Flow Boiling of a Dilute Emulsion In Smooth and Rough Microgaps 3031277724, 9783031277726

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Mechanical Engineering Series

Brandon M. Shadakofsky Francis A Kulacki

Flow Boiling of a Dilute Emulsion In Smooth and Rough Microgaps

Mechanical Engineering Series Editor-in-Chief Frank A. Kulacki, Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN, USA

The Mechanical Engineering Series presents advanced level treatment of topics on the cutting edge of mechanical engineering. Designed for use by students, researchers and practicing engineers, the series presents modern developments in mechanical engineering and its innovative applications in applied mechanics, bioengineering, dynamic systems and control, energy, energy conversion and energy systems, fluid mechanics and fluid machinery, heat and mass transfer, manufacturing science and technology, mechanical design, mechanics of materials, micro- and nano-science technology, thermal physics, tribology, and vibration and acoustics. The series features graduate-level texts, professional books, and research monographs in key engineering science concentrations.

Brandon M. Shadakofsky • Francis A. Kulacki

Flow Boiling of a Dilute Emulsion In Smooth and Rough Microgaps

Brandon M. Shadakofsky Department of Mechanical Engineering University of Minnesota Minneapolis, MN, USA

Francis A. Kulacki Department of Mechanical Engineering University of Minnesota Minneapolis, MN, USA

ISSN 0941-5122 ISSN 2192-063X (electronic) Mechanical Engineering Series ISBN 978-3-031-27772-6 ISBN 978-3-031-27773-3 (eBook) https://doi.org/10.1007/978-3-031-27773-3 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

This book describes an advance in the understanding of heat transfer and fluid flow in flow boiling of water and a dilute emulsion in a small gap flat channel, or microgap. Measurements are made in microgaps of 200, 500, and 1000 μm hydraulic diameter with mass flux of 150, 350, and 550 kg/m2s. The emulsions comprise droplets of FC-72 suspended in water at volume fractions of 0.1, 0.5, 1, and 2% without the presence of a surfactant. Systematic measurements are conducted for a smooth surface and three microporous surfaces of 708, 633, and 412 μm thickness and bulk porosity of 0.354, 0.410, and 0.413, respectively. In flow boiling of water on a smooth surface, the single-phase heat transfer coefficient increases with increasing mass flux and decreasing gap size. After onset of nucleate boiling and prior to transition to the critical heat flux, heat transfer coefficients collapse to one curve. Critical heat flux increases with increasing gap size and mass flux. The effects of the liquid sub-cooling, applied heat flux, mass flux, and gap size on the two-phase heat transfer coefficient are correlated using the Nusselt, Jakob, Reynolds, and boiling numbers, with 98% of the experimental data within ±30% of the predicted Nusselt number. In flow boiling of emulsions on a smooth surface, increasing the volume fraction to 0.1–0.5% enhances cooling in some cases, but increasing volume fraction to 1–2% provides no additional benefit and decreases heat transfer in some experiments. The emulsion improves heat transfer compared to that for water for larger gap sizes and lower mass flux. The heat transfer coefficient for the emulsion generally increases with increasing wall temperature. Based on these observations, it is posited that two heat transfer mechanisms coexist: (1) conduction in a thin film of FC-72 impairs heat transfer owing to the low conductivity of FC-72; (2) mixing due to boiling of the FC-72 increases the heat transfer coefficient. From these two mechanisms, correlations are developed for the emulsion heat transfer coefficient and the ratio of the emulsion and water heat transfer coefficients. These correlations include a new dimensionless number, GCpd/kd, to account for conduction in the thin film and sensible heat advected from the wall. A very good fit is seen for the heat transfer coefficient, and 95.7% of the experimental data are within v

vi

Preface

±10% of the correlation. For heat transfer coefficients normalized by water values, 58.7% of the data falls within ±30% of the predicted value, and the correlation captures the trend of the data well. In flow boiling of water on a porous surface, enhanced heat transfer is measured at larger mass flux and gap sizes. The best heat transfer for the porous surfaces is consistently displayed on a surface of 708 μm thickness with 0.354 bulk porosity (Porous Surface 1). Pressure drop for the porous surfaces is generally larger than that for the smooth surface, and the largest pressure drops are measured for a surface with 633 μm thickness and 0.410 bulk porosity (Porous Surface 2). In boiling of emulsions on the porous surfaces, Porous Surface 1 shows both enhanced and degraded heat transfer. For Porous Surface 2, the emulsions enhance heat transfer for much of the data set, and this is especially pronounced for smaller gaps. The emulsions also decrease the measured pressure drop on Porous Surface 2 for the cases where heat transfer is increased. Porous Surface 3 (412 μm thickness and 0.413 bulk porosity) shows similar behavior for the emulsions and water for most of the data set. Better emulsion heat transfer behavior for Porous Surface 2 is likely due to the open pore network seen from both the edge and top. The open pore network allows FC-72 droplets to flow down into the porous structure and nucleate bubbles. The resulting vapor can also release more easily in this open structure. To summarize these findings, regime maps are presented to show where the emulsions either enhance or degrade heat transfer on each surface. Minneapolis, MN, USA

Brandon M. Shadakofsky Francis A. Kulacki

Contents

1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

2

Experimentation and Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Validation of Experimental Methodology . . . . . . . . . . . . . . . . . . .

7 20

3

Flow Boiling of Water in a Microgap . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Flow Regimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3 Flow Boiling Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . 3.1.4 Comparison with Microchannels . . . . . . . . . . . . . . . . . . . . 3.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25 25 25 27 30 31 33

4

Flow Boiling of Dilute Emulsions in a Microgap . . . . . . . . . . . . . . . . 4.1 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Effect of System Properties . . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Visualization of Pool Boiling . . . . . . . . . . . . . . . . . . . . . . 4.1.3 Flow Boiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.4 Mechanisms in Pool Boiling . . . . . . . . . . . . . . . . . . . . . . . 4.1.5 Roesle-Kulacki Pool Boiling Model . . . . . . . . . . . . . . . . . 4.1.6 Bulanov Pool Boiling Model . . . . . . . . . . . . . . . . . . . . . . 4.1.7 The Rozentsvaig-Strashinskii Flow Boiling Model . . . . . . . 4.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43 43 44 50 52 56 57 60 63 66

5

Flow Boiling on a Porous Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1 Description of Porous Media . . . . . . . . . . . . . . . . . . . . . . 5.1.2 Methods of Creating Porous Surfaces . . . . . . . . . . . . . . . . 5.1.3 Boiling on Microporous Surfaces . . . . . . . . . . . . . . . . . . . 5.2 Experimental Results: Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Experimental Results: Dilute Emulsions . . . . . . . . . . . . . . . . . . . .

77 77 77 78 79 82 88

vii

viii

Contents

6

Physical Mechanisms and Correlation . . . . . . . . . . . . . . . . . . . . . . . . 103

7

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Flow Boiling on Smooth Surfaces . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Flow Boiling on Porous Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Summation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

111 111 112 114

Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

Nomenclature

*

Area, m2 Archimedes number, ðρeff - ρb Þgρd D3 =μ2eff Series constant Specific work due to body forces, W/kg Boiling number, q″/Ghfg Body force vector, N

*

Constant Constant pressure specific heat, J/kgK Constant volume specific heat, J/kgK Bubble diameter, m Hydraulic diameter, m Droplet diameter, m Specific work due to interaction with other phases, J/kg Specific internal energy, J/kg Source flow strength, m3/s Force, N

A Ar a B Bl b C Cp Cv D Dh d E e F

F f G → g H h hfg ifg I J Ja K k

Friction factor, Eq. (4.24) Mass flux, kg/m2s Gravity vector, m/s2 Height of the microgap, m Heat transfer coefficient, W/m2K Latent heat of evaporation, J/kg Latent heat, J/kg Applied current, A Nucleation rate, 1/m3s Jakob number based on subcooling, Cp(Tsat - Ti)/hfg Porous layer permeability Thermal conductivity, W/mK ix

x

L l

Nomenclature

*

Boundary layer thickness, m Pipe length, m Force due to interaction with other phases, N

→

Mass, kg Mass flow rate, kg/m3s Total number of droplets in a boundary layer Nusselt number, hDh/kf Number of boiling droplets in a boundary layer Number of droplets that deposit on a hot surface Pressure, Pa Prandtl number, ν/α Probability that a droplet boils Energy, J Volumetric flowrate, m3/s Heat, W Radius, m Rayleigh number, Prgβρ2 d3wire ðT- T 1 Þ=μ2 Reynolds number, ρDhum/μ Radial coordinate, m Strain rate, s-1 Stefan number, C p d ðT- T sat Þ=ifg Temperature, K Traction tensor, N/m2 Film thickness, m Velocity vector, m/s

M m m_ N Nu nb nd P Pr p Q Qflow q R Ra Re r S St T T t U u u u′ V Vapplied Vd v W w x Y y y* z

x-direction velocity, m/s Mean velocity, m/s Velocity fluctuation, m/s Volume, m3 Applied voltage, V Volume of droplet, m3 y-direction velocity, m/s Width of the microgap, m z-direction velocity, m/s Stream wise coordinate, m Eigenfunction Normal direction, m Dimensionless vertical coordinate, y* = 2y/H, Eqs. (2.5) and (2.7) Span wise coordinate, m

Nomenclature

Greek Symbols α αk β Γ ΔT ΔWcr δ δij ε εdiss η ηcoll λ μ ν ρ σ τ ϕ φ

Thermal diffusivity, k/ρCp, m2/s Volume fraction for the kth phase Thermal expansion coefficient, K-1 Mass production rate, kg/m3s Tw - Tsat, K Work of formation of a critical size bubble, J Uncertainty Kronecker delta Disperse phase volume fraction Turbulent energy dissipation Kolmogorov length scale, m Collision efficiency Eigenvalue Dynamic viscosity, Ns/m2 Kinematic viscosity, m2/s, μ/ρ Density, kg/m3 Surface tension, N/m2 Boundary layer residence time, s Porous layer porosity, Eq. (5.1) Number of collisions between droplets and bubbles in a chain reaction

Subscripts 0 1 b c coll cond cr Dh d e eff f film g i k kj m

Reference state The surroundings Disperse component, vapor Continuous component From collisions From condensation Of critical size Based on the hydraulic diameter Disperse component, liquid Exposed to continuous component flow Effective value for the emulsion Liquid In the oil film Vapor Inlet For the kth phase For the kth phase relative to the jth phase Mean

xi

xii

Nomenclature

min mix o pore s sat solid T void w wire

Minimum Due to mixing Covered by an oil film At the pore scale Surface Saturated condition Porous surface solid Turbulent Porous surface void space Wall Pertaining to the wire

Superscripts ′ ″

Dummy variable Flux

Other Symbols ∂ ∂ ∂ ∇ =bi ∂x þ bj ∂y þb k ∂z

Cartesian gradient operator

ðÞ

Average

Chapter 1

Introduction

Though the first studies of boiling as a mode of cooling date to the 1700s, research conducted on the topic increased dramatically with the rise of nuclear energy and rocket research beginning in the 1940s [1, 2]. From that time, the subject has proven to be a fruitful area of study, but there are still many aspects of the boiling mechanism that are not well understood. To underscore this point, in 1963 Westwater published a paper titled “Things We Don’t Know About Boiling Heat Transfer” which raised questions pertaining to boiling that were unanswered at the time [3]. This theme also was discussed by Lienhard in 1988 in commemorating the 25th anniversary of Westwater’s paper [4]. While many of the questions raised then have been answered, others remain. Research on boiling continues seeking to describe the heat transfer mechanisms present during bubble nucleation, growth, and departure from a heated surface. Much of the difficulty is attributable to boiling being an unsteady process that is in thermodynamic disequilibrium with strong coupling between fluid motion and heat transfer. In addition, difficulty arises from experiments demonstrating conflicting results, possibly due to measurements that were not well controlled, poor experimental design, large experimental uncertainty, or lack of control of thermal boundary conditions [5]. The state of affairs was such that some researchers questioned whether understanding the physical mechanisms is feasible, as noted by Dhir, who argued for the use of computational fluid dynamics for prediction rather than mechanism-based correlations [6]. However, recent investigations continue on the physical mechanisms of heat transfer in pool boiling [7], flow boiling in microchannels [8–12], and bubble nucleation in flow boiling [13], to name a few. Though the questions about heat transfer mechanisms in pool boiling and flow boiling at the conventional scale (characteristic dimension ~3 mm and larger) remain unresolved and important, the boiling curve and flow regimes for these applications have been well-characterized for a variety of fluids. Consider the pool boiling curve shown in Fig. 1.1a. On this curve, several letters are marked corresponding to transition to a new fluid state, and these states are qualitatively depicted in © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 B. M. Shadakofsky, F. A. Kulacki, Flow Boiling of a Dilute Emulsion In Smooth and Rough Microgaps, Mechanical Engineering Series, https://doi.org/10.1007/978-3-031-27773-3_1

1

2

1

Introduction

Fig. 1.1 (a) Pool boiling curve for water at atmospheric pressure. (b) Flow structure for each respective point on the pool boiling curve [2]

Fig. 1.1b. From points A to B and potentially further along the dotted line shown, single-phase natural convection is the mode of heat transfer. At point B, bubbles start to nucleate and grow on the surface indicating the presence of two-phase heat transfer. Point B is commonly denoted the onset of nucleate boiling (ONB) and is at a wall temperature higher than the corresponding saturation temperature of the fluid (100 °C here). In both pool and flow boiling, it is often necessary for the surface temperature to be higher than the saturation temperature of the fluid before nucleation begins. Thus, the system exists in a metastable state until the wall temperature is high enough to nucleate bubbles larger than a critical size. The difference between the wall temperature at ONB and the saturation temperature is termed the surface superheat. The fluid near the wall generally demonstrates a larger superheat in pool boiling than in flow boiling. It is possible for point B to be further along the dotted line shown, depending on the surface geometry, pressure, fluid temperature, and the type of fluid. Once ONB is reached, the system will rapidly transition from point B to B′. Heat transfer mechanisms present during boiling are much more efficient than in natural convection, resulting in a much larger heat transfer coefficient once ONB is reached. This will cause the surface temperature to decrease quickly if the heat flux is constant. The temperature difference between locations B and B′ is the temperature

1

Introduction

3

overshoot. It is desirable to limit this overshoot in thermal design, and the overshoot is not present in all systems. Between points B′ and C, nucleate boiling is the dominant heat transfer mode. In this regime, small bubbles nucleate on the surface and grow and depart, and the heat transfer mechanisms associated with the bubble growth and departure are very efficient at transferring heat from the heated surface to the fluid. As the wall temperature or heat flux increases, the frequency of bubble growth and release increases, resulting in higher heat transfer coefficients with increasing wall temperature. As the wall temperature or heat flux increases further to point C, neighboring bubbles start to interact and form larger vapor structures on the wall. These vapor structures slightly inhibit heat transfer, causing a change in the slope of the boiling curve. As the wall temperature increases even further to point D, these vapor structures cover large portions of the wall, limiting the ability of liquid to wet the wall. Because heat transfer is much less efficient in gases than in liquids, the wall temperature increases dramatically from point D to D′ without increasing the heat flux. The heat flux dissipated at point D is termed the critical heat flux (CHF). If CHF is reached, failure of the surface (or system part) cooled is often the result. Generally, the portion of the boiling curve between points D and E cannot be accessed unless the wall temperature is carefully controlled. In this region, the wall is covered by a vapor film, but liquid will periodically break through the vapor to rewet portions of the wall. Point E is denoted the Leidenfrost point,1 and it marks the transition to stable film boiling where heat transfer is characterized primarily by conduction and convection within a vapor film. The film boiling region extends from point E to F and beyond. This discussion elucidates the strong coupling between two-phase flow behavior and heat transfer, with flow behavior dependent on the heat transfer and heat transfer dependent on flow behavior. This coupling is not present in single-phase heat transfer wherein the flow behavior can be determined first (under the assumption of constant thermophysical properties) and then used to determine the heat transfer. Although the discussion above revolves around pool boiling, the fluid-thermal coupling is also present in flow boiling. In that case fluid flow behavior is slightly different owing to the presence of mean flow and shear. The typical flow regimes present in flow boiling are shown in Fig. 1.2. When nucleation begins in flow boiling, small bubbles are formed and release from the surface. These bubbles largely remain independent of each other, and the

The Leidenfrost point is the transition to stable film boiling. For surfaces at or above the Leidenfrost point, the surface temperature is significantly higher than the saturation temperature of the fluid. This results in a vapor film covering the entire wall above which liquid is suspended and inhibited from contacting the wall. If a surface is at the Leidenfrost point and the surface temperature decreases slightly, the vapor film collapses, and nucleate boiling is reestablished. Thus, the Leidenfrost point is the minimum temperature at which film boiling can occur. The corresponding heat flux is the minimum film boiling heat flux. More information on the Leidenfrost temperature can be obtained in either [1, 2] or reference books specifically related to film boiling.

