Computational fluid dynamics in food processing [Second edition] 9781138568310, 1138568317

Citation preview

Computational Fluid Dynamics in Food Processing Second Edition

Contemporary Food Engineering Series Editor

Professor Da-Wen Sun, Director Food Refrigeration & Computerized Food Technology National University of Ireland, Dublin (University College Dublin) Dublin, Ireland http://www.ucd.ie/sun/ Emerging Technologies for Food Quality and Food Safety Evaluation, edited by Yong-Jin Cho and Sukwon Kang Operations in Food Refrigeration, edited by Rodolfo H. Mascheroni Advances in Food Extrusion Technology, edited by Medeni Maskan and Aylin Altan Modified Atmosphere and Active Packaging Technologies, edited by Ioannis Arvanitoyannis Juice Processing: Quality, Safety and Value-Added Opportunities, edited by Victor Falguera and Albert Ibarz Physical Properties of Foods: Novel Measurement Techniques and Applications, edited by Ignacio Arana Fermentation Processes Engineering in the Food Industry, edited by Carlos Ricardo Soccol, Ashok Pandey, and Christian Larroche Engineering Aspects of Cereal and Cereal-Based Products, edited by Raquel de Pinho Ferreira Guine, and Paula Maria dos Reis Correia Enhancing Extraction Processes in the Food Industry, edited by Nikolai Lebovka, Eugene Vorobiev, and Farid Chemat Thermal Food Processing: New Technologies and Quality Issues, Second Edition, edited by Da-Wen Sun Advances in Fruit Processing Technologies, edited by Sueli Rodrigues and Fabiano Andre Narciso Fernandes Biosensors in Food Processing, Safety, and Quality Control, edited by Mehmet Mutlu Edible Oils: Extraction, Processing, and Applications, edited by Smain Chemat Engineering Aspects of Membrane Separation and Application in Food Processing, edited by Robert W. Field, Erika Bekassy-Molnar, Frank Lipnizki, and Gyula Vatai Engineering Aspects of Food Emulsification and Homogenization, edited by Marilyn Rayner and Petr Dejmek Advances in Meat Processing Technology, edited by Alaa El-Din A. Bekhit Engineering Aspects of Food Biotechnology, edited by Jose A. Teixeira and Antonio A. Vicente High Pressure Processing of Fruit and Vegetable Juices, edited by Milan Houška and Filipa Vinagre Marques da Silva Trends in Fish Processing Technologies, edited by Daniela Borda, Anca I. Nicolau, and Peter Raspor Food Biofortification Technologies, edited by Agnieszka Saeid Advances in Postharvest Fruit and Vegetable Technology, edited by Ron B.H. Wills and John Golding Computational Fluid Dynamics in Food Processing, Second Edition, edited by Da-Wen Sun For more information about this series, please visit: Contemporary-Food-Engineering/book-series/CRCCONFOOENG

https://www.crcpress.com/

Computational Fluid Dynamics in Food Processing Second Edition

Edited by

Da-Wen Sun

CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2019 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed on acid-free paper International Standard Book Number-13: 978-1-138-56831-0 (Hardback) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www​ .copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-7508400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com

Contents Series Preface.....................................................................................................................................ix Preface to the Second Edition............................................................................................................xi Editor............................................................................................................................................................xiii Contributors................................................................................................................................................. xv

Section I  CFD Applications in Cold Chain Facilities Chapter 1 CFD Aided Retail Cabinets Design..............................................................................3 Giovanni Cortella Chapter 2 CFD Optimization of Perturbed Air Curtains for Refrigerated Display Cabinets..... 23 Jean Moureh Chapter 3 CFD Modeling to Improve the Performance of Industrial Cooling of Large Beef Carcasses..................................................................................................................61 Mulugeta A. Delele, Kumsa D. Kuffi, Bart Nicolai, and Pieter Verboven Chapter 4 CFD Modeling of Heat and Mass Transfer in a Hydrofluidization System During Food Chilling and Freezing............................................................................ 87 Juan Manuel Peralta and Susana E. Zorrilla Chapter 5 Improving the Performance of a Partially Loaded Cold Store by CFD.....................105 Fumihiko Tanaka and Fumina Tanaka Chapter 6 CFD Investigation of Fresh Produce Cooling Processes and Effects of Package Stacking.......................................................................................................121 Umezuruike Linus Opara, Alemayehu Ambaw, and Tarl Berry Chapter 7 Optimization of Ventilation Ports of Packaging for Fresh Produce Using CFD...... 149 Hiroaki Kitazawa Chapter 8 Optimization of Horticultural Carton Vent Hole Design by CFD..............................169 Umezuruike Linus Opara, Tarl Berry, and Alemayehu Ambaw

v

vi

Contents

Section II  CFD Applications in Thermal Processing and Heat Exchangers Chapter 9 Three-Dimensional CFD Modeling of Continuous Industrial Baking Process........ 193 Weibiao Zhou and Nantawan Therdthai Chapter 10 Improving Bread-Baking Process Under Different Oven Load Conditions by CFD Modeling..................................................................................................... 225 N. Chhanwal, J. A. Moses, and C. Anandharamakrishnan Chapter 11 CFD Applications of Food Packaging Sterilization and Filling............................... 243 Giuseppe Vignali and Filippo Ferrari Chapter 12 CFD Analysis of Food Pasteurization Processes.........................................................261 Padma Ishwarya and C. Anandharamakrishnan Chapter 13 CFD Determination of F Values During Thermal Processing of Still Cans............ 289 Won Byong Yoon and Hyeon Woo Park Chapter 14 CFD Modeling of Thermal Processing of Particulate Foods.................................... 305 Massimiliano Rinaldi, Matteo Cordioli, and Davide Barbanti Chapter 15 CFD Modeling of Natural-Convection Heating Processes....................................... 319 Ferruh Erdogdu, Huseyin Topcam, Fabrizio Sarghini, and Francesco Marra Chapter 16 CFD Modeling of Convective Drying of Cylindrical Fruit Slices..............................339 Alexandros Vouros, Dimitrios Tzempelikos, Dimitrios Mitrakos, and Andronikos Filios Chapter 17 CFD Modeling of Convection Flow in Pan Cooking................................................ 365 Yvan Llave and Noboru Sakai Chapter 18 CFD Analysis of Thermal Processing of Intact Eggs................................................. 389 Behzad Abbasnezhad, Mohsen Dalvi-Isfahan, and Nasser Hamdami Chapter 19 Applications of CFD for Optimization of Cabinet Dryers........................................ 415 Yasaman Amanlou and Mohammad Hadi Khoshtaghaza

vii

Contents

Section III  CFD Applications in Other Food Processes Chapter 20 CFD Design and Optimization of Biosensors in the Food Industry..........................439 Agnese Piovesan, Jeroen Lammertyn, Bart Nicolai, and Pieter Verboven Chapter 21 Analysis and Simulation of Pasta Dough Extrusion Process by CFD....................... 463 Fabrizio Sarghini Chapter 22 Computational Modeling of Radio Frequency Thawing of Frozen Food Products..... 487 Francesco Marra, Tesfaye Faye Bedane, Oriana Casaburi, Ozan Altin, Rahmi Uyar, and Ferruh Erdogdu Chapter 23 CFD Application for the Evaluation of Food Texture...............................................509 Won Byong Yoon and Hwabin Jung Chapter 24 CFD Study of Top-Spray Fluidized Bed Coating Process........................................ 531 Wasan Duangkhamchan, Frederik Ronsse, and Jan G. Pieters Chapter 25 Operation of Biofilm Reactors for the Food Industry Using CFD............................ 561 Luciana C. Gomes, João Miranda, and Filipe J. Mergulhão Index............................................................................................................................................... 591

http://taylorandfrancis.com

Series Preface CONTEMPORARY FOOD ENGINEERING Food engineering is the multidisciplinary field of applied physical sciences combined with the knowledge of product properties. Food engineers provide the technological knowledge transfer essential to the cost-effective production and commercialization of food products and services. In particular, food engineers develop and design processes and equipment in order to convert raw agricultural materials and ingredients into safe, convenient, and nutritious consumer food products. However, food engineering topics are continuously undergoing changes to meet diverse consumer demands, and the subject is being rapidly developed to reflect market needs. In the development of food engineering, one of the many challenges is to employ modern tools and knowledge, such as computational materials science and nanotechnology, to develop new products and processes. Simultaneously, improving quality, safety, and security remain critical issues in food engineering study. New packaging materials and techniques are being developed to provide more protection to foods, and novel preservation technologies are emerging to enhance food security and defense. Additionally, process control and automation regularly appear among the top priorities identified in food engineering. Advanced monitoring and control systems are developed to facilitate automation and flexible food manufacturing. Furthermore, energy saving and minimization of environmental problems continue to be important food engineering issues, and significant progress is being made in waste management, efficient utilization of energy, and reduction of effluents and emissions in food production. Consisting of edited books, the Contemporary Food Engineering book series attempts to address some of the recent developments in food engineering. Advances in classical unit operations in engineering applied to food manufacturing are covered as well as such topics as progress in the transport and storage of liquid and solid foods; heating, chilling, and freezing of foods; mass transfer in foods; chemical and biochemical aspects of food engineering and the use of kinetic analysis; dehydration, thermal processing, nonthermal processing, extrusion, liquid food concentration, membrane processes and applications of membranes in food processing; shelf-life, electronic indicators in inventory management, and sustainable technologies in food processing; and packaging, cleaning, and sanitation. The books are aimed at professional food scientists, academics researching food engineering problems, and graduate level students. The editors of the books are leading engineers and scientists from many parts of the world. All the editors were asked to present their books in a manner that will address the market need and pinpoint the cutting-edge technologies in food engineering. Furthermore, all contributions are written by internationally renowned experts who have both academic and professional credentials. All authors have attempted to provide critical, comprehensive, and readily accessible information on the art and science of a relevant topic in each chapter, with reference lists to be used by readers for further information. Therefore, each book can serve as an essential reference source to students and researchers in universities and research institutions. Da-Wen Sun Series Editor

ix

http://taylorandfrancis.com

Preface to the Second Edition Computational Fluid Dynamics (CFD) uses applied mathematics, physics and computational software to provide quick and efficient simulation and visualization of fluid flow and heat transfer. CFD analysis aims to solve the governing equations describing fluid flow (i.e., the continuity equation and the set of Navier–Stokes equations) and any additional conservation equations, such as energy balance, in order to predict the profiles of velocity, temperature, pressure, and other parameters. As many processes in the food industry involve fluid flow and heat and mass transfer, CFD provides a powerful early-stage simulation tool for gaining a qualitative and quantitative assessment of the performance of food processing, allowing engineers to test concepts all the way through the development of a process or system. By experimenting and analyzing the significance and effects of various design parameters and working conditions on the computer, better understanding of the dynamics and the underlying physics of a food process or phenomenon can be achieved, leading to the optimization of existing and new processes and the overcoming of the need to test the design with each modification. Therefore, the food industry has used CFD widely in its continual quest for process and product improvement. As the first book in the area, the first edition of Computational Fluid Dynamics in Food Processing was published in 2007, with the main aims to present a comprehensive review of CFD applications for the food industry and pinpoint the research and development trends in the development of the technology, to provide the engineer and technologist working in research, development, and operations in the food industry with critical, comprehensive and readily accessible information on the art and science of CFD, and to serve as an essential reference source to undergraduate and postgraduate students and researchers in universities and research institutions. This will continue to be the purpose of this second edition. In the second edition, in order to reflect the most recent research and development trends in the technology, only a few original chapters are updated with latest developments. Therefore, this new edition mostly contains new chapters covering the analysis and optimization of cold chain facilities, simulation of thermal processing and modeling of heat exchangers, and CFD applications in other food processes.

xi

http://taylorandfrancis.com

Editor Born in Southern China, Professor Da-Wen Sun is a global authority in food engineering research and education. He is a Member of the Royal Irish Academy, the highest academic honour in Ireland; a Member of Academia Europaea (The Academy of Europe), one of the most prestigious academies in the world; a Foreign Member of the Polish Academy of Sciences, the highest lifetime honour bestowed by the Polish government; a Fellow of the International Academy of Food Science and Technology; a Fellow of the International Academy of Agricultural and Biosystems Engineering; and a Full Member (Academician) of the International Academy of Refrigeration. He is also the founder and Editor-in-Chief of Food and Bioprocess Technology, one of the most prestigious food science and technology journals; Series Editor of Contemporary Food Engineering book series with already over 50 volumes published; and the Founder and President of the International Academy of Agricultural and Biosystems Engineering (iAABE). In addition, he served as the President the International Commission of Agricultural and Biosystems Engineering (CIGR), the world largest organization in the field, in 2013–2014, and is now Honorary President of CIGR. He has significantly contributed to the field of food engineering as a researcher, as an academic authority and as an educator. His main research activities include cooling, drying and refrigeration processes and systems, quality and safety of food products, bioprocess simulation and optimization, and computer vision/ image processing and hyperspectral imaging technologies. Especially, his many scholarly works have become standard reference materials for researchers in the areas of hyperspectral imaging, computer vision, ultrasound assisted freezing, vacuum cooling, computational fluid dynamics modeling, etc. Results of his work have been published in over 900 papers including more than 500 peer-reviewed journal papers indexed by Web of Science, with an average citation of over 35 per paper (Web of Science h-index = 91, SCOPUS h-index = 94). Among them, 50 papers have been selected by Thomson Reuters’s Essential Science IndicatorsSM as Highly Cited/Hot Papers in Field, ranking him No. 2 in the world in Agricultural Sciences. He has also edited 17 authoritative books. In addition, Professor Sun has been named Highly Cited Researcher in the last three consecutive years (2015–2017) by Clarivate Analytics (formerly Thomson Reuters). He received a first class BSc Honours and MSc in Mechanical Engineering, and a PhD in Chemical Engineering in China before working in various universities in Europe. He became the first Chinese national to be permanently employed in an Irish University when he was appointed College Lecturer at National University of Ireland, Dublin (University College Dublin) in 1995, and was then continuously promoted in the shortest possible time to Associate Professor, Professor, and Full Professor. Dr. Sun is now the Full Professor of Food and Biosystems Engineering and Director of the Food Refrigeration and Computerised Food Technology Research Group at University College Dublin (UCD). As a leading educator in food engineering, Professor Sun has significantly contributed to the field of food engineering. He has trained many PhD students, who have made their own c­ ontributions to the industry and academia. He has also given lectures on advances in food engineering on a regular basis in academic institutions internationally and delivered keynote speeches at international conferences. In recognition of his significant contribution to Food Engineering worldwide and for his outstanding leadership in the field, the International Commission of Agricultural and Biosystems Engineering (CIGR) awarded him the “CIGR Merit Award” in 2000, in 2006, and again in 2016. The Institution of Mechanical Engineers (IMechE) based in the UK named him xiii

xiv

Editor

“Food  Engineer of the Year 2004.” In 2007 he was presented with the only “AFST(I) Fellow Award” in that year by the Association of Food Scientists and Technologists (India). In 2008 he was awarded “CIGR Recognition Award” in honour of his distinguished achievements as the top one percent of Agricultural Engineering scientists in the world. In 2010 he received the “CIGR Fellow Award”; the title of Fellow is the highest honour in CIGR, and is conferred to individuals who have made sustained, outstanding contributions worldwide. In March 2013, he was presented with the “You Bring Charm to the World Award” by Hong Kong-based Phoenix Satellite Television, with other award recipients including the 2012 Nobel Laureate in Literature and the Chinese Astronaut Team for Shenzhou IX Spaceship. In July 2013 he received “The Frozen Food Foundation Freezing Research Award” from the International Association for Food Protection (IAFP) for his significant contributions to enhancing the field of food freezing technologies, the first time that this prestigious award was presented to a scientist outside the USA. In June 2015 he was presented with the “IAEF Lifetime Achievement Award”, this IAEF (International Association of Engineering and Food) award highlights the lifetime contribution of a prominent engineer in the field of food, and in February 2018, he was conferred with the honorary doctorate degree by Universidad Privada del Norte in Peru.

