to be employed in the power production industry. Numerous benefits come with the SOFCs technology, including fuel flexibility, high conversion efficiency, and clean energy service [5]. They are suitable for numerous applications, consisting off-grid power production, integrated systems, and transportation applications, and can assist as a substitute energy source for internal combustion engines. Many industries, particularly manufacturing, have been drawn to examine the potential of fuel cells as a power generation technology [6]. The fuel cell is an electrochemical method that produces energy directly from fuel chemicals like methanol and hydrogen without the need for any additional procedures [7]. The technology's key advantage is that it does not need combustion for energy conversion. As an environmentally clean technology, using renewable fuels such as ethanol, methanol, and hydrogen, which are not difficult to produce and naturally available through the fermentation process, causes fuel cell technology to be categorized as a trustworthy and sustainable energy source [8]. Furthermore, the use of this technology reduces reliance on fossil fuels such as gasoline. Type of fuel used, operating temperature, and electrolyte usage are a few of the criteria used to categorize fuel cell technology. In large-scale

Solid Oxide Fuel Cells

213

applications (such as power generation plants with high energy conversion and cogenerative energy production from waste heat), SOFCs are now established for commercialization after molten carbonate fuel cells (MCFCs) and phosphoric acid fuel cells (PAFCs) [9]. Hydrogen and carbon monoxide (𝐶𝑂, it is known as a direct carbon fuel cell) were the first fuels used in SOFCs. When the operating temperature hits 800°C, the redox reaction starts, and the oxide ion flows to the anode side through a solid electrolyte to produce electricity [10]. Because of the low emissions of waste gases, the SOFC application generated low noise during operation and had a modest impact on air pollution. Furthermore, the high working temperature of SOFCs allows this system to be used in a wide range of fuel types and consumption. Additionally, the high working temperature of SOFC causes waste heat generation that can be recovered as a component of a cogeneration system, such as a steam turbine power plant or a combined heat and power (CHP) system [11]. In this chapter, we first discuss various fuel cells before concentrating on SOFC and its components (sections 2 and 3). The modeling of SOFC encompassing fluid, heat transfer, and electrochemistry is then presented in section 4. The primary design criteria for a SOFC are presented in section 5. This can greatly assist us in creating a model-based artificial intelligence (AI) for this complicated device. In section 6, we talk about how a SOFC performs and the various factors that influence it. In part 7, we go over hybrid systems that use SOFC to generate both heat and electricity. The conclusion is presented in section 8.

2. Fuel Cell Types Different types of fuel cells are in varying stages of development. The most common division is the kind of electrolyte utilized in fuel cells, which includes [12]: 1. 2. 3. 4. 5.

polymer electrolyte fuel cell (PEFC), alkaline fuel cells (AFC), PAFC, MCFC, SOFC.

Primary Cell Elements Water Management for Products Product Heat Control

Yes, plus purification to remove trace CO and CO2 Carbon-based Evaporative Circulation of the Electrolyte and Process Gas

Yes, plus purification to remove trace CO

Process Gas plus a liquid coolant

Carbon-based Evaporative

Yes

65 − 220℃ 𝑂𝐻 −

Platinum Metal

AFC Mobilized or Immobilized Potassium Hydroxide in asbestos matrix Transition metals

Yes

40 − 80℃ 𝐻+

Platinum Carbon or metal

Catalyst Interconnect

Working Temperature Charge Carrier Hydrocarbon fuel external reformer CO to hydrogen external shift conversion

Carbon

PEFC Hydrated Polymeric Ion Exchange Membranes

Electrodes

Electrolyte Materials

Process Gas + Liquid Cooling Medium or Steam Production

Graphite-based Evaporative

Yes

Yes

205℃ 𝐻+

Platinum Graphite

Carbon

PAFC Immobilized Liquid Phosphoric Acid in SiC

Process Gas + Internal Reforming

Stainless-based Gaseous Product

No

Nickel and Nickel Oxide Electrode material Stainless steel or Nickel 650℃ 𝐶𝑂3= No, just for some fuels

MCFC Immobilized Liquid Molten Carbonate in LiAIO2

Table 1. Overview of principal distinctions of the fuel cells [13]

Process Gas + Internal Reforming

Ceramic Gaseous Product

Perovskite and Perovskit/metal cermet Electrode material Nickel, ceramic, or steel 600 − 1000℃ 𝑂= No, for some fuels and cell designs No

SOFC Perovskites (Ceramics)

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The electrolyte that is employed mostly determines the fuel cell's working temperature range. The operating temperature and the cell useful life affect the physicochemical and thermomechanical properties of materials used in fuel cell parts (i.e., electrodes, electrolytes, interconnect, etc.). Table 1 provides a summary of the main characteristics of the different types of fuel cells [13].

3. Main Components of SOFCs The main SOFC components are made from a combination of electrolytes and two different electrodes (anode and cathode). As seen in Figure 1 [14], a ceramic-based solid electrolyte is sandwiched between the porous electrodes. The oxide ion in the cathode electrode of SOFCs is created by a working process involving the reduction of oxygen. The fuel oxidation process is finished, and an electron is created, as the oxide ion travels from the cathode side via the solid electrolyte. The process of creating electrical energy is finally completed by the electron traveling along the external wire.

Figure 1. A schematic of a SOFC [14].