1

4

1

Introduction

Fig. 1.2 Flow regimes for flow boiling in a horizontal tube [2]

flow is termed bubbly flow. As thermodynamic quality increases, either with increasing position downstream or an increase in local wall temperature/heat flux, the flow transitions to plug flow or slug flow, where the bubbles start to agglomerate and form larger slugs. At a fixed location, the wall periodically sees vapor slugs passing with a thin liquid layer below them and with successive slugs separated by liquid bridges. As quality increases further, the flow can transition to either wavy flow or annular flow. In wavy flow, the vapor and liquid separate, with the vapor occupying the top of the pipe and the liquid occupying the bottom due to gravity. Ripples can often be seen on the interface between the vapor and liquid. This flow regime is also denoted stratified flow if these ripples are not present. Stratified flow is seen generally at lower flow rates and wavy flow at high flow rates. Because these regimes are dependent on gravity, they are not seen when flow is in the vertical direction. In annular flow, a thin liquid film wets the entire wall surface and surrounds a core of vapor. Heat transfer coefficients are generally large when annular flow is present owing to heat transfer in this thin liquid film. However, as the wall temperature or heat flux increases, the film will further thin until portions of the wall become covered by vapor patches, and the system will transition to critical heat flux. Though this classification of flow and heat transfer regimes is used here, others exist with transitions to sub-states between those described. Not all systems will demonstrate all of these flow regimes. Specific regimes present depend largely on the mass flux, temperature (or heat flux), pressure, wall geometry, and the hydraulic diameter of the flow conduit. In experiments, specific flow regimes are often created by combining the liquid and vapor (a gas is often used) upstream to create flows with a given thermodynamic quality, or void fraction in some cases. The flow of the two components creates a superficial velocity for each. For flow boiling, the current focus of research has recently shifted from largescale to small-scale conduits. Most of this research has been conducted for microchannels (channels with W/H < 10), with research on flow boiling in microgaps (channels with W/H > 10) conducted only recently. Some applications for flow boiling in microchannels range from miniature refrigeration systems to cooling of PEM fuel cells [14]. The application that may prove to be the most important in the future is cooling of high-performance electronics. As the power

1

Introduction

5

density of modern computer chips continues to increase, it has become necessary to explore cooling means other than forced gaseous convection. Both single-phase and two-phase cooling strategies are being explored, with studies focused on boiling in microchannels and microgaps showing that the heat transfer coefficient increases with decreasing channel/gap size. Other means of increasing boiling heat transfer have been studied and shown to be effective, including the use of microporous surfaces or an emulsion (a mixture of two immiscible fluids) in pool and/or flow boiling. Thus far neither of these have been applied at the small scale. In the case of boiling emulsions, relatively few investigations exist, and almost the entirety of them have been conducted for pool boiling. Each of these areas individually or in combination may be a viable method of improving cooling in electronic applications. More investigation is needed, however, before any of them can be applied in design. In this context, the thermal engineer as an applied scientist has two objectives: to better understand the mechanisms of boiling heat transfer and to apply fundamental knowledge to the design of systems that take advantage of any enhancement in heat transfer while minimizing any drawbacks due to the boiling process. Both depend on the existence of a large and robust experimental database. To these ends the focal objectives of this book are: • To review the relevant literature on boiling in microgaps, of emulsions and on porous surfaces • To build a large experimental database for flow boiling of emulsions in microgaps with smooth and microporous surfaces and to compare heat transfer performance to that of water under similar flow boiling conditions • To draw conclusions from the experimental data about the physical mechanisms for flow boiling of emulsions • To determine correlations for boiling of water and emulsions in microgaps that can be used for thermal design

Chapter 2

Experimentation and Procedure

Flow boiling experiments were conducted with a flow loop in which the mass flux, concentration of the disperse component, inlet bulk temperature, and wall temperature were controlled (Fig. 2.1). The flow loop includes a recirculation loop with a heater to control the temperature of the fluid in the fluid reservoir. A second heater is located just before the entrance to the test section to account for any heat losses to the surroundings while the fluid flows from the reservoir to the test section. The inlet fluid temperature for a given experimental run is thus set using these two heaters which are controlled with proportional integral derivative (PID) controllers. Total volumetric flow of the emulsion is determined by collecting a volume of fluid and measuring the amount of time required for that volume of fluid to collect. Additional details of the experimental procedure are given in [15]. The emulsions consist of suspended droplets of FC-721 in distilled water without a surfactant. Prior to each series of measurements, the water is degassed by boiling for 30 minutes to remove dissolved gases. It is then cooled to 30 °C before the FC-72 is added. The emulsion is prepared by pumping the mixture through the check valve in the emulsion preparation loop (Fig. 2.2). As the mixture flows through the check valve, the FC-72 breaks up into small suspended droplets. The mixture flows through this preparation loop for 5 minutes and then is transferred to the fluid reservoir (Fig. 2.1) which is maintained at 30 °C. Once the emulsion is created, the droplet diameter is independent of the length of time the emulsion is processed in the loop [16]. The measured distribution of droplet diameters is shown in Fig. 2.3. The distribution has a mean and standard deviation of 10.7 μm and 4.4 μm, respectively, and skewness of 1.5.

1

FC-72 is a thermally and chemically stable, dielectric Flourinert™ Electronic Liquid produced by 3M™ and intended to be used for leak detection and cooling of electronic equipment. At atmospheric pressure, the saturation temperature of FC-72 is 56 °C. See Appendix A for a list of thermophysical properties. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 B. M. Shadakofsky, F. A. Kulacki, Flow Boiling of a Dilute Emulsion In Smooth and Rough Microgaps, Mechanical Engineering Series, https://doi.org/10.1007/978-3-031-27773-3_2

7

8

2

Experimentation and Procedure

Key Valve Rotameter

P

Pressure Transducer

T

Thermocouple

T

Flow Direction

qpreheat 2

PID qpreheat 1

Fluid Reservoir

PID

Test Section T Condenser

Fig. 2.1 Experimental flow loop Fig. 2.2 Emulsion preparation loop

P

P

T

2

Experimentation and Procedure

Fig. 2.3 Measured distribution of emulsion droplet diameter

9 0.21 0.18

Probability

0.15 0.12 0.09 0.06 0.03 0.00 0

5

10

15

20

25

30

35

d [µm]

The test section includes a long entry length upstream of the heated wall to achieve fully developed laminar flow prior to the flow entering the heated section (Fig. 2.4). The mass flux is limited to less than 550 kg/m2s, and the largest gap hydraulic diameter is 1000 μm (Table 2.1). This combination of mass flux and hydraulic diameter are chosen to assure that laminar flow is present for all experimental trials. The test section also has a long exit region downstream of the heated portion. It has been shown experimentally that the design of the inlet and outlet manifolds affects the heat transfer performance in two-phase flow [17]. Thus, the length of the exit region is set to minimize the impact of the exit manifold design in the measurements reported in this book. A constant heat flux is applied to the lower surface in the heated portion of the test section with four Al-Ni heaters. The heaters are placed inside a Garolite™ G-102 box to limit the amount of heat loss to the surroundings. The heaters are in contact with a copper substrate through a thermal grease, and the top surface of the copper plate is exposed to the flowing fluid in the microgap. The copper plate has nine holes drilled to within 0.5 mm of the top surface, and E-type thermocouples are fixed in the holes to measure the surface temperature. The copper substrate used in the smooth plate experiments was finished with 2000 grit sandpaper. To create the microporous surfaces, a mixture of 3 M™ L-20227 copper powder, polypropylene carbonate, propylene carbonate, and methylethylketone (MEK) are sprayed onto the copper substrate. The copper powder, MEK, polypropylene carbonate, and propylene carbonate are combined in proportions of 202.1:86.5:6.7:1 by weight, respectively. The MEK evaporates at atmospheric pressure and is used to

2 Garolite™ G-10 has the properties ρ = 1800 kg/m3, k = 0.288 W/mK and in-plane and out-ofplane coefficient of thermal expansion of 9.9 × 10-6/°C and 11.9 × 10-6/°C, respectively.

10

2

Experimentation and Procedure

Fig. 2.4 (a) Test section. (b) Laboratory setup Table 2.1 Values of experimental quantities Parameter DH (μm) G (kg/m2-s) ε (%) Surfaces

Quantities 200, 500, 1000 150, 350, 550 0, 0.1, 0.5, 1, 2 1 smooth, 3 porous

decrease the viscosity of the mixture for spraying. The polypropylene carbonate and propylene carbonate strengthen the bond between the copper powder and the copper substrate and combine with oxygen during an oven brazing process to form H2O and CO2, leaving only the copper powder on the substrate. Prior to the brazing process, the mixture is sprayed onto the substrate using an Iwata CM-B airbrush at a pressure of 40 psig. The substrates are left at atmospheric conditions overnight to allow the MEK to evaporate. The substrates are then brazed

2

Experimentation and Procedure

Fig. 2.5 Temperature profile in the oven brazing cycle

11

Oven Temperature [°C]

1000 800 600 400 200 0 0

20

40

60

80

100

120

140

Time [min]

in a vacuum oven held at 0.01 mTorr and reaching a maximum temperature of 850 °C. The temperature-time profile of the brazing process is shown in Fig. 2.5, and images via scanning electron microscopy (SEM) of each brazed surface are shown in Figs. 2.6, 2.7 and 2.8. The mass of copper powder applied to each surface and various surface characteristics are shown in Table 2.2. The porosity is measured by converting the SEM images to black and white images wherein the black pixels represent voids and the white pixels the solid material. This requires the assumption that the porosity is uniform normal to the image plane, so it can be calculated using void and solid area rather than volume. This technique was previously applied to measure the porosity of frost layers in frost growth and melting studies [18, 19]. In the conversion process the software calculates a grayscale threshold to determine which gray pixels should be converted to black or white. At times, this threshold may result in solid areas from the SEM images being converted to black void pixels. Two examples of this are shown in Fig. 2.9 by the red circles demonstrating two areas where solid material can clearly be seen in the pore in the SEM image but whose grayscale value is determined to be void by the computer algorithm. In these examples, it can be argued that the areas in question should be counted as void because the solid material is behind the plane in view, and the porosity here is a planar measurement. However, if the user determines that a specific area has been counted as void and should be solid, or vice versa, the user can vary the threshold grayscale value and compare the original and converted images until the conversion is suitable.

12

2 Experimentation and Procedure

Fig. 2.6 SEM images for porous surface 1. (a) to (c) are images from the top with magnification of ×150, ×350, and ×550, respectively. (d) to (f) are images from the side with magnification of ×70, ×150, and ×300, respectively

2

Experimentation and Procedure

13

Fig. 2.7 SEM images for porous surface 2. (a) to (c) are images from the top with magnification of ×150, ×350, and ×550, respectively. (d) to (f) are images from the side with magnification of ×70, ×150, and ×300, respectively

14

2

Experimentation and Procedure

Fig. 2.8 SEM images for porous surface 3. (a) to (c) are images from the top with magnification of ×150, ×350, and ×550, respectively. (d) to (f) are images from the side with magnification of ×70, ×150, and ×300, respectively Table 2.2 Porous surface characteristics Surface 1 2 3

Surface area (in × in) 0.992 × 0.961 0.989 × 0.993 0.983 × 0.997

Coating volume (ml) 1.1 0.75 0.4

Coating mass (g) 1.308 0.844 0.611

Surface porosity 0.354 0.410 0.413

Coating depth (μm) 708 633 412

2

Experimentation and Procedure

15

Fig. 2.9 Conversion of the surface 3 top view SEM image into black and white. The red circles denote areas where the solid is determined to be void by the computer algorithm. (a) Original SEM image. (b) Converted black and white image

To measure the porosity, the SEM images were split into 25 segments, converted to black and white, and the porosity for each segment was calculated. The converted images and porosity distribution for each image are shown in Figs. 2.10, 2.11, and 2.12. The porosity distribution and average porosity for each surface are slightly different for the top and side views. The average porosity measured from the top view of each surface is that shown in Table 2.2. The temperature and pressure of the flowing fluid are measured upstream and downstream of the test section. The temperature is measured using type E thermocouples, and the pressure is measured with pressure transducers (Omega, PX-309). After the temperature and pressure measurements are taken downstream of the test section, the fluid flows through a heat exchanger to condense the vapor before returning to the inlet reservoir.

2 Experimentation and Procedure

16

a

d

b

e

c

f 0.30

0.20 0.15 0.10 0.05 0.00 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 f

Probability

Probability

0.25

0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 0.2

0.3

0.4

0.5

0.6

f

Fig. 2.10 Porosity measurement for porous surface 1. (a) to (c) are the original SEM image, converted black and white image and porosity distribution, respectively, for the side image at ×70 magnification. (d) to (f) are the original SEM image, converted black and white image and porosity distribution, respectively, for the top image at ×150 magnification

2

Experimentation and Procedure

17

a

d

b

e

c

0.25

f

0.15 0.10

0.20 Probability

Probability

0.20

0.25

0.15 0.10

0.05

0.05

0.00 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 φ

0.00 0.2

0.3

0.4

0.5

0.6

φ

Fig. 2.11 Porosity measurement for porous surface 2. (a) to (c) are the original SEM image, converted black and white image and porosity distribution, respectively, for the side image at ×70 magnification. (d) to (f) are the original SEM image, converted black and white image and porosity distribution, respectively, for the top image at ×150 magnification

18

2

a

d

b

e

Experimentation and Procedure

f

c

0.30

0.40 0.35

0.25

0.25 0.20 0.15

Probability

Probability

0.30 0.20 0.15 0.10

0.10 0.05 0.00 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 φ

0.05 0.00 0.2

0.3

0.4

0.5

0.6

φ

Fig. 2.12 Porosity measurement for porous surface 3. (a) to (c) are the original SEM image, converted black and white image and porosity distribution, respectively, for the side image at ×70 magnification. (d) to (f) Are the original SEM image, converted black and white image and porosity distribution, respectively, for the top image at ×150 magnification

2

Experimentation and Procedure

Table 2.3 Uncertainty estimates

19

Parameter Vapplied

Uncertainty ±1.5%

H

±13 μm

I

±1.5%

P

±1.0%

Q

±3–5%

T

±1.0 °C

G

±2–5%

h

±3–14%

q″

±2.1%

ε

±3–6% of measurement

All temperature and pressure measurements are collected with a custom LabVIEW® program.3 Once the copper surface temperature reaches steady state, measurements are recorded for 5 s at a sampling frequency of 50 Hz. The program then calculates the mean temperature and pressure at each measurement location from the respective 250 individual measurements. The program also acquires heater power, surface area, and heat loss as inputs by the user and calculates the net applied heat flux and heat transfer coefficient. The heat transfer coefficient is h=

q00net Tw - Tf

ð2:1Þ

where the wall temperature is taken to be the mean of the nine wall temperature measurements and the fluid temperature is the mean of the inlet and outlet fluid temperature. The uncertainty for measured and calculated items is given in Table 2.3. For quantities that include multiple uncertainty sources, the total uncertainty is determined by the square root of the sum of the squares.

3

Temperature and pressure measurements are collected using a National Instruments (NI) USB-9171 data acquisition device (DAQ) and an NI USB-6000 DAQ, respectively.

20

2

Experimentation and Procedure

Fig. 2.13 Channel geometry

y

x L

H

z

W

Heat flux is determined by multiplying the voltage and current output from the power supply and dividing by the surface area. The area for each surface is measured using a micrometer whose uncertainty is negligible compared to that of the voltage and current. Thus, the uncertainty in applied heat flux contains only these two sources.

2.1

Validation of Experimental Methodology

To increase confidence in the experimental results, it is necessary to quantify the uncertainty associated with each measured parameter (Table 2.3) and heat loss to the surroundings and to demonstrate that the apparatus produces results that are expected and repeatable. Because the flow loop and microgap are designed to provide fully developed laminar flow at the entrance to the heated surface, an analytical expression for temperature in the microgap can be obtained. This expression can be compared to single-phase water measurements to demonstrate that the apparatus is functioning as expected and to quantify heat losses. For laminar, steady, incompressible, fully developed flow of a Newtonian fluid heated by one constant heat flux wall in a microgap (flat plate channel), the temperature distribution in the stream wise and wall-normal directions (Fig. 2.13) is [ ( ) ( ) 2Hq}w 3 (2y)2 1 2y 4 1 2y 39 x þ T ðx, yÞ = T i þ kf 32 H 64 H 8 H 2240 H Re Dh Pr ( )# 1 X 32 2 þ Cn Y n ðyÞ exp λ x 6H Re Dh Pr n n=1 ð2:2Þ

2.1 Validation of Experimental Methodology Table 2.4 Eigenvalues and constants for the power series solution

n 1 2 3 4 5 6 7

21

λn 4.2872 8.3037 12.3106 16.3145 20.3171 24.3190 28.3232

a1 2.3715 9.9307 11.2041 12.0152 12.5437 12.8984 13.1439

Cn 0.0687 -0.0301 0.0304 -0.0299 0.0291 -0.0281 0.0272

Yn(-1) -0.9052 0.4919 -0.7426 0.9207 -1.0578 1.1681 -1.2529

and the Nusselt number is [

#-1

( ) 1 ( ) 26 X H 32 NuðxÞ = Cn Y n λ2n x þ exp 140 n = 1 2 6H Re Dh Pr Z x 1 Nuðx0 Þdx0 Nu-ðxÞ = x 0

ð2:3Þ ð2:4Þ

where Yn is represented by a power series Y n ð y* Þ =

1 X

am y * m

ð2:5Þ

m=0

and the constants am are given by the recurrence relations a0 = 1

a2 = - a 0

λ2n 2

a3 = - a 1

λ2n 6

am =

λ2n ða - am - 2 Þ mðm - 1Þ m - 4

ð2:6Þ

The constants Cn are, Z Cn =

1 -1

[ Y n ð y* Þ * -

3 *2 32 y

Z

1 -1

] * 1 *4 39 dy þ 64 y þ 18 y* þ 2240

ð2:7Þ

Y 2n ðy* Þdy*

The first seven values of λn, a1, Cn and the value of the eigenfunctions at the heated wall are shown in Table 2.4. A full derivation of the solution is given in [15]. The mean wall temperature obtained from Eq. (2.2) is compared in Fig. 2.14a to measurements for water. The analytical expression and the experimental results follow the same trend, but there is an offset between the experimental data and the

22

2

a 210

b 180

180

150 120

2

q″net [kW/m ]

q″ [kW/m2]

150 120 90 60

Experimentation and Procedure

90 60 30

30 0 50

60

70

80

90

Tw [°C]

100

0 50

60

70 80 Tw [°C]

90

100

Fig. 2.14 Comparison between the mean wall temperature from the analytical temperature expression (line), Eq. (2.2), and single-phase experimental results (circles). Dh = 1000 μm, G = 262 kg/m2s, Ti = 51 °C. (a) Without accounting for heat losses. (b) Accounting for heat losses in experimental results

Table 2.5 Heat loss to surroundings

Tw (°C) 45 50 55 60 65 70 75 80 85 90 95 100

q00loss (kW/m2) 7.0 8.7 10.5 12.2 14.0 15.7 17.5 19.2 21.0 22.7 24.5 26.2

analytical result which represents heat loss to the surroundings. If these losses are subtracted, the analytical temperature equation and the experimentally measured wall temperature are in accord (Fig. 2.14b). As a check for the measured heat losses, the approximate heat loss is calculated via a one-dimensional conduction model [15]. Though the conduction in the test section walls may be two- or three-dimensional, the low thermal conductivity of Garolite™ and the long conduction paths in the transverse and axial directions result in the resistance to conduction heat losses being significantly lower in the wallnormal direction. A one-dimensional conduction model provides a good approximation of the heat lost to the surroundings, and the approximation yields heat losses in good agreement with the measured losses. Heat losses are accounted for in all experimental results (Table 2.5).