Contributors Behzad Abbasnezhad Food Science and Technology Department College of Agriculture Isfahan University of Technology Isfahan, Iran Ozan Altin Department of Food Engineering Ankara University Ankara, Turkey Yasaman Amanlou Biosystems Engineering Department Tarbiat Modares University Tehran, Iran Alemayehu Ambaw Postharvest Technology Research Laboratory South African Research Chair in Postharvest Technology Stellenbosch University Stellenbosch, South Africa C. Anandharamakrishnan Director, Indian Institute of Food Processing Technology (IIFPT) Thanjavur, India Davide Barbanti Department of Food Science University of Parma Parma, Italy

Oriana Casaburi Department of Industrial Engineering University of Salerno Fisciano, Italy N. Chhanwal Food Engineering Department Institute of Chemical Technology Mumbai, India Matteo Cordioli Department of Food Science University of Parma Parma, Italy Giovanni Cortella Polytechnic Department of Engineering and Architecture University of Udine Udine, Italy Mohsen Dalvi-Isfahan Faculty of Agriculture Department of Food Science and Technology Jahrom University Jahrom, Iran Mulugeta A. Delele BIOSYST-MeBioS University of Leuven Heverlee, Belgium

Tesfaye Faye Bedane Department of Industrial Engineering University of Salerno Fisciano, Italy

Wasan Duangkhamchan Functional Foods, Department of Food Technology and Nutrition Faculty of Technology Mahasarakham University Maha Sarakham, Thailand

Tarl Berry Postharvest Technology Research Laboratory South African Research Chair in Postharvest Technology Stellenbosch University Stellenbosch, South Africa

Ferruh Erdogdu Department of Food Engineering Ankara University Ankara, Turkey

xv

xvi

Filippo Ferrari Department of Engineering and Architecture University of Parma Parma, Italy Andronikos Filios Department of Mechanical Engineering University of West Attica Athens, Greece Luciana C. Gomes LEPABE Department of Chemical Engineering Faculty of Engineering University of Porto Porto, Portugal Nasser Hamdami Food Science and Technology Department College of Agriculture Isfahan University of Technology Isfahan, Iran Padma Ishwarya Indian Institute of Food Processing Technology Thanjavur, India Hwabin Jung Department of Food Science and Biotechnology College of Agricultural and Life Science Kangwon National University Chuncheon, South Korea Mohammad Hadi Khoshtaghaza Biosystems Engineering Department Tarbiat Modares University Tehran, Iran Hiroaki Kitazawa Postharvest Science and Technology Unit Division of Food Processing and Distribution Research Food Research Institute National Agriculture and Food Research Organization (NARO) Tsukuba, Japan Kumsa D. Kuffi BIOSYST-MeBioS University of Leuven Heverlee, Belgium

Contributors

Jeroen Lammertyn Faculty of Bioscience Engineering Department of Biosystems Mechatronics-Biostatistics-Sensors Division Katholieke Universiteit Leuven Leuven, Belgium Yvan Llave Department of Agro–Food Science Niigata Agro–Food University Niigata, Japan Francesco Marra Dipartimento di Ingegneria Industriale Universita degli studi di Salerno Fisciano, Italy Filipe J. Mergulhão LEPABE Department of Chemical Engineering Faculty of Engineering University of Porto Porto, Portugal João Miranda CEFT Department of Chemical Engineering Faculty of Engineering University of Porto Porto, Portugal Dimitrios Mitrakos Greek Atomic Energy Commission Athens, Greece J. A. Moses Computational Modeling and Nanoscale Processing Unit Indian Institute of Food Processing Technology Thanjavur, India Jean Moureh Chargé de Recherche HDR/Researcher, Irstea Unité de Recherche Génie des Procédés Frigorifiques Antony, France

xvii

Contributors

Bart Nicolai Faculty of Bioscience Engineering Department of Biosystems Mechatronics-Biostatistics-Sensors Division Katholieke Universiteit Leuven Leuven, Belgium Umezuruike Linus Opara Postharvest Technology Research Laboratory South African Research Chair in Postharvest Technology Stellenbosch University Stellenbosch, South Africa Hyeon Woo Park Department of Food Science and Biotechnology College of Agricultural and Life Science Kangwon National University Chuncheon, South Korea Juan Manuel Peralta Instituto de Desarrollo Tecnológico para la Industria Química (INTEC) Universidad Nacional del Litoral – CONICET Santa Fe, Argentina Jan G. Pieters Department of Biosystems Engineering Faculty of Bioscience Engineering Ghent University Gent, Belgium Agnese Piovesan Faculty of Bioscience Engineering Department of Biosystems Mechatronics-Biostatistics-Sensors Division Katholieke Universiteit Leuven Leuven, Belgium Massimiliano Rinaldi Department of Food Science University of Parma Parma, Italy Frederik Ronsse Department of Biosystems Engineering Faculty of Bioscience Engineering Ghent University Gent, Belgium

Noboru Sakai Department of Food Science and Technology Tokyo University of Marine Science and Technology Tokyo, Japan Fabrizio Sarghini University of Naples Federico II Department of Agricultural Sciences Portici, Italy Fumihiko Tanaka Department of Bio-production Environmental Sciences Faculty of Agriculture Kyushu University Fukuoka, Japan Fumina Tanaka Department of Bio-production Environmental Sciences Faculty of Agriculture Kyushu University Fukuoka, Japan Nantawan Therdthai Department of Product Development Faculty of Agro-Industry Kasetsart University Bangkok, Thailand Huseyin Topcam Department of Food Engineering Ankara University Ankara, Turkey Dimitrios Tzempelikos Department of Mechanical Engineering University of West Attica Athens, Greece Rahmi Uyar Department of Food Engineering Siirt University Siirt, Turkey Pieter Verboven BIOSYST-MeBioS University of Leuven Heverlee, Belgium

xviii

Contributors

Giuseppe Vignali Department of Industrial Engineering University of Parma Parco Area delle Scienze Parma, Italy

Weibiao Zhou Food Science and Technology Programme Department of Chemistry National University of Singapore Singapore

Alexandros Vouros Department of Mechanical Engineering Educators School of Pedagogical and Technological Education (ASPETE) Athens, Greece

Susana E. Zorrilla Instituto de Desarrollo Tecnológico para la Industria Química (INTEC) Universidad Nacional del Litoral – CONICET Santa Fe, Argentina

Won Byong Yoon Department of Food Science and Biotechnology College of Agricultural and Life Science Kangwon National University Chuncheon, South Korea

Section I CFD Applications in Cold Chain Facilities

http://taylorandfrancis.com

1

CFD Aided Retail Cabinets Design Giovanni Cortella

CONTENTS 1.1 Introduction........................................................................................................................... 4 1.2 The Retail Cabinet.....................................................................................................................4 1.2.1 Classification..................................................................................................................4 1.2.1.1 Storage Temperature.................................................................................... 4 1.2.1.2 Geometry..................................................................................................................5 1.2.1.3 Refrigeration Equipment................................................................................. 6 1.2.1.4 Air Circulation................................................................................................ 7 1.2.1.5 Energy Consumption.................................................................................................. 7 1.2.2 Standardized Temperature Tests....................................................................................7 1.2.3 Air Curtains................................................................................................................... 9 1.3 Applications of CFD to Display Cabinets.......................................................................................10 1.3.1 Modeling Product Temperature Distribution.............................................................. 10 1.3.2 Modeling Airflow..................................................................................................................11 1.3.2.1 Air Curtains...................................................................................................... 12 1.3.2.2 Shelves.........................................................................................................................12 1.3.2.3 Evaporator and Rear Ducts...............................................................................13 1.3.3 Modeling the Influence of Air Humidity..................................................................... 13 1.3.4 Modeling Interactions with the Ambient Conditions.....................................................13 1.3.4.1 Radiation....................................................................................................... 13 1.3.4.2 Ambient Air Movement....................................................................................13 1.3.5 Glass Doors Fogging and Defogging.................................................................................14 1.3.6 Humidification............................................................................................................. 14 1.4 CFD Codes......................................................................................................................................... 15 1.4.1 Methodology................................................................................................................ 15 1.4.1.1 Preprocessing................................................................................................ 15 1.4.1.2 Solving....................................................................................................................16 1.4.1.3 Postprocessing.............................................................................................. 16 1.4.2 Turbulence Models................................................................................................................16 1.4.3 Mass Transfer.............................................................................................................. 16 1.4.4 Validation..................................................................................................................... 17 1.5 Conclusions.............................................................................................................................. 18 References......................................................................................................................................... 18

3

4

Computational Fluid Dynamics in Food Processing

1.1 INTRODUCTION In retail stores, refrigerated cabinets are used to display perishable food. For merchandizing purposes, the main function of such equipment is the effective display of products to make them visible and easily accessible to customers. At the same time, food should be maintained at the prescribed temperature and preserved from radiant heat. The safety and quality of perishable foodstuffs are strongly affected by inappropriate storage temperature and by uneven temperature fluctuations, which are regrettably encountered to a large extent in display cabinets [1–3]. For this reason, from the point of view of storage conditions, retail cabinets are considered to be one of the weakest links in the cold chain, and only the typical short residence time of food in such appliances reduces the risk of quality loss. It is therefore essential that the efficacy of retail cabinets in terms of food preservation is improved. The people who can play an important role in this improvement are the manufacturer, the person in charge of installation and maintenance, and the shop manager. The cabinet is certified by the manufacturer to comply with the testing standards currently in place for a specified climate class defined by ambient temperature and relative humidity. Actually, the performance of display cabinets in terms of food temperature is strongly affected by ambient conditions, particularly air velocity and direction, and radiative heat load [4–7]. For this reason, particular care is necessary for the installation, and furthermore, accurate maintenance and operation are essential to accomplish correct food storage conditions. The manufacturer is the only person who can take advantage of Computational Fluid Dynamics (CFD). Thus, the contents of this chapter will mainly focus on problems related to the design of retail cabinets, giving only some suggestions about installation and proper use.

1.2 THE RETAIL CABINET The main features of a retail cabinet can be summarized with the following statements: • Food should be displayed in the most efficient way to promote selling; • Correct food storage temperature should be ensured, with temperature fluctuations reduced as much as possible. The preservation and the display functions are contrasting requirements, because the best way to protect the product from temperature fluctuations is to protect it from the shop environment, thus keeping it out of sight of customers. Furthermore, the manufacturer must operate an optimization process aiming to fulfill another important requirement, which is low energy consumption. In fact, while retaining the preserving function, a better display function usually requires higher energy consumption. Low energy consumption is becoming increasingly important, and the manufacturer should make huge efforts to comply with all these requirements.

1.2.1 Classification Retail cabinets are classified according to various criteria [4–6,8]. Among them, the most important are the storage temperature and the cabinet geometry, which are the key factors for the choice of the most suitable unit. Another important classification can be made according to the kind of air circulation, which is crucial for certain food. Finally, a further classification can be made according to energy consumption. 1.2.1.1 Storage Temperature Retail cabinets are intended to host almost every kind of perishable food, from frozen food at −18°C to some kinds of fruit and pastry at +10°C. For this reason they are usually classified as “low temperature” cabinets in the case of storage and display of frozen food, and “medium temperature”

CFD Aided Retail Cabinets Design

5

cabinets in the case of storage and display of chilled food. A more detailed classification is defined in the testing standards currently in place and will be discussed in the section 3.II.A. 1.2.1.2 Geometry As regards geometry, retail cabinets can be [4]: • Closed (in the presence of doors or sliding covers/glasses) or open; • Vertical multideck (Figure 1.1), horizontal single deck (Figure 1.2) or horizontal serve-over counters; or • A combination of these (e.g., a horizontal open-top cabinet combined with a vertical multideck closed cabinet). Of course, the various geometries of cabinets are not suitable for all foods and temperatures. As an example, open cabinets are not suitable for frozen food, due to heat infiltration from the ambient;

FIGURE 1.1  Vertical, multi-deck display cabinet.

6

Computational Fluid Dynamics in Food Processing

FIGURE 1.2  Horizontal display cabinet.

if it is necessary to use open cabinets, then horizontal open-top cabinets are to be preferred, while vertical open cabinets are to be avoided. 1.2.1.3 Refrigeration Equipment Display cabinets are designed to maintain the correct storage temperature of food. Therefore, they are not capable of reducing the temperature of products if they are too warm when loaded [4,6]. However, the cabinets’ refrigeration equipment is forced to perform heavy duty because of the huge amount of heat due to air infiltration, radiative heat transfer and product manipulation by the customers. Depending on the refrigerating equipment, display cabinets can be classified as incorporated condensing units and remote condensing units. In the cabinets with incorporated condensing units, also named “stand alone,” the whole vapor compression refrigerating equipment is contained within the cabinet, which only needs a power supply connection and a drainage piping. In the remote condensing units the cabinet is connected to a refrigerating unit that usually supplies several cabinets, both at low and medium temperatures. The remote condensing units can be further distinguished depending on the refrigerating system as a compression-type refrigerating system or an indirect type-refrigerating system. In the cabinets of the first category only the expansion valve and the evaporator are contained in the cabinet, which is fed with liquid refrigerant from a centralized refrigerator. Because the compression-type refrigeration system is complex and affords limited flexibility under changes to supermarket layout, it is typically used only in medium to large size stores. However, this configuration is preferable because of its enhanced energy efficiency. The recent issue with halocarbon refrigerants is pushing interest toward employing systems of the second category, in which a secondary refrigerant circulating system is installed between a central refrigerating system (usually placed in an outbuilding) and the cabinets. This configuration reduces dramatically the amount of refrigerant circulated [9] and allows the use of toxic or flammable refrigerants with lower environmental impact (e.g., ammonia) at the expense of a more complicated circuitry [10]. This secondary refrigerant can be a single-phase mixture of water and antifreeze additives or a two-phase fluid like ice slurry or carbon dioxide. The reduction of the amount of refrigerant circulated is also pushed by the issue of environmental impact of refrigerants [11,12]. For this reason, new low-GWP (Greenhouse Warming Potential) are being adopted both in incorporated and remote condensing units, leading to the need for a re-design of the evaporators. In this case, CFD can be effectively employed in the design of such heat exchangers.

CFD Aided Retail Cabinets Design

7

1.2.1.4 Air Circulation A further classification can be made with reference to air circulation inside the cabinet. Cold air distribution can be ensured by forced or natural circulation, the choice depending mostly on the kind of foodstuff. As a general rule, forced air circulation is preferable because it is much more effective in transferring the refrigerating power, thus enabling the correct operation of almost every kind of display cabinet. Natural air convection should be preferred for the display of unwrapped sensitive food like meat, pastry and ice cream, where water loss coupled with heat transfer on the food surface can give rise to significant quality damage due to dehydration. It is mostly used on horizontal serve-over units, where air stratification helps reduce warm air infiltration inside the load volume. 1.2.1.5 Energy Consumption Supermarkets are intensive users of energy in all countries. Electricity consumption in large supermarkets represents a substantial share (about 4%) of the national electric energy use in the United States and in France. A large part of this consumption, varying from 50% to 70%, is due to air conditioning and refrigeration cases [13,14]. In the United States, typical supermarkets with approximately 3700 to 5600 m2 of sales area consume about 2 to 3 million kWh annually for total store energy use [15]. The national average electricity intensity (the annual electricity use divided by the size of the facility) of a grocery store in the United States is about 565 kWh m−2 per year [1,16], and 400 kWh m−2 per year for Europe [13]. These figures are a real challenge for energy savings, and the supermarket chains are spending a substantial proportion of money on the yearly energy consumption compared to the investment costs. For this reason the evaluation and certification of the energy consumption of display cabinets is becoming an essential step in the future development of such equipment. Legislation is considering this issue, and in many countries laws are in force for a compulsory energy labelling of display cabinets.

1.2.2 Standardized Temperature Tests Various testing standards for retail display cabinets are currently in place (e.g., the EN Standard 23953 [17,18] in Europe and the ASHRAE Standards 72 [19] in the United States). The objective of such standards is to specify “requirements for the construction, characteristics and performance of refrigerated display cabinets used in the sale and display of foodstuffs,…. to specify test conditions and methods for checking that the requirements have been satisfied, as well as classification of the cabinets, their marking and the list of their characteristics to be declared by the manufacturer” [18]. Apart from the requirements about construction, the main scope of these standards includes classifying retail cabinets as a function of their storage temperature and giving instructions for measuring their energy consumption. Specific conditions for the “temperature test” are thus defined in the standards. The cabinet is loaded with packages made of a specified composition of water, cellulose and additives. It is placed in a test room (Figure 1.3) where air temperature and humidity, air velocity and radiant heat are controlled. The temperature of a certain number of “measure packages” is recorded over a period of 24 hours after having reached steady state. Various temperature classes are identified, depending on the load temperature measured during such tests. As an example, the European standard identifies the temperature classes through the definition of the highest and lowest temperatures of the warmest and coldest packages, as reported in Table 1.1 [18]. The test room conditions are identified through the definition of the ambient psychrometric conditions (climate classes), as reported in Table 1.2 [18]. For all of them, air velocity and radiant heat are the same. In particular, air velocity shall lie between 0.1 and 0.2 m/s parallel to the plane of the cabinet display opening and to the longitudinal axis. Radiant heat shall be controlled by the definition of the wall temperature and emissivity, and the level of illumination.