The design cell structure divides the SOFC configurations into two categories: planar and tubular. An electrode with a cathode and anode, a solid electrolyte, a connector, and a sealant are components of both kinds of SOFCs. The popular configuration is planar SOFC architecture used for single-cell and

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stack fabrication. The ability to achieve great power density performance with a cheap production cost is one of the benefits of planar SOFC design. SOFC components with flat design plates are easy to produce, as shown in Figure 2 (A). Since the planar SOFC design is less costly and more quickly produced than the tubular SOFC design, companies generally utilize it. Additionally, this design is excellent for creating a compact SOFC stack for mobile applications and transportation.

(a)

(b) Figure 2. (A) A schematic diagram of a Planar SOFC and (B) Tubular SOFC [15].

The tubular SOFC architecture is appropriate for manufacturing as a stationary power-generating plant system since this design is great for largescale and medium applications. The tubular SOFC design is shown in Figure

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2(B) and integrates all components to create a closed-end ceramics tube design structure. The basic design structure is a tubular geometry structure. The benefits of the tubular SOFC structure comprise a straightforward sealing technique, a high capacity to tolerate great thermal stress, a strong mechanical resistance load fluctuation, and increased tolerance to multiple fuel supply methods. The high expense of the manufacturing process and large ohmic losses, which lower the ionic conductivity of the electrolyte, impose limitations on the tubular SOFC structure.

3.1. Electrode An electrode component is essential for performing the redox reaction for energy generation. The oxidation of the fuel occurs on the anode side, whilst the reduction of the oxidant occurs on the cathode side. The porous structure is necessary for high redox reaction efficiency, as well as chemical stability and compatibility. Additionally, the most important ingredient in boosting the SOFC's effectiveness for energy generation is the electrode's capacity to adapt to the other components, notably the electrolyte [11].

3.1.1. Anode An important aspect of SOFC technology is the microstructure of the anode material, which influences electrochemical performance when the cells are manufactured under ideal conditions. Fuels such as hydrogen and natural gas are oxidized at the anode. As a result of the high temperature inside the cell, an anodic material must have good stability, a great level of electronic conductivity, effective thermal adaptability with other cell components, sufficient electrocatalytic efficiency to cause oxidation reactions, and enhanced porosity for efficient carrier gas transport. Reduced polarization losses of the oxidation reaction enable SOFCs with good performance [15]. 3.1.2. Cathode The cathode electrode is where the oxidant reduction process happens. On the other side of the anode is a cathode sandwiched by an electrolyte in the center. The primary purpose of the SOFC cathode is to regulate the entire cell, which impacts the output system's performance. Typically, poisoning and corrosion concerns produced by external factors such as oxidant from the air around the cathode electrolyte cause loss of cathode electrolyte performance. Cathode

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corrosion, for example, occurs when the cathode is exposed to humidity and carbon dioxide in the air over a long-lasting period. Perovskite materials based on lanthanum are the most common cathode materials utilized in SOFC nowadays. Early SOFC cathode materials included magnetite, platinum, other noble metals, and other minerals. Due to their physical and chemical instability, compatibility issues with electrolytes, and, in the platinum case, they are no longer being explored because of the high price. Currently, doped lanthanum manganites comprise the basis of the majority of cathodes. Strontium-doped LaMnO3 (LSM) is employed in hightemperature SOFCs (with an operating temperature of around 1000℃) [16].

3.2. Electrolyte An electrolyte serves as the "heart" of fuel cell technology. Because of the crucial function of this cell element in the total system arrangement and its principal role in energy generation, electrolyte consumption is one way to recognize the types of fuel cell technology. For instance, solid polymer electrolyte membranes, such as poly (vinyl alcohol), polyamide, and others, are used as the electrolyte in fuel cells that operate at lower temperatures, such as alkaline fuel cells, polymer electrolyte membrane fuel cells, and direct alcohol fuel cells (methanol and ethanol). A harder and denser electrolyte is critical and necessary for fuel cell technologies working in high-temperature such as SOFCs. These electrolyte materials can be ceramic-based, such as zirconia. The primary functions of solid electrolytes are to initiate the cellular reaction from the redox process, prevent electron movement inside the electrolyte, act as a filter for oxidant and fuel, and distinguish between reduction and oxidation processes. The relationship between electrolyte conductivity and temperature is seen in Figure 3.

3.3. Interconnect In general, there are two types of connection materials for SOFC: conducting ceramic (perovskite) materials for use at high temperatures (900–1000°C) and metallic alloys for use at lower temperatures. In theory, there is approximately 1.23 V of open circuit potential produced by a single SOFC cell. The creation of a SOFC stack is essential for high-voltage applications. As shown in Figure 2 (A), the SOFC stack structure comprises two or more SOFC single cells

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connected through a bipolar plate interconnect component to stack the whole single cell. Compatibility with the electrode component, as well as strong physical and chemical resistance under redox circumstances, are crucial factors to consider when selecting a connection material [11].

Figure 3. Temperature effects on the conductivity of electrolytes [13].

3.4. Sealants Sealants are utilized to eliminate leakage difficulties in single cells or stacks of SOFCs to improve performance. This element ensures that the SOFC system can resist high temperatures, maintain stability in redox reactions, and ensure long operational consistency to prevent thermal stresses. The researcher proposes bonded compliant seals, compressive seals, and stiff seals as different forms of sealants [13].