2.1

a

Validation of Experimental Methodology

b

700

600

Run 1,G = 156 kg/m2s

600

500

Run 2,G = 160 kg/m2s Run 3,G = 157 kg/m2s

500

q″net [kW/m2]

q″net [kW/m2]

23

400 300 200

400

Run 1,G = 345 kg/m2s Run 2,G = 357 kg/m2s Run 3,G = 349 kg/m2s

300 200 100

100 0 50

65

80

95 Tw [°C]

110

125

140

0 30

45

60

75

90

105

120

Tw [°C]

Fig. 2.15 Comparison of the boiling curves for three experimental runs on the smooth surface. (a) Water, Ti = 51 °C, Dh = 1000 μm, (b) 1% emulsion, Ti = 30 °C, Dh = 500 μm

To demonstrate repeatability, water and emulsion experiments were conducted at nominally the same mass flux. These experiments were run on separate days following the same experimental procedure. The resulting boiling curves (Fig. 2.15) demonstrate that the apparatus produced repeatable results when boiling water and emulsions on the smooth surface. Prior to conducting experiments on the porous surfaces, the surfaces were conditioned by running repeated experiments [20]. Each surface was conditioned by running one or two experiments, after which each surface produces repeatable results when boiling water (Fig. 2.16) as well as boiling emulsions (Fig. 2.17). The results shown in Fig. 2.17 are from experiments conducted both before and after the rest of the emulsion data set was generated. Thus Fig. 2.17 demonstrates that the surfaces did not degrade over the course of measurements.

24

600

q″net [kW/m2]

b

700

500

Run 1, G = 353 kg/m2s Run 3, G = 357 kg/m2s Run 4, G = 356 kg/m2s

400

Run 5, G = 352 kg/m2s

300

500

100

100 55

70

85

100

Run 3, G = 349 kg/m2s Run 5, G = 349 kg/m2s

300 200

40

Run 1, G = 355 kg/m2s Run 2, G = 358 kg/m2s Run 4, G = 354 kg/m2s

400

200

0 25

Experimentation and Procedure

700 600

Run 2, G = 348 kg/m2s

q″net [kW/m2]

a

2

0 25

115

40

55

70

c

100

115

130

145

700 Run 1, G = 343 kg/m2s

600

q″net [kW/m2]

85 Tw [°C]

Tw [°C]

Run 2, G = 354 kg/m2s Run 3, G = 353 kg/m2s

500

Run 4, G = 343 kg/m2s

400

Run 5, G = 344 kg/m2s

300 200 100 0 25

40

55

70

85

100

115

130

Tw [°C]

Fig. 2.16 Demonstration of surface conditioning for (a) porous surface 1, (b) porous surface 2, and (c) porous surface 3. Water, Ti = 30 °C, Dh = 500 μm

600 Run 1, G = 349 kg/m2s

500 q″net [kW/m2]

Fig. 2.17 Comparison of the boiling curves for three experimental runs on porous surface 1. 1% emulsion, Ti = 30 °C, Dh = 500 μm

400

Run 2, G = 346 kg/m2s Run 3, G = 354 kg/m2s

300 200 100 0 25

40

55

70

85 Tw [°C]

100

115

130

145

Chapter 3

Flow Boiling of Water in a Microgap

3.1

Literature Review

Research on flow boiling at the small scale has mostly focused on boiling in microchannels and has led to several reviews [5, 14, 21–24]. Owing to the high aspect ratio in a microgap (channel width/gap height), boiling in microgaps leads to different flow regimes and heat transfer behavior than in a microchannel (small aspect ratio).

3.1.1

Flow Regimes

Flow regimes present in microgaps have been investigated by Bar-Cohen et al. [25– 28], Harirchian and Garimella [29, 30], and Alam et al. [31–35]. Bar-Cohen et al. [25–28] assume that the Taitel-Dukler [36] flow regime map for flow boiling at the conventional scale is applicable for microgap flow. This map uses superficial gas and liquid velocities to plot the transition between bubbly, intermittent (generally slug or plug), stratified, and annular flow. Bar-Cohen and Rahim [26] plot the flow regimes for R113 flowing in gaps of 0.1 < Dh < 100 mm, with 100 < G < 400 kg/m2s and 0.01 to 0.9 thermodynamic quality. The maps show that for the 0.1 mm and 1 mm gaps, the majority of the data falls in the annular flow regime. At very low quality, intermittent flow is present, with the data shifting closer to annular flow with increasing mass flux. Bar-Cohen and Rahim [26] also plot the data from the experiments of Yang and Fujita [37] and Lee and Lee [38] for R113 flowing in 0.4 mm and 1 mm gaps, respectively, to gain insight on how the flow regime affects heat transfer behavior. For the 1 mm gap with 52 < G < 208 kg/m2s, the entirety of the data falls in the annular flow regime. For the 0.4 mm gap with G = 100 and 200 kg/m2s, most of the © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 B. M. Shadakofsky, F. A. Kulacki, Flow Boiling of a Dilute Emulsion In Smooth and Rough Microgaps, Mechanical Engineering Series, https://doi.org/10.1007/978-3-031-27773-3_3

25

26

3

Flow Boiling of Water in a Microgap

data falls in the annular regime, though some low-quality data points fall in the intermittent flow regime. Previous R113 maps show that annular flow is more prevalent for smaller gap sizes, and thus the presence of intermittent flow in the smaller gap of [37] and not in the larger gap of [32] may be due to differences in the system pressure. The 0.4 mm gap experiments were conducted at a pressure of 219 kPa, and those of the 1 mm gap were conducted at 108 kPa. Flow regimes present during boiling heat transfer have been measured via highspeed videography by Harirchian and Garimella [29, 30] and Alam et al. [31– 35]. Harirchian and Garimella investigated boiling of FC-771 in microchannels and a microgap of Dh = 707 μm, with 225 < G < 1420 kg/m2s. Between bubbly and annular flow, they observe several sub-regimes of intermittent flow. In addition to slug flow, they observed churn flow (a regime similar to slug flow but with smaller, irregular vapor structures and much more chaotic mixing than in slug flow) and wispy-annular flow (a flow regime similar to annular flow characterized by a thicker liquid film on the wall and large wave structures that allow the vapor to entrain larger droplets in the vapor core). In the microgap of width 5850 μm, they report that a multiplicity of these regimes can exist side-by-side due to the large aspect ratio (Fig. 3.1). At low wall heat flux, bubbly flow predominates. Bubbly flow is replaced by intermittent churn and wispyannular flow as wall heat flux increases, followed by churn-annular flow at still higher heat fluxes. As the mass flux increases, the bubbly flow regime is present over a much wider range of heat flux. Harirchian and Garimella further point to the dissimilarity between the flow regimes in the 100–250 μm channels and the 400–5850 μm wide channels to differentiate microchannels and microgaps based on flow regime. Alam et al. observe bubbly, slug, and annular flow in microgaps of 12.7 mm width and 80–1000 μm height. For the same heat and mass fluxes, bubbly flow tends to dominate in the larger gaps, and the flow regime shifts to slug then annular flow with decreasing gap height [31, 32, 35]. They also note that the flow condition was unsteady, with varying flow regimes present at the same experimental condition. At a given gap size, mass flux and wall heat flux, bubbly, slug, and annular flow were observed sequentially as bubbles nucleated, grew, coalesced, and flowed downstream [32, 33, 35]. The research of Harirchian and Garimella [29, 30] and Alam et al. [31–35] show similar trends to those predicted in [25–28]. Though the trends are similar, comparisons have not yet been made between the flow regime seen via the use of videography and that predicted by the Taitel-Dukler map for a given experimental condition. Therefore, the accuracy of the Taitel-Dukler map at the small scale has not yet been proven.

FC-77 is one of several Fluorinert™ fluids manufactured by 3M™, Inc., St. Paul, Minnesota. Fluorinert™ fluids are perfluorinated or fully fluorinated compounds, with all available carbon bond sites occupied by fluorine atoms. An example of a fully fluorinated compound is FC-72, whose chemical composition is C6F14. FC-77 is a perfluorinated compound whose chemical composition is C8F16O. Data are available for thermodynamic and transport properties of FC-77 at multimedia.3 m.com/mws/media/64893O/fluorinert-electronic-liquid-fc-77.pdf 1

3.1

Literature Review

27

C/W C/W C/W

B

1420

B B C

B B

C/A

B/S C/A

S

B

1050

B

G (kg/m2s)

B B S

B

630

B/S B

B S C/A

B/S S

225

B B/S B/S B/S S S

0

C/W C/A

B/S C/A

B

C/W

C/W C/W C/W C/A C/A

C/W C/W C/W C/A C/A

5850 Pm 2200 Pm 1000 Pm 400 Pm 250 Pm 100 Pm

C/A C/A C/A

5850 Pm 2200 Pm 1000 Pm 400 Pm 250 Pm 100 Pm

C/A C/A C/A

C/A

100

5850 Pm 2200 Pm 1000 Pm 400 Pm 250 Pm 100 Pm

C/W C/W C/W

B/S B

5850 Pm 2200 Pm 1000 Pm C/A 400 Pm 250 Pm 100 Pm

200

300

400

qs (kW/m2)

B: Bubbly S: Slug C: Churn W: Wispy-annular B/S: Intermittent bubbly/slug flow C/W: Intermittent churn/wispy-annular flow C/A: Intermittent chum/annular flow : Single-phase flow

A: Annular

Fig. 3.1 Flow regimes present for flow boiling of FC-77 in microchannels and microgaps of 400 μm height and varying width [29]

3.1.2

Heat Transfer

Like flow boiling at the conventional scale, heat transfer at the small scale is dependent on the flow regime. Bar-Cohen and Rahim [26] and Alam et al. [35] show that changes in the slope of the boiling or heat transfer coefficient curve correlate with changes in the flow regime (Fig. 3.2). It is seen that higher heat transfer coefficients are measured as the flow transitions from bubbly to slug and annular flow due to the effectiveness of evaporation in the thin liquid film around the wall.

28

3

Flow Boiling of Water in a Microgap

b 50000 Annular flow

ht (W/m2K)

40000

Partial dryout

30000 20000 10000 Subcooled Bubbly boiling flow 0 0 10

G=390kg/m2s Gap=300Pm

Slug/Transition flow 20

30 40 qseff (W/cm2)

50

60

70

30000 Annular flow

ht (W/m2K)

25000

Slug/Transition flow

20000 15000 10000 5000

Bubbly flow

Subcooled boiling

G=390kg/m2s Gap=1000Pm

0 0

10

20

30

40 50 qseff (W/cm2)

60

70

80

90

Fig. 3.2 Heat transfer coefficient associated with various flow regimes for flow boiling of deionized water in gaps with 300 μm and 1000 μm height [35]

Heat transfer is also affected by gap size, mass flux, fluid used, inlet subcooling (the difference between the saturation temperature and the bulk inlet temperature), and the wall condition. Heat transfer for various gap sizes was investigated in [31, 32, 39–41]. The boiling curve generally shifts to lower wall temperatures, and the heat transfer coefficient increases with decreasing gap size especially at wall temperatures near ONB. This is probably due to the early transition to annular flow in smaller gaps. Although higher heat transfer coefficients are seen near ONB, the early transition to annular flow also results in an earlier transition to CHF. Thus, at higher wall temperature and heat flux, smaller gaps can have decreased heat transfer coefficients than larger gaps at the same heat flux, and CHF values are generally lower for smaller gaps [39]. The effect of the mass flux was studied in [31, 41–44]. In the single-phase region, increasing mass flux decreases the wall temperature and increases the heat transfer

3.1

Literature Review

29

coefficient, as is typical at the conventional scale. However, the higher wall temperatures for lower G mean that boiling is initiated at lower heat flux, which can result in larger heat transfer coefficients at low heat flux for lower mass flux [31]. Increasing mass flux also delays the onset of CHF due to the effectiveness of single-phase cooling at higher flow rate, as well as the prevalence of bubbly flow and the delayed transition to annular flow (Fig. 3.1). The geometry of the entry and exit manifolds has a significant impact on the heat transfer and fluid flow characteristics [17]. Therefore, comparison of multiple fluids can only be achieved when they are used in the same experimental setup. Water and FC-72 were investigated in [40], and water and Novec 7200 and 7300 were studied in [41, 42]. In these studies, it is shown that the use of water results in larger heat transfer coefficients in both single- and two-phase flow owing to its higher specific heat, latent heat of vaporization, and thermal conductivity. However, the use of FC-72, Novec 7200, and Novec 73002 offer two distinct advantages: these are all dielectric fluids that can be brought into direct contact with functioning electronics for cooling, and the saturation temperature of these cooling fluids can be tuned by modifying the chemical composition of the fluid. The maximum operating temperature for reliable operation of most contemporary electronic devices, i.e., processors and memory chips, is ~95 °C, and thus the lower saturation temperature of FC-72 (56 °C) and Novec 7200 (76 °C) at atmospheric pressure make them attractive fluids for cooling of high-performance electronics. This difference in saturation temperature adds one additional difficulty in determining the impact of different fluid properties on heat transfer. The difference in saturation temperature means that various fluids experience varying levels of subcooling for the same inlet temperature, and subcooling has also been shown to have an impact on boiling heat transfer [39, 41–44]. For a given fluid, the heat transfer coefficient increases at a given heat flux for increasing inlet temperature (or decreasing subcooling) due to boiling initiating at lower heat flux. This is a benefit to heat transfer at lower heat flux, but decreasing subcooling is a detriment to heat transfer at higher heat flux; CHF decreases with decreasing subcooling owing to the earlier transition to annular flow and dry out [39]. Wall condition and the design of the experimental apparatus also significantly impact both the fluid flow and heat transfer behavior. Most microgap research is performed for a gap asymmetrically heated on one wall, with variations of the inlet and outlet flow geometries. Symmetric and asymmetric heating were studied by Geisler and Bar-Cohen [39] on aluminum and silicon heaters. Symmetric heating for a single pair of heaters and for three in-line heater pairs at uniform and nonuniform

The Novec™ HFE fluids are produced by 3M™, Inc. as an alternative to their Fluorinert™ FC fluids. The Novec™ fluids are hydrofluoroethers (HFEs), which are segregated chains, with one perfluorinated part of the chain being separated via an oxygen atom, or ether, from a portion of the chain that is fully hydrogenated, with all carbon bond sites being occupied by hydrogen. The Novec™ fluids have a much lower global warming potential than the Fluorinert™ fluids. Novec 7200 and 7300 have chemical compositions of C4F9OC2H5 and C7H3F13O, respectively. Their thermal and fluid transport properties can be obtained at https://www.3m.com/3M/en_US/novec-us/

2

30

3

Flow Boiling of Water in a Microgap

axial (or zonal) heat flux profiles was investigated by Janssen et al. [41, 42]. The effect of surface roughness was investigated by Alam et al. [34] and Geisler and Bar-Cohen [39]. Increasing surface roughness increases the number of nucleation sites available to nucleate bubbles, thereby decreasing the temperature at ONB and increasing heat transfer thereafter. Surface roughness has little effect on CHF as the gap size decreases.

3.1.3

Flow Boiling Mechanisms

The mechanisms associated with boiling in microgaps have not been conclusively investigated to date. However, slug flow is one of the prevalent flow regimes in microgaps, and the heat transfer mechanisms present in slug flow in microchannels have received some attention [8–12, 45–48]. In studies by Moghaddam et al. [8–12], a device was constructed to measure heat transfer and wall temperature as a slug passes over the wall. The bubble that formed the slug was nucleated upstream of the test section and passed through an adiabatic channel that contains the heat flux and temperature sensors. The local wall temperature and heat flux measurements as a slug passes over the sensors are shown in Fig. 3.3. As the front of the slug passes over the sensor, the wall temperature decreases and the local heat transfer increases dramatically. The authors attribute this to evaporation in the thin film of liquid separating the slug and the channel wall. After part of the slug has passed, the wall temperature increases, demonstrating a decrease in local heat transfer coefficient. The authors assume that this is indicative of partial dry out of the liquid film and the decreased heat transfer associated with the wall being partially covered by vapor. After the rear of the slug passes the sensor, the wall temperature decreases again, though not as dramatically as when the front of the slug

Fig. 3.3 Local wall temperature and heat flux measurement as a slug passes a microchannel wall [11]

3.1

Literature Review

31

reaches the sensor. This decrease in temperature is followed by a gradual increase in temperature until it reaches an asymptotic value consistent with liquid convection in the microchannel. The authors note that this decrease and increase of temperature are caused by the gradual wetting of the dry wall after the slug passes. It is possible that transient heat conduction is the primary heat transfer mode. This mechanism has been modeled in pool boiling [49, 50]. Bigham and Moghaddam [10] demonstrate that their heat transfer results in the section labeled T.H.C. in Fig. 3.3 are predicted well by the model in [50]. Thus, they infer that the dominant heat transfer mechanism directly following the passing of the slug is transient heat conduction. These physical mechanisms are very similar to those assumed in [45–47] in the development of a three-zone model for heat transfer in microchannels. In this model, it is assumed that as a slug passes, thin film evaporation is the dominant heat transfer mode and can lead to partial dry out of the wall in the rear of the slug. In front of and behind the slug, heat transfer is governed by single-phase liquid convection. The basic three-zone model has been updated to include various other parameters including more detail for the slug geometry [48].