8

Computational Fluid Dynamics in Food Processing

FIGURE 1.3  A display cabinet during a standardized temperature test.

TABLE 1.1 Temperature Classes According to the EN 23953 Standard Highest Temperature of the Warmest Package (°C)

Lowest Temperature of the Coldest Package (°C)

Lowest Temperature of the Warmest Package (°C)

–

−18

–

−18

L3

−15 −12 −12

–

−15

M0

+4

M1

+5

M2

+7

−1 −1 −1

H1

+10

+1

H2

+10

−1

− − − − −

Class L1 L2

S

Special classification

It should be noted that compliance of a retail cabinet with the standards does not mean that the correct storage temperature will be kept during normal operation in the retail store, even if the cabinet has been set up and situated in accordance with the recommendations of the manufacturer (“normal conditions of use”). This is mostly due to the dissimilar thermal properties of foodstuffs and test packages, and to some differences in ambient conditions (i.e., air velocity, air temperature, radiative heat load). The EN standard 23953-2 [18] highlights this argument in the Annex B “Comparison between laboratory and in-store conditions.” It states thus: “The complete range of various climate

9

CFD Aided Retail Cabinets Design

TABLE 1.2 Climate Classes According to the EN 23953 Standard Test Room Climate Class 0 1 2 3 4 5 6 7 8

Dry Bulb Temperature (°C)

Relative Humidity (%)

20 16 22 25 30 40 27 35 24

50 80 65 60 55 40 70 75 55

conditions and various ways of loading in stores cannot be simulated in the laboratory. For these reasons, specific climate classes and loading are defined for tests in the laboratory to classify cabinets and to make comparisons. For open refrigerated display cabinets, test results in laboratory cannot be directly transposed in stores.” For this reason it is crucial that the cabinet is installed and operated with awareness. For the same reason, designers can make great use of CFD because they can check different configurations, thereby saving the huge amount of time required for the standardized tests (at least a couple of days each), and they can predict the performance of the apparatus at operating conditions different from the standardized ones.

1.2.3 Air Curtains In an open cabinet, refrigerated air curtains are established at the cabinet opening when cooling of the load is achieved via forced air distribution. The reason for the choice of this position is the need to reduce heat transfer from the external environment by creating a barrier between the load volume and the external ambience. Heat transfer through the solid walls surrounding the load volume can be effectively cut by means of adequate insulating material. On the contrary, load is subject at the opening to both radiative and convective heat transfer from the ambient. Both cause heating of the food surface. Radiative heat transfer takes place between the load surface and the room walls, lights and all other objects surrounding the opening. It plays an important role, since emissivity of the food packaging and of the surrounding objects is usually high (in the range 0.8–0.9). It has been measured that the temperature of the exposed surface of frozen food can increase up to 5–10 K due to the absorption of radiant heat. Radiant heat can be reduced by using low emissivity materials for food packaging, high efficiency (low temperature) lights in the environment, and shielding coatings on the glass door surfaces, if any [20]. Convective heat transfer is due to the temperature difference between the load volume and the environment. Air movement caused by natural convection unavoidably causes infiltration of warm air through the opening, which is enhanced in the presence of even slight air movements in the room. The air curtain is capable of effectively restraining the convective heat transfer and the warm air infiltration, in the meantime reducing the surface heating due to radiation. In the case of open cabinets, more than one air curtains are used, the temperature of the external air curtain being higher than that of the internal one for the sake of a better flow stability. Air from the curtains is then extracted through a grille and forced by fans through a finned cooling coil where heat is removed. The surface temperature of the cooling coil is usually below the dew point

10

Computational Fluid Dynamics in Food Processing

temperature of air; thus water condensation takes place. In the frequent case of surface temperature of the coil below 0°C, frost formation takes place, which requires cyclical coil defrosting operations. Finally, refrigerated air is supplied to a plenum and then through a honeycomb to the supply grille, thus creating the air curtain or curtains. In the case of closed cabinets, usually only one air curtain is established, which flows close to the internal surface of the door. When the door is open, the air curtain helps prevent warm air infiltration. When the door is closed, the air curtain extracts heat from the load volume and particularly from the food surface, which is still subject to radiant heat. Air curtains will be discussed more in detail in the section 3.III.B.1 and in Chapter 2.

1.3 APPLICATIONS OF CFD TO DISPLAY CABINETS CFD is a successful tool for the designer of display cabinets, who can take advantage of this tool to improve load temperature distribution, predict the flow pattern of air and its efficacy, reduce warm air entrainment and improve product refrigeration [21]. As previously mentioned, the main concern arises from the necessity to ensure an effective display, while preserving the optimal storage conditions and achieving the lowest energy consumption. The manufacturer must face this challenge and find the solution that best fits such requirements. Air movement inside the cabinet plays the key role in this challenge, essentially because it is in charge of product refrigeration. Thorough comprehension of the phenomena associated with airflows in display cabinets is itself a difficult task, due to the various interdependent factors that act simultaneously. Often a trial and error process has to be established, requiring numerous experimental tests that entail spending a huge amount of time and money. Numerical modeling performed by a skilled person can be a viable alternative, once its reliability has been validated against experimental data. Sensitivity analyses can be easily executed, efforts can be directed to optimize the most critical components, and improvements in the performance of the whole cabinet can be achieved in a much shorter time than through experimental testing. Furthermore, the performance of the cabinet at different ambient conditions (e.g., temperature, humidity, air velocity) or operating conditions (e.g., load arrangement) can be predicted with sufficient accuracy, thus leading to a better awareness of the possible performance of the unit in the actual conditions at the retail store. In the following, the most important applications of CFD to retail cabinets are briefly described and the possible advantages of numerical modeling are discussed.

1.3.1 Modeling Product Temperature Distribution Product temperature inside a display cabinet suffers from an uneven distribution, both from left to right and from back to front of the shelves. Temperature differences up to about 5 K for chilled food and about 10 K for frozen food can be encountered, which can be unacceptable. The difference from the left to the right side is often due to uneven air distribution, and will be discussed later on. The main reasons for the difference from back to front are the proximity of the cooling coil to the back/bottom of the load volume and the effect of radiant heat on the front surface. Radiant heat can account for up to 12% [22] of the total load, and therefore cannot be neglected. Furthermore, as radiation is concentrated on the surface, it leads to a significant local temperature increase. Experimental tests [23] showed a reduction of up to 10 K of the surface temperature of the upper layer of products in a horizontal frozen food cabinet thanks to the application of a low emissivity shield. This is because food packaging has an average emissivity of about 0.9, which is also the value required by the EN standard for the test packages. The main problem when simulating the product temperature distribution resides in the necessity to adopt a transient state model. In fact, heat exchanges through radiation and with the cooling coil are both time-dependent phenomena, linked to the shop opening time, to the presence of covers or night curtains, to the on-off cycling of the refrigerating equipment and to the defrosting operations.

CFD Aided Retail Cabinets Design

11

FIGURE 1.4  Temperature of the warmest and of the coldest packages during a temperature test.

Figure 1.4 reports as an example the temperature of the warmest and the coldest test packages measured at different locations in a frozen food cabinet. In addition to the influence of the location, temperature fluctuation due to the defrosting operations is also clearly visible. The defrosting operations can be performed by heating the coil or simply by switching off the refrigerating equipment. The missed refrigerating power leads to a step increase in food temperature, which requires a few hours to completely recover. For this reason, modeling the product temperature distribution inside a cabinet should be performed via a transient state simulation adopting a reliable model of radiation. In this case, it is not convenient to model concurrently the airflow pattern in the air curtains, because of the great disparity between the time constants of the two phenomena. A satisfactory transient model of the airflow should require a time step of a few hundredths of a second, whereas for the food temperature a few minutes could be enough. When modeling the load temperature distribution, the air curtain could be simulated as a convective boundary condition with an average convective coefficient evaluated by means of previous simulations or through classical correlations. In this case, the CFD model becomes a much simpler coupled conduction-convection model that can also be easily solved with in-house codes [23,24].

1.3.2 Modeling Airflow From the point of view of the designer, the effective simulation of the airflow pattern inside the whole display cabinet is the most interesting result. However, there are too many factors regarding the geometry of the cabinet, the operating conditions of the cabinet, and the ambient conditions thatinteract and influence the performance of the unit. This would require a very complex model with an almost unpredictable accuracy that probably could not fit the actual operating conditions well [25]. A solitary paper is present in the literature with a simulation of a whole vertical open chilled cabinet in 3D, with the purpose of obtaining steady-state temperature distribution in the product [26]. The whole cabinet, including the load, the air curtains, the air ducts and a portion of the ambient, is included in the domain, and the authors claim reasonable agreement with the load temperature distribution obtained from spot thermocouple measurements and infrared camera images. It is much more effective to split the whole flow course into a few sections and set up simplified models where some variables can be disregarded, after verification by means of a sensitivity analysis. With such models it will become almost impossible to closely reproduce the operation of the whole cabinet; however, they will be much more effective for a quick comparison of various configurations [25,27–29]. The most widely used simplified models relate to the air curtain, the air distribution between two shelves, the airflow at the evaporator and the airflow in the rear ducts. In all of these, load surface

12

Computational Fluid Dynamics in Food Processing

can be considered as an adiabatic surface at the storage temperature. The effect of radiation on the load surface can be considered through a suitable increase in the food surface temperature. Usually simulations are performed for a cabinet fully loaded, because this operating condition is required for the standard test and is the most common in supermarkets. 1.3.2.1 Air Curtains The function of the air curtain has already been introduced, and will be further detailed in Chapters 4 and 5. It is indeed the most investigated part of the display cabinet, because of its crucial influence in the performance of the unit, in terms of both product temperature and energy consumption. This is mostly due to the warm air infiltration, which accounts for 60% to 75% of the total refrigeration load [4,30]. In fact, as soon as the air curtain leaves the air discharge, entrainment of warm air takes place due to the increase in the width of the curtain. Because of the necessity to respect the mass balance, a portion of the flow rate will be lost at the air return and will overspill at the bottom of the cabinet, thus causing the so-called “cold feet effect.” The induction factor α is defined for a single air curtain as the ratio of the mass flow rate of ambient air entrained to the total mass flow rate at the return grille [4,29].

α=

−t t m ambient ≅ return discharge (1.1)  mreturn tambient − tdischarge

It can be computed also in the case of multiple air curtains, through the calculation of the average values of air temperature weighed with the respective mass flow rates and of back panel flow [31]. The induction factor is commonly considered for the evaluation of the effectiveness of the air curtain, especially because the variables required for its calculation are easily measurable. It has been found to depend upon several factors, among which the most important are the initial turbulence intensity, the Reynolds number and the velocity profile at the air discharge [32]. Early simulations of the air curtains were performed using in-house codes in 2D domains. As an example, Cortella [33] utilized a finite element code based on the streamfunction-vorticity formulation, with a turbulence model similar to an LES procedure. Transient simulations were performed in a 20,000 grid points domain of a vertical open cabinet for chilled food. The induction factor and the refrigerating power were found to be in good agreement with experimental values, and some suggestions could be given to enhance curtain stability. Ge and Tassou [34] also used an in-house code based on finite differences, which took into account the moisture content in the air curtain. The authors derived from this model some correlations for the estimation of the heat flow rate and of the return air temperature at various conditions. The employment of commercial codes made simulations much easier, because the main problems of computational efficiency and user friendliness of in-house codes were overcome. In the last decade many authors published 2D simulations of air curtains in horizontal and vertical cabinets, with the aim of predicting the air flow pattern and evaluating the curtain efficacy at various conditions [29,35–41,42], including the airflow from the back panel [43]. A 3D simulation of air curtains has been developed by D’Agaro et al. [29] and will be discussed more in detail in 3.3.4. In all the studies mentioned here, CFD has proven to be a successful tool for the optimization of the air curtain. 1.3.2.2 Shelves In open vertical cabinets, air curtains are deeply influenced by the shape, length and loading of shelves. In regard to loading, the best air curtain efficacy is encountered when the cabinet is fully loaded, which is the standard test and design condition and the most common condition in

CFD Aided Retail Cabinets Design

13

retail stores. In regard to geometry, at the design stage a lot of experimental tests or CFD simulations are required to minimize air curtain disruption at the front of the shelves [44]. Some interest is also raised from the employment of air guiding strips (airfoils) at the edge of the shelves to guide the air curtain and reduce the disruption effect [45]. They showed to be effective to a large extent with some geometries and are worth further investigation through CFD simulations. 1.3.2.3 Evaporator and Rear Ducts Uneven distribution of air at the evaporator ducts is crucial because it could lead to an uneven air curtain velocity at the air discharge, thus causing differences in product temperature from left to right in the load volume. Foster et al. [44] investigated the flow of air as it exited the evaporator and entered the rear duct. The effects of a dead space were identified and modifications were suggested in order to reduce the formation of vortices and to improve air distribution in the back plenum. Similar simulations can be performed on different geometries of cabinets, and not only the shape of the rear ducts but also the position of the evaporator and of the fans can be investigated [46–51]. More details are given in Chapter 4.

1.3.3 Modeling the Influence of Air Humidity Commercial codes give the user the opportunity to include moisture content in the air flow models, in order to investigate both heat and mass entrainment in the cabinet. Some authors did use this feature when performing their simulations [26,34,35]. Actually, presence of humidity is crucial for the cabinet performance, because humidity entrainment leads to performance detriment due to evaporator frosting. However, the increase in computer power requirements due to the inclusion of moisture content in the CFD model can be avoided by estimating the latent heat from a mass balance on the water vapor content of the air curtain, once the induction factor and the humidity ratio of the ambient air are known, and assuming that air is saturated at the evaporator outlet. More details about the numerical methodology are given in Section 3.4.3.

1.3.4 Modeling Interactions with the Ambient Conditions Display cabinets operation, especially for open cabinets, is crucially influenced by ambient conditions [52]. Radiant heat, ambient air velocity and direction are the most important variables that must be considered when designing such units. 1.3.4.1 Radiation In the previous section the effect of radiant heat has been described, and some suggestions have been given on how to reduce radiant heat gain on the load surface. In regard to simulations, it has been clarified that radiation has to be accounted for only when simulations of the load temperature distributions are being performed, whereas it is unnecessary for the evaluation of airflow patterns when load surface can be considered as a constant temperature surface. 1.3.4.2 Ambient Air Movement Air velocity in the ambient environment and its direction are also crucial for the performance of the cabinet, and for this reason standard tests prescribe both of them. Furthermore, air flow visualizations performed on the air curtains during cabinet testing showed that 3D effects take place and can be significant, even with still air in the ambient. For these reasons, we realize that it is necessary to investigate more thoroughly the 3D effects in the air curtains. Typically almost all papers in the literature describe 2D simulations, for the sake of CPU time and memory requirement reduction, assuming that simulations are performed on the median section and that end effects can

14

Computational Fluid Dynamics in Food Processing

be negligible. In fact, especially for short length cabinets, end effects can be significant, and lead to uneven air curtain velocity and food temperature distribution. D’Agaro et al. [29] performed 3D simulations on a 2.44 m long vertical cabinet for frozen food and investigated the effect of longitudinal air movement. The authors report that 3D flow structures that may originate from slow air movements in the ambient are responsible for 20% decay in the performance of the unit between a 2 m and a 1 m long cabinet, thus underlining the importance of 3D simulations in the design of short to medium cabinets. Another important interaction between the cabinet and the ambient is the accumulation of cold air that overspills the return air grille and accumulates on the floor in front of the unit. This situation is named “cold feet effect” because of the unpleasant sensation on the customer who walks close to vertical open cabinets. Some authors [53] tried to simulate the whole sales area of a store, but the model was too complex and time-consuming. For this reason they moved to a simplified model of a chilled aisle, simulated on the three symmetry planes, and investigated different ventilation and heating strategies. More details on the topic are reported in Chapter 4.

1.3.5 Glass Doors Fogging and Defogging On closed display cabinets with doors, mist deposition occurs on the internal side of the door each time it is open, especially for frozen food cabinets. In the case of transparent doors, a quick defogging must be achieved to recover product visibility through the glass. For this purpose, an air curtain is established flowing along the internal glass surface, and an electric heater is sometimes embedded in the multiglazed door. Demisting time can be estimated through the application of CFD. D’Agaro et al. [54] coupled a CFD commercial code with an in-house code for the evaluation of the air flow pattern and of the water layer evolution, respectively. More details on the numerical procedure are given in Section 3.4.3. The computation enables the prediction of the water layer height during condensation when the door is open and during evaporation in the presence of electrical heaters. Various parameters both of the refrigerated cabinet (e.g., geometry, air curtain velocity and temperature) and of the glass door (e.g., geometry, global heat transfer coefficient, and presence of electrical heaters) can be considered. The model also takes into account condensation as a thin film or a collection of water droplets. Results showed the model to be reliable for the evaluation of the entity of defogging time reduction that might be expected with different solutions. Mist formation can also occur at the external side of the glass door at high relative humidity ambient conditions. Usually electrical heaters are employed to limit the occurrence by increasing the glass surface temperature. More recently some investigations considered the chance to take advantage of the air conditioning supply flow to heat up the glass without electrical heaters.