4. Modeling of SOFC: Fluid, Heat Transfer, and Electrochemistry For modeling a planar SOFC with co-flow channels, Chnani (2007) proposed an approach [17]. He used an electrical analogy to create fluidic and thermal

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sub-models. This approach allows for the representation of gas flows and thermodynamic behavior in comparable circuits, allowing for stacking numerous identical models. This benefit is clear for a stack module: the thermal circuit represents the temperature gradient among cells. The illustration of the stack modeling is shown in Figure 4. The solid and gas temperatures are calculated using the transient thermal model. The partial pressures of chemical species were computed using the fluidic model. With the parameters from these two sub-models, the electric (electrochemical) model calculated the stack voltage and polarisations. The cell was separated into seven isothermal volumes (as illustrated in Figure 5) for thermal behavior modeling, comprising cathode interconnect, cathode channel, electrolyte/ cathode interface, electrolyte, electrolyte/anode interface, anode channel, and anode interconnect.

Figure 4. Schematic of stack modeling [17].

Any system's mathematical modeling may be separated into three stages [18]: 1. Dynamic 2. Off-design operation, and 3. Design point All of the modeling layers are depicted graphically in Figure 6. Design point modeling is the most generic and has the widest range of applications. It is mainly used for selecting devices or system assessments. In most situations, only a basic understanding of the procedure is required.

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Figure 5. Heat transfer and heat sources for a SOFC [17].

Off-design operations are those technologies, things, or systems for which sufficient attributes are already known. A more thorough model which relies on real operational data of the represented item is necessary to characterize the off-design system operation. The outcome of calculating design points is typically utilized as a reference state for estimating off-design operations. The transient behavior modeling of the objects is the most challenging and intricate undertaking. This requires acquiring all available comprehensive information regarding the object's technological solution. Aside from realworld features, an extra understanding of time-dependent factors is required (heat accumulation, mass accumulation, etc.). The usual current-voltage curve is influenced by several factors that affect fuel cell performance. There are two types of parameters: thermal-flow parameters and architecture parameters. To effectively simulate SOFC behaviors, it is necessary to classify those parameters and their impact on fuel cell operating characteristics. Only the thermal-flow parameters can be altered during normal cell operation. As a result, the flow parameters primarily concern the fuel cell's off-design functioning. In contrast, we have complete freedom to adjust the cell's design characteristics throughout the building stage (thicknesses, electrolyte type, etc.). Architecture parameters may change only at the design point stage and need to be preserved at their nominal levels. Degradation processes will

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impact the architectural parameters only when the fuel cell's long-term operation is taken into account.

Design point

Off-design operation

Dynamic

Figure 6. The levels of mathematical modeling.

5. Application of Artificial Intelligence for Modeling of SOFC: Design Parameters The multi-physics processes occurring on the fuel cell surfaces influence SOFC performance modeling. Inside the cell, heat transfer, electrochemical processes, mass, and charge movement are all carried out. Many mathematical models of the SOFC exist, with the majority of them relying on mathematical explanations of electrochemical, chemical, and physical features. Anode and cathode porosities, inlet and outlet gas compositions at anode and cathode, cell temperature, electrolyte thickness, electrolyte material, and other factors all influence cell operating conditions. Fuel cells have a very basic construction, but modeling their operation is challenging. This is because of the enormous number of constants that must be calculated. Different types of SOFCs are under development. Additionally, new fuel cell layers are always being researched and may be made from a variety of materials (YSZ, SDC, etc.). Moreover, the layers that make up the cathode and anode might have varying porosity and could be made up of many layers. As a result, almost any technological solution might lead to extensive and multidisciplinary study in the quest for model coefficients. A model that has been constructed and validated is typically only valid for one technological

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solution and cannot be utilized for other reasons. Different characteristics that impact SOFC efficiency are shown in Figure 7 [18]. Solid Oxide Fuel Cell

Flows

Architecture

Oxidant

Electrolyte

Type

Flow

Material

Planar

Pressure

Thickness

Tubular

Composition

Temperature Fuel

Sintering Temperature Cathode

Flow Pressure Composition

Anode

Material

Material

Thickness

Thickness

Porosity

Porosity

Area

Area

Figure 7. Design parameters for SOFCs.

It is possible to simulate a stack's performance using a well constructed three-dimensional model. Nevertheless, because all spatiotemporal factors in a stack might impact the voltage-current features, it is challenging to discover the best arrangement of many stack characteristics due to the high time costs. Models of one- and two-dimensional mechanisms must take complicated mathematical equations into account, and fitting accuracy is also not very good. While just a few parameters may be improved by orthogonal experimental designs, they are not very efficient. The aforementioned circumstances make it possible to estimate SOFC performance with artificial intelligence (AI) tools like neural networks and machine learning algorithms at a significantly reduced cost [19]. AI is used in numerous researches to identify non-linear relationships between input parameters (design parameters) and outputs (power generation, thermal efficiency, overall efficiency, etc.). This section aims to clarify which input variables should be

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used to simulate a SOFC's behavior. Therefore, we explore the earlier research done by AI for SOFC modeling. The network structure depicted in Figure 8 was proposed by Rauh and Auer [20]. They simulated the behavior of a SOFC by considering the following components as the input vector: • • • •

detectable stack temperatures ϑm,(1,1,1),k and ϑm,(1,3,1),k at the gas inlet and outlet manifolds, electric current Ik, inlet temperatures ϑCG,m,k and ϑAG,m,k at the cathode and anode sides of the stack, and mass fluxes of nitrogen and hydrogen 𝑚̇𝑁2,𝑘 , and 𝑚̇𝐻2,𝑘 at the anode.