3.1.4

Comparison with Microchannels

Both microchannels and microgaps are now considered for cooling highperformance electronics. For this reason, both have been studied on the same platform by Alam et al. [33, 35] and Harirchian and Garimella [51] to determine which provides more effective cooling. Alam et al. found that heat transfer coefficients in the microgap are larger than in the microchannel at the same experimental condition and that CHF is greater in the microgap (Fig. 3.4). It is important to note that the microgap hydraulic diameter (375 μm) is slightly greater than that of each microchannel (270 μm) but the total volume available for flow is equivalent in the microgaps and microchannels. In addition to providing larger heat transfer coefficients, the microgap produces more consistent temperature measurements in both the axial and lateral directions

a 70000

b 35000

G=420 kg/m2s

60000

40000

Microchannel

25000 ht (W/m2K)

50000 ht (W/m2K)

G=970 kg/m2s

30000 Microchannel heat sink Microgap heat sink

30000

Microgap

20000 15000

20000

10000

10000

5000 0

0 0

10

20

30

40

50 2

qseff (W/cm )

60

70

80

0

10

20

30 40 qseff (W/cm2)

50

60

70

Fig. 3.4 Heat transfer coefficient comparison for boiling in microchannels and microgaps. (Reprinted from Alam et al. [33])

32

3

Flow Boiling of Water in a Microgap

Fig. 3.5 Axial and lateral temperature measurements in microgaps and microchannels. (Reprinted from Alam et al. [35])

(Fig. 3.5). The temperature is more uniform in the microgap because the vapor is able to expand in both the lateral and axial directions as bubbles grow. In the microchannels, the bubbles are confined by the microchannel width and are only able to expand in the axial direction. As a bubble grows and constricts flow in a single channel, liquid will flow to surrounding channels with lower resistance. This results in a nonuniform flow and temperature distribution in the microchannels. The temperature measurements in Fig. 3.5 are time-averaged measurements. However, Alam et al. demonstrate that both microchannels and microgaps exhibit variation in the wall temperature. The amplitude of this variation is significantly larger in microchannels. Unsteady wall temperature measurements were also reported in microgaps by Sheehan and Bar-Cohen [52]. Alam et al. also demonstrate unsteady pressure drop measurements in both the microchannels and microgap. The average pressure drop and the amplitude of variations are lower in the microgap than in the microchannels. Finally, microgaps can provide one additional benefit for cooling of electronics as noted by Bar-Cohen and Wang [53]. With microchannels, a thermal interface material must be used at the interface between the microchannel base and the electronic substrate being cooled. This interface represents the largest resistance to heat transfer in some electronics. If a microgap is used for cooling, the cooling fluid can be brought into direct contact with the electronics, eliminating this large resistance to heat transfer.

3.2

3.2

Experimental Results

33

Experimental Results

The boiling curve, heat transfer coefficient, and pressure drop are shown below for all experiments conducted at an inlet temperature of 30 °C (Figs. 3.6, 3.7, and 3.8). Although the nominal mass flux for each run is 150, 350, or 550 kg/m2s, the actual mass flux for a given experiment is generally within ±10 kg/m2s of the nominal value. The measured mass flux for each experiment is given in Appendix B. The

Fig. 3.6 Boiling curves for water on the smooth surface, Ti = 30 °C. ΔT = Tw - Tsat

Fig. 3.7 Heat transfer coefficient for water on the smooth surface, Ti = 30 °C

34

3

Flow Boiling of Water in a Microgap

Fig. 3.8 Pressure drop for water on the smooth surface, Ti = 30 °C

boiling curves are also presented to view the effect of the mass flux and the hydraulic diameter (Figs. 3.9 and 3.10). The ONB is indicated by a change in the slope of the boiling curve as the heat transfer mechanism shifts from single-phase to two-phase forced convection. It can be seen, therefore, that boiling starts with little or no surface superheat at all hydraulic diameters and mass flux. Prior to ONB, increasing the mass flux increases the slope of the boiling curve for each gap (Fig. 3.9). The increased slope is a result of higher heat transfer for larger mass fluxes (Fig. 3.11). At G = 150 kg/m2s, the boiling curves for Dh = 500 and 1000 μm are nearly equivalent in the single-phase region, but the boiling curve for Dh = 200 μm shifts downward to higher wall temperatures (Fig. 3.9a). For G = 350 and 550 kg/m2s, the single-phase results are nominally equivalent for all Dh (Fig. 3.10b, c). For each gap size and mass flux, the two-phase results are nearly equivalent except when CHF is either approached or reached. The approach to CHF is shown by a decreasing slope of the boiling curve, with the curve shifting toward significantly higher wall temperatures with increasing heat flux. For the smallest gap, CHF is reached at relatively low wall temperatures, with CHF occurring at ONB in the Dh = 200 μm gap at G = 150 kg/m2s and at mean wall temperatures less than 110 °C for G = 350 and 550 kg/m2s (Fig. 3.9a). Increasing hydraulic diameter delays the approach to CHF. This is seen most clearly in Fig. 3.10a, where CHF is achieved at the ONB for Dh = 200 μm and at ~450 kW/m2 for Dh = 500 μm. For Dh = 1000 μm, CHF is approached but does not occur in the range of applied heat flux. The heat transfer data indicates three distinct regions: (1) a developing region where heat transfer increases with increasing wall temperature; (2) heat transfer levels off and remains fairly constant until boiling initiates; and (3) following ONB heat transfer increases dramatically. When CHF is approached or achieved, heat transfer levels out a second time.

3.2 Experimental Results

600 500 q″net [kW/m2]

b

700 G = 150 kg/m2s 2 G = 350 kg/m s

G = 550 kg/m2s q″net [kW/m2]

a

35

400 300 200 100 0 25

700 600

G = 150 kg/m2s 2 G = 350 kg/m s

500

2 G = 550 kg/m s

400 300 200 100

40

55

70

85

100

115

0 25

130

40

55

70

Tw [°C] –75

–60

–45

–30 –15 ΔT [°C]

q″net [kW/m2]

c

85

100

115

130

0

15

30

Tw [°C] 0

15

30

–75

–60

–45

–30 –15 ΔT [°C]

700 600

G = 150 kg/m2s 2 G = 350 kg/m s

500

G = 550 kg/m s

2

400 300 200 100 0 25

40

55

70

85

100

115

130

0

15

30

Tw [°C] –75

–60

–45

–30 –15 ΔT [°C]

Fig. 3.9 Boiling curves for water on a smooth surface, Ti = 30 °C. (a) to (c) are for Dh = 200, 500, and 1000 μm, respectively

As previously noted, heat transfer increases with increasing G at each Dh. However, the curves approach one another at each Dh once boiling initiates, except where CHF is approached (Fig. 3.11). For G = 150 kg/m2s, the heat transfer coefficients for all hydraulic diameters are nominally the same until CHF is approached (Fig. 3.12a). However, for G = 350 and 550 kg/m2s, decreasing hydraulic diameter leads to an increase in heat transfer in single-phase flow (Fig. 3.12b, c). For example, at G = 350 kg/m2s, decreasing Dh from 1000 to 200 μm increases the heat transfer coefficient by ~25%. Because the boiling curves are nearly equivalent for constant mass flux, these results may suggest that the difference between the wall temperature and fluid temperature decreases with decreasing gap size.

36

b

700

Flow Boiling of Water in a Microgap

700

600

Dh = 200 Pm Dh = 500 Pm

600

Dh = 200 Pm Dh = 500 Pm

500

Dh = 1000 Pm

500

Dh = 1000 Pm

q″net [kW/m2]

q″net [kW/m2]

a

3

400 300 200

300 200 100

100 0 25

400

40

55

70

85

100

115

0 25

130

40

55

70

Tw [°C] –75

–60

–45

–30 –15 ΔT [°C]

q″net [kW/m2]

c

85

100

115

130

0

15

30

Tw [°C] 0

15

30

–75

–60

–45

–30 –15 ΔT [°C]

700 600

Dh = 200 Pm Dh = 500 Pm

500

Dh = 1000 Pm

400 300 200 100 0 25

40

55

70

85

100

115

130

0

15

30

Tw [°C] –75

–60

–45

–30 –15 ΔT [°C]

Fig. 3.10 Boiling curves for water on a smooth surface, Ti = 30 °C. (a) to (c) are for G = 150, 350, and 550 kg/m2s, respectively

Pressure drop measurements demonstrate that with increasing wall temperature, the pressure drop either stays constant or decreases slightly prior to the ONB (Fig. 3.13), possibly due to the slight decrease in dynamic viscosity and density as the film temperature increases. Once boiling is initiated, the pressure drop is most strongly affected at lower mass flux. This is not clearly seen in Fig. 3.13a owing to the early approach to CHF at all G. However, Fig. 3.13b, c shows that the pressure drop increases at the initiation of boiling for G = 150 kg/m2s but stays constant for G = 350 and 550 kg/m2s.

3.2 Experimental Results

b

14000

14000

12000

G = 150 kg/m2s 2 G = 350 kg/m s

12000

G = 150 kg/m2s 2 G = 350 kg/m s

10000

2 G = 550 kg/m s

10000

2 G = 550 kg/m s

h [W/m2K]

h [W/m2K]

a

37

8000 6000

8000 6000

4000

4000

2000

2000

0 25

40

55

70

85

100

115

0 25

130

40

55

–75

–60

–45

–30 –15 ΔT [°C]

h [W/m2K]

c

70

85

100

115

130

0

15

30

Tw [°C]

Tw [°C] 0

15

–75

30

–60

–45

–30 –15 ΔT [°C]

14000 12000

G = 150 kg/m2s G = 350 kg/m2s

10000

2 G = 550 kg/m s

8000 6000 4000 2000 0 25

40

55

70

85

100

115

130

0

15

30

Tw [°C] –75

–60

–45

–30 –15 ΔT [°C]

Fig. 3.11 Heat transfer coefficient for water on a smooth surface, Ti = 30 °C. (a) to (c) are for Dh = 200, 500, and 1000 μm, respectively

38

10000

h [W/m2K]

b

12000

8000

Dh = 200 Pm Dh = 500 Pm Dh = 1000 Pm

6000 4000

Dh = 200 Pm Dh = 500 Pm Dh = 1000 Pm

8000 6000 4000 2000

2000 0 25

12000 10000

h [W/m2K]

a

3 Flow Boiling of Water in a Microgap

40

55

70

85

100

115

0 25

130

40

55

–75

–60

–45

–30 –15 ΔT [°C]

h [W/m2K]

c

70

85

100

115

130

0

15

30

Tw [°C]

Tw [°C] 0

15

–75

30

–60

–45

–30 –15 ΔT [°C]

14000 12000

Dh = 200 Pm Dh = 500 Pm

10000

Dh = 1000 Pm

8000 6000 4000 2000 0 25

40

55

70

85

100

115

130

0

15

30

Tw [°C] –75 –60

–45

–30 –15 ΔT [°C]

Fig. 3.12 Heat transfer coefficient for water on a smooth surface, Ti = 30 °C. (a) to (c) are for G = 150, 350, and 550 kg/m2s, respectively

3.2 Experimental Results

a

b

24 20

14

G = 150 kg/m2s G = 350 kg/m2s

12

G = 150 kg/m2s G = 350 kg/m2s

G = 550 kg/m2s

10

G = 550 kg/m2s

ΔP [kPa]

16 ΔP [kPa]

39

12 8

8 6 4

4

2 0

0 25

40

55

70 85 Tw [°C ]

100

115

130

25

40

55

70 85 Tw [°C ]

100

115

130

–75

–60

–45

–30 –15 ΔT [°C]

0

15

30

–75

–60

–45

–30 –15 ΔT [°C]

0

15

30

c

ΔP [kPa]

14 12

G = 150 kg/m2s G = 350 kg/m2s

10

G = 550 kg/m2s

8 6 4 2 0 25

40

55

70 85 Tw [°C ]

100

115

130

–75

–60

–45

–30 –15 ∆T [°C]

0

15

30

Fig. 3.13 Pressure drop for water on a smooth surface, Ti = 30 °C. (a) to (c) are for Dh = 200, 500, and 1000 μm, respectively

Pressure drop also shows a strong correlation with hydraulic diameter (Fig. 3.14). In single-phase flow, decreasing Dh increases the pressure drop. At smaller Dh, the pressure drop also increases dramatically once boiling initiates. However, the effect of boiling on pressure drop decreases with increasing Dh and the pressure drop only slightly increases when boiling begins for G = 150 kg/m2s in the 1000 μm gap. For G = 350 and 550 kg/m2s, the pressure drop stays constant at the initiation of boiling for Dh = 500 and 1000 μm.

40

a

3

b

10

14

Dh = 200 Pm Dh = 500 Pm

12

Dh = 200 Pm Dh = 500 Pm

Dh = 1000 Pm

10

Dh = 1000 Pm

6

ΔP [kPa]

ΔP [kPa]

8

Flow Boiling of Water in a Microgap

4

8 6 4

2 2 0

0 25

40

55

70

85

100

115

130

25

40

55

70

Tw [°C ] –75

–60

–45

–30 –15 ΔT [°C]

c

100

115

130

0

15

30

–75

–60

–45

–30 –15 ΔT [°C]

0

15

30

24 20 16

ΔP [kPa]

85

Tw [°C ]

Dh = 200 Pm Dh = 500 Pm Dh = 1000 Pm

12 8 4 0 25

40

55

70

85

100

115

130

0

15

30

Tw [°C ] –75

–60

–45

–30 –15 ΔT [°C]

Fig. 3.14 Pressure drop for water on a smooth surface, Ti = 30 °C. (a) to (c) are for G = 150, 350, and 550 kg/m2s, respectively

The heat transfer coefficient is presented in dimensionless form via the Nusselt number in Fig. 3.15. Previous studies have shown that in flow boiling, the Nusselt number is a function of the Reynolds and Boiling numbers [13, 17], and these two dimensionless groups are used here to account for the effect of the hydraulic diameter, mass flux, heat flux, latent heat, and other properties. It is assumed that the Prandtl number should also be considered, but the measurements reported in this book were all conducted with water, and therefore the Prandtl number is not included in this analysis. For the two-phase data, the Nusselt number is almost linearly dependent on ReBl, and the hydraulic diameter and mass flux are well accounted for in the Reynolds and Boiling numbers (Fig. 3.15). The data points that do not follow this trend are instances where CHF is approached or reached.

3.2

Experimental Results

41

Fig. 3.15 Nusselt number as a function of the Reynolds and Boiling numbers for two-phase heat transfer on the smooth surface. Ti = 30 °C

21 G [kg/m2s] Dh [μm] 150 350 550 200 500 1000

18 15

Nu

12 9 6 3 0

0

0.15

0.3

0.45

0.6

0.75

0.9

0.9

1.05

ReBl

Fig. 3.16 Nusselt number as a function of the Reynolds and Boiling numbers at various inlet temperatures

30 Ti = 30°C Ti = 51°C Ti = 70°C

25

Nu

20 15 10 5 0

0

0.15

0.3

0.45 0.6 ReBl

0.75

Data sets were also generated at inlet temperatures of 51 and 70 °C to study the effect of the inlet temperature. The trends in these data sets largely follow those discussed above for the 30 °C inlet temperature data set, so the heat transfer coefficient is only presented here in nondimensional form (Fig. 3.16). The singlephase data is neglected in Fig. 3.16, but the entire data sets are tabulated in [15].

42

Flow Boiling of Water in a Microgap

100 Ti = 30˚C Ti = 51˚C Ti = 70˚C

Numeasured

Fig. 3.17 Comparison between the measured Nusselt number and the Nusselt number predicted by Eq. (3.1). The solid line represents equivalence between the measured and predicted Nusselt numbers

3

+30% –30%

10

1 1

10 Nupredicted

100

Figure 3.16 shows that the boiling results have a strong dependence on inlet temperature. Although the 30 and 51 °C data sets show similar measured Nusselt numbers, as the inlet temperature continues to increase, the Nusselt number increases dramatically. This is a result of boiling occurring at lower heat fluxes and the smaller difference between the wall and fluid temperatures. The 51 and 70 °C data sets also show an almost linear dependence on ReBl. When the Jakob number is used to account for the level of subcooling, the data can be correlated by the Jakob, Reynolds, Boiling, and Nusselt numbers: Nu = 4:04Ja - 0:615 Re 0:909 Bl0:866

ð3:1Þ

There is very good agreement between the measured Nusselt number and that predicted by Eq. (3.1), with 98% of the boiling data within ±30% of the predicted Nusselt number and 83% of the data within ±15% (Fig. 3.17). The majority of the data that falls outside of these bounds represents data where CHF is approached.

Chapter 4

Flow Boiling of Dilute Emulsions in a Microgap

4.1

Literature Review

Boiling heat transfer in mixtures has been extensively investigated, and most research has focused on boiling in mixtures of miscible liquids. Several reviews have arisen from this research [54–57]. Over the last 30 years, research has focused on boiling in mixtures of immiscible liquids. Whereas heat transfer coefficients are generally lower in miscible mixtures than in the separate components, larger heat transfer coefficients can be obtained in boiling of immiscible mixtures, particularly emulsions. This suggests that systems involving high heat flux could benefit from boiling emulsions rather than single-component fluids. The following sections elaborate current understanding of heat transfer in pool and flow boiling of dilute emulsions. Discussion is restricted to emulsions comprising two components, but more generally emulsions can contain more than two components. The effects of various system and fluid properties, e.g., droplet size, droplet concentration, use of stabilizing agents, etc., are described with respect to their effects on the underlying thermodynamics and energy transport. Currently proposed mechanisms governing pool boiling of emulsions are described, followed by various techniques used to model pool and flow boiling of dilute emulsions (ε < 5%). The earliest investigation of boiling of emulsions was conducted by Mori et al. [58] and involved pool boiling of oil-in-water and water-in-oil emulsions on a horizontal wire. The emulsions they studied were stabilized using surfactants. The four oils studied, KF96, KF54, n-dodecane, and n-undecane, have saturation temperatures much higher than that of water at atmospheric pressure. In their experiments, the temperature of the emulsion was held at 100 °C. Mori et al. find that when water is the disperse component (water-in-oil), boiling of the emulsion always progresses at lower surface temperatures compared to that of the oil. They also find that the water-in-oil emulsions require surface superheats of © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 B. M. Shadakofsky, F. A. Kulacki, Flow Boiling of a Dilute Emulsion In Smooth and Rough Microgaps, Mechanical Engineering Series, https://doi.org/10.1007/978-3-031-27773-3_4

43

44

4

Flow Boiling of Dilute Emulsions in a Microgap

~40–100 °C to initiate boiling on the wire surface. Because they use a transparent test apparatus, initiation of boiling could be observed by noting bubbles on the wire surface. Initiation of boiling is also accompanied by a shift in the slope of the boiling curve. When oil is the disperse component (oil-in-water), boiling initiates at much lower surface superheats, often of 15–30 °C. Presumably boiling is able to initiate at much lower temperatures owing to the high water fraction (with much lower saturation temperature) in the emulsion. They also find that their results depend on the type of surfactant. They utilized Tween 80 and sodium oleate to stabilize the oil-in-water emulsions and Span 80 to stabilize the water-in-oil emulsions. When experiments are conducted with sodium oleate, the surfactant reduces single-phase natural convection prior to boiling initiation, and this effect is more pronounced with increasing volume fraction of oil. However once boiling initiates, the presence of the sodium oleate shifts the boiling curve to lower surface temperatures compared to those experiments without the surfactant. When Tween 80 is used, heat transfer coefficients are lower in both the natural convection and boiling regimes compared to those in water. Another early investigation by Ostrovskiy [59] investigated boiling of water-inR113, water-in-benzene, and water-in-butyl alcohol emulsions on a vertically oriented wire. Ostrovskiy did not utilize a surfactant, and the emulsion was continually stirred to maintain the suspension. The water-in-R113 experiments result in measured heat transfer coefficients almost equivalent to those measured for boiling of R113 without the disperse component. Similar results are found for water-in-butyl alcohol and at higher heat fluxes in water-in-benzene. One interesting observation that Ostrovskiy makes is that the dependence of the heat transfer coefficient on heat flux is very similar to that of turbulent free convection. Ostrovskiy notes that the emulsions were preheated prior to running the experiments, but he does not indicate at what temperature experiments are performed. Keeping in mind the large surface superheats required to initiate boiling [58], it has been suggested that the results are similar to that for free convection because boiling was not initiated [60].