1.3.6 Humidification Unwrapped food products like fruits and vegetables are subject to dehydration when displayed in open cabinets. This is due to air dehumidification that takes place on the cooling coil surface, especially when forced convection cabinets are employed. The importance of relative humidity on the shelf life of products is well known, and all efforts are made to limit quality decay and weight loss when possible. In display cabinets, air dehumidification can be limited by choosing appropriate air velocity and temperature at the design stage; however, the solution is not fully satisfactory. Another approach is derived from the air conditioning plants, and from some vegetable refrigerated storage rooms, where air humidification is sometimes exploited through water spray. This technique has the disadvantage of possible bacteria growth, and therefore requires strict control from the microbiological point of view. Tests have been performed on humidification equipment that uses water mist sprayed over the products’ surface above each shelf and the well [55]. Results were encouraging, since weight loss was reduced at the expense of a slightly higher refrigeration load requirement.

CFD Aided Retail Cabinets Design

15

This device is already commercially available and supplied upon request by display cabinet manufacturers; however, it has not yet been thoroughly investigated. Commercial codes are available to treat heat and mass transfer, and some research has been performed in the similar field of weight loss during blast chilling [56]. Thus in the near future some research work will be probably devoted to this interesting topic.

1.4 CFD CODES Computational Fluid Dynamics (CFD) is based on the solution of the governing flow (i.e., the continuity and the Navier–Stokes) equations of the energy conservation equations, and sometimes on the conservation of other factors (e.g., water moisture). It has become popular only recently, when the availability of more powerful and affordable computers made it possible to investigate practical problems that were previously too computationally expensive. When applied to display cabinets, CFD can model fluid flow, conductive, convective and radiative heat transfer, and moisture transfer. In addition to numerous in-house codes, there are a number of commercial codes that can now cope with a high level of complexity. However, most of them are general purpose software designed for use in many different research fields. Therefore, sometimes robustness is enhanced to the detriment of accuracy, which still needs to be improved [57].

1.4.1 Methodology Every CFD simulation can be split into three consecutive phases: preprocessing, solving, postprocessing [57]. 1.4.1.1 Preprocessing Preprocessing starts with the choice of the computational domain to be simulated, includes the mesh generation and the definition of material properties, and ends with the application of boundary conditions. It is a crucial phase for obtaining reliable results. The users must be fully aware of the physics of the problem, because in this phase they set up the model of their practical problem. The choice of the domain to be investigated needs to be carefully considered in order to include all possible effects on the object of investigation. As an example, CFD simulation of an open display cabinet requires a portion of the external ambient to be included in the computational domain, in order to evaluate correctly the warm air entrainment and the cold air overspill. Two dimensional or three dimensional domains can be considered for display cabinets. Until now, almost all the simulations of air curtains have been performed in 2D, because of the necessity to reduce the computational load. However, D’Agaro et al. [29] have shown that in short-length cabinets the end effects cannot be disregarded, thus demonstrating that in certain cases 3D simulations could be necessary. For the simulation of air ducts (e.g., rear ducts, evaporator, and fans) 3D simulations are usually indispensable, because of their complicated geometry. The dimension of the elements in the grid influences the level of accuracy of the solution. Usually the dimension must be reduced in the portions of domain where an accurate solution is required (e.g., in the presence of turbulence or of high velocity gradients) or close to solid boundaries, where the requirements of the turbulence model must be satisfied. Of course the computational time increases with the number of elements in the domain, thus suggesting the limiting of grid refinements to those areas where it is strictly necessary. For an accurate simulation, it should be necessary to check that the solution is not “grid dependent” (i.e., it does not depend on the dimension of the elements). Otherwise, mesh refinements are still required. Once all the properties of the various solid and fluid substances have been identified, the boundary conditions must be defined. This is another important step in the simulation, theeffect of which on the solution can be significant. Usually it is necessary to introduce assumptions at this step,

16

Computational Fluid Dynamics in Food Processing

because the available boundary conditions rarely match the actual conditions. In many cases, different boundary conditions must be checked, the results compared and a sensitivity analysis performed for the identification of the best conditions. More specific information about different boundary conditions used to simulate display cabinets is reported in Chapter 4. 1.4.1.2 Solving The solution of the governing equations requires their discretization and an iterative process to obtain an approximation of the value of each variable at specific points in the domain. Calculation is stopped when the residuals in the calculation of the balance of one or more properties are below a specified value, and the solution is said to converge. Reaching convergence is not trivial, and the choice of the threshold value of residuals is not easy. Some suggestions are given in Chapter 4. Another main concern about solving in CFD simulation is the choice between steady-state or transient calculations. The choice depends on the phenomena to be investigated, and some suggestions have been given in the previous sections depending on the object of the simulation. In general, transient simulations should be performed only in the case where the time evolution of a phenomenon is under investigation, because convergence must be reached at each time step and therefore they are much more time-consuming. 1.4.1.3 Postprocessing When the solution reaches convergence, a distribution of the values of all the variables throughout the whole domain is produced. Such values must be processed to obtain visualizations and some require numerical results (e.g., the induction factor, the refrigerating power, etc.). The postprocessing phase is thus essential for the evaluation of the simulation results and an important tool for their most thorough understanding. In fact, the postprocessor also performs calculations and balances, thus giving further precious information.

1.4.2 Turbulence Models Turbulence models must be adopted to take into account the turbulence effects, which cannot be evaluated through a direct simulation. In fact, direct simulation of turbulence in large domains as those used for display cabinets would require a really huge amount of memory and CPU time. There are many turbulence models available, and unfortunately the choice of the model significantly affects the results. Literature can be helpful in this respect, but experience is fundamental. The basic turbulence models are the so-called “two equations models,” which are the default choice for many commercial codes. Among these, the k-ε and the RNG k-ε models are the most widely used. Although easy to implement, they require the previous evaluation of the turbulence kinetic energy and dissipation rate, which is a matter of difficult measurements or experience. Furthermore, they are not considered as the best choice because of the poor accuracy sometimes encountered. Other models are those based on the Reynolds stresses and the Large Eddy Simulation (LES). The former was found to be accurate [48] even if it required a quite fine mesh. The latter was successfully used by Cortella et al. [33] in the framework of a streamfunction-vorticity in-house code. Some more suggestions, particularly on the initial turbulence intensity, will be given in Chapter 4, while a deeper discussion of turbulence models is left to specific literature.

1.4.3 Mass Transfer It has already been pointed out in Section 3.3.3 that the moisture content of the air is a critical factor influencing the performance of display cabinets, because humidity entrainment involves an additional latent heat that shall be removed at the cooling coil. Furthermore, also in the case of chilled

CFD Aided Retail Cabinets Design

17

cabinet, the surface temperature of the cooling coil is often below 0°C, thus leading to frost formation and the need for cyclical defrosting operations. The evaluation of the latent heat does not strictly require a coupled heat and mass transfer simulation. The induction factor can be once again considered from the evaluation of the water mass balance in the air curtain

α=

− xdischarge x m ambient ≅ return (1.2)  mreturn x ambient − x discharge

where x is the humidity ratio (kgvap/kgdry air). The ambient humidity ratio is known, while the discharge humidity ratio can be easily estimated by assuming saturation for the discharge air [2,29]. On the contrary, there are some particular cases where coupled heat and mass transfer must be simulated, as in the simulation of door fogging and defogging in closed display cabinets. This topic has already been introduced in Section 3.3.5. In the following, more details are given on the numerical procedure, which involves coupling of two different codes for the dry heat and flow and for the mass transfer [54]. The problem is split into two phases, the first regarding the dew deposition on the internal face of the glass when the door is open, and the second regarding the defogging operation once the door is closed. In regard to the heat transfer, the evaluation of the local heat transfer coefficient for the air flow on the internal face of the glass is performed with a single phase solver. In fact, the phase change during evaporation is limited to a thin layer on the solid surface, and therefore it is accounted for through proper boundary conditions. Conductive heat transfer through the multiglazed glass can be solved by means of a steady state network of thermal resistances, which can also take into account radiation in the air cavities, thus leading to a very simple conduction problem easily solvable with simple in-house codes. Finally, the external heat transfer coefficient can be effectively estimated by means of the classical empirical correlations for steady state natural convection on a vertical plate. The different domains and solvers are coupled through an exchange of boundary conditions, thus leading to a more flexible algorithm. In regard to the mass transfer, an in-house code was used, where the latent heat contribution due to condensation or evaporation appeared as a heat source or sink, respectively, placed at the interface between the solid and the fluid domain. Thermal and mass balances can be established at the interface and solved taking advantage of the heat and mass transfer analogy. A detailed description of this procedure is given in [54]. It is interesting to note that in this model the water layer can be considered as a continuous film or as a number of droplets, the geometry of which changes during the condensation and evaporation processes. Furthermore, the effect of electric heaters can be accounted for in order to speed up the demisting process. The simulation showed to be reliable when compared to experimental tests, especially using the droplet model.

1.4.4 Validation It is common opinion that CFD simulations must be validated, and this is especially true in the case of display cabinets, where the simulation of such a complex problem requires a number of assumptions to set up the model. Usually validation is performed against experimental tests in controlled conditions, like those in accordance with the standards in force. The variables that can be compared are essentially load temperature, air temperature and air velocity [59]. Measurements of load temperature can be easily performed, and the effect of radiative heat transfer can be highlighted by means of infrared thermal imaging systems. Measurements of air temperature can be easily performed at the discharge and return grille, although it is quite complicated to measure air temperature along the air curtain. Infrared systems

18

Computational Fluid Dynamics in Food Processing

cannot visualize air temperature, because it is transparent under infrared radiation. Some images taken with infrared cameras and able to show air temperature are actually infrared visualizations of the cabinet end wall temperature. Accurate measurements of air velocity are difficult, especially along the air curtain. At the discharge and return grille, the use of hot wire anemometers allows for a sufficiently accurate evaluation of the velocity distribution, even if important information about direction and turbulence is lost. Anemometers placed along the air curtain are susceptible to disturbing the airflow pattern, thus providing an incorrect evaluation. Axell [60] reported a strong influence of the distance and shape of the sensors, and claimed to have measured values in “good qualitative agreement” with the numerical results. Much more reliable results can be obtained using the Particle Image Velocimetry (PIV), which is a very accurate method for flow pattern measurements. Air has to be seeded, the field of investigation is lighted with a laser sheet and a number of subsequent images are taken by a digital video camera placed perpendicular to the laser plane. Processing of the images allows for the identification of the movement of each seeding particle, thus leading to the complete flow pattern recognition. Rather than for CFD validation, this is a valuable tool for the adoption of the best CFD boundary conditions, especially at the discharge air (air velocity and direction, turbulence intensity), which are crucial to obtain reliable results.

1.5 CONCLUSIONS Retail display cabinet design can take great advantage of CFD, in terms of both time and money savings. It is rather difficult to replicate experimental results, due to flow complexity and to difficulties in reproducing the actual ambient conditions. However, CFD is very effective for sensitivity analyses, and can be very helpful to compare the performance at different operating conditions and find the optimal design of the unit. In the near future CFD will surely grow in popularity, and probably it will be much easier to perform even complicated simulations, due to the increasing computational power. 3D simulations will be more affordable, and larger computational domains will permit a more thorough evaluation of the influence of ambient air, as an example. Nevertheless, a lot of critical assumptions or choices must be made to perform a CFD simulation, and the outcomes will always depend on the judgment of the operator. Furthermore, commercial codes tend to improve robustness at the expense of accuracy every time convergence is difficult, thus leading to incorrect results. For these reasons CFD must be always operated by skilled people, the results accurately assessed and, whenever possible, boundary conditions and results of some reference cases should be validated by comparison with experimental tests.

REFERENCES 1. Spiess W.E.L., Boehme T., Wolf W., Quality changes during distribution of deep-frozen and chilled foods: Distribution chain situation and modeling considerations, In: Food Storage Stability, Taub I.A. and Singh R.P., Eds, CRC Press, Boca Raton, FL, USA, 399–417, 1997. 2. Morelli E., Noel V., Rosset P., Poumeyrol G., Performance and conditions of use of refrigerated display cabinets among producer/vendors of foodstuffs, Food Control, 26: 363–368, 2012. 3. Sergelidis D., Abrahim A., Sarimvei A., Panoulis C., Karaioannoglou P., Genigeorgis C., Temperature distribution and prevalence of Listeria spp. in domestic, retail and industrial refrigerators in Greece, International Journal of Food Microbiology, 34(2): 171–177, 1997. 4. Rigot G., Meubles et Vitrines Frigorifiques, Pyc Edition, Paris, 1990. 5. Gac A., Gautherin W., Le Froid dans les Magasins de Vente de Denreés Périssables, Pyc Edition, Paris, France, 1987. 6. American Society of Heating, Refrigerating and Air Conditioning Engineers, Handbook 2006 Refrigeration, ch. 46, Retail Food Store Refrigeration and Equipment, ASHRAE, Atlanta, 2006.

CFD Aided Retail Cabinets Design

19

7. Billiard F., Gautherin W., Heat Balance of an open type freezer food display cabinet, In: Proceedings of the International Conference “Cold Chain Refrigeration Equipment by Design,” International Institute of Refrigeration Comm. B1, B2, D1, D2/3, Palmerston North, New Zealand, 322–332, 1993. 8. IIR-International Institute of Refrigeration, Recommendations for the Processing and Handling of Frozen Foods, IIR/IIF Paris, 1986. 9. Sharma V., Fricke B., Bansal P., Supermarket refrigeration system charge reduction using cascade systems, In: Proceedings of the 11th IIR Gustav Lorentzen Conference on Natural Refrigerants: Natural Refrigerants and Environmental Protection, GL 2014, pp. 956–962, 2014. 10. Sawalha S., Perales Cabrejas C., Likitthammanit M., Rogstam J., Nilsson P.O., Experimental investigation of NH3/CO2 cascade system and comparison with R-404A system for supermarket refrigeration, In: Proceedings of the 22nd International Congress of Refrigeration, IIR–IIF, Beijing, 2007. 11. Gullo P., Elmegaard B., Cortella G., Energy and environmental performance assessment of R744 booster supermarket refrigeration systems operating in warm climates, International Journal of Refrigeration, 64: 61–79, 2016. 12. Gullo P., Cortella G., Theoretical evaluation of supermarket refrigeration systems using R1234ze(E) as an alternative to high-GWP refrigerants, Science and Technology for the Built Environment, 22(8): 1145–1155, 2016. 13. Orphelin M., Marchio D., Computer aided energy use estimation in supermarkets, In: Proceedings of the Building Simulation Conference, Prague, Czech Republic, 1997. 14. Arias J., Energy Usage in Supermarkets—Modelling and Field Measurements, Division of Applied Thermodynamics and Refrigeration, Department of Energy Technology, Royal Institute of Technology PhD thesis, 2005. 15. Baxter V., Advanced Supermarket Refrigeration/Heat Recovery Systems, Vol. 2, Country Reports, I.H.P. Programme, Oak Ridge, USA, 2003. 16. Anon., Energy Star, Putting Energy into Profits, Guide for Small Business, Washington, D.C., 2003. 17. European Standard EN ISO 23953–1:2015 Refrigerated display cabinets; Part 1: Vocabulary. 18. European Standard EN ISO 23953–2:2015 Refrigerated display cabinets; Part 2: Classification, requirements and test conditions. 19. ASHRAE Standard 72–2014—Method of Testing Open and Closed Commercial Refrigerators and Freezers. 20. Faramarzi R.T., Woodworth-Szieper M.L., Effects of low-emissivity shields on the performance and power use of refrigerated display case, ASHRAE Transactions, 105(1): 533–540, 1999. 21. Smale N.J., Moureh J., Cortella G., A review of numerical models of airflow in refrigerated food applications, International Journal of Refrigeration, 29: 911–930, 2006. 22. Faramarzi R.T., Efficient display case refrigeration, ASHRAE Journal, 41: 46–54, 1999. 23. Bobbo S., Cortella G., Manzan M., The temperature of frozen food in open display freezer cabinets: Simulation and testing, In: Proceedings of the 19th International Congress of Refrigeration, IIR/IIF, The Hague, Netherlands, 697–704, 1995. 24. Comini G., Cortella G., Saro O., Finite element analysis of coupled conduction and convection in refrigerated transport, International Journal of Refrigeration, 18: 123–131, 1995. 25. Cortella G., CFD-aided retail cabinets design, Computers and Electronics in Agriculture, 34: 43–66, 2002. 26. Madireddi S., Agarwal R.K., Computation of three-dimensional flow field and heat transfer inside an open refrigerated display case with an air curtain, In: Proceedings of IIR International Conference Commercial Refrigeration, Vicenza, I, 2005. 27. Morillon C., Penot F., La modélisation: Une aide à la conception thermoaéraulique des meubles frigorifiques de vente, Revue Générale du Froid, 968: 48–53, 1996. 28. Stribling D., Tassou S.A., Marriott D., A two-dimensional computational fluid dynamic model of a refrigerated display case, ASHRAE Transactions, 103(1): 88–94, 1997. 29. D’Agaro P., Cortella G., Croce G., Two- and three dimensional CFD applied to vertical display cabinets simulation, International Journal of Refrigeration, 29: 178–190, 2006. 30. Axell M., Fahlen P., Climatic influence on display cabinet performance, In: Proceedings of IIR International Conference New Technologies in Commercial Refrigeration, Urbana, USA, Hrnjak P.S., Ed., 181–190, 2002. 31. Yu K., Ding G., Chen T., A correlation model of thermal entrainment factor for air curtain in a vertical open display cabinet, Applied Thermal Engineering, 29: 2904–2913, 2009. 32. Navaz H.K., Henderson B.S., Faramarzi R., Pourmovahed A., Taugwalder F., Jet entrainment rate in air curtain of open refrigerated display cases, International Journal of Refrigeration, 28: 267–275, 2005.