Figure 8. Proposed network to analyze the SOFC stack's electric power characteristics [20].

Wang and Wang [21] stated that it might be inferred that there is a complex nonlinear pattern between the real-time temperature, SOFC output voltage, water vapor, oxygen, and hydrogen inlet molar flow rates, as shown in Figure 9. Low temperature and low current result in a lower delivered voltage by the SOFC. The SOFC output voltage increases when both the current and temperature are high. Temperature-dependent activation and

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ohmic polarization losses are reduced by raising the load current, whereas ohmic polarization and activation losses drop as the SOFC temperature rises.

Hydrogen Input

Molar flow rate

Oxygen input Molar flow rate

Output voltage

Water vapor input

Molar flow rate

Real time temperature

Figure 9. The proposed neural network by Wang and Wang.

The following variables were chosen as inputs for an AI-based model: current density, aging time, cathode and anode temperatures, and air and hydrogen flow rates. Meanwhile, the SOFC voltage was the output by the neural network autoregressive with external input (NNARX) model [22], as illustrated in Figure 10.

Figure 10. NNARX model to simulate the SOFC.

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Figure 11 shows a different network design, the output variable for the network architecture was output voltage, considering the furnace temperature, load current, hydrogen flow rate, and airflow rate as input parameters, as proposed by Song et al. [19].

Figure 11. Proposed model to analyze the SOFC.

A hybrid-ANN model with 13 input parameters was built by Jarosław and Konrad [23], incorporating a few non-numerical parameters. 31 voltagecurrent density curves (583 experimental data points) were utilized in total as the training data points. The fuel cell voltage was the model's output, and the network input parameters needed to create it were as follows: • • • • • • • • •

Electrolyte temperature (℃). Electrolyte thickness (µm); Anode porosity, dimensionless; Anode thickness (mm); Anode inlet He flow density (ml/min/cm2); Anode inlet H2 flow density (ml/min/cm2); Cathode inlet N2 flow density (ml/min/cm2); Cathode inlet O2 flow density (ml/min/cm2); Current density (A/cm2);

6. SOFCs Performance Analysis This chapter introduces the empirical equations to predict the SOFCs performance based on the operating variables.

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6.1. Pressure Effect SOFC performance could be enhanced by rising the cell pressure. The effect of pressure on cell performance at 1000 °C is roughly represented by the following equation [13]. 𝑝

∇V𝑝 (𝑚𝑉) = 59 log (𝑝2) 1

(1)

The aforementioned correlation is based on the idea that overpotentials decrease with increased pressure and are influenced by gas pressures, where p1 and p2 are distinct cell pressures.

6.2. Temperature Effect Figure 12 illustrates how SOFC performance is influenced by temperature. The graph represents a two-cell stack using air and fuel made up of 67% hydrogen, 22% carbon dioxide, and 11% oxygen. At 800°C, the sharp reduction in cell voltage as a function of current density represents the solid electrolyte's increased ohmic polarization (i.e., low ionic conductivity) at this temperature. By raising the operating temperature to 1,050°C, the ohmic polarization decreases, and at the same time, the current density at a specific cell voltage rises. Analyzing the data in Figure 12 indicates a larger reduction in cell voltage by lowering the temperature to 800-900°C than the temperature of 900-1,000°C at a steady current density. This investigation shows that temperature and current density have a strong correlation with voltage gain with regard to temperature. The following relationship explains the voltage gain [13]. ∇𝑉𝑇 (𝑀𝑉) = 𝐾(𝑇2 − 𝑇1 ) ∗ 𝐽

(2)

where 𝐽 is the current density in 𝑚𝐴/𝑐𝑚2. The following K values are figured from multiple references utilizing a fuel composition of 67% 𝐻2/22% CO/11% 𝐻2 𝑂, and an air oxidant, as presented in Table 2 [13].

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Table 2. K Values for ΔVT 𝐾 0.008 0.006 0.014 0.068 0.003 0.009

𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒(℃) ~1000 1000 − 1050 900 − 1000 800 − 900 900 − 1000 800 − 900

Figure 12. Performance of a two-cell stack with 67% H2, 22% CO, and 11% H2O/Air [13].

6.3. Current Density Effect The SOFC voltage level is decreased by increasing the current density, which results in ohmic and concentration losses. The extent of this loss is expressed by the following equations. ∇𝑉𝑗 (𝑀𝑉) = −0.73∆𝐽

(3)

where J is the cell's operational condition's current density (mA/cm2). Air electrode-supported (AES) cells by Siemens Westinghouse show the performance illustrated in Figure 13.

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Figure 13. AES cell voltage-current characteristics (1.56 cm Diameter, 50 cm Active Length) [13].