4.1.1

Effect of System Properties

Research has shown that many system properties, such as the two fluids present in the emulsion, heating surface geometry, temperature, droplet size/distribution, concentration, and use of surfactants, affect heat transfer. Consider first fluid properties. If some of the property dependences of single-phase systems apply to two-phase systems, one would expect that the Nusselt number is dependent on either the Rayleigh number in pool boiling or the Reynolds and Prandtl numbers (Peclet number) in flow boiling. Additional dimensionless parameters account for the effect of latent heat and surface tension, e.g., the boiling or Jakob number and the Bond or Weber number [61]. The way the two fluids in the emulsion interact will also affect heat transfer. Consider, for example, FC72-in-water and pentane-in-water emulsions.

4.1

Literature Review

45

Fig. 4.1 Pool boiling curve for FC-72 in water emulsions [70]. Equations (5.2 ) and (5.3) noted are Eqs. (4.1) and (4.2) here, respectively

Roesle and Kulacki [62] measured the heat transfer coefficient for pool boiling of FC72-in-water and pentane-in-water emulsions on a small diameter horizontal wire. Droplets of the disperse components (pentane and FC72) produce a poly-disperse emulsion with a mean diameter of 8 μm [62]. Their results for FC72-in-water (Fig. 4.1) demonstrate some interesting trends. In the natural convection portion of the curve prior to initiation of boiling, heat transfer coefficients for ε = 0.1% are close to those predicted by the Morgan correlation [63] for natural convection of water on a cylinder: Nu = 1:02Ra0:148

ð4:1Þ

As the volume fraction of FC72 is increased, the heat transfer coefficient decreases, and Morgan’s correlation no longer approximates the data. For dilute emulsions, mixture properties are nearly equivalent to those of the continuous component, and therefore the decrease in the heat transfer coefficient is probably not caused by the effect of disperse component on bulk mixture properties. FC72 has a higher density and lower thermal conductivity than water, and Roesle and Kulacki conclude that it settles onto the wire, decreasing the heat transfer coefficient. Once boiling initiates, the opposite trend is seen. Larger heat transfer coefficients are measured for increasing volume fractions of FC72. All emulsion data sets demonstrate larger two-phase heat transfer coefficients compared to those for water, as predicted by the Rohsenow correlation [64] (Eq. (4.2)) for boiling on a horizontal cylinder, where h = q/(Twire - T1) [62]: #16 ( )1 [ Cp ðT wire - T sat Þ σ q 3 ( ) = 0:013 hfg Pr μf hfg g ρf - ρg

ð4:2Þ

At the onset of boiling, the FC72 data for ε = 0.1% also demonstrate a slight overshoot in temperature. This overshoot decreases with increasing volume fraction

46

4

Flow Boiling of Dilute Emulsions in a Microgap

Fig. 4.2 Pool boiling curve for pentane in water emulsions [70]. Equations (5.2) and (5.3) noted are Eqs. (4.1) and (4.2) here, respectively

and is nonexistent for ε = 1%. Roesle and Kulacki do not explain what may have caused this overshoot. However, the role of mass transfer may be able to explain this phenomenon [55]. When the FC72 droplet nears the heated wire, phase change occurs, and bubbles of FC72 vapor rise from the wire. If the wire temperature is low enough that the water cannot boil, boiling can then only progress when more FC72 droplets contact the wire. For very dilute emulsions, this may lead to a time delay in the next stage of bubble nucleation with the observed overshoot of temperature until the heat flux is large enough to cause a larger fraction of the FC72 to boil. At larger volume fractions, there is more FC72 to rewet the wire when a vapor bubble leaves, leading to either a decreased or no temperature overshoot. For pentane-in-water emulsions, trends are similar but with some marked differences (Fig. 4.2). Although natural convection heat transfer coefficients in the pentane-in-water emulsions are lower than those for water, the decrease is significantly smaller compared to that in the FC72-in-water results. This may be due to the lower density of pentane compared to water, thereby making it less likely that it would coat the wire and decrease heat transfer coefficients owing to its lower thermal conductivity. The pentane-in-water emulsions demonstrate larger heat transfer coefficients after the onset of boiling compared to those in water, and the data collapse to a single curve at high wire temperatures. This is not seen in the data for FC72-inwater because the applied heat flux is greater in the pentane studies. It is possible this occurs because the wire temperature is high enough to cause boiling of the continuous water phase. The low volume fraction pentane-in-water emulsions do not exhibit a temperature overshoot, but the temperature overshoot is observed for ε = 0.5% and 1%. It is possible that mass transfer is also contributing to this effect. Because pentane has a lower density than water, as the wire temperature increases, the increased buoyancy force causes more pentane to rise above the surrounding water than would otherwise occur at lower temperatures. This effect would be exaggerated at higher volume fractions of pentane and could lead to a larger temperature overshoot. Although mass

4.1

Literature Review

47

Fig. 4.3 Heat transfer coefficient, α, as a function of wall temperature. Data sets 1 and 2 are for water/ PES-5 emulsions with d = 1.5 μm and 35 μm, respectively. ΔT = Tw Tsat [67]

transfer plays a role in single-component, single-phase heat transfer, it may be essential to understanding single- or two-phase heat transfer in dilute emulsions. Very few emulsion studies have been conducted with varying bulk temperatures. One such investigation is that of Bulanov et al. [65]. Water-in-PMS300 emulsions with ε = 0.8 and 3.2% show that at a bulk temperature of 40 °C in single-phase convection, the emulsion demonstrates nominally the same heat transfer coefficient as PMS300 alone. However, when the surface is ~20 °C above the saturation temperature of water, the emulsion starts to boil, and the heat transfer coefficient is nearly twice that of the PMS300 up to wall temperatures of 230 °C. When the bulk temperature is increased to 99 °C so that the water droplets are nearly at the saturation temperature, the heat transfer coefficient for PMS300 alone nearly doubles in the natural convection regime. The heat transfer coefficient in the emulsion is also larger compared to natural convection values at 40 °C. However, the heat transfer coefficient decreases until wall temperatures are ~140 °C and increases thereafter. This effect is seen in both the ε = 0.8% and 3.2% emulsions, although the decrease in the heat transfer coefficient is less for ε = 0.8%. Even though heat transfer coefficients decrease at lower wall temperatures, they were larger in the 99 °C data set for all wall temperatures. In [66], the emulsion temperature is varied from 30 to 65 °C, but the results are not dependent on it. Gasanov and Bulanov report the effect of droplet size on the heat transfer coefficient in water-in-PES5 [67] and water-in-VM1S oil emulsions [68]. In both investigations, they classify the emulsions as either “coarse grained” (d ~ 20–30 μm) or “fine grained” (d ~ 1–2 μm). In natural convection, droplet size does not affect the heat transfer coefficient (Fig. 4.3). However, the boiling curve tends to shift to lower surface temperatures for the coarse-grained emulsions, and the temperature at the onset of nucleate boiling is higher in the fine-grained emulsions. This is to be expected owing to the effect of surface tension, which increases the pressure inside the droplet:

48

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P - P1 =

σ d

ð4:3Þ

Because the pressure inside the droplet increases with decreasing diameter, the saturation temperature of the disperse component is higher for the fine-grained emulsions. Boiling in the fine-grained emulsions in [67] initiates at a wall temperature ~70 °C higher than in the coarse-grained emulsions (Fig. 4.3). For water droplets of this size, the rise in the saturation temperature compared to atmospheric conditions would be ~5–10 °C, and thus it is clear that surface tension alone does not account for the large surface temperature required to initiate boiling in [67]. In [68], the difference in surface temperature required to initiate boiling is ~10 °C. Figure 4.3 also shows two additional features in the water-in-PES5 emulsions of [67] that do not appear in the water-in-VM1S oil emulsions of [68]. The fine-grained emulsions demonstrate a small temperature overshoot at the onset of boiling that gradually decreases as the heat flux increases. This feature has also been demonstrated in the pentane-in-water and FC72-in-water emulsions [62]. At high heat flux, the coarse-grained and fine-grained emulsions collapse to a single curve. Once boiling is initiated in the water-in-VM1S oil emulsions, the fine-grained and coarse-grained emulsion heat transfer curves are separated by a consistent temperature difference [68]. It can be expected that the droplet size distribution will also impact heat transfer. In developing an analytical model of boiling in emulsions, Bulanov [69] utilizes statistical mechanics to include the effect of the bubble nucleation rate. Because the nucleation rate is probabilistic, the droplet size distribution plays a role in determining the nucleation rate. The effect of droplet size distribution has not, however, been investigated experimentally. Most experimental studies and models assume that the emulsion is monodisperse [16, 69]. However, the results in [62] are for a droplet size distribution that is non-Gaussian [70], and the experimental results of Bulanov et al. are for emulsions that are almost bi-disperse [71]. Most emulsion experiments involve studying the impact of volume fraction of the dispersed component on heat transfer coefficients. Increasing the volume fraction generally shifts the boiling curve to the left such that higher heat transfer coefficients are seen at the same wall temperatures for higher volume fraction of the dispersed component (Fig. 4.1). As noted previously, mass transfer may also play a role in both single-phase and two-phase heat transfer and cause a decrease in heat transfer coefficients depending on the fluids used and geometry of the surface. Bulanov et al. [71] systematically vary the volume fraction and measure heat transfer coefficients for a range of wall temperatures in water-in-PES5 emulsions (Fig. 4.4). For ε ≤ 1%, an increase in the heat transfer coefficient by a factor of two to four is measured. However, for ε > 1%, no increase in the heat transfer coefficient is found for a wide range of wall temperatures. As noted previously, a study of the use of surfactants was conducted in [58]. The use of activated carbon in emulsions of water-in-PES5 and n-pentane-in-glycerin, zeolites in a water-in-PES4 emulsion, and sodium hydrate and trisodium phosphate surfactants in a water-in-PES5 emulsion was subsequently investigated by Bulanov

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Fig. 4.4 Heat transfer coefficient as a function of water volume fraction, εd, in water-in-PES5 emulsions [71]. Data sets 1–5 correspond to wall temperatures of 100, 190, 205, 220, and 235 °C, respectively. Data sets 6–8 correspond to emulsions stabilized with 1% (by weight) tri-sodium phosphate at wall temperatures of 100, 190, and 220 °C, respectively

and Gasanov [67]. They find that when water-in-PES5 emulsions are stabilized with activated carbon, the boiling curve shifts to lower wall temperatures by ~10–15 °C. The heat transfer results are also relatively insensitive to the amount of carbon added in the range 0.045–0.3% by weight. When n-pentane-in-glycerin emulsions are stabilized with 0.3% activated carbon, the presence of the carbon delays onset of boiling and shifts the boiling curve to higher wall temperatures by ~10 °C. Bulanov and Gasanov theorize that nucleation of bubbles occurs on small floccules in the emulsions that adsorb atmospheric gas [72]. Thus, they attribute these results to activated carbon forming the floccules in the water-in-oil emulsions and the formation of floccules being hindered in oil-in-oil emulsions. When water-in-PES5 emulsions are stabilized with 0.6% and 2% NaX zeolites by weight, the use of the zeolites inhibits the onset of boiling, with the temperature at the onset of nucleate boiling increasing with increasing mass of zeolite added. They attribute this to adsorbed water by the zeolite rather than atmospheric gases, thus limiting the number of possible nucleation sites. At higher heat flux, the results for emulsions with and without zeolites collapse to the same curve. When a water-in-PES5 emulsion is stabilized with either sodium hydrate or trisodium phosphate, Bulanov and Gasanov state that at low volume fraction of the dispersed component, the presence of the surfactant leads to an increase in the wall temperature required to initiate boiling. They also state that at either high temperature or large volume fraction of the disperse component, the addition of a surfactant results in larger heat transfer coefficients and an increase in critical heat flux. Bulanov et al. also investigate the effect of trisodium phosphate on water-inPES5 emulsions, and their results are shown in Fig. 4.4. They find that the presence of trisodium phosphate has no effect on the heat transfer coefficient [71]. From these studies, it is not clear how the presence of either surfactants or other stabilizing agents affect the heat transfer coefficient.

50

4.1.2

4

Flow Boiling of Dilute Emulsions in a Microgap

Visualization of Pool Boiling

Visualization of pool boiling has been limited to photography to track bubble formation and transit around and from a heated surface. While qualitative in nature, these observations give some insight into physical mechanisms, bubble kinematics, and bubble morphology along the boiling curve. There are, however, two significant challenges to using visualization techniques: (1) small droplets in the emulsion scatter incident light, making the mixture opaque and difficult to observe, and (2) the index of refraction of many of the liquids studied, e.g., water, FC72, pentane, and VO1C oil, are nearly identical, making it difficult to differentiate between the two liquid components. Though these difficulties exist, videography has been applied to study boiling of FC72-in-water [73], pentane-in-water [73, 74], pentanein-glycerin [74], and water-in-VO1C oil emulsions [75]. In the following, several observations are elaborated. In [73] it is demonstrated that for boiling of pentane-in-water emulsions, large bubbles attach to the wire at low heat flux, and as the heat flux increases, bubble size decreases (Figs. 4.5 and 4.6). The pentane droplets have diameters of 4–22 μm with an average of ~8 μm and in the bulk of the emulsion are subcooled, Tsat - T1 = 13 ° C. No spontaneous vaporization in the liquid phase away from the wire is observed. Vapor bubbles nucleate on the wire and grow prior to lift off at various diameters on departure. It is speculated that the large bubbles seen are a result not of boiling of individual droplets but of droplets of pentane attaching to the wire, agglomerating with other droplets, and then boiling. Also evident in Fig. 4.6 are bubbles that form at the surface, collect with other bubbles to form a packet or cluster, and then lift off of the surface without coalescing to form a single large bubble. It is shown that at higher heat fluxes, bubbles can form at the surface and be propelled downward and away from the wire, rather than simply rising off of the wire. This is the source of the bubbles that are present below the wire in images (c) and (d).

80

h / (kW m–2 °C–1)

70 60

experiment

d

Eq. (1)

50 c

40

b

30 a

20 10 0 60

70

80

90

100

110

120

130

Twire / °C

Fig. 4.5 Heat transfer coefficient for pool boiling of a pentane/water emulsion on an electrically heated wire of 10.1 μm diameter. ε = 0.2%, T1 = 23.5 °C [70]. Equation (1) noted is Eq. (4.1) here. Letters denoting locations on the heat transfer coefficient curve correspond to bubble images in Fig. 4.6

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Fig. 4.6 Bubbles in boiling pentane-in-water emulsions on a heated wire [70]. ε = 0.2%, T1 = 23.5 °C. Heat flux increases from (a) to (d) as labeled in Fig. 4.5. Optical resolution is 4.5 μm/pixel at a frame rate of 30 s-1

The pentane-in-water results obtained in [74] demonstrate many of the same trends. At lower heat flux, large bubbles are seen attached to the wires, while at higher heat flux attached bubbles tend to decrease in size and increase in number, and at high heat fluxes some of them are driven downward and away along the wire. Bubbles are also observed to form on the wire and coalesce to form larger bubbles. This may provide an alternate mechanism for the formation of large bubbles, although it was not demonstrated that most of the large bubbles form in this manner. Spontaneous vaporization in the liquid away from the wire is not observed. To this point observations suggest that bubbles are formed at the heated surface, not in either the bulk of the emulsion or the thermal boundary layer on the heated surface. Owing to the near equivalence of the indices of refraction of the liquid droplets and water, only bubbles can be imaged and droplet behavior cannot be observed. To observe droplet mechanics and heat transfer, other imaging techniques may be necessary. Similar bubble behavior is observed for emulsions of FC72-in-water. Figures 4.7 and 4.8 are images of boiling on a 10 μm DIA wire at several points along the boiling curve. The bulk temperature of the fluid is 35 °C, and imaging is similar to that in [74]. Bubbles first become visible on the wire, while the heat transfer data shows the first sign of boiling (Fig. 4.8a). As heat flux increases, more bubbles form, grow larger (Fig. 4.8b), and detach from the wire with increasing frequency. An interesting behavior is that some bubbles depart the wire with significant velocity. Figure 4.8c shows a bubble initially attached to the near side of the wire departing from the wire and initially travelling downward before rising in front of the wire due to buoyancy. The bubble also shrinks visibly owing to condensation as it rises out of the frame.

52

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h / (kW m–2 °C–1)

25

20

Experiment Eq. (1) Eq. (2)

c d b

15

10 a 5 50

60

70

80

90

100

110

120

130

Twire / °C

Fig. 4.7 Heat transfer coefficient for heated wire in an FC72-in-water emulsion; 0.1% FC72 by volume, and T1 = 35 °C [70]. Letters denote images in Fig. 4.8. Equations (1) and (2) noted are Eqs. (4.1) and (4.2) here, respectively, and are calculated using the properties of water

At high heat flux bubbles that nucleate on the heated wire detach at a much smaller diameter than at lower heat flux (Fig. 4.8d). Because of the high temperature of the wire, it is not clear whether the bubbles that nucleate on the wire are FC72 or water. The detached bubbles visible in Fig. 4.8 have diameters of 50–100 μm and could be the result of boiling of individual FC72 droplets with diameters 10–20 μm. As is seen in the second frame of Fig. 4.8d, some bubbles that nucleate on the wire surface are propelled downward, and thus the dispersed bubbles seen throughout the frame could be the result of this process instead. The elongation of the bubble in the second frame (middle image) is an artifact of the rolling shutter in the image sensor. It is likely that processes are occurring that are either too small or too fast to capture. The small number of bubbles observed in Fig. 4.8d could not be responsible for such a large change in the heat transfer coefficient.