20

Computational Fluid Dynamics in Food Processing

33. Cortella G., Manzan M., Comini G., CFD simulation of refrigerated display cabinets, International Journal of Refrigeration, 24: 250–260, 2001. 34. Ge Y.T., Tassou S.A., Simulation of the performance of single jet air curtains for vertical refrigerated display cabinets, Applied Thermal Engineering, 21: 201–219, 2001. 35. Van Oort H., Van Gerwen R.J.M., Air flow optimisation in refrigerated display cabinets, In: Proceedings of the 19th International Congress of Refrigeration, IIR/IIF, The Hague, Netherlands, 446–453, 1995. 36. Baléo J.N., Guyonnaud L., Solliec C., Numerical simulation of air flow distribution in a refrigerated display case air curtain, In: Proceedings of the 19th International Congress of Refrigeration, IIR/IIF, The Hague, Netherlands, 681–688, 1995. 37. Laguerre O., Moureh J., Srour S., Derens E., Commere B., Predictive modelling for refrigerated display cabinets, In: Proceedings of IIR International Conference Advances in the Refrigeration Systems, Food Technologies and Cold Chain, Sofia, BG, 480–487, 1998. 38. Cortella G., Manzan M., Comini G., Computation of air velocity and temperature distributions in open display cabinets, In: Proceedings of IIR International Conference Advances in the Refrigeration Systems, Food Technologies and Cold Chain, Sofia, BG, 617–625, 1998. 39. Wu Y., Xie G., Chen Z., Niu L., Sun D.-W., An investigation on flowing patterns of the airflow and its characteristics of heat and mass transfer in an island open display cabinet with goods, Applied Thermal Engineering, 24: 1945–1957, 2004. 40. Cortella G., D’Agaro P., Air curtains design in a vertical open display cabinet, In: Proceedings of IIR International Conference New Technologies in Commercial Refrigeration, Urbana, USA, Hrnjak P.S., Ed., 55–63, 2002. 41. Cui J., Wang S., Application of CFD in evaluation and energy-efficient design of air curtains for horizontal refrigerated display cases, International Journal of Thermal Sciences, 43: 993–1002, 2004. 42. Gaspar P.D., Carrilho Gonçalves L.C., Pitarma R.A., Experimental analysis of the thermal entrainment factor of air curtains in vertical open display cabinets for different ambient air conditions, Applied Thermal Engineering, 31: 961–969, 2011. 43. Wu X., Chang Z., Yuan P., Lu Y., Maa O., Yin X., The optimization and effect of back panel structure on the performance of refrigerated display cabinet, Food Control, 40: 278–285, 2014. 44. Foster A.M., Madge M., Evans J.A., The use of CFD to improve the performance of a chilled multi-deck retail display cabinet, International Journal of Refrigeration, 28: 698–705, 2005. 45. Sun J., Tsamos K., Tassou S.A., CFD comparison of open-type refrigerated display cabinets with/​ without air guiding strips, Energy Procedia, 123: 54–61, 2017. 46. Marinetti S., Cavazzini G., Fedele L., De Zan F., Schiesaro P., Air velocity distribution analysis in the air duct of a display cabinet by PIV technique, International Journal of Refrigeration, 35: 2321–2331, 2012. 47. Rossetti A., Minetto S., Marinetti S., A simplified thermal CFD approach to fins and tube heat exchanger: Application to maldistributed airflow on an open display cabinet, International Journal of Refrigeration, 57: 208–215, 2015. 48. Marinetti S., Cavazzini G., Lauri I., Testa S., Minetto S., Numerical and experimental analysis of the air flow distribution in the cooling duct of a display cabinet, International Journal of Refrigeration, 42: 8–13, 2014. 49. Rossetti A., Minetto S., Marinetti S., Numerical modelling and validation of the air flow maldistribution in the cooling duct of a horizontal display cabinet, Applied Thermal Engineering, 87: 24–33, 2015. 50. Ge Y.T., Tassou S.A., Hadawey A., Simulation of multi-deck medium temperature display cabinets with the integration of CFD and cooling coil models, Applied Energy, 87: 3178–3188, 2010. 51. Ge Y.T., Tassou S.A., The impact of geometric structure and flow arrangement on the performance of CO2 evaporators in multi-deck medium temperature display cabinets, International Journal of Refrigeration, 35: 142–149, 2012. 52. Laguerre O., Hoang M.H., Flick D., Heat transfer modelling in a refrigerated display cabinet: The influence of operating conditions, Journal of Food Engineering, 108: 353–364, 2012. 53. Foster A.M., Quarini G.L., Using advanced modelling techniques to reduce the cold spillage from retail display cabinets into supermarket stores to maintain customer comfort, In: Proceedings of the Institution of Mechanical Engineers, Part E - Journal of Process Mechanical Engineering, 215: 29–38, 2001. 54. D’Agaro P., Croce G. Cortella G., Numerical simulation of glass doors fogging and defogging in refrigerated display cabinets, Applied Thermal Engineering, 26: 1927–1934, 2006.

CFD Aided Retail Cabinets Design

21

55. Brown T., Corry J.E.L., James S.J., Humidification of chilled fruit and vegetables on retail display using an ultrasonic fogging system with water/air ozonation, International Journal of Refrigeration, 27: 862–868, 2004. 56. Hu Z., Sun D.-W., CFD simulation of heat and moisture transfer for predicting cooling rate and weight loss of cooked ham during air-blast chilling process, Journal of Food Engineering, 46: 189–197, 2000. 57. Xia B., Sun D.-W., Application of computational fluid dynamics in the food industry: A review, Computer and Electronics in Agriculture, 34: 5–24, 2002. 58. Moureh J., Flick D., Airflow characteristics within a slot-ventilated enclosure, International Journal of Heat and Fluid Flow, 26: 12–24, 2005. 59. Laguerre O., Hoang M.H., Osswald V., Flick D., Experimental study of heat transfer and air flow in a refrigerated display cabinet, Journal of Food Engineering, 113: 310–321, 2012. 60. Axell M., Fahlen P.O., Tuovinen H., Influence of air distribution and load arrangements in display cabinets, In: Proceedings of the 20th International Congress of Refrigeration, IIR/IIF, Sydney, AU, paper 152, 1999.

http://taylorandfrancis.com

2

CFD Optimization of Perturbed Air Curtains for Refrigerated Display Cabinets Jean Moureh

CONTENTS 2.1 Introduction......................................................................................................................... 24 2.2 Energy Consumption and Food Safety Aspects of RDC.................................................... 24 2.3 Numerical Modeling................................................................................................................24 2.4 Airflow Design and Research Methodology of RDC..............................................................25 2.5 Aims and Objectives................................................................................................................26 2.6 Experimental Setup and Procedure......................................................................................... 27 2.6.1 Air Curtain Facility......................................................................................................... 27 2.6.2 Non-Intrusive Experimental Facilities...................................................................... 29 2.6.2.1 Laser Doppler Velocimetry (LDV)............................................................... 29 2.6.2.2 Particle Image Velocimetry (PIV)............................................................. 30 2.6.3 General Features of the Flow Field.................................................................................... 32 2.7 Numerical Modeling Approaches............................................................................................ 33 2.7.1 CFD Numerical Modeling........................................................................................... 34 2.7.1.1 Governing Equations and Hypothesis...................................................... 34 2.7.1.2 Boundary Conditions........................................................................................... 36 2.7.2 Global Modeling Approach................................................................................................ 37 2.7.2.1 Governing Equations................................................................................................37 2.7.2.2 Air Curtain Performance................................................................................. 40 2.8 Results and Discussion.................................................................................................................................41 2.8.1 Without External Perturbation..................................................................................... 42 2.8.1.1 Jet Characteristics and Airflow Patterns....................................................... 42 2.8.1.2 Global Exchanges Through Air Curtain.......................................................44 2.8.2 With External Lateral Flow...................................................................................45 2.8.2.1 Effect of ELF on Airflow Patterns................................................................ 45 2.8.2.2 Turbulence Modeling Performance............................................................ 47 2.8.2.3 Effect of the ELF on the Jet Deflection.....................................................49 2.8.2.4 Effect of ELF on the Jet Decay..................................................................... 50 2.8.2.5 Effect of ELF on the Velocity Profiles.......................................................... 51 2.8.2.6 Effect of ELF on the Global Exchanges Through Air Curtain................... 53 2.9 Conclusions.............................................................................................................................. 55 Nomenclature.................................................................................................................................... 56 References......................................................................................................................................... 58

23

24

Computational Fluid Dynamics in Food Processing

2.1 INTRODUCTION In many industrial applications, air curtains formed by plane air jets are used to provide a dynamic barrier for reducing and controlling the heat and mass transfer between two adjoining areas with different levels of temperature, humidity and pollution. Air curtains are used to create refrigerated spaces [1,2], open minienvironments for sensitive high-quality products [3], or to reduce the spreading of fire smokes in underground tunnels [4,5]. One of the relevant applications is the vertical open Refrigerated Display Cabinet (RDC) widely used in supermarkets. Within this context, the air curtain plays a key role in keeping food at prescribed regular temperatures, while allowing an energy-saved control and open access for customers. As air curtains play a very important role in the cold preservation of display cabinets, much research has been made in this field, including experimental studies [6–8], computational fluid dynamics (CFD) simulations [9–16] and global modeling approaches [17–19]. The majority of these studies take into consideration only an idealized scenario in which no perturbation affects the dynamic behavior of the air curtains. However, these devices are generally used in open spaces like supermarkets, and are very sensitive to external perturbations generated by human activities, such as pressure difference due to door opening, parasitic air draughts, action of air conditioning system, etc. Such perturbations may strongly affect the stability, the air tightness, the transfer mechanisms and therefore the efficiency of the air curtain due to a lack of confinement and an increase of energy consumption [16]. D’Agaro et al. [9] indicated that the incidence of external air currents on air entrainment needs further investigation. Therefore, the flow characteristics, efficiency and performance are yet to be understood, especially with consideration of external perturbations, which one would encounter in practical industrial applications.

2.2 ENERGY CONSUMPTION AND FOOD SAFETY ASPECTS OF RDC In 2002 it was estimated that there were 322,000 supermarkets and 18,000 hypermarkets worldwide and that the refrigeration equipment in these supermarkets used on average 35–50% of the total energy consumed in these supermarkets [20]. In supermarkets, refrigerated display cabinets are the most common method of keeping chilled food at the required temperature and allowing the customer almost unrestricted access to the food. In a typical RDC, the air jet flows from nozzle inlet located at the top front to a nozzle exit located at the bottom front of the case, acting as a thermal barrier between the warm ambient air and the chilled compartment. Due to their design, RDC are very sensitive to ambient conditions and are considered as the weakest link of the cold chain. It has been shown that mean food temperatures among chilled cabinets can range from –1°C to +16°C [21]. These higher values could be explained by the fact air curtains are easily disturbed by the outside ambient air, which in addition results in higher temperature rise and more power consumption. These disadvantages are difficult to overcome since the European testing standard, EN441, was established for steady ambient conditions where the surrounding velocity is below 0.15 m/s.

2.3 NUMERICAL MODELING Many authors [11–15] have shown computational fluid dynamics (CFD) to be a valuable tool to rapidly provide design options to improve airflow within display cabinets. In their studies, the authors use the CFD models to optimize RDC design or to minimize energy losses through the air curtain by testing the influence of the main factors, which include the dimensions of the nozzle inlet, the nozzle exit, the length of air curtains, the initial velocity, turbulent intensity and temperature of air curtains and the temperature and velocity of the ambient environment. Smale et al. [14] offer a review on the importance of the complementary role of the CFD approach and its ability to handle the complex configurations of refrigerating facilities, including

CFD Optimization of Perturbed Air Curtains for Refrigerated Display Cabinets

25

RDC. The  authors stress the importance of validating CFD models, which necessitates rigorous comparisons with experimental data. D’Agaro et al. [9] perform 2D and 3D CFD simulations to investigate the effects of the cabinet length, the air curtain and longitudinal ambient air movement on air flow pattern and temperature distribution in a frozen food vertical display cabinet. The authors pointed out the importance of the 3D effects. The computed refrigerating power shows that even low room air velocity of 0.2 m/s, due to its interaction with the end-wall vortices, has a significant impact on cabinet performance. The introduction of the ambient air movement affects the return air temperature and consequently the refrigerating power, which has been estimated to increase about 30%. A similar result was found by Gaspar et al. [6], who conducted an experiment to study the heat transfer rate and thermal entrainment factor of air curtains in a RDC in different ambient air conditions. In this study, the high values of thermal entrainment observed at the sidewall locations can be attributed to sidewall effects, as the air curtain is unable to restrict the free entry of external air at the extremities of the RDC. The results of Gaspar et al. [6] also show that the increase of ambient air velocity magnitude from 0.2 to 0.4 m/s, even parallel to the plane of the equipment’s frontal opening, promotes thermal interaction between the conservation zone and ambient air masses by disturbance of aerothermodynamics barrier provided by air curtain. The total heat transfer rate increases 53% due to increase of air infiltration load across the air curtain. However, it’s worth noting that the validation of the majority of CFD models reported in the literature [7,11,12,16] are obtained by comparisons with test results limited to temperature and humidity (no velocity measurements were performed). Even when velocity measurements have been performed, they are limited to some velocity profiles [1], which is not enough to validate complex 3D airflow patterns [2]. Thus, there is a need to use more advanced non-intrusive techniques like PIV and LDV in order to obtain high enough resolution to characterize air flow patterns and velocity profiles and turbulence levels. The obtaining of such results allows a better understanding of airflow characteristics and also improves the quality of CFD validation. Two important physical parameters appear in the bibliography analysis and have been studied in general by all others: (1) thermal entrainment, reflecting the energy loss, and (2) the air curtain tightness, which is responsible for the temperature or pollution infiltration to the confined cavity. According to Howell and Adams [22], 75% of the refrigeration load related to an RDC is induced by the air curtain entrainment, which could be viewed as a global air exchange with the ambient. The results obtained by Navaz et al. [17] indicate that lowering the Reynolds number of the air curtain reduces the entrainment rate. However, sufficiently high momentum should still exist to enforce the integrity of the air curtain structure. A similar result was found by Moureh et al. [18] and Flick et al. [19], who developed a global analytical model to predict jet velocities and temperature profiles along a turbulent jet used to seal/confine a heated cavity. In a forced convection regime, the thermal entrainment (i.e., energy loss) becomes proportional to the flow rate of the jet. Amin et al. [8] proposed an original approach combining experimental technique and a global analytical model to quantify the steady state infiltration rate of RDC. The infiltrating rate was defined as the part of entrained flow drawn into the nozzle exit. This technique is based upon the concentration measurements of a tracer gas at three locations: nozzle inlet, nozzle exit and the ambient.