6.4. Impurities Effect The usual impurities in coal gas are ammonia (𝑁𝐻3 ), hydrogen chloride (𝐻𝐶𝑙), and hydrogen sulfide (𝐻2 𝑆). Part of the mentioned substances may damage the SOFCs' performance. An oxygen-blown coal gas was used in the first trials, which had 37.2% CO, 34.1% H2, 0.3% CH4, 14.4% CO, 13.2% H2O, and 0.8% N2. These experiments revealed no decay in the existence of 5,000 ppm 𝑁𝐻3. 1 ppm HCl impurity level also disclosed non-detected deterioration. When 𝐻2 𝑆 levels reached 1 ppm, performance dropped immediately, but it quickly settled into a normal linear deterioration. Additional testing revealed that eliminating 𝐻2 𝑆 from the fuel stream nearly brought the cell back to its starting state. Silicon (𝑆𝑖) is also studied as a contaminant, which similarly can be found in coal gas. The deposition of Si all over the cell is realized to be improved (~50%) by high fuel 𝐻2 𝑂 content. 𝑆𝑖 is reacted by the subsequent reaction [13]: 𝑆𝑖𝑂2 (𝑠) + 2𝐻2 𝑂(𝑔) → 𝑆𝑖(𝑂𝐻)4 (𝑔)

(4)

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𝐻2 𝑂 is consumed as 𝐶𝐻4 reforms to 𝐶𝑂 and 𝐻2. This encourages the inversion of the aforementioned equation, which permits the deposition of 𝑆𝑖𝑂2 downstream, most likely on exposed nickel surfaces. However, the H2O component of oxygen-blown coal gas is only around 13%, and this is not expected to allow for significant Si transfer.

7. Hybrid Systems with SOFC For power generation and as a CHP system, SOFC is utilized in a variety of industrial applications. Figure 14 illustrates a schematic of a cogeneration system consisting of a combined dual-loop organic Rankine cycle (ORC) setup for recovering waste heat from a SOFC system [24]. The integrated system's working principles may be summarized as follows.

Figure 14. A SOFC system with a dual-loop ORC system for waste heat recovery [24].

The air necessary for the fuel cell is compressed (AC, State 9) and heated (APH, State 10) in the preheater before participating cathode in the electrochemical processes. After passing via a preheater, the needed fuel (methane) is delivered into a fuel cell after being gasified by LNG (State 4′′) (FPH, State 6). After leaving the anode, the high-pressure fuel is transported

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to the SOFC stack after being combined in a mixer with recycled water vapor (and other outputs) (State 7). The fuel and warm air mix in the fuel-cell stack go through electrochemical redox reactions to generate electricity. The excess air from the cathode (State 11) and the unburned fuel from the anode (State 12′) are then completely burnt in the afterburner (AB) to create hightemperature combustion gases, which are then supplied into the gas turbine (G.T, State 14) to provide further electrical power. The exhaust gases from the gas turbine enter the waste-heat recovery system (WHR, State 17) where they are used as a heat source for the organic Rankine cycle system (ORC1) before being vented to the atmosphere (State 18). Because of the enormous temperature differential between the gas turbine exhaust gas and the cryogenic (LNG) thermal sink, it is necessary to employ another ORC system (ORC2) as a bottoming cycle for ORC1 to maximize power production and heat recovery from such a big temperature difference. In another study, the SOFC system was used as a CHP system, as depicted in Figure 15 [25]. The design is based on a common model that can be found online at Cycle Tempo [26]. The system includes an afterburner, a SOFC stack, and an external reforming unit (ER) (AB). It shows a typical SOFC system architecture that operates at 750 °C, which is a moderate temperature. In the afterburner (AB), the anode off-gas is completely oxidized when the fuel gas flow is combined with the cathode outlet. Because there is always an extra cathode airflow to cool down the stack, the off-gasses of the cathode have more oxygen than necessary for the afterburner. A gas flow divider (S1) is added to provide just a small amount of oxidant flow to the burner in order to ensure that the AB exhausts are heated to the right design temperature. After the off-gasses from the burner pass via the heat exchanger (HE1) and Reformer (ER), which preheats the incoming fuel, fuel, and steam are mixed prior to entering the Reformer. The Second half of the cathodic off-gas that was separated in S1 is combined with AB off-gases in the mixer M2. Before the cathode intake gas in the high-temperature heat exchanger (HE2) reaches M2, this cathodic stream heats it to stack input temperature. M2 gas outputs are directed to heat exchanger HE3, which offers intermediate air input flow preheating. In S2, the gas flow leftover heat is partitioned. Part of the S2 output advances HE6, which performs low-temperature heating from room temperature, while the balance of the gas from S2 is used to warm up the water stream in three steps: superheater (HE6) (HE4), evaporator (HE5), and economizer (HE7). Earlier than getting to the cogeneration unit (CH), the two separated streams in S2 are remixed in mixer M3 prior to being vented into

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the atmosphere via blower B. The system thermal output is the heat extracted in CH.

Figure 15. A CHP design for SOFC system [25].