4.1.3

Flow Boiling

Investigations of flow boiling in dilute emulsions have been reported only recently. The findings of three investigations which find significant augmentation of heat transfer coefficients are summarized. As with pool boiling, the mechanism of bubble nucleation remains undetermined, and the role of droplet-surface interactions is unresolved. Gasanov and Bulanov [75] investigate flow boiling of water-in-vacuum oil (VO1C oil) emulsions in a peripherally heated 16 mm DIA pipe with inlet bulk temperature ~25 °C and mass flux of 12 kg/m2s. Water concentrations are 0.1% ≤ ε ≤ 1.5% by volume, and droplet size is denoted as either coarse (20 < d < 30 μm) or fine grained (1 < d < 2 μm). As seen in pool boiling, the

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Fig. 4.8 Images of heated wire during boiling in FC72-in-water emulsion, 0.1% FC72 by volume: (a) onset of boiling; (b) attached bubbles at higher heat flux; (c) rapid bubble detachment; and (d) boiling at high heat flux, average bubble rise velocity is 0.0087 m/s [70]. The experimental condition for each image is noted in Fig. 4.7

fine-grained emulsions boil at higher wire temperatures than the coarse grained emulsions. They find that the critical heat flux decreases with increasing water fraction and increasing droplet size at a given concentration. They attribute this to a vapor film forming more easily owing to either a higher volume of water in larger droplets or higher concentration. Heat transfer coefficients for both the coarse and fine-grained emulsions exhibit significant increases once boiling commences (Fig. 4.9). Bulanov et al. [76] boiled water-in-organosilicon fluid (PES4) emulsions at a mass flow of 0.006 kg/s in an 8.4 mm DIA pipe with an inlet temperature of 60 °C. The mass percent of PES4 was varied between 3% and 33% by weight. They find that heat transfer coefficients shift to lower wall temperatures with increasing volume fraction. They note that increases in the heat transfer coefficient are seen up to 33% by weight (Fig. 4.10), whereas previous pool boiling studies demonstrate increases in heat transfer coefficient only up to ε ~ 1% (Fig. 4.4). The 12, 20, and

54

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0.6

α, kW/(m2 K)

0.5

–1 –2 –3

0.4

0.3

0.2 50

100

150

200

250

300

Tw, °C

Fig. 4.9 Convective heat transfer coefficients, α, in peripherally heated pipe flow [75]. Qflow = 2.5 × 10-6 m3/s. (1) VO-IC oil; (2) coarse-grained water-in-VO1C oil emulsion; (3) fine-grained water-in-VO1C oil emulsion. ε = 1%

Fig. 4.10 Heat transfer coefficients, α (kW/m2K), versus temperature difference between heated surface and bulk fluid (K) [76]: (1) PES4 fluid; (2) water; (3)–(7) emulsions by weight percent of PES4, 3.0, 6.0, 12.0, 20.0, 33.0, respectively

33% data sets all fall within experimental scatter of each other, so it is possible that improvement is only seen up to ε ~ 12%. This is a marked difference from the trends seen in pool boiling. Bulanov et al. also note that boiling begins at the saturation temperature of water, whereas the pool boiling results discussed previously and the flow boiling study [75] require a significant superheat to initiate boiling. Recent flow boiling experiments have been reported in microgap channels 30 mm wide with gaps of 0.1 mm [77] and 0.25 mm [78]. The design of the microgap in [77] was such that unsteady filling and emptying of the emulsion in the channel was demonstrated, making it difficult to draw conclusions on the heat transfer behavior. However, in [78] FC72-in-water and pentane-in-water emulsions were prepared in advance and pumped through the microgap at 133 kg/m2s (0.006 L/min) with a flow development length of 70 mm. Emulsions with ε = 0.1, 1, and 2% were investigated with a bulk inlet temperature of 25 °C. The dominant droplet size in the emulsion was 5–7 μm. The increasing volume fraction of FC72 initiates boiling at lower wall temperatures, with the onset of nucleate boiling occurring at wall temperatures of ~85 and 75 °C in the 1% and 2% emulsions, respectively. At 20–30 °C wall

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1.0 0.1 % FC-72

(h-ho)/ho

0.8

1.0 % FC-72 2.0 % FC-72

0.6

0.4

0.2

0.0 70

80

90

100

110

Wall Temperature [C] Fig. 4.11 Augmentation of average heat transfer coefficient for the FC72-in-water emulsions relative to water, h0. Tsat = 56 °C for FC72 at 1 atm [78]. H = 0.25 mm Qflow = 0.006 L/min

superheat, these temperatures are also lower than those normally required to initiate pool boiling. The heat transfer coefficient is 70% larger in the 2% emulsion compared to that in water at temperatures below the saturation temperature of water. This enhancement is attributed to mixing caused by the turbulent motion of the boiling droplets. For the pentane-in-water emulsions, no enhancement in heat transfer is measured up to ε = 1%. Figure 4.11 shows the augmentation of heat transfer coefficient achieved for the FC72-in-water emulsions. Morshed et al. [79] report experiments on flow boiling of FC72-in-water emulsions in a single 5 mm × 0.360 mm microchannel and in five parallel 0.5 mm × 0.5 mm microchannels. For both flow configurations, the channels were bottom-heated. Similar to pool boiling studies of FC72-in-water emulsions [62], the emulsions exhibited decreasing single-phase heat transfer coefficients with increasing volume fraction of FC72. This effect is observed only for the single microchannel and is not evident in the data for parallel microchannels. The researchers note that owing to the design of the single channel, the emulsion comes into contact with one hot surface, whereas it contacts three hot surfaces in each parallel microchannel. They conclude that FC72 accumulates on the bottom of the channel, but this affects heat transfer more significantly in the single microchannel due to the emulsion contacting only one hot surface. In contrast to the flow boiling studies mentioned above, once boiling initiates, they do not measure any enhancement in the heat transfer coefficient. They also measured the axial temperature distribution and find that the temperature change in the axial direction is not as large as observed in boiling of water.

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4.1.4

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Flow Boiling of Dilute Emulsions in a Microgap

Mechanisms in Pool Boiling

Boiling can occur via either spontaneous homogeneous nucleation in the bulk of a liquid or heterogeneous nucleation at a heated surface or other existing nucleation site. For spontaneous nucleation of bubbles, the emulsion temperature must be close to the kinetic limit of superheat, which is often hundreds of degrees Celsius above the saturation temperature [80]. Although a high level of superheat has been demonstrated experimentally, the temperatures measured to initiate boiling are much lower than the kinetic limit of superheat, so it is unlikely that spontaneous nucleation is occurring in the emulsions. It is likely that droplets in emulsions are boiling by either contact with a heated surface or interactions between a superheated droplet and a bubble or both. When a superheated droplet contacts a heated surface with available nucleation sites, boiling will occur, and it may be reasonable to assume that the mechanisms present are the same as those that govern pool boiling of single component liquids. There are four generally agreed-upon mechanisms: thin film evaporation, contact line heat transfer, transient conduction, and micro-convection [7]. After a bubble nucleates on the surface, a thin film of liquid exists between the edges of the curved bubble and the surface. Evaporation in this thin film and heat transfer at the contact line between the bubble surface and the heated surface contribute much of the energy transfer from the surface and the bubble. As the bubble becomes larger, more of the surface is exposed to vapor in its interior, and transient conduction between the vapor phase and the surface becomes gradually more important. Transient conduction to the surrounding liquid is also generally considered to be important during this phase of growth. After the droplet has completely evaporated and the bubble lifts off the surface, the space once filled by the bubble is replenished by the surrounding liquid, and this replenishment process results in micro-convection between the liquid and the surface. Although these may be the dominant processes taking place between the bubble and the heated surface, it is likely that before the entire droplet evaporates, there is interaction between the growing bubble and the droplet. It may be that the outward movement of the bubble surface causes movement in the droplet, resulting in convection within the droplet. An alternative energy transfer mechanism may be evaporation at the heated surface and at the surface between the bubble and the surrounding liquid. The interaction between the droplet and a bubble growing on a surface has not apparently been investigated thus far. After a droplet boils, interaction between the vapor bubble and another superheated droplet can cause the droplet to subsequently boil. It is not clear how this interaction takes place, but several mechanisms have been proposed. Bulanov et al. [81] theorize that the droplet boils very rapidly, and the rapid outward movement of the bubble surface produces a shock wave. The droplets exist in a metastable state so that as the shock wave passes surrounding droplets, the pressure of the wave disturbs the superheated droplets and causes them to boil. The amplitude of this wave decreases with distance from the original bubble but is sufficient to start a chain

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reaction of boiling droplets. Bulanov et al. utilize the theory of point explosions to determine the amplitude of the resulting shock wave. Roesle and Kulacki [60] contend that thermal diffusion is too slow to produce shock waves. They attribute this chain boiling process to physical contact between a bubble and a droplet. In a dilute emulsion with droplets of diameter O(10-6 m), the distance between individual droplets may be small. If this distance is less than the diameter of the bubble, the bubble surface will contact every droplet within one bubble diameter of its center. The contact between the bubble and the droplet can disturb the metastable droplet and cause it to boil. If there are many droplets that are contacted by the bubble, a chain reaction of boiling droplets can be started through simple contact. Regardless of which proposed mechanism causes boiling, the speed with which the droplets boil and interact with surrounding droplets is important in determining the rate of formation of new bubbles. As more bubbles form either at a surface or in the bulk of the fluid at microscopic nucleation sites, the turbulence of the boiling process will enhance energy transport. Thus, increasing the speed of the chain activation process will increase heat transfer. The chain activation process is limited by the rate at which individual droplets boil, and this process takes place via two distinct mechanisms that cause a bubble to expand: inertia-driven growth caused by the difference between the pressure inside the bubble and the surrounding fluid and thermally driven growth caused by heat diffusion coupled with phase change and mass transfer at the vapor/liquid interface [82]. When a single droplet boils, the bubble formation process involves both of these stages with the initial growth being inertial and the later stages of growth being thermally driven [83]. These two mechanisms would both contribute to the bubble growth rate, thus setting the speed of the chain activation process.

4.1.5

Roesle-Kulacki Pool Boiling Model

Roesle and Kulacki describe a model formulation based on the RANS equations [16, 60, 70]. Their numerical technique splits every variable in the mass, momentum, and energy conservation equations into the mean value and fluctuation around the mean. For example, velocity in the x-direction would be represented u = u þ u0

ð4:4Þ

where u is the mean velocity and u′ is the fluctuation around the mean. The differential equations are averaged, generally using ensemble averaging. Because the average of the fluctuations for each variable is zero, the differential equations are solved for the mean motions. This formulation results in terms that will include the * * average of two fluctuations multiplying each other, e.g., from Uk Uk in the advection terms, and this average is not necessarily equal to zero. Constitutive equations are

58

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therefore required to model these terms. In the momentum equations, these terms are the Reynolds stress, and they are often modeled in a manner similar to viscous stress. For their numerical model, Roesle and Kulacki consider three phases: the liquid continuous phase, the droplet (liquid disperse) phase, and the bubble (vapor disperse) phase. They do not consider the situation where the temperature of the emulsion is high enough to boil the continuous phase. They further assume each phase is an incompressible Newtonian fluid. Thus, the continuity equation is written ( * ) ∂ðαk Þ Γ þ ∇ . αk Uk = k ρk ∂t

ð4:5Þ

For the continuous phase, there is no mass production, and Γc = 0. The mass production for the droplet and bubble phase must be equal and have opposite signs. Mass production is positive for the bubble phase when boiling occurs so _ and Γd = - m. _ that Γb = m, To determine the mass transfer rate, the various sources of mass production are boiling by contact with heated surfaces, boiling by bubble-droplet collisions, boiling via spontaneous nucleation, and condensation in subcooled regions of flow. From experiments, it is unclear whether most droplets boil upon contact with or away from the heated surface. However, it is assumed numerically that the surface temperature is sufficiently greater than the saturation temperature of the disperse component such that if any droplets contact it, they boil immediately. This is effectively accomplished by setting the boundary condition so that the mass transfer of the droplet phase at the surface equals the mass transfer of the bubble phase away from the surface. If a droplet boils either at the surface and then rises into the free stream or away from a surface, it can then interact with other superheated droplets that have not yet boiled, thereby causing nucleation in surrounding droplets. To determine the rate of nucleation and the mass production via this process, Roesle and Kulacki utilize statistical mechanics to determine the nucleation rate and collision efficiency as droplets and bubbles translate toward and slide around each other. This collision efficiency is used to find the mass production rate due to collisions between droplets and bubbles |* | * | 3ðRd þ Rb Þ2 | _ coll = αb αd ρd |Ud - Ub |ηcoll φ m 4R3b

ð4:6Þ

where ηcoll is the collision efficiency and φ is the average number of collisions between droplets and bubbles in a chain reaction of boiling droplets. They next consider spontaneous nucleation of bubbles. They find that the temperature of most emulsions is well below the kinetic limit required for spontaneous nucleation to occur, and they neglect this as a means of mass production. They finally consider condensation of bubbles in portions of the emulsions that are subcooled below the saturation temperature of the disperse component. They

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account for convection of a sphere in a quiescent medium and the latent heat of the disperse component to find the mass transfer rate via condensation: [ ] k _ cond = min - 3αb c 2 ðT sat- T Þ, 0 m hfg Rb

ð4:7Þ

The total rate of mass transfer is the sum of these sources. In the momentum equation, gravity is taken to be the only body force present, and the Boussinesq approximation is applied to the body force term. The momentum equation takes the form ( * ) ∂ αk Uk ∂t

] [ ( * * ) )( * * ) αk ( 2 T* μ þ μk,T ∇Uk þ ∇ Uk - ∇ . Uk I þ ∇ . αk Uk Uk = ∇ . ρk k 3 *

X F kj α * - k ∇P þ αk g ½1 - βk ðT - T k,0 Þ] þ ρk ρ j = b , c, d , j ≠ k k ð4:8Þ For determining the forces between phases, it is assumed that for dilute emulsions the droplets and bubbles do not exchange momentum. Therefore, only the forces * between the droplets and the continuous phase, F dc , and the bubbles and the * continuous phase, F bc , are needed. When considering the interphase forces, virtual mass, lift, and rotational and Stokes drag forces are considered. However, it is assumed that the virtual mass, lift, and rotational forces are negligible and the interphase forces are modeled as Stokes drag: * ) 18αd μeff (* U U d c d 2d * * * ) 18αb μeff (* Ub - Uc F bc = - F cb = 2 db *

*

F dc = - F cd = -

ð4:9Þ ð4:10Þ

The momentum equation also contains a term involving the turbulent viscosity, μk, T. This term is a model for the Reynolds stress that arises due to the RANS averaging procedure. As the RANS formulation arose to solve turbulent fluid dynamics, an analogy is drawn between the motions of boiling droplets and turbulent eddies to determine the turbulent viscosity. For the continuous phase, _ μc,T = 0:1m

ρc 2 R ρb b

ð4:11Þ

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Flow Boiling of Dilute Emulsions in a Microgap

Owing to the large spacing between individual droplets or bubbles (dilute dispersions), shear stress cannot transmit through turbulent motion, and the turbulent viscosity in the droplet and bubble phases is set equal to zero. For the energy equation, it is first assumed that the three phases are in thermodynamic equilibrium. With this assumption, the mixture temperature can be obtained without modeling interphase heat transfer. Rather than writing the equation in terms of internal energy, specific heat and Fourier’s law of conduction are used to write the mixture energy equation in terms of temperature: X * ∂T X _ fg αk ρk C v,k þ αk ρk Cv,k Uk . ∇T = ∇ . ½ðk eff þ k T Þ∇T ] - mh ∂t k k

ð4:12Þ

The turbulent conductivity, kT, arises due to the RANS formulation similarly to turbulent viscosity. As is often done in single-component fluids, the Reynolds analogy is utilized to determine this conductivity. Thus, the turbulent conductivity is set equal to the turbulent viscosity scaled by the specific heat. This model has the drawback of being difficult to implement, computationally expensive, and containing many simplifying assumptions. However, because it can solve the differential equations and account for many of the interactions between phases, it may be able to elucidate the complex physical mechanisms taking place in boiling of dilute emulsions. For example, Roesle and Kulacki [16, 70] consider the effect of increasing the collision efficiency by scaling their collision efficiency model by a parameter Kη. For emulsions with a lower volume fraction, increasing the collision efficiency increases heat transfer due to the increased number of nucleating bubbles. However, for ε = 1 or 2%, increasing the collision efficiency can have the effect of decreasing heat transfer at higher wall temperatures (Fig. 4.12). The decreased heat transfer is attributed to increased vapor in the thermal boundary layer surrounding the wire.