2.4 AIRFLOW DESIGN AND RESEARCH METHODOLOGY OF RDC In RDC, there are several factors affecting the complexity of refrigerated air curtains flow, due to the nature of the regime flow, thermal and geometrical aspects. According to Field and Loth [23], with typical RDC dimensions and the corresponding jet flow rates, the Reynolds number is about 5,000 and the typical air curtain lengths are about ten jet widths. Therefore, the air curtain flows reside in the transitional flow regime, which is not well understood, and little information

26

Computational Fluid Dynamics in Food Processing

was available concerning the velocity profiles. In addition, the transitional flow is more complex to predict, since classical turbulence model RANS are more adapted to fully developed turbulence. Unlike free turbulent jets, refrigerated air curtains experience aerodynamic and thermal asymmetric design; one side has a cold temperature and no stagnant air within a confined space, while the ambient side has a high temperature and lower velocities. Another complexity concerning the thermal aspect is the fact that refrigerated air curtains are negatively buoyant jets, which combine the effects of forced convection and natural convection due to density difference. In addition, the entrainment of warm air from the ambient causes the air curtain to become warmer as it falls down the cabinet. Thus the predominance of natural convection decreases progressively along the cabinet. The measurements of [Field and Loth, 2006] indicated negatively-buoyant acceleration following the jet exhaust, followed by a more linear curtain growth characteristic of isothermal wall jets. This increases the edge instabilities, which increase the mixing and entrainment into the air curtain. Finally, the geometry employed is complex and specific to a particular display case. The free turbulent shear flow developed by the jet is strongly affected by aerodynamic interactions with shelves, loading arrangements of products, back flow panel and secondary recirculation developed as semi-confined flow within the cabinet. Given this complexity, the global studies cited above performed on specific cases, which behave as black-boxes, could be considered empirical approaches since the main geometric and air flow parameters are fixed. Consequently, it was difficult to develop a fundamental understanding of the underlying fluid dynamics of air curtains in general and thus to derive universal recommendations aiming to improve their design. In order to perform more fundamental studies related to fluid dynamics of the air curtain while eliminating case-specific flow features particular to each manufacturer, some authors perform investigations on more simplified air curtain geometries, such as isothermal wall jet [23,24] or plane jet confining rectangular empty cavities [18,19,25].

2.5 AIMS AND OBJECTIVES Previous studies only assessed the efficiency of air curtain devices in quiescent ambient conditions. Some fundamental studies have also been extended by a number of researchers to jets discharged in non-quiescent surroundings with “co-flow” [26,27] and “cross-flow” [28,29]. However, to the best of our knowledge, the flow configuration of a perturbed air curtains resulting from an aerodynamic interaction with an external lateral flow has not yet been studied in detail either experimentally or numerically. The aim of this research is to experimentally and numerically characterize the dynamic behavior and the confinement effectiveness of an air curtain used to confine a rectangular cavity and subjected to external perturbation. This study is performed on a reduced-scale model representing an idealized configuration of a RDC, which is formed by an isothermal simple jet plane, and investigates the influence of the main parameters related to the jet, cavity and the lateral perturbation. This allows a more fundamental study of the physics of an air curtain, while avoiding the more casespecific geometries used by many authors [7,11,13,30]. The study focuses on the near field region (x/e < 10), which includes the transition zone where strong interactions are expected between the jet core, cavity and external lateral flow, due to this region’s strong relevance to RDC. Velocity measurements are performed by means of LDV and PIV techniques. The numerical approach was performed using computational fluid dynamics (CFD) Fluent code with the standard k-ɛ model, and the more advanced RSM. The main purpose is to acquire reliable data on the physics of the air curtain development and transfer mechanisms with and without external perturbation. It also allows a critical evaluation of the performance of these models and therefore validation of the numerical model by comparisons with LDV and PIV measurements. The analysis of experimental and numerical data obtained with and without external perturbation make it possible to quantify the effect of the perturbation on the main jet characteristics related to maximum velocity decay, growth rate, self-similarity, as well those related to air flow patterns,

CFD Optimization of Perturbed Air Curtains for Refrigerated Display Cabinets

27

jet stability and confinement effectiveness. The numerical developed model was then validated with PIV measurements and with the available results in terms of the thermal entrainment and infiltration rate in the literature. The validated CFD model was then combined with an original modeling approach based on entrainment spill mechanism of the jet. This enables the construction of a global model used to predict heat or mass fluxes exchanged between cavity, air curtain and the ambient with and without external perturbation. In addition to the RDC case, studying transitional disturbed plane jets can provide further understanding of the fundamental nature of the flow physics, leading to improvements in various practical applications where air curtains evolve in non-quiescent ambient.

2.6 EXPERIMENTAL SETUP AND PROCEDURE 2.6.1 Air Curtain Facility The experimental setup shown in Figure 2.1 is a scaled-down (1:5) model of a cavity representing a generic configuration of an open display cabinet with respect to Reynolds dimensionless number, defined as Re = e U/v. It represents an air curtain confining cavity subjected to an external lateral flow (ELF) under isothermal conditions. Using a scaled -down model as a generic configuration of a RDC is very instructive to characterize the fundamental nature of flow field while eliminating case-specific issues particular to each manufacturer. The key benefit and originality of this facility derives from its ability to obtain simultaneously the control of the air curtain flow and the ELF. The cavity is of 0.4 m height and 0.5 m width with an adjustable back wall enabling different depths ranging from 0.15 m (which corresponds to an air curtain confining a cavity) to 0 m, representing a plane wall jet that corresponds to a fully stocked RDC [31]. In this paper, only the configuration with a cavity depth of 0.15 m is considered. The experimental device is composed of two airflow separate circuits related to the air curtain and to the ELF. Airflows for both air curtain and ELF are provided by two centrifugal fans, which can deliver a nominal flow rate of 0.5 m3s−1 with pressure loss of ΔP = 1469 Pa for the air curtain and 1.25 m3s−1 for the lateral flow with ΔP = 1959 Pa. Both airflow circuits are put into two closed

FIGURE 2.1  Experimental scaled-down test facility of a display cabinet: (a) settling chamber, (b) smooth contraction nozzle, (c) rectangular channel, (d) cavity wall, and (e) exit of the recycled jet. Blue vertical arrow: Air curtain; red horizontal arrow: External Lateral Flow (ELF).

28

Computational Fluid Dynamics in Food Processing

recycled air loops. This configuration also reduces the amount of injected tracer particles needed to achieve better measurement. The main dimensions and the axis system are presented in Figure 2.2. Cartesian coordinates are used, x axis for streamwise direction related to the air curtain flow, y axis for transverse direction and the third z axis for lateral or span-wise evolution where the ELF flows. The origin is fixed in the middle of the nozzle inlet and in the (x-y) mid-plane of the air curtain (Figure 2.2b). In the air curtain airflow circuit, the air jet blows from top to bottom (Figure 2.2a). The rectangular settling chamber contains two honey-comb flow straighteners and four perforated screens of progressively finer mesh sizes of 4 × 10 −3 m, 3 × 10 −3 m, 2 × 10 −3 m and 1 × 10 −3 m are put in order to ensure the uniformity of the mean velocity with a low turbulence level. A rectangular channel (of section 0.04 m × 0.5 m) leading to the jet nozzle inlet is connected to the settling chamber with a smooth contraction ratio of 1/5. The aspect ratio (l/e) of the channel is 12.5. The air curtain length extended to 10 jet widths (H/e = 10) downstream to better focus the initial stages of the plane jet development in the near field region. Data were acquired in

FIGURE 2.2  Sketch of the scale model: (a) front view, (b) coordinate system, and (c) top view.

CFD Optimization of Perturbed Air Curtains for Refrigerated Display Cabinets

29

TABLE 2.1 Geometrical Characteristics of the Jet and the Cavity e (nozzle inlet width) D (cavity depth) H (cavity height) L (cavity length)

0.04 m 0.15 m 0.4 m 0.5 m

the turbulent regime at a Reynolds number based on the slot exit (e) of 0.04 m thickness, giving Re ≈ 8000. In the ELF circuit, the air is injected in a rectangular horizontal channel of dimensions 0.4 m height, 0.5 m width and 2.4 m length. To control the uniformity of the ELF flow, 0.5 m of the channel entrance has been devoted to a settling chamber composed of a honeycomb and a set of perforated plates (Figure 2.2c). The distance between the last perforated plate and the lateral side of the air curtain, which corresponds to the beginning of the interaction with the ELF, is 0.7 m. At z = –0.25 m, located downstream of the interaction with the air curtain, the air flow rate of the ELF is extracted in a channel in order to form a closed loop. The scaled-down experimental model walls are made of Plexiglas of higher optical quality material, which is advantageous for LDV and PIV image recording since the laser sheet can be directed through the wall cavity surface, allowing the flow field to be free of optical obstructions. The geometrical dimensions characteristics of the scaled-down model are summarized in Table 2.1. In this study three external lateral flow velocities (Ulf) have been chosen: 0 ms−1 (unperturbed air curtain), 0.5 ms−1 and 1 ms−1, which correspond to the ratios Ulf /U0 of 0 (unperturbed air curtain), 0.16 and 0.33, respectively. To investigate the three-dimensional effect of the ELF on the air curtain flow in the lateral direction, four positions were selected for PIV measurements: distances of 0.05 m, 0.1 m, 0.25 m and 0.4 m from the lateral side where the ELF comes in, which correspond to z/L = 0.4, z/L = 0.3, z/L = 0 (mid-plane) and z/L = –0.3, respectively.

2.6.2 Non-Intrusive Experimental Facilities Two experimental techniques, Laser Doppler Velocimetry (“LDV”) and Particle Image Velocimetry  (“PIV”), have been used to characterize the mean velocity field and its fluctuating components. For both techniques, the flow was seeded by white atomized oil particles of 4 × 10 −6 m that scatter light as the flow carries them through the measurement volume of LDV or the laser sheet of PIV. The atomizer was set in a box placed in the air curtain jet loop before entering the settling chamber. 2.6.2.1 Laser Doppler Velocimetry (LDV) One-dimensional Laser Doppler Velocimetry (Laservec) produced by TSI (Shoreview, MN, USA) manufacturer was used. The LDV consists of an LDP-100 probe and the raw data are processed using an IFA 600 signal processor. This measurement technique does not interfere with the flow and is able to correctly resolve the sign, as well as the magnitude of velocity, and determine mean velocity and its fluctuation. It comprised a 50 × 10 −3 W laser diode emitting a visible red beam at a 690 × 10 −9 m wavelength, a beam splitter, a Bragg (acousto-optic) cell, a focusing and receiving lens to collect scattered light from the measurement point and a photomultiplier. The accuracy is considered to be below 1%. For the present experiments, a maximum of 10,000 samples was specified for each point measured, with a maximum sampling time of 2 min. The data acquisition was stopped depending on which of these two events occurred earlier. The data rate varied between 100 and

30

Computational Fluid Dynamics in Food Processing

1000 Hz for all measurements. The probe was carried on an automatic three-dimensional displacement system that provides a position resolution of ±0.5 × 10 −3 m in three directions. 2.6.2.2 Particle Image Velocimetry (PIV) The 2D-PIV was used to provide instantaneous velocity field measurements in vertical crosssections of the flow downstream of the air curtain. This technique is non-intrusive and measures the velocities of micron-sized particles following the flow. The PIV system used for the determination of the velocity fields was essentially composed of a CCD camera of 1375 × 1086 pixel resolution (LaVision sense M2/E 12 bits) with an objective Nikon (60 mm), a pulsed Nd:Yag laser with the energy of 15 mJ/pulse (Double cavity ) and a ‘‘LaVision” correlator. The laser light is passed through suitable optics to form a light sheet with approximately 1.5 mm thickness. The whole system is driven by the software ‘‘Davis V7.2.” The laser light scattered from the seeded particles is imaged on a camera and a 64 × 64 pixel region is used on the first pass and a 32 × 32 pixel region with 50% overlap is used on the second pass. The time delay between two laser pulses was 3.5 ms and the time delay between the capture of two pairs of pictures was 200 ms. For all measurement cases 1,000 pairs of images are used for each velocity measurement to allow good accuracy in statistical calculations of the mean flow and turbulence fluctuation. To validate the 2D behavior of the air curtain device, Figure 2.3 shows the quasi-uniformity of inlet velocities and turbulence intensities at (x/e = 1; y/e = –0.5) along the jet nozzle (–0.5 < z/L < 0.5). Furthermore, Figure 2.4 confirms the top-hat character of the jet obtained in the mid-plane (z/L = 0) within the jet nozzle (–1 < y/e < 0). To assess the uniformity of the ELF, air velocity measurements were performed within the duct, upstream of the interaction with the air curtain maintained at 0m/s along the x direction at z = 0.44 m and y = 0.15 m (Figure 2.5). The obtained results show the quasi-uniformity of the velocities (Ulf = –1.05 ms –1 ± 2.5%) and turbulence intensities (4.4% ± 0.1%).

FIGURE 2.3  Inlet velocities and turbulence intensities at (x/e = 1; y/e = –0.5) along the jet nozzle inlet (–0.5 < z/L < 0.5).

CFD Optimization of Perturbed Air Curtains for Refrigerated Display Cabinets

31

FIGURE 2.4  Profile of inlet velocities (U0) in the mid-plane (z/L = 0) within the jet nozzle (–1 < y/e < 0) at x/e = 1.

FIGURE 2.5  Velocity and turbulence intensity measurements in the ELF at z = 0.44 m and y = 0.15 m.

32

Computational Fluid Dynamics in Food Processing

2.6.3 General Features of the Flow Field On the basis of the present investigation and the results reported by many authors [18,19,32], a recirculating air curtain developed in a relatively quiescent ambient behaves as a free jet. The corresponding flow field, schematically represented in Figure 2.6, consists of two, linearly growing mixing layers separated by a diminishing potential core. As can be seen, the two main regions identified in this figure may be defined as follows: the first region is referred to as the potential core region, in which the axial component of velocity is essentially a constant, (Ucl = U 0; where Ucl is the mean axial velocity along the centerline of the jet and U 0 is the mean velocity at the nozzle exit), and the zone of fully established flow, which originates at about the location where the two mixing layers meet. In the fully turbulent region, velocity profiles at various distances from the nozzle inlet are similar. According to Reichardt [33], the self-similar profiles could be approximated by the following Gaussian/ exponential function:



2     U/ U m = exp  − ln(2).  y (2.1)   y1/ 2   

The normalised velocity half-widths are given by y0.5

e

 x  = K y  x + 0  (2.2) e e

where Ky is the jet spreading rate and x0 is the virtual origin. y0.5 represents the distance at which the velocity is one-half the value of the maximum velocity Um:

U (x) =

1

2

Um( x )

Figure 2.7 displays instantaneous flow visualization via PIV tomography of the shear layer within the cavity. It shows the onset and development of initial eddies of Kelvin–Helmholtz (K–H) instabilities that dominate the early stages of air jet transition process and play a relevant

FIGURE 2.6  Schematic view of the plane turbulent jet regions.

CFD Optimization of Perturbed Air Curtains for Refrigerated Display Cabinets

33

x /e = 3

x /e = 4

FIGURE 2.7  PIV visualization of Kelvin–Helmholtz instability for unperturbed jet (Ulf = 0 ms–1) at the mid-plane (z/L = 0).

role in enhancing mixing and entrainment between the jet and the ambient. The roll-up and pairing process of the K–H instability that leads to the formation of larger structures represent the principal mechanisms governing the growth of the shear mixing layer. The dominance of largescale structures diminish as they convect downstream due to the generation of a broader range of smaller eddies. Downstream of the jet nozzle inlet, the jet spreads out, which causes a decrease in air jet velocity and an increase of the mass flow rate of the jet by entrainment mechanisms from both sides: ambient and cavity. This process continues until the jet flows approach the nozzle exit located at the bottom of the cavity at x/e = 10. At this level, the global flow rate exceeds the recirculated part. Therefore, the jet splits into three different air flow components. The main or central part of the jet, which corresponds to the mass flow rate of the jet (m 0), is drawn into the nozzle exit to continue the steady flow operation of the jet. The outer part of the air curtain is spilled back to the ambient surroundings in order to balance the quantity of air that was entrained by the air curtain on the outside. The inner part of the air curtain is spilled into the cavity and entrains the formation of a global recirculation within the cavity, as observed by many authors [17,19,25].

2.7 NUMERICAL MODELING APPROACHES In this study, two complementary modeling approaches were performed. The first is based on the CFD numerical predictions, which enable better understanding of the local air flow characteristics, while the second deals on the global fluxes exchanged between the air curtain, the ambient and the cavity.