In a combined cycle, the biomass gasifier (as the feeder) is paired with a SOFC in model (a) [27]. Model (a) waste heat is reused in a Sterling Engine (SE) to improve power generation (Model (b)) and exergy efficiency. The extra power generated by the SE is utilized in a PEME to make hydrogen in the last suggested model (Model (c)). The SE is selected as the primary waste heat recovery system for generating power and distributing hot water, while the gasifier produces the necessary fuel for the SOFC. First, ambient air blows into an air heat exchanger (AHX) (points 1 and 2) by an air blower. The air is then mixed at the mixing unit with recirculated cathode off-gases before entering the cathode (points 3a, 3b, and 3). A fuel blower blows syngas into the mixer after biomass and air are delivered into the gasifier (points 5 and 6). Before entering the anode portion, anode exhaust gases are recirculated and blended with blown fuel (points 7, 8, 9b, and 9). Unburned cathode and anode

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gases burn in the afterburner after electrochemical processes in the SOFC, and hot exhaust gases pass via the AHX, respectively (points 10b, 4a, and 11). The exhaust flue gases from SOFC may be used in the SE since they are warm enough. Therefore, the off-gases are repurposed as a heat source for the SE before being released into the environment (points 12 and 13), Figure 16.

Figure 16. The proposed multigeneration system combined with SOFC [27].

In another application, as illustrated in Figure 17, SOFC was employed in a combined system comprising an ORC, a single-effect absorption chiller, and a heating system as proposed by Al-Sulaiman et al. [28]. Waste heat from the SOFC heats the organic fluid in the ORC. The ORC's waste heat is then utilized to heat and cool the building. Cooling is provided by a single-effect absorption chiller, and a heat exchanger generates steam utilizing the ORC waste heat.

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Figure 17. Multigeneration plant with SOFC and ORC [28].

Conclusion Fuel cells generate energy directly from fuel using electrochemical processes, bypassing the efficiency limitations of Carnot engines. This might result in unprecedented levels of power-generating efficiency. The disadvantage is that chemical processes are inherently irreversible, which reduces fuel cell efficiency to some level. There are several uses for fuel cell technology, including personal gadgets, micro capacity units, transportation, and utility provider for residential and industrial sites. The proper way to convert the chemical energy of hydrocarbon fuels into electrical energy are SOFCs, which function at high temperatures. There has been a spike in interest in them in recent years for use in clean distributed generating systems. Any system mathematical modeling can be divided into three stages. The most versatile and general modeling technique is design point modeling. Technologies, items, or systems that have suitable qualities are known to be used in off-design procedures. It is required to categorize factors and their impact on operational characteristics in order to successfully simulate SOFC behaviors. Modeling the transient behavior of the modeled elements is the

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most challenging and complicated undertaking. The technological solution for the object must be thoroughly researched, which calls for gathering all available information. Flow and architecture are the two categories of design parameters for modeling a SOFC. The composition of the inlet and outlet gases at the anode and cathode, the porosity of the anode and cathode, the electrolyte material, the electrolyte thickness, the cell temperature, and other variables all affect the cell operating conditions. A number of industrial applications use SOFCs for power production and as CHP systems. This method offers a potentially effective solution for cogeneration operations.

Acknowledgments The first author acknowledges the University of Southern Denmark (SDU), Department of Mechanical and Electrical Engineering (DME). Aalto University’s Department of Mechanical Engineering is acknowledged by the second author.

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Index

A analytical modelling, 89, 110 artificial intelligence, 213, 222, 223 automotive, 72, 73, 85

B baseline correction, 2 biomass sample, ix, 1, 2, 10, 26, 27, 29, 31, 35, 37, 42, 44, 45, 46, 47, 48 boiling, vii, 49, 113, 114, 115, 116, 129, 130, 135, 136, 137, 138, 139, 140, 144, 145, 147, 151, 156, 161, 162, 183 bubble(s), vii, ix, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 134, 135, 136, 137, 138, 163, 164 bubbles dynamic behavior, ix, 113, 114, 131, 132, 135, 163 buoyancy, 10, 21, 22, 23, 24, 119, 123

C calcium, 38, 53, 54, 56, 57, 58, 59, 60, 194, 195, 196 calcium oxide, 53, 56, 57, 58, 59, 60 calibration, 2, 4, 7, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 25, 29 catalyst(s), ix, 53, 54, 55, 56, 57, 58, 59, 60, 214 catalytic, vii, 51, 53, 54, 55, 56, 60 centrifugal, 119, 125, 128 characterization, vii, ix, 1, 42, 48, 50, 51, 60 clean energy, 64, 212

climates, viii, 165 compressor, 165, 168, 169, 170, 171, 173, 174, 177, 178, 180, 181 condensation, vii, ix, 6, 114, 115, 116, 139, 140, 141, 144, 156, 157, 160, 162, 164, 171, 178, 180, 183 conversion, 4, 10, 11, 31, 32, 35, 38, 42, 43, 48, 51, 64, 65, 68, 69, 80, 81, 84, 85, 86, 91, 96, 97, 166, 167, 212, 214, 237 crucibles, 3, 4, 5, 6, 10, 22, 23, 27, 28, 47

D density, 67, 76, 93, 95, 104, 113, 114, 136, 152, 159, 186, 193, 194, 216, 225, 226, 227, 228 departure and lift off diameters, ix, 113, 135 derivative thermal analysis (DTG), 4, 6, 26, 27, 29, 48, 49, 50, 53, 54, 58, 59 derived, 46, 96, 101, 102, 106, 110, 123, 125, 128 design, x, 2, 64, 65, 67, 70, 83, 84, 85, 86, 87, 94, 107, 110, 111, 129, 175, 182, 188, 189, 193, 205, 208, 211, 213, 215, 216, 220, 221, 222, 223, 226, 231, 232, 234, 235 dynamics, vii, 27, 113, 136, 196