4.1.6

Bulanov Pool Boiling Model

Bulanov [69] developed an analytical solution for pool boiling on a heated wire. The quiescent medium is similar to that shown in Fig. 4.13. The heated wire has a surface temperature greater than the saturation temperature of the disperse component, Ts, which is also greater than the temperature of the surrounding pool, T1. As the disperse component droplets enter the thermal boundary layer surrounding the wire, they start to boil, rise through the boundary layer, and interact with droplets above the boundary layer that had not previously boiled. Statistical thermodynamics is used first to determine the number of droplets within the thermal boundary layer that will boil. For a monodisperse emulsion, the probability that a single droplet of diameter d and volume Vd will boil is

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Fig. 4.12 Heat transfer coefficient variation with increasing collision efficiency for FC72-in-water emulsions, T1 = 28 °C. (a) ε = 1%. (b) ε = 2%. (Adapted from [16])

bubble

T = T∞ T = Ts Heated wire q thermal boundary layer droplet

Fig. 4.13 Boiling of disperse emulsion considered by Bulanov [69, 60]

62

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Flow Boiling of Dilute Emulsions in a Microgap

p = 1 - expð- JV d τÞ

ð4:13Þ

and that the number of droplets, nb, within the boundary layer that boil is nb = Np = N ½1- expð- JV d τÞ]

ð4:14Þ

where N is the total number of droplets within the thermal boundary layer, J is the bubble nucleation rate, and τ is the time of residence of bubbles in the boundary layer. The number of droplets within the boundary layer can be determined if the disperse component volume fraction, ε, and the volume of the thermal boundary layer are known. Bulanov assumes the boundary layer has a thickness L and surface area As. The nucleation rate, time of residence, and boundary layer thickness are unknown a priori. The residence time and boundary layer thickness are determined from force and energy balances. Bulanov assumes that bubbles within the boundary layer experience two forces: Stokes drag and a buoyancy due to the difference in density between the emulsion and vapor bubbles of the disperse phase. He further assumes that the bubbles are traveling at a constant speed as they rise through the boundary layer so the speed of the bubbles can be determined by equating these two forces: u=

ðρeff - ρb ÞgD2 18μeff

ð4:15Þ

If the boundary layer thickness is defined as L = uτ, Eq. (4.15) can be used to determine the boundary layer thickness in terms of the residence time: L=

ðρeff - ρb Þgd 2 τ ( )2= 18μeff ρb=ρd 3

ð4:16Þ

In Eq. (4.16), the bubble diameter, D, is replaced by the droplet diameter, d, via conservation of mass. Next, it is assumed that the droplets enter the thermal boundary layer at their saturation temperature such that the energy required to boil N droplets is given by the latent heat of vaporization: Q = εAs Lρd hfg ½1- expð- JV d τÞ]

ð4:17Þ

The heat flux can then be determined by dividing by the surface area and the residence time. The fitting factor, C, accounts for approximations in the model formulation: q″ = C

ερd ðρeff - ρb Þgd 2 h fg ½1 - expð - JV d τÞ] ( )2=3 ρ b μeff =ρd

ð4:18Þ

4.1

Literature Review

63

With heat flux in terms of the heat transfer coefficient, Eq. (4.18) can be rewritten using the non-dimensional Nusselt, Archimedes (a metastability group), Prandtl, and Stefan numbers: Nu = C

ArPr ½1- expð- JV d τÞ] St

ð4:19Þ

This formulation is valid only for large values of superheat and very low droplet concentrations, and it is modified to show how it can be used when these assumptions are not met. Probability distribution functions are also provided for various droplet diameter distributions so that the model can be used for emulsions that are not monodisperse. Consistency between his predicted and measured results is achieved by varying the nucleation rate and fitting parameters in the model to fit each experiment, not by measuring the nucleation rate for a given experiment and then using it as an input for the model. Although Bulanov shows that his model can match experimental results, it has been shown that several assumptions in the formulation of it are internally inconsistent [60]. Setting aside this inconsistency, there are two additional deficiencies. First, because the model does not hold any ties to the differential equations and involves an ad hoc model for the forces and energy required to initiate boiling, it does not have the ability to inform either the physical mechanisms or the dynamics of the boiling process. Therefore, it cannot capture any of the myriad effects that have been demonstrated experimentally. Second, the formulation does not include a way to determine directly the nucleation rate. The nucleation rate is generally a complex function of the thermodynamic conditions, as well as surface properties and geometry of the system of interest, and predicting the nucleation rate a priori to input it into the model remains a significant challenge. Nevertheless, Bulanov’s theory of the nucleation and chain boiling processes represents an important step forward.

4.1.7

The Rozentsvaig-Strashinskii Flow Boiling Model

The Rozentsvaig-Strashinskii model determines the temperature at which bubbles will start to nucleate in turbulent flow of a monodisperse emulsion [84]. It assumes that portions of the droplet surface are deformed slightly, causing a local decrease of the capillary pressure. This decrease in the capillary pressure decreases the superheat temperature required to cause nucleation. Two deformation mechanisms are considered. The resonance model. For droplets with diameter greater than the turbulent Kolmogorov length scale, η, it is assumed that the turbulent kinetic energy of vortices of size η is able to deform the droplet surface. Thus, it is required that the turbulent kinetic energy of a vortex of size η be greater than the work of formation of a bubble whose size, Dcr, is large enough to grow:

64

4

Flow Boiling of Dilute Emulsions in a Microgap

mc ðu0 Þ ≥ σD2cr 2

ð4:20Þ

It is assumed that the minimum droplet size that can undergo nucleation via this mechanism is equivalent to the Kolmogorov length scale. Hence the mass of the vortex in the continuous component, mc, in terms of this minimum diameter is ρc ðu0 Þ d3min ≥ σD2cr 2

ð4:21Þ

The total turbulent kinetic energy is linked to the energy dissipated by vortices of this size ðu0 Þ ≈ ðεdiss d min Þ =3 2

2

ð4:22Þ

To determine the turbulent kinetic energy dissipated, Rozentsvaig and Strashinskii consider turbulent flow in a pipe of diameter Dh and equate the dissipation and the wall shear stress: πD2h lρc εdiss = τw πDh lU 4

ð4:23Þ

The wall shear stress is related to the friction factor via the Blasius equation for turbulent flow in a round pipe: ( )0:25 μc 0:3164 = 0:3164 f= UDh ρc Re 0:25

ð4:24Þ

With the use of Eq. (4.24), Eq. (4.23) can be rearranged to obtain an equation for the dissipation: εdiss =

2:75 0:158μ0:25 c U 1:25 0:25 D h ρc

ð4:25Þ

Having obtained an equation for the dissipated turbulent kinetic energy, Rozentsvaig and Strashinskii insert Eq. (4.25) into Eq. (4.21) and assume equality to determine the minimum diameter of droplets that would boil via this mechanism: - 0:05 d min = CΔW 0:27 cr μc

ð4:26Þ

Note that ΔWcr is used to generalize the work of formation term in Eq. (4.21). For a metastable droplet, the work of formation is

4.1

Literature Review

65

ΔW cr =

16π 3 σ 3 ( )2 3ðPsat - Pf Þ2 1 - ρg =ρf

ð4:27Þ

Finally, it is assumed that the surface tension is linearly related to temperature, the viscosity is exponentially dependent on temperature, and the saturation pressure is ( Psat = C exp -

C1 T þ C2

) ð4:28Þ

Thus, Rozentsvaig and Strashinskii obtain an expression for the minimum droplet size that will boil via the resonance mechanism as a function of the temperature of the emulsion: ( ) ðC 4 - C5 T Þ0:81 0:05C 0 d min = C h ( ) i0:54 exp - T C1 exp - TþC P f 2

ð4:29Þ

The gradient model. For droplets whose diameter is smaller than the Kolmogorov length scale, Rozentsvaig and Strashinskii note that at that scale, the dynamics are largely governed by viscous shear associated with the turbulent fluctuations. Thus, they assume that the shear stress is able to deform the droplet surface and the energy associated with the deformation must be larger than the work of formation of a critical bubble radius, dcr: μc

∂u0 3 d ≥ σd2cr ∂r min

ð4:30Þ

For isotropic turbulence, the derivative of the turbulent fluctuations is related to the dissipated turbulent kinetic energy: ∂u0 = ∂r

r--------------2εdiss ρc 15μc

ð4:31Þ

Equation (4.30) can be rearranged to solve for dmin. With the use of Eqs. (4.25) and (4.31), - 0:21 d min = CΔW 0:33 cr μc

ð4:32Þ

Substituting the expression for the work of formation given by Eq. (4.27) and utilizing the same assumptions regarding surface tension, viscosity, and saturation pressure, the minimum diameter that will boil via the gradient mechanism is dmin = C h

( ) C4 - C5 T 0:21C 0 ) i0:66 exp - T C1 exp - TþC - Pf 2 (

ð4:33Þ

66

4

Flow Boiling of Dilute Emulsions in a Microgap

Rozentsvaig and Strashinskii compare the model results to measurements from [85] for water-in-PES5 emulsions with droplet diameters of 1.5 and 35 μm. It is shown that the resonance model provides good agreement with the temperature at the onset of nucleate boiling for droplets with d = 35 μm, and the gradient model predicts well the temperature for droplets with d = 1.5 μm. However, the experimental results that are referenced are for pool boiling, and thus there would be no turbulence present to nucleate bubbles via these turbulent flow mechanisms prior to the initiation of boiling. After the onset of nucleate boiling, they state that for a laminar flow, the boiling process would cause local turbulence that would further nucleate bubbles via these mechanisms. This mechanism relies on the use of the Kolmogorov length scale based on the large-scale flow behavior and the Reynolds number based on the pipe scales (see Eqs. (4.24) and (4.25)). If the turbulence is due solely to boiling of droplets, it is not clear that the turbulent kinetic energy and dissipation should scale with the pipe scales. In the resonance and gradient regimes, the mechanisms rely on a determination of dissipation of turbulent kinetic energy. To determine the dissipation, Rozentsvaig and Strashinskii equate the dissipation and the wall shear stress, which are distinct mechanisms for the diffusion of energy. The dissipation describes the amount of energy diffused at the molecular scale due to the transport of energy from large vortices to small vortices in the turbulent region of the boundary layer (the turbulent core). The wall shear stress describes the momentum diffused in the near-wall region of the boundary layer (the viscous sublayer) due to viscosity and the presence of the wall. Equating these two mechanisms therefore represents an inconsistency in this model.

4.2

Experimental Results

In flow boiling of dilute emulsions, the heat transfer coefficient typically demonstrates three regions based on the wall temperature (Fig. 4.14). In region I, the wall temperature is lower than the saturation temperature of the disperse component, 56 °C for FC-72, and single-phase heat transfer is present in both components. In this region, heat transfer coefficients are typically similar to those for water at the same experimental conditions. However, emulsion heat transfer coefficients can be lower than those for water depending on the volume fraction, flow rate, and gap size. In region II, the wall temperature is between the saturation temperature of the disperse and continuous components. In this region the disperse component will start to boil at wall temperatures slightly above its saturation temperature with a corresponding shift in the slope of the boiling and heat transfer coefficient curves. Although in general the heat transfer coefficient increases with increasing wall temperature, and Fig. 4.14 shows much larger heat transfer coefficients for the emulsion than water, it is possible that measured heat transfer coefficients are lower than in water at the same wall temperature. Depending on the volume fraction, mass flux, and gap size, the emulsion heat transfer coefficient in this region can be

4.2

Experimental Results

67

Fig. 4.14 Typical heat transfer coefficient curves for emulsions compared to those for water. Ti = 30 °C, Dh = 1000 μm, G = 350 kg/m2s. ΔT = Tw - Tsat

larger or smaller relative to that of water over the whole range of wall temperature, or less than water at lower wall temperatures and greater than water at higher wall temperatures. Thus, heat transfer is quite complex in this region. In region III, part of the wall has reached the saturation temperature of the continuous component, and boiling is present in the disperse and the continuous components. This is signified by another shift in the slope of the boiling and heat transfer coefficient data. Because the disperse component accounts for less than 5% of the volume in a dilute emulsion, the heat transfer in this region is typically dominated by boiling of the continuous component. The following figures show more fully the impact that the volume fraction, gap size, and mass flux have on heat transfer and pressure drop. At G = 350 kg/m2s and Dh = 200 μm, the emulsion boiling curves all shift to higher wall temperatures relative to water (Fig. 4.15a), indicating a decrease in heat transfer for the emulsion. For Tw < 80 °C, the heat transfer coefficient is independent of the volume fraction and ~30% lower than that for water. At higher wall temperatures, the heat transfer coefficient increases for the 0.1% and 0.5% emulsions but is still much less than that for water.

68

b

350 300

q"net [kW/m2]

Flow Boiling of Dilute Emulsions in a Microgap

250

Water

e = 1%

e = 0.1%

e = 2%

700 600

e = 0.5%

q"net [kW/m2]

a

4

200 150 100 50

Water

e = 1%

e = 0.1%

e = 2%

e = 0.5%

500 400 300 200 100

0 26

41

56

71 Tw [°C]

86

101

116

0 26

41

56

71 Tw [°C]

86

101

116

–30

–15

0

15 DT [°C]

30

45

60

–30

–15

0

15 DT [°C]

30

45

60

c

700

q"net [kW/m2]

600 500

Water

e = 1%

e = 0.1%

e = 2%

e = 0.5%

400 300 200 100 0 26

41

56

71 Tw [°C]

86

101

116

–30

–15

0

15 DT [°C]

30

45

60

Fig. 4.15 Boiling curves for emulsions on the smooth surface, Ti = 30 °C, G = 350 kg/m2s. (a) to (c) are for Dh = 200, 500, and 1000 μm, respectively. ΔT = Tw - Tsat

For Dh = 500 μm, the boiling curve for the 0.1% emulsion shifts to slightly lower wall temperatures (Fig. 4.15b) with a corresponding increase in the heat transfer coefficient compared to that for water as the wall temperature increases (Fig. 4.16b). The 1% emulsion shows decreased heat transfer, but the boiling curve and heat transfer coefficient for the 0.5% and 2% emulsions are nearly the same as those for water. For Dh = 1000 μm, the boiling curve shifts to lower wall temperatures for all ε, with the largest shift occurring at the lower volume fractions (Fig. 4.15c). Thus, the heat transfer coefficient is larger compared to that in water in all emulsion trials at this gap size (Fig. 4.16c). For the 0.1% emulsion, the heat transfer coefficient is more than 50% larger than that for water at the same experimental condition.

Experimental Results

4.2

69

a 12000

8000

ε = 1%

ε = 0.1%

ε = 2%

10000

ε = 0.5%

h [W/m2K]

h [W/m2K]

10000

b 12000 Water

6000 4000

8000

Water

ε = 1%

ε = 0.1%

ε = 2%

ε = 0.5%

6000 4000 2000

2000 0 26

41

56

71 86 Tw [°C]

101

116

0 26

41

56

71 86 Tw [°C]

101

116

–30

–15

0

15 30 ΔT [°C]

45

60

–30

–15

0

15 30 ΔT [°C]

45

60

c 12000 10000

Water

ε = 1%

ε = 0.1%

ε = 2%

h [W/m2K]

ε = 0.5%

8000 6000 4000 2000 0 26

41

56

71 86 Tw [°C]

101

116

–30

–15

0

15 30 ΔT [°C]

45

60

Fig. 4.16 Heat transfer coefficient for emulsions on the smooth surface, Ti = 30 °C, G = 350 kg/m2s. (a) to (c) are for Dh = 200, 500, and 1000 μm, respectively

Though the heat transfer in the flowing emulsions is at times like that for water, the pressure drop is always affected by the presence of the disperse component. The pressure drop increases with increasing volume fraction regardless of gap size (Fig. 4.17). The 2% emulsion pressure drop is generally 3–5 kPa higher than that for water. The disperse component constitutes less than 5% of the total volume, and when it starts to boil, the pressure drop does not increase, e.g., Figs. 4.16c and 4.17c where the heat transfer coefficient increases with increasing wall temperature and the pressure drop stays constant. When the continuous component starts to boil, the pressure drop can increase dramatically (Fig. 4.17a). Although the pressure drop is slightly lager for the emulsions at all Tw, for the range of Tw where the emulsions exhibit increased heat transfer compared to that for water, there is no associated additional pressure penalty.

70

b

21 18 15

ΔP [kPa]

Flow Boiling of Dilute Emulsions in a Microgap

Water

ε = 1%

ε = 0.1%

ε = 2%

15 12

ε = 0.5%

Water

ε = 1%

ε = 0.1%

ε = 2%

ε = 0.5%

ΔP [kPa]

a

4

12 9

9 6

6 3

3 0 26

41

56

71 Tw [°C]

86

101

116

0 26

41

56

71 Tw [°C]

86

101

116

–30

–15

0

15 ΔT [°C]

30

45

60

–30

–15

0

15 ΔT [°C]

30

45

60

c

15

ΔP [kPa]

12

Water

ε = 1%

ε = 0.1%

ε = 2%

ε = 0.5%

9 6 3 0 26

41

56

71 Tw [°C]

86

101

116

–30

–15

0

15 ΔT [°C]

30

45

60

Fig. 4.17 Pressure drop for emulsions on the smooth surface, Ti = 30 °C, G = 350 kg/m2s. (a) to (c) are for Dh = 200, 500, and 1000 μm, respectively

Mass flux and gap size also strongly affect the emulsion heat transfer, and this is shown for a fixed ε in the following figures. Similar to flow boiling in water, the emulsion boiling curves shift leftward with increasing mass flux. However for the 200 and 500 μm gaps, the boiling data shift to higher wall temperatures for G = 350 and 550 kg/m2s compared to that for water (Fig. 4.18a, b). This is a result of the emulsion measurements exhibiting a significantly lower heat transfer coefficient (Fig. 4.19a, b). The heat transfer coefficient is constant and shows little evidence of boiling of the disperse component. For G = 150 kg/m2s, the boiling curve is almost equivalent to that of water for Dh = 200 μm and shifts to slightly lower wall temperatures for Dh = 500 μm. For the 200 μm gap, the emulsion heat transfer coefficient is less than that for water but

4.2

a

Experimental Results

71

b

600 G [kg/m2s]

500

Fluid

400

e = 1%

G [kg/m2s]

600

150 350 550

q"net [kW/m2]

Water

q"net [kW/m2]

700

300 200 100

Fluid

500

150 350 550

Water e = 1%

400 300 200 100

0 26

41

56

71 86 Tw [°C]

101

116

131

0 26

41

56

71 86 Tw [°C]

101

116

131

–30

–15

0

15 30 DT [°C]

45

60

75

–30

–15

0

15 30 DT [°C]

45

60

75

c

700

q"net [kW/m2]

600 500

G [kg/m2s] Fluid

150 350 550

Water e = 1%

400 300 200 100 0 26

41

56

71 86 Tw [°C]

101

116

131

–30

–15

0

15 30 DT [°C]

45

60

75

Fig. 4.18 Boiling curves for water and 1% emulsions on the smooth surface, Ti = 30 °C. (a) to (c) are for Dh = 200, 500, and 1000 μm, respectively

increases slightly with increasing Tw (Fig. 4.19a). For Dh = 500 μm, the heat transfer coefficient is slightly larger than that for water at higher wall temperatures. In these two water runs, CHF is reached but is significantly delayed in the corresponding emulsion cases. For Dh = 1000 μm, the boiling data shift to lower wall temperature for all values of mass flux with the largest shift occurring for G = 150 kg/m2s and decreasing with increasing mass flux (Fig. 4.18c). The 150 and 350 kg/m2s mass flux experiments demonstrate lager emulsion heat transfer coefficients compared to water for Tw between the saturation temperatures of the two fluids (Fig. 4.19c). At G = 550 kg/m2s, the heat transfer coefficient increases with increasing wall temperature and becomes larger than that for water at Tw ~ 75 °C.