34

Computational Fluid Dynamics in Food Processing

2.7.1 CFD Numerical Modeling 2.7.1.1 Governing Equations and Hypothesis The description of airflow development is based on the conservative law of mass and momentum. The solved equations can be written as follows:

Mass conservation:





∂U j = 0 (2.3) ∂x j

∂U jUi 1 ∂P ∂ =− + ∂x j ρ ∂xi ∂x j

Momentum conservation:

 ∂Ui   v ∂x − ui u j  (2.4) j

Passive transport scalar equation: The general equation form of the convection-diffusion of a passive scalar tracer in steady state without chemical reaction is written as: ∂U jC ∂x j



=

∂ ∂x j

 v ∂C   Sc ∂x − u j c  + S (2.5)   j

where C is the mean mass fraction of the passive tracer, S is the source term and ui u j and u j c are, respectively, the unknown Reynolds stresses and mass fluxes. The obtaining of these quantities depends on the turbulence closure. For the case investigated, two levels of turbulence modeling closure have been employed: • on one hand, with the standard two-equation k-ɛ model described by Launder and Spalding [34]; • on the other hand, with a second-moment closure with the Reynolds stress model (RSM). a) The standard k-ε model Using the Boussinesq hypothesis, the Reynolds stresses can be described as follows:  ∂U ∂U j  2 − u i u j = vt  i + − kδ ij (2.6) ∂xi  3  ∂x j



The eddy (turbulent) viscosity νt is obtained from: vt = Cµ fµ



k2 (2.7) ε

The turbulence kinetic energy k and the dissipation rate ε are determined using the following transport equations respectively:

Ui

∂k ∂ = ∂xi ∂xi

 vt  ∂k   v +  + Pk − ε (2.8) σ k  ∂xi  

CFD Optimization of Perturbed Air Curtains for Refrigerated Display Cabinets

Ui

∂ε ∂ = ∂xi ∂xi

35

 vt  ∂ε  ε  v +  + (C1 Pk − C2 ε ) (2.9) σ ε  ∂xi  k 

Pk represents the shear production term:  ∂U ∂U j  ∂Ui Pk = vt  i + (2.10)  ∂xi  ∂x j  ∂x j



The model coefficients in the standard k-ε model are: (Cµ , C1 , C2 , σ k , σ ε ) = (0.09, 1.44, 1.92, 1.0, 1.3) (2.11)



b) The RSM The transport equations for Reynolds turbulent stress are obtained by subtracting the product of the mean velocities by the time-averaged Navier–Stokes equations from the product of instantaneous velocities by instantaneous Navier–Stokes equations. This gives rise to: ∂ui u j

Uk

∂x k

=−

∂ ∂x k

 ∂(ui u j )  p ∂u ∂u j p  ∂u ∂u  ui u j uk + (δ kj ui + δ ik u j ) − v  + Pij −  i + j  − 2v i (2.12) ρ ∂x k  ρ  ∂xj ∂xi  ∂x k ∂x k 

where Pij = −ui uk

∂U j ∂x k

− u j uk

∂Ui represents the production term. ∂x k

The diffusive transport term was represented by a simplified form of the generalized gradient diffusion hypothesis as:

−

∂ (ui u j )   p ∂  ∂  νt ∂ ui u j uk + (δ kj ui + δ ik u j ) − ν = (ui u j ) (2.13)  ρ ∂ x k  ∂x k  σ k ∂x k ∂x k  

p  ∂ ui ∂ u j  +   represents the pressure-strain term leading to a redistribution process ρ  ∂ xj ∂ xi  within the Reynolds-stresses towards an isotropic state. It is modeled by Wilcox formulation [35], which is recommended to shear and swirling flows. The dissipation term was assumed isotropic, and was approximated by:



2ν

∂ui ∂u j 2 = δ ij ε (2.14) ∂x k ∂x k 3

The dissipation rate was computed via the ε transport equation as described by the standard k-ε model [34]. It implies the isotropy of the dissipation process at smallest length scales.

36

Computational Fluid Dynamics in Food Processing

2.7.1.2 Boundary Conditions The computational domain may be surrounded by inflow, outflow boundaries and solid walls. At the two inlet sections concerning the jet and the external flow, uniform distribution is assumed for velocity components, transport variables, kinetic energy of turbulence (k0), the energy dissipation rate and the dissipation rate (ε 0). The turbulence quantities are imposed by means of two parameters: the turbulence intensity as obtained from experiments, and the hydraulic diameter, assuming a fully developed duct flow upstream. For the RSM, turbulence is assumed to be isotropic: 2 (u i u j = k0δ ij ). For the air curtain, the magnitude of the inlet velocity was tacked constant for all 3 performed simulations at 3 ms–1 and 6 ms–1 for the nozzle inlet width of e = 4 10 –2 m and 6 ms–1 for 2 10 –2 m. This allows the finding of: • Two different Reynolds numbers: Re = 8000 and Re = 6000 for e = 4 10 –2 m, and Re = 8000 for e = 2 10 –2 m. • Two different jet aspect ratios: H/e = 10 for e = 4 10 –2 m and H/e = 20 for e = 2 10 –2 m. For the external lateral perturbation, different ratios of Ulf /U0 were simulated, ranging from 0 to 0.33 for H/e = 20 and from 0 to 0.66 for H/e = 10. At the outlet boundaries related to the air curtain and to external flow, the air flow rate is imposed with respect to the mass balance, while the velocity profiles are unknown. Based on the present model, the non-diffusion outlet boundary conditions for velocity and concentration are assumed. These have been extensively analysed and proven to be a correct and reasonable assumption for air flow within ducts. The near wall region was modeled using the standard logarithmic wall function. The boundary conditions are summarized in Table 2.1 and indices (τ, η, λ) represent the local coordinate system of the wall, where τ is the tangential coordinate, η is the normal coordinate, and λ is the binormal coordinate. Then the local Reynolds stresses at the wall-adjacent cells were computed from:



u′2 u′ u′ uτ′2 u′ 2 = 1.098, η = 0.247, λ = 0.655, and τ η = 0.255. (2.15) k k k k

The values of k used at the boundaries are obtained from a transport equation of turbulence kinetic energy similar to the one in the standard k-ε model. For reasons of computational convenience, this equation is solved globally (on the domain), even though the values of k thus computed are needed only near the wall. The boundary condition for k imposed at the wall is:



∂k = 0 (2.16) ∂n

where n is the local coordinate normal to the wall. The production of kinetic energy and its dissipation rate ε at the wall-adjacent cells, which are the source terms in the k equation, are computed on the basis of the local equilibrium hypothesis. The different boundary conditions for different simulations were summarized in the Table 2.2. The governing equations are solved using the finite-volume ANSYS Fluent® CFD code [36] in a staggered grid system and the SIMPLER algorithm for pressure–velocity coupling. For the spatial discretization, a second-order accurate upwind differencing scheme is used for the momentum, all convective-diffusively transported variables and Reynolds stress components. A three-dimensional, non-uniform hexahedral grid was used in this study, with high-density mesh in regions near the inlet, outlet, walls and jet boundaries where high gradients are expected. The growth ratio between two adjacent cells does not exceed 20%.

CFD Optimization of Perturbed Air Curtains for Refrigerated Display Cabinets

37

TABLE 2.2 Boundary Conditions Inlet (jet)

U0 = 3 and 6 (m/s) I0x = 5%, Dh = 0.074 (m) k0 = 3/2 (U0I0x)2

(

)

2 k0δ ij 3 Ulf = 0, 0.2, 0.5, 0.7, 1.0, 1.2, 1.5, 1.8 and 2 m/s I = 5%, Dh = 0.44 ∂u/∂n = 0 (1/s) Ui = 0

ε 0 = Cµ0.75 k01.5 / 0.07 DH ui u j =

Inlet (ELF) Outflow Wall (no slip condition) Wall treatment

(a)

ρ Cµ1/ 4 k 1p/ 2 y p u p Cµ1/ 4 k 1p/ 2 1 , y* = u* = ln( E y* ), u* = κ τ w /ρ µ

(b)

cavity

FIGURE 2.8  Mesh topology in (a) xy and (b) yz cross sections.

The numerical results are obtained with 1.5 million cells. It was observed that increasing the grid to larger than this value does not affect the numerical results. A view of the used mesh in two crosssections showing the jet and the cavity domain is given in the Figure 2.8. The computations were run on the PC station, with total CPUs of 8, and 10 Go of RAM. The convergence was established after 10,000 iterations, which “take[s] approximately 2 days.”

2.7.2 Global Modeling Approach Due to the strong 3D effect exerted by the ELF of the jet behaviour described in the paragraph 2.8.2, the air curtain flow loses its initially two-dimensional character and thus experiences substantial variations along the cavity in the lateral direction. Therefore, a global modeling approach appears more appropriate to characterize the fluxes exchanged between the whole cavity, ambient and the air curtain. 2.7.2.1 Governing Equations To evaluate exchanges through the air curtain with and without lateral flow, a global modeling approach based on the entrainment-spill mechanism was built. This model considers: • Four compartments supposed to be homogeneous in temperature or concentration: cavity (c), ambient (a), jet nozzle inlet (0) and jet nozzle exit (s) (Figure 2.9). Each compartment is represented by an indice. • Seven fluxes exchanged between the compartments (Figure 2.9). Each flux involves two compartments and is represented by their respective indices. For example, the ac flux represents the flux flowing from ambient (a) to the cavity (c).

38

Computational Fluid Dynamics in Food Processing Ambient T

Jet inlet

Uo

a

Jet Exit

ca oa as os cs

To

T

s

ac oc Tc Cavity

FIGURE 2.9  Schematic view of the seven air fluxes exchanged between the four compartments.

In a turbulent regime (Sct = Prt), heat and mass transfer are driven by forced convection and turbulent diffusion, while molecular diffusion is neglected. As a consequence, all the fluxes defined above are proportional to the Reynolds number of the jet. This finding was observed by many authors [18,19,32,37]. For simplicity, we consider dimensionless fluxes by dividing them by the air mass flow rate of the jet m 0 . Assuming heat and mass transfer analogy, non-dimensional temperature and concentration are similar. This also concerns heat and mass fluxes exchanged between the four compartments. For example: m 0 ca represents the mass flux of air molecules flowing from cavity c to the ambient a. The heat and mass fluxes transferred from the cavity to the ambient could be written as: m 0 C p ca Tc and m 0 ca Cc, respectively (where T = 0°C represents the enthalpique reference). This representation reflects the physics of a jet. At the nozzle exit level, the mass rate of flow that is entrained by the jet is spilled out into the cavity (ac + oc) and into the ambient (oa + ca). In addition, the recirculated part flowing into the nozzle exit, which represents the mass rate of the jet (m 0), contains three components: os, as and cs, which come from the three compartments: jet nozzle inlet, ambient and cavity. Among these air fluxes, two are particularly important: • The air flux flowing from the jet nozzle inlet to the jet nozzle exit: os represents the capacity of the air curtain to seal the cavity. Higher values of os close to 1 indicate lower exchanges between the air curtain and its surroundings. • The air flux flowing from the ambient into the cavity by the spilled air: ac characterizes the air tightness efficiency of the air curtain. It also represents the level of the cavity protection against ambient contaminants, such as seeds, dust, smoke, etc. For example, if Ca represents the mass concentration of contaminant in the ambient, the quantity of contaminants carried into the cavity could be expressed as: Ca m 0 ac. • In the case of a retail display cabinet, (ca Tc + oa T0) represents the spillage of cold air from the case to the store. The conservation of (total mass flow rate of the “air + tracer gas” mixture) mass at the nozzle inlet, nozzle exit and cavity, allowsfor three relations:

oc + os + oa = 1 → as + os + cs = 1 → oc + ac + cs + ca (2.17)

To identify the seven unknown air fluxes involved in this model, a numerical approach based on the transportation of tracer gas within the studied system is developed by using the CFD model built with the RSM. Two numerical but independent simulations were performed with and without a source term for the gas tracer within the cavity. The momentum equations for velocity and pressure were solved first, and the transport equation for the tracer was then solved based on the converged velocity results.

CFD Optimization of Perturbed Air Curtains for Refrigerated Display Cabinets

39

Obtaining concentrations of the tracer within the compartments makes it possible to write four additional relations: • The first simulation consists of injecting a constant concentration of the tracer gas in the jet discharge (C01) and computing, by the CFD model, the corresponding concentrations of the cavity (Cc1), ambient (Ca1) and jet exit (Cs1). The mass conservation of tracer gas at the nozzle exit and the cavity result in:

os.C01 + cs. Cc1 + as.Ca = (as + os + cs).Cs1 (2.18)



oc.C01 + ac.Ca + = (oc + ac).Cc1 (2.19) • The second simulation consists of injecting a constant concentration of the tracer gas in the jet (C02), and applying a uniform source term of gas tracer S (kg/m3.s) within the cavity domain in such a way to obtain: C02 = Cc 2 (2.20)



Several trials were required to obtain the appropriate value of S . As in the first simulation, the mass conservation of tracer gas at the nozzle exit and the cavity result in:

os.C02 + cs. Cc 2 + as.Ca 2 = (as + os + cs).Cs 2 (2.21)



oc.C02 + ac.Ca + S .Vc / m 0 = (oc + ac).Cc 2 (2.22) In these equations, the mass concentration of gas tracer at the nozzle exit is computed as: Cs 2 =



m m

gas tracer

gas tracer

+ m

(2.23) air

In the cavity, the mass concentration of gas tracer was calculated as the numerical average value:



Cc =

∫ C dv (2.24) Vc

Where Vc represents the volume of the cavity and is equal to 0.022 m3. By combining (2.20) and (2.22), it is possible to determine the air flux ac as: ac =

 SV c (2.25) m 0 (Cc 2 − Ca )

Solving of the algebraic Equations (2.17), (2.18), (2.19), (2.21) and (2.22) with MATLAB software allow for the finding of the seven unknown mass-air fluxes depicted in Figure 2.9. This methodology is applied under different external velocity perturbations.

40

Computational Fluid Dynamics in Food Processing

In the particular case of no external lateral flow and assuming a symmetrical jet hypothesis, we can write:

ac = ca and oc = oa = as = cs = (1 − os) / 2 (2.26)

2.7.2.2 Air Curtain Performance Prior to the results presentation, a few concepts and definitions should be introduced, in view of the analysis and the assessment of the sealing performance of the air curtain. The objective is to build dimensionless parameters related to heat or mass exchanges through air curtains as a function of characteristic fluxes defined above (Figure 2.9). By replacing concentrations by temperatures in the studied system (Figure 2.9), the heat balance of the cavity domain and the jet can be expressed as:

oc(To − Tc ) = ac(Tc − Ta ) (2.27)



Q j / m 0 C p = (To − Ts ) = cs(Tc − Ta ) + as(To − Ta ) (2.28) By combining Equations (2.27) and (2.28) and after manipulating, one can find:



To − Ts (Q j ) (m 0 C p ) ac.cs ac.as = = + + as (2.29) Tc − Ta Tc − Ta oc oc

This quantity corresponds to a dimensionless form of the energy loss of the jet required to provide a given level of thermal sealing, i.e., the temperature difference between the cavity and the ambient. This quantity is inversely proportional to the thermal confinement efficiency (TCE), defined as the ratio between the thermal confinement level induced by the air curtain and the corresponding heat leakage:



T − Ta T − Ta TCE =  c (2.30) = c (Q j ) (m 0 C p ) T0 − Ts To − Ts reflect lower TCE levels of the air curtain. Tc − Ta In the particular case of a symmetrical jet (Equation (2.26)), the Equation (2.29) can be expressed:

This means that higher values of



To − Ts (Q j ) (m 0 C p ) 1 − os = = 2 ac + (2.31) Tc − Ta Tc − Ta 2

The right term of Equation (2.31) shows the relative importance of the two characteristic fluxes: ac and (1-os)/2 in TCE. By defining a heat transfer coefficient h and a Nusselt number Nu related to the air curtain as follows:

Q j = hHe(Tc − Ta ) (2.32)

CFD Optimization of Perturbed Air Curtains for Refrigerated Display Cabinets

Nu =

41

Q j hH = (2.33) λ λ (Tc − Ta )

the relation (31) could also be written as:



To − Ts (Q j ) (m 0 C p ) Nu = = (2.34) Tc − Ta Tc − Ta Re Pr

Cpµ ρU o e and Pr = . λ µ In a forced convection regime, many authors [18,19,32,37,38] concluded that (Nu/Re Pr) depends only on the ratio (H/e). Another important quantity that was characterized by many researchers [8,17,23,25,39] is the infiltration rate or thermal entrainment defined by the ratio: where Re =

TE =

To − Ts (2.35) To − Ta

TE varies between 0 and 1 and can be interpreted as the efficiency of an air curtain in infiltrating the outside air. The higher values of TE represent higher infiltrations; those are undesirable. In lower limit, TE → 0 occurs when Cs → C0. In our model, this corresponds to os → 1 and as → 0. This means that the infiltrated part entrained from the ambient goes to zero and the cavity is completely sealed. In contrast, TE → 1 occurs when Cs → Ca. Therefore, at the nozzle exit the air is entirely entrained from the ambient and similarly no portion of the air curtain reaches the nozzle exit. In our model, this corresponds to as → 1 and os → 0. This means the air curtain ceases to seal the cavity, due to its breaking by external forces, for example. Evidently, such a situation is highly undesirable in regards to the cavity sealing purposes. In our model, TE could be written as:



 T − To  TE = as + cs  c (2.36)  Ta − To 

The first term “as” represents the direct infiltration flowing directly from the ambient to the nozzle exit. The second term represents the portion of “cs” originating from the ambient. It could be viewed as an indirect infiltration flowing from the ambient to the nozzle exit but passing through  Tc − To  is induced by exchanges between the cavity and ambient. Note that the cavity. The ratio   Ta − To  the simplified model elaborated by Amin et al. [8] neglects exchanges between the cavity and the ambient. As a consequence, Tc = To and TE = as.