E efficiency, ix, x, 63, 64, 68, 69, 72, 73, 74, 76, 77, 79, 80, 81, 82, 83, 84, 90, 97, 98, 99, 101, 105, 106, 110, 111, 140, 165, 167, 169, 170, 171, 172, 176, 177, 178, 181, 211, 212, 217, 223, 232, 234

240 electricity, 64, 68, 71, 72, 76, 77, 79, 80, 83, 90, 91, 93, 165, 166, 168, 171, 177, 182, 183, 211, 212, 213, 231 electrochemistry, 213, 219 energy, viii, ix, x, 3, 5, 29, 32, 33, 44, 46, 48, 49, 50, 51, 54, 60, 63, 64, 65, 68, 71, 72, 74, 76, 77, 78, 80, 82, 83, 84, 85, 86, 89, 93, 97, 99, 104, 110, 111, 112, 114, 135, 136, 140, 145, 148, 162, 163, 165, 166, 167, 170, 172, 173, 176, 177, 179,180, 181, 182, 183, 186, 196, 206, 207, 208, 209, 211, 212, 213, 215, 217, 218, 234, 235, 236, 237, 245 energy conversion, ix, 3, 64, 68, 89, 93, 181, 211, 212, 213 energy transition, 212 entropy, vii, ix, 111, 136, 139, 140, 141, 142, 143, 144, 160, 161, 162, 163 entropy generation, ix, 139, 140, 141, 144, 162, 163 environment(s), 50, 54, 71, 79, 80, 99, 156, 166, 168, 173, 176, 178, 207, 212, 233 evaporator, x, 165, 167, 168, 169, 170, 171, 172, 173, 175, 176, 182, 231

F flow boiling, ix, 114, 115, 116, 130, 131, 135, 136, 137, 138, 139, 140, 141, 145, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 162, 163, 164 flow condensation, 140, 156, 157, 158, 159, 160, 161, 163 fluid, 124, 130, 132, 133, 136, 137, 141, 167, 168, 169, 170, 171, 172, 173, 175, 176, 179, 185, 186, 189, 191, 196, 197, 200, 202, 206, 207, 208, 213, 219, 233, 237 force balance analysis, ix, 113, 119, 135 force(s), ix, 64, 79, 91, 93, 113, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 128, 129, 130, 135, 136, 137, 164, 204 fuel cells, viii, 211, 212, 213, 214, 215, 218, 222, 234, 235, 236

Index fundamentals, 59, 60, 61, 65

G gas, 5, 7, 10, 11, 13, 16, 21, 22, 24, 25, 27, 29, 31, 32, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 50, 51, 72, 73, 74, 76, 77, 79, 86, 181, 214, 217, 220, 222, 224, 227, 229, 230, 231, 237 generation(s), vii, 54, 64, 71, 76, 79, 82, 83, 86, 106, 113, 139, 141, 143, 144, 162, 175, 177, 182, 187, 197, 207, 211, 213, 217, 218, 236 generator(s), vii, ix, 63, 65, 66, 71, 73, 74, 77, 79, 80, 81, 83, 84, 85, 86, 87, 96, 97, 99, 104, 107, 108, 109, 111, 112, 180 geothermal, 82, 194, 208, 209, 235 granulometry, 2 ground heat exchanger, 185, 186, 188, 189, 191, 200, 205, 208, 209

H heat pump, x, 96, 101, 104, 165, 166, 167, 168, 169, 177, 178, 180, 181, 182, 183, 185, 188, 205, 207, 208, 209 heat transfer, 4, 5, 23, 27, 69, 89, 90, 103, 110, 113, 114, 115, 135, 136, 137, 138, 139, 140, 144, 145, 148, 149, 150, 152, 153, 155, 157, 158, 159, 160, 162, 163, 164, 169, 170, 172, 173, 174, 175, 183, 185, 187, 189, 190, 196, 198, 200, 202, 204, 205, 208, 213, 221, 222 heat transfer coefficient, 110, 113, 114, 140, 164, 172, 173, 174, 200 heat transfer enhancement, 135, 139, 140, 162, 163 heating rate, 2, 9, 10, 13, 16, 20, 22, 23, 25, 43, 46, 47, 48, 57 heating/cooling, 83, 89, 92 helical coil(s), 140, 141, 142, 145, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 173, 183 hydrodynamic, 119, 124, 128

Index hydrogen, 45, 48, 51, 212, 213, 214, 217, 224, 225, 226, 227, 229, 232, 235, 236, 237

I impurities, 229 industrial, ix, 2, 48, 49, 54, 60, 63, 71, 72, 79, 83, 114, 139, 140, 145, 211, 230, 234, 235 industry, 54, 63, 64, 71, 72, 73, 80, 212 instrument(s), 1, 5, 6, 7, 8, 10, 12, 29, 32, 33, 35, 47, 48, 49, 50 interconnect, 214, 215, 218, 219, 220

M measurement(s), ix, 1, 2, 4, 5, 6, 7, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 31, 47, 50, 78, 86, 131 medical, 82, 83, 87 microelectronics, 79 micro-fin tubes, 139, 140, 141, 147, 155, 156, 162, 163, 164 modeling, viii, ix, x, 50, 84, 85, 86, 89, 90, 93, 107, 110, 135, 136, 137, 180, 181, 182, 185, 186, 188, 193, 194, 205, 207, 208, 211, 213, 219, 220, 221, 222, 224, 234, 235, 236, 237 multi-layer soil, x, 185, 186, 190

N niobium, 53, 54, 55, 57, 58, 59, 60 niobium pentoxide, 53, 55, 57, 58, 59, 60 numerical analysis, 186

P performance, viii, ix, 12, 47, 60, 63, 71, 76, 79, 80, 81, 82, 83, 85, 86, 90, 93, 94, 96, 97, 99, 100, 101, 102, 103, 105, 106, 107, 109, 111, 112, 139, 141, 145, 162, 163, 164, 165, 166, 167, 168, 177, 178, 179, 180, 182, 183, 185, 188, 189, 208,

241 209, 216, 217, 219, 221, 222, 223, 226, 227, 228, 229, 237 photovoltaic, x, 80, 81, 82, 86, 165, 166, 167, 169, 171, 172, 180, 181, 182, 183 power generation, x, 64, 72, 84, 85, 89, 92, 96, 97, 99, 111, 211, 212, 213, 223, 230, 232 preparation, 2, 10, 11, 29, 57, 59, 60 pressure, 7, 114, 119, 120, 124, 125, 128, 129, 130, 135, 136, 137, 138, 139, 140, 141, 142, 153, 160, 162, 163, 164, 169, 187, 227, 230 production, vii, ix, 46, 48, 51, 53, 56, 57, 59, 60, 63, 64, 67, 71, 75, 76, 77, 79, 82, 91, 99, 166, 211, 212, 213, 214, 216, 231, 235 pump(s), viii, 101, 165, 166, 167, 168, 180, 181, 182, 185, 186 PV/T system, 166, 167, 175, 177, 181

R recovery, 55, 64, 72, 73, 75, 76, 83, 84, 85, 181, 230, 231, 232, 237 refrigerant, 144, 156, 163, 167, 168, 169, 170, 172, 173, 174, 175, 176, 179, 182

S sealants, 219 sensors, 4, 7, 79, 82, 85 solar, viii, x, 72, 79, 80, 81, 82, 86, 165, 166, 167, 168, 169, 171, 173, 175, 176, 177, 178, 180, 181, 182, 183, 212, 235 solar energy, x, 86, 166, 171, 177, 178, 180, 235 solid oxide fuel cell, x, 211, 212, 236, 237 solid(s), viii, x, 3, 14, 53, 57, 59, 77, 90, 207, 211, 212, 213, 215, 218, 220, 227, 236, 237 space, 71, 77, 86, 103, 165, 167, 181, 209 spectrometer, 6, 29, 35 spectrometry, 28, 29, 48, 50, 51 subcooled, vii, 113, 114, 115, 116, 129, 135, 136, 137, 138, 163, 164 support, vii, ix, 53, 55, 57, 58, 59, 235

242 synthesis, 50, 57 systems, viii, ix, 50, 71, 72, 75, 76, 79, 80, 81, 82, 84, 85, 86, 114, 136, 137, 165, 166, 167, 168, 182, 183, 188, 207, 208, 212, 213, 221, 230, 234, 235

T thermal analysis, ix, 1, 2, 3, 4, 6, 15, 29, 48, 49, 50, 56, 61, 182, 208, 209, 212 thermal performance, 155, 156, 161, 185, 186, 188, 189, 198, 199, 204, 205, 208, 209 thermobalance, 54, 57 thermoelectric, vii, ix, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 76, 77, 80, 81, 82, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94, 95, 96, 97, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112 thermoelectric generators, 63, 64, 65, 71, 76, 77, 80, 81, 83, 84, 85, 86, 97, 105, 111 thermoelectricity, ix, 64, 72, 89, 93, 111

Index thermogravimetric (TG), vii, ix, 1, 2, 3, 4, 5, 6, 7, 8, 23, 27, 28, 29, 47, 48, 49, 50, 51, 53, 56, 57, 58, 59 thermogravimetric analysis (TGA), vii, ix, 1, 2, 10, 11, 12, 13, 15, 21, 26, 46, 47, 49, 50, 53, 54, 56, 57, 58, 59 thermogravimetry, 2, 5, 50, 61

V volume(s), 10, 12, 165, 171, 175, 178, 179, 181, 187, 207, 220

W waste heat, 64, 72, 73, 76, 82, 83, 84, 85, 181, 211, 212, 213, 230, 232, 233 waste(s), 2, 47, 48, 55, 64, 72, 73, 74, 76, 82, 83, 84, 85, 97, 181, 211, 212, 213, 230, 231, 232, 233, 237 water heating, 166, 168, 181, 182 water tank, 166, 168, 173, 179, 180

Editors’ Contact Information

Dr. Mamdouh El Haj Assad, PhD Professor Sustainable and Renewable Energy Engineering Department University of Sharjah United Arab Emirates [email protected].

Dr. Ali Khosravi Aalto University Espoo, Finland [email protected].

Dr. Mehran Hashemian Urmia University Urmia, Iran [email protected].