2.8 RESULTS AND DISCUSSION In this part, experimental and numerical results obtained with the two modeling approaches, CFD and the global model, are compared and contrasted. The comparisons concern jet characteristics, air flow pattern and global exchange through the air curtain with and without external lateral flow.

42

Computational Fluid Dynamics in Food Processing

2.8.1 Without External Perturbation 2.8.1.1 Jet Characteristics and Airflow Patterns Figure 2.10 illustrates a typical cross-section in the mid plane (z/L = 0) showing numerical and experimental PIV results of velocity vectors related to the 2D flow induced by the air curtain surrounded by the cavity and the ambient. A qualitatively reasonable agreement is observed between predicted and experimental results concerning the main airflow related to the air curtain and the global recirculation within the cavity, which could be viewed as a secondary flow. The presence of the circulation cell in the cavity affects the air jet trajectory, which is slightly deviated towards the ambient. In comparison with experimental data, the RSM predicts a more stretched recirculation. The high rate of mixing induced by this recirculation could potentially entrain the homogenisation of temperature or concentration in case of heat or mass transfer with the ambient. In Figure 2.11, related to the centreline jet velocity decay in the mid-plane (z/L = 0), experimental results exhibit a potential core that extends up to x/e = 3. This finding accords with previous work

FIGURE 2.10  Velocity vectors for unperturbed jet (Ulf = 0 ms–1) at the mid-plane (z/L = 0): comparison between numerical (RSM) and experimental (PIV) results.

FIGURE 2.11  Decay of the dimensionless centerline jet velocity at the mid-plane (z/L = 0): comparisons between experimental and numerical results.

CFD Optimization of Perturbed Air Curtains for Refrigerated Display Cabinets

43

concerning free jet [40] or air curtains [41]. Comparisons between turbulence models and experimental data clearly show that k-ɛ model significantly overpredicts the length of the potential core, and therefore fails to predict the jet centerline decay in the transition zone. On the contrary, a good agreement is observed with the RSM predictions concerning the jet centerline decay in the initial and the transition zones. A critical comparison between the two turbulence models is provided in the paragraph 2.8.2.2. The unnormalized and normalized streamwise velocity profiles at selected downstream locations are shown in Figures 2.12a and 2.12b. Figure 2.12a compares numerical and experimental results, while Figure 2.12b compares experimental data with the theoretical profile obtained by Gaussian-exponential function (Equation 2.1). In Figure 2.12a, numerical and experimental results related to the position x/e = 5, which corresponds to the half-length of the air curtain, confirm the jet deviation outwards. However, local differences are observed between numerical and experimental values concerning velocity profiles near the nozzle exit at x/e = 9, even if the trends of these two profiles are similar. In fact, the RSM profile exhibits unphysical deviation of the jet outwards at x/e = 9, which could be attributed to the effect of the recirculation into the cavity on the jet airflow. We also noted a reasonable agreement between experimental and numerical data concerning velocity profiles. Figure 2.12b shows that downstream of the potential core (x/e > 3), the mean velocity profiles are Gaussian and become approximately selfsimilar, especially in the free part of the air curtain flowing into the ambient. Due to the confinement effect and the interaction with the recirculation into the cavity, differences are observed between

FIGURE 2.12  (a) Unnormalized and (b) normalized streamwise velocity profiles at the mid-plane (z/L = 0) for unperturbed air curtains.

44

Computational Fluid Dynamics in Food Processing

FIGURE 2.13  Half-width growth of the jet at the mid-plane (z/L = 0).

experimental and theoretical values related to the inner part of the air curtain developed into the cavity. In addition, the good agreement with the theoretical formulation proposed by Reichardt [33] justifies the assumption made by many authors to assimilate the air curtain to a plane free jet. All the self-similar profiles conform closely to a Gaussian relation (Equation 2.1). Likewise, the streamwise variations (Figure 2.13) of the normalized velocity half-widths, y0.5/e, conform to the far-field theoretical relationship (Equation 2.2). A quasi-linear regression approximation of this experimental growth rate curve gives a value of the slope Ky = dy0.5/dx = 0.13, which is slightly higher than values generally quoted in the literature [40]. This could be easily explained by the fact that our investigations concern the near field region, while the majority of studies in the literature concern the far field region. We also notice that the RSM slightly underestimates the jet expansion. 2.8.1.2 Global Exchanges Through Air Curtain Assuming heat and mass transfer analogy makes it possible to validate the global model by comparing numerical results with experimental data obtained from literature related to heat transfer through air curtains. Figure 2.14a and 2.14b present comparisons between our model and experimental T − Ts T − Ts Nu 1 and o or theoretical data related to TE = o = = respectively. Qualitatively, T0 − Ta Tc − Ta Re Pr TCE a good agreement between numerical and experimental data is observed for H/e = 10 and 20. The differences were on the same order of magnitude as those related to experimental data provided by the different authors. The results confirm the quasi-proportionality of exchanges through the air curtain in regard to the H/e ratio. An increase of H/e from 10 to 20 entrains an increase of  To − Ts   To − Ts   T − T  and  T − T  from 0.16 and 0.32 to 0.32 and 0.34 respectively. Two times higher values 0 a c a for these quantities mean that the jet is two times less efficient in terms of energy loss and thermal sealing because of the higher amount of infiltrated ambient air. In addition to these quantities, the global model developed in this study permits quantification of the various dimensionless fluxes exchanged between all compartments for H/e = 10 and 20 (Table 2.3). Overall, predicted values confirm the quasi-symmetry of the air fluxes exchanged from both sides of the air curtain. (oc ≈ oa ≈ cs ≈ as). However, this symmetry is less more pronounced for e = 0.02 m (H/e = 20) than for e = 0.04 m (H/e = 10). As indicated above, these results confirm the importance of the H/e parameter on air fluxes across the air curtain. For the studied configuration, the air flux exchanged between the ambient and the cavity “ac” is twice as important for H/e = 20 than for H/e = 10, where it increases from 0.16 to 0.315. Conversely, increasing H/e causes a reduction of the “os” flux by 50% because of the infiltrated ambient air.

45

CFD Optimization of Perturbed Air Curtains for Refrigerated Display Cabinets

To − Ts T − Ts and (b) o vs H/e: Comparisons between our model and experiT0 − Ta Tc − Ta mental or theoretical data quoted in literature.

FIGURE 2.14  Evolution of (a)

TABLE 2.3 Air Fluxes Obtained with the Global Model for Unperturbed Jet (e; U0; H/e; Re) (0.02; 3; 20; 8.103) (0.04; 3; 10; 16.103)

ac

oc

os

cs

as

ca

oa

0.0315 0.016

0.25 0.16

0.45 0.68

0.287 0.16

0.263 0.16

0 0.016

0.3 0.16

2.8.2 With External Lateral Flow 2.8.2.1 Effect of ELF on Airflow Patterns In an attempt to investigate the three-dimensional effects of the ELF on the air curtain, Figure 2.15 shows mean flow velocity vector fields for perturbed air curtain at Ulf = 1 m/s in four planes: 0.05 m, 0.1 m, 0.25 m and 0.4 m from the lateral side where the ELF comes in, which correspond to z/L = 0.4, z/L = 0.3, z/L = 0 and z/L = –0.3 respectively. The results related to PIV, RSM and k-ɛ are depicted in three columns (a, b and c, respectively) and ordered from top to bottom in the

46

Computational Fluid Dynamics in Food Processing

FIGURE 2.15  Airflow patterns in x-y plane at different z-locations, for perturbed air curtain (U0 = 3 m/s and Ulf = 1 m/s): comparison between (a) PIV, (b) RSM, and (c) k-ɛ model.

ELF/lateral direction. This representation enables direct comparisons between numerical results obtained with RSM and k-ɛ with the PIV data for the different locations. The results clearly show a strong 3D effect along the axis of the ELF. In comparison with Figure 2.10, which could be considered as a reference case (without perturbation), the results of Figure 2.15 suggest that the highest effect occurred at the lateral side of the air curtain, which corresponds to the beginning of the interaction between the air curtain and the lateral flow (z/L = 0.5). Among the presented data, Figure 2.15a (z/L = 0.4) exhibits the strongest effect of the external perturbation on the air curtain. As can be seen, the jet is completely deflected towards the outside and the cavity is locally unsealed. In this plane, the jet deviates immediately downstream of the exit nozzle and breaks at x/e = 0.6 approximately, which in turn prevents the formation of the recirculation within the cavity.

CFD Optimization of Perturbed Air Curtains for Refrigerated Display Cabinets

47

With increased distance downstream of the lateral edge of the jet, the effect of the perturbation on the air curtain is progressively reduced. At z/L = 0.3 (Figure 2.15a), the jet conserves its vertical trajectory until x/e = 2, when it begins to deviate. In the lower part (2 < x/e < 10), the jet exhibits a strong curvature. The interaction with the lateral flow enhances the lateral spread of the jet, especially at the bottom level (x/e = 10). Therefore, a great part of the air curtain is deflected towards the outside and the cavity is partially sealed. By increasing the jet deflection, the air spilling into the cavity is reduced and the corresponding global recirculation is less active and entrained to the bottom. For actual RDC, this behavior for the air curtain is highly undesirable because it amplifies the ‘cold feet’ effect; a much larger mass of air from the cold air curtain overspills the bottom of the cabinet [9]. At the mid plane (z/L = 0) no noticeable effects due to the ELF were observed on the jet behavior, which conserves its stability (Figure 2.15a). As a consequence, the airflow related to the air curtain and to the recirculation within the cavity is very close to the baseline. Further downstream (z/L = –0.3) the jet conserves its stability but it is slightly deviated inside the cavity. Due to the ELF effect, experimental (Figure 2.15a) and RSM results (Figure 2.15b) confirm the presence of an external vortex loop (EVL), developing in the outer shear layer of the jet in the ambient side. This EVL, which could be viewed as an additional secondary stress induced ELF-flow with swirl effects, results in a complex shear flow instead of simple free shear layer when compared with an unperturbed jet. This EVL strongly interacts with the air curtain, implying a substantial increase of streamline curvature associated with a strong 3D effect along the air curtain in the lateral direction. As can be seen, this EVL located initially near the jet inlet nozzle at z/L = 0.4 is convected downstream along the ELF direction and thus it moves progressively to the bottom area of the jet at z/L = –0.3. For actual RDC configurations, this EVL induced by the ELF would enhance mixing processes between refrigerated air curtain and warm ambient, implying an increase of energy consumption and air temperature in the conservation zone above the higher limit for the proper conservation of food products. 2.8.2.2 Turbulence Modeling Performance Despite the complexity of airflows, the results obtained with the RSM (Figure 2.15b) show a reasonably good agreement between numerical and experimental data. This concerns jet deviation and stability, airflow patterns and their evolution under the ELF. The same figure also shows the poor predictions given by the k-ɛ model (Figure 2.15c) and underlines its inability to predict the general behavior of air motion related to the air curtain sheared laterally. At z/L = 0.4, when experimental and RSM results show a jet deflected outside the cavity, the k-ɛ predicts a jet deflected inwards. Conversely, when experimental and RSM results show a slight deflection of the jet inside the cavity at z/L = –0.3, the k-ɛ predicts a slight jet deflection outwards. In addition, the k-ɛ overestimates the stability of the jet at z/L = 0.3 in comparison with PIV results. The failure of the k-ɛ model predictions could be explained by the complexity of the airflow resulting from the interaction between the air curtain and the ELF, implying a complex shear layer instead of a simple free shear layer including a high streamline curvature effect. For these complex flows, different authors [35,42,43] agree on the inadequacy of k-ε model to predict airflow patterns and underline its limitation by comparison with experimental data. Gibson and Rodi [44] showed that the standard k-ε model lacks sensitivity to curvature in contrast to the full Reynolds stress model. Leschziner and Rodi [45] derived after some simplifications the expression of the Cµ coefficient in the Reynolds stress transport equations in curvilinear coordinates. Cµ is not a constant, as in the standard k-ε models, but depends strongly on streamline curvature. In a comparative review, Nallasamy [43] concludes that the use of RSM models to account for curvature effects and secondary flows would improve the confidence in turbulence closure models. Leschziner [46] pointed out that k-ɛ model does not respond correctly to curvature strain, normal straining and rotation and is more appropriate for flows in which a single shear stress is the dominant dynamic link between turbulence and the mean flow. A similar observation was formulated by Bsara and Jakirlic [47],

48

Computational Fluid Dynamics in Food Processing

who consider that even if the performance of k-ɛ model could be regarded as acceptable in the flows dominated by the mean shear, it fails to capture important flow features in most of the flows departing from the thin shear layer approximation: flows induced by streamline curvature, swirling flows, flows with stagnant regions, etc. The poor results given by the k-ɛ model could also be explained by the fact that it’s more appropriate for fully developed isotropic turbulence, which is not the case with anisotropic K–H vortices due to their similar topologies and alignment of their rotational axis in the inner field region (Figure 2.4). The additional rotating, shear and swirling effects due to streamline curvature and the EVL impose a strong anisotropy on the eddy viscosity field. Eddy viscosity has no longer an isotropic, scalar nature as enforced by the k-ɛ formulation, but a tensorial one. To better illustrate the anisotropic effect in the inner field region, Figure 2.16 shows the Urms and Wrms (root mean square velocity fluctuation in x and z directions: streamwise and lateral directions) profiles obtained with LDV in the mid plane (z/L = 0) at x/e = 2 without and with ELF (Ulf = 1 m/s). Without perturbation, a strong anisotropy is observed between streamwise and lateral components. This concerns outer shear layers in the ambient and the cavity sides as well as the peak values, where Urms values are almost 60% higher than Wrms values. Under the ELF effect, the Urms and Wrms values become closer, especially in the outer shear layer in the ambient side, due to the direct influence of the ELF. The ratio between the peak values decreased to 30% for the outer shear layer in ambient side and to 53% in the cavity side. Obviously, the ELF enhances the isotopy of turbulence but with vanishing

FIGURE 2.16  Effect of the ELF on RMS velocity fluctuations (LDV) in the mid plane (z/L = 0) at x/e = 2: comparison between (a) unperturbed and (b) perturbed air curtain (Ulf = 1 m/s).

CFD Optimization of Perturbed Air Curtains for Refrigerated Display Cabinets

49

effect from the ambient side where the ELF flows to the cavity side. These strong modifications affecting the behavior of normal stresses, including attenuation and amplification of the turbulence anisotropy, reflect the importance of the pressure-strain term (Equation (2.10)), which controls the redistribution of turbulence energy among the normal stresses in the RSM. Conversely, the k-ɛ does not resolve normal-stress anisotropy. In spite of comprising two principal directions (X: related to air curtain and Z: related to ELF), this configuration displays all features of a three-dimensional flow, necessitating solution of the transport equation for all three velocity components and all six Reynolds stress components. Note that the orientation of the jet deflection occurs in the Y direction, where no dominant mean flow is present. As a consequence, the wrong predictions given by the k-ɛ model concerning the jet deflection in the Y direction only result in the selective influence of the anisotropic Reynolds-stress field on the mean flow. This point highlights the superiority of the RSM, as it only enables resolving Reynolds-stress anisotropy. All these aspects justify the use of the second moment closure instead of the two equation turbulence models in this near field region (x/e