72

4

a 14000

h [W/m2K]

10000

b G [kg/m2s] Fluid

14000

Water

Fluid

6000

150 350 550

Water

10000

ε = 1%

8000

ε = 1%

8000 6000

4000

4000

2000

2000

0 26

G [kg/m2s]

12000

150 350 550

h [W/m2K]

12000

Flow Boiling of Dilute Emulsions in a Microgap

41

56

71 86 Tw [°C]

101 116 131

0 26

41

56

71 86 Tw [°C]

101 116 131

–30 –15

0

15 30 ΔT [°C]

45

–30 –15

0

15 30 ΔT [°C]

45

60

75

60

75

c 14000 G [kg/m2s]

12000 h [W/m2K]

10000

Fluid

150 350 550

Water ε = 1%

8000 6000 4000 2000 0 26

41

56

71 86 Tw [°C]

101 116 131

–30 –15

0

15 30 ΔT [°C]

45

60

75

Fig. 4.19 Heat transfer coefficient for water and 1% emulsions on the smooth surface, Ti = 30 °C. (a) to (c) are for Dh = 200, 500, and 1000 μm, respectively

The effect of hydraulic diameter on the boiling curve and heat transfer coefficient is shown in Figs. 4.20 and 4.21. At G = 150 kg/m2s, the emulsion boiling curves are almost equivalent to those for water for Dh = 200 and 500 μm, and the boiling curve shifts to lower wall temperature for Dh = 1000 μm (Fig. 4.20a). This corresponds to larger heat transfer coefficients compared to that for water in the 500 and 1000 μm gaps and a lower value for the 200 μm gap (Fig. 4.21a). For G = 350 and 550 kg/m2s, the boiling curve shifts to higher wall temperature for Dh = 200 and 500 μm and slightly lower wall temperature for the 1000 μm gap (Fig. 4.20b, c). Thus, the heat transfer coefficient is decreased for the 200 and 500 μm gaps. The heat transfer coefficient increases with decreasing gap size for flow boiling of water, but the reverse is true for the emulsions, with the largest value occurring for Dh = 1000 μm at each mass flux.

a

Experimental Results

b

700 600

q"net [kW/m2]

73

500

Dh [mm] Fluid

700 600

200 500 1000

Water

q"net [kW/m2]

4.2

e = 1%

400 300 200

500

Dh [mm] 200 500 1000

Fluid Water e = 1%

400 300 200 100

100 0 26

41

56

71 86 Tw [°C]

101

116

131

0 26

41

56

71 Tw [°C]

86

101

116

–30

–15

0

15 30 DT [°C]

45

60

75

–30

–15

0

15 DT [°C]

30

45

60

c

700

q"net [kW/m2]

600 500

Dh [mm] Fluid

200 500 1000

Water e = 1%

400 300 200 100 0 26

41

56

71 86 Tw [°C]

101

116

131

–30

–15

0

15 30 DT [°C]

45

60

75

Fig. 4.20 Boiling curves for water and 1% emulsions on the smooth surface, Ti = 30 °C. (a) to (c) are for G = 150, 350, and 550 kg/m2s, respectively

Figures 4.22 and 4.23 show that the pressure drop for the 1% emulsion is almost always larger than that measured for water. The water and emulsions exhibit the same trend of increasing pressure drop with increasing mass flux (Fig. 4.22) and decreasing hydraulic diameter (Fig. 4.23). The pressure drop is similar for Dh = 500 and 1000 μm for both the emulsions and water (Fig. 4.23). However, the emulsions demonstrate a wider range of pressure drop when viewing the pressure drop as a function of Dh, where the difference between the pressure drop for Dh = 200 and 1000 μm at each mass flux is greater for the emulsions than for water. In Fig. 4.24, the water and 1% emulsion data for Dh = 500 μm and G = 150 kg/m2s are presented in comparison with measurements of Janssen and Kulacki [78] and Morshed et al. [79], which offer a limited comparison for similar experimental conditions. Flow boiling was also studied by Gasanov and Bulanov [75] and Bulanov, Skripov, and Khmylnik [76]. Comparison with these studies is not feasible owing to significant differences in the hydraulic diameter, heater geometry, and mass flux.

74

4

Flow Boiling of Dilute Emulsions in a Microgap

a 12000

b 14000 Dh [μm]

8000

Fluid

Fluid

10000

Water ε = 1%

6000 4000

200 500 1000

Water ε = 1%

8000 6000 4000

2000 0 26

Dh [μm]

12000

200 500 1000

h [W/m2K]

h [W/m2K]

10000

2000 41

56

71 86 Tw [°C]

–30 –15

0

15 30 ΔT [°C]

101 116 131

45

60

75

0 26

41

56

71 86 Tw [°C]

101

116

–30

–15

0

15 30 ΔT [°C]

45

60

c 14000 12000 h [W/m2K]

10000

Dh [μm] Fluid

200 500 1000

Water ε = 1%

8000 6000 4000 2000 0 26

41

56

71 86 Tw [°C]

–30 –15

0

15 30 ΔT [°C]

101 116 131

45

60

75

Fig. 4.21 Heat transfer coefficient for water and 1% emulsions on the smooth surface, Ti = 30 °C. (a) to (c) are for G = 150, 350, and 550 kg/m2s, respectively

In Fig. 4.24, the results of this investigation and that of Janssen and Kulacki are similar. The boiling curves measured by Morshed et al. are shifted to much higher wall temperatures for a nearly identical inlet temperature of 25 °C, and the boiling curves are relatively insensitive to ε. The Janssen-Kulacki data show continuously increasing heat transfer performance with increasing ε, which is not shown in the data of our investigation at the higher flow rate of G = 350 kg/m2s. The emulsion data in this investigation show larger heat transfer coefficients for lower G. It is possible that for varying ε, a trend similar to that in Janssen’s data would be measured in our microgap at a lower mass flux of 150 kg/m2s. Because Morshed et al. measure a boiling curve for water that is also shifted to much higher wall temperatures, the difference in results for both water and emulsions may be due to a difference in their experimental setup. It is likely that this is caused by two factors.

Experimental Results

4.2

b 15

35 30

Fluid

25 ΔP [kPa]

G [kg/m2s]

G [kg/m2s] 150 350 550

12

Fluid

Water

Water

ε = 1%

ε = 1%

ΔP [kPa]

a

75

20 15

9

150 350 550

6

10 3

5 0 26

41

56

71 86 Tw [°C]

101

116

131

–30

–15

0

15 30 ΔT [°C]

45

60

75

15

Fluid

150 350 550

12

ε = 1%

c

0 26

41

56

71 86 Tw [°C]

101

116

131

–30

–15

0

15 30 ΔT [°C]

45

60

75

18 G [kg/m2s]

ΔP [kPa]

Water

9 6 3 0 26

41

56

71 86 Tw [°C]

101

116

131

–30

–15

0

15 30 ΔT [°C]

45

60

75

Fig. 4.22 Pressure drop for water and 1% emulsions on the smooth surface, Ti = 30 °C. (a) to (c) are for Dh = 200, 500, and 1000 μm, respectively

Janssen and Kulacki and this investigation employ long flow development lengths upstream and exit lengths downstream of the heated section, whereas the entrance and exit of the channel are located immediately upstream and downstream of the heated section in the Morshed et al. apparatus. Although the hydraulic diameter is similar, Morshed et al. use a channel that is 0.36 mm × 5 mm in cross section making their channel much narrower than either that employed here (25.4 mm wide) or in Janssen and Kulacki’s experiments (30 mm). Their channel may be experiencing confinement effects that are not demonstrated for boiling in the larger gaps.

76

b

21 18 15

ΔP [kPa]

Flow Boiling of Dilute Emulsions in a Microgap

24 Dh [μm]

Dh [μm] Fluid

200 500 1000

20

Fluid

16

ε = 1%

200 500 1000

Water

Water ε = 1%

ΔP [kPa]

a

4

12 9

12 8

6

4

3 0 26

41

56

71 86 Tw [°C]

101

116

131

0 26

41

56

71 86 Tw [°C]

101

116

–30

–15

0

15 30 ΔT [°C]

45

60

75

–30

–15

0

15 30 ΔT [°C]

45

60

Fluid

200 500 1000

c

35 Dh [μm]

30

Water

ΔP [kPa]

25

ε = 1%

20 15 10 5 0 26

41

56

71 86 Tw [°C]

101

116

131

–30

–15

0

15 30 ΔT [°C]

45

60

75

Fig. 4.23 Pressure drop for water and 1% emulsions on the smooth surface, Ti = 30 °C. (a) to (c) are for G = 150, 350, and 550 kg/m2s, respectively 800 700 600 q"net [kW/m2]

Fig. 4.24 Comparison of Dh = 500 μm, G = 150 kg/m2s emulsion boiling data with that of Janssen and Kulacki [78] (Dh = 500 μm, G = 133 kg/m2s) and Morshed et al. [79] (Dh = 672 μm, G = 129 kg/m2s)

Janssen, Kulacki [107], e=0.1% Janssen, Kulacki [107], e=1% Janssen, Kulacki [107], e=2% Morshed et al. [108], water Morshed et al. [108], e=0.5%

500 400

Morshed et al. [108], e=1% This study, water This study, e=1%

300 200 100 0 25

40

55

70

85

100 115 130 145 160

Tw [°C]

Chapter 5

Flow Boiling on a Porous Surface

5.1

Literature Review

Investigations of boiling on structured and unstructured surfaces have appeared recently owing to the effectiveness of these structures for increasing heat transfer and delaying the transition to CHF. Many of them have been conducted for structured surfaces used in microgaps and microchannels [86–100]. Because the literature is so large for boiling on structured and unstructured surfaces and the present focus is boiling on unstructured microporous surfaces, attention will be given here to this subset of the literature. The reader can consult [98, 101–103] for more complete lists of the relevant literature.

5.1.1

Description of Porous Media

A porous medium consists of solid material interspersed with interstitial void spaces (pores) through which fluid can flow. A representative volume of a heterogeneous porous medium is shown in Fig. 5.1. If a porous medium is deposited on a wall with bulk flow above it, flow must be considered at the macroscopic and pore levels. Generally, flow and heat and mass transport in a porous medium are dependent on the local fluid pore size, porosity, and permeability. The bulk porosity, ϕ, of a porous medium is defined as the ratio of void volume to solid volume in a representative elementary volume in the medium. A common assumption in measuring porosity is that the solid and void cross-sectional areas are constant in one direction and that the porosity can be approximated by the void and solid areas rather than volume:

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 B. M. Shadakofsky, F. A. Kulacki, Flow Boiling of a Dilute Emulsion In Smooth and Rough Microgaps, Mechanical Engineering Series, https://doi.org/

77

78

5

Flow Boiling on a Porous Surface

Fig. 5.1 Typical heterogeneous porous medium

ϕ=

V void A ≈ void V solid Asolid

ð5:1Þ

The permeability, K, relates to the momentum loss due to flow at the pore scale, which has one component associated with viscous losses and one associated with inertia. The pressure drop at the pore scale is related to the permeability [104]: ∇Ppore = -

5.1.2

* ρC || * || * μU - 1= |U |U K K2

ð5:2Þ

Methods of Creating Porous Surfaces

Various techniques have been developed for creating microporous surfaces. One popular technique is that developed and patented by You et al. [105–112]. You et al. deposit alumina (Al2O3), silver, or diamond flakes on substrates. First the flakes are mixed with a binder, e.g., Omegabond™ 101, and an alcohol, e.g., methyl-ethylketone, that evaporates at atmospheric pressure. The mixture is either dripped onto the surface with a pipette or paint brush or sprayed onto it with an airbrush, depending on the substrate size. It is allowed to sit at atmospheric pressure until the alcohol evaporates, leaving a mixture of flakes and the binder. The van der Waals force is the primary adhesive force between the mixture and the substrate. The pore size and porosity of this porous surface can be varied by using various flake sizes. Usually, a range of pore sizes is seen for a given flake size, but the dominant pore size is on the order of the flake size. The coating thickness can be set by varying the

5.1

Literature Review

79

amount of mixture applied to the substrate, and often the thickness also increases with the size of the flakes. This technique was also utilized to deposit Al2O3 and TiO2 surfaces for flow boiling in vertically oriented 11 mm diameter tubes [113] and to deposit aluminum particles for pool boiling between parallel plates [114, 115]. A second technique for depositing microporous surfaces was developed by El-Genk and Ali [20]. In this process, electrochemical deposition is used to deposit the surface and increase the bond strength between the surface and substrate. Two copper plates are connected to a voltage supply and oriented horizontally and parallel to each other in an electrolyte solution of sulfuric acid and copper sulfate. Voltage is applied to drive a chemical reaction, where the copper cathode will serve as the substrate on which the porous surface is deposited. In this reaction, the copper and hydrogen in the electrolyte solution are stripped of electrons which travel to the copper cathode and cause the copper to deposit on the surface and hydrogen atoms near the surface to combine with free electrons to form hydrogen bubbles. This reaction proceeds in two steps. A high voltage is applied so that 3 A/cm2 flows between the copper cathode and anode. In this step the majority of the copper atoms are deposited, but the bond between the surface and substrate is relatively weak. The released hydrogen bubbles at the cathode form semi-regular circular pores. The thickness of the layer is set by the length of time this voltage is applied with surfaces of 95–230 μm thickness resulting from 15 to 44 s of applied voltage. The porosity of the surface is insensitive to the time in this stage. In the second step, the current density is set to be very low and held for approximately 10 or more minutes. The bonds between the surface and the substrate and between individual copper atoms strengthen, resulting in a very robust surface. The porosity decreases as additional copper atoms fill out the structure. At the end of the first step, the bonded copper atoms form more dendritic structures, and after the second step, the small-scale structures are more rounded. This also increases the wettability of the surface. In previous work by Parker and El-Genk [116–118], the surfaces were created by bonding a graphite surface to a heated substrate.

5.1.3

Boiling on Microporous Surfaces

Boiling on microporous surfaces generally offers three benefits compared to boiling on smooth surfaces. Superheat at ONB is much lower on the microporous surfaces, with a correspondingly low, or often nonexistent, overshoot of temperature before boiling begins. This is attributed to the nucleation site characteristics and the ability of the porous surface to trap air that can serve as bubble embryos. Also, CHF is much higher on porous surfaces, more than double that on a smooth surface at the same condition in some cases [108]. Two mechanisms are often considered for increasing CHF on these surfaces. First, the porous surface increases the frequency of bubble release and decreases the bubble diameter. This has been supported with visual evidence in pool boiling [116]. Second, the pore network on the microporous surface can serve to wick

80

5 35

a

Heat Flux (W/cm2)

30

50 ΔTsub = 0 K

ΔTsub = 10 K

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Flow Boiling on a Porous Surface

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Surface Superheat, ΔTsat (K)

30

35

0 –15 –10 –5

0

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10 15 20 25 30 35

Surface Superheat, ΔTsat (K)

Fig. 5.2 Pool boiling curves for smooth copper and porous graphite surfaces [117]

fluid to the heated surface via surface tension and capillary pressure. This decreases the ability of vapor to wet the surface and cause a transition to CHF. The benefit is a decrease in the wall temperature and a corresponding increase in the heat transfer coefficient. These benefits are shown in Fig. 5.2 at various levels of subcooling. This figure also shows that, as in pool boiling on smooth surfaces, subcooling has a significant effect on the boiling curve. In the nucleate boiling region just after ONB, increasing subcooling decreases the wall temperature and increases the slope of the boiling curve. As the heat flux increases, the impact of subcooling decreases, and the slope of the boiling curve is seen to be the same for various levels of subcooling. At high heat flux, CHF is seen to be a linear function of subcooling. Subcooling in pool boiling on microporous surfaces was investigated in [111, 112, 116–118], and these trends are consistent among the various studies. In addition to subcooling, it is known that pressure, heater size, and heater orientation impact pool boiling heat transfer on smooth surfaces. On microporous surfaces, the effect of system pressure was studied by You et al. [111, 112], and the trends for the microporous surfaces are similar to trends for smooth surfaces. Increasing system pressure generally decreases superheat at ONB and increases CHF, with the impact on CHF being more dramatic on the microporous surfaces.

5.1

Literature Review

81

40

30

Plain surface data

Microporous surfaces

20

Microporous surfaces CHF (W/cm2)

Incipient superheat (K)

30

Porous nonconducting surfaces

Porous nonconducting surfaces

20

Plain surface data 10

CHF = 20.62 + 3.11 In (dm) – 0.25(In(dm))2 – 0.016 (In (dm))2

10

0

0 0

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30

40

50

60

Mean particle diameter (μm)

70

80

0

10

20

30

40

50

60

70

80

Mean particle diameter (μm)

Fig. 5.3 Superheat at ONB and CHF as a function of surface thickness, denoted as particle diameter for diamond flake microporous surfaces [108]

The effect of heater size was investigated by Rainey and You [110]. As in pool boiling on smooth surfaces, critical heat flux decreases with increasing heater area until a transition point is reached, after which CHF is insensitive to it. The transition point is approximately equivalent to that determined for pool boiling on smooth surfaces [119]. The effect of heater orientation on pool boiling on a smooth surface was investigated in [110, 118]. Increasing the surface angle generally shifts the boiling curve to slightly lower temperatures up to ~135°; thereafter the heat transfer coefficient diminishes, and the boiling curve shifts to significantly higher wall temperatures. On microporous surfaces, Rainey and You [110] report a relative insensitivity to change in heater angle throughout much of the boiling curve. El-Genk and Parker [118] report that the maximum heat transfer coefficient is insensitive to surface orientation and that the heat transfer coefficient at higher wall temperatures decreases with increasing heater angle. This is consistent with decreasing CHF with increasing angle, as is shown for both smooth and microporous surfaces. Finally, pore size, porosity, and thickness of the surface coating will likely impact heat transfer. The effect of surface thickness was investigated in [20, 108] although the process used for creating the porous coatings resulted in variations of both porosity and pore size with increasing thickness. Chang and You [108] found that increasing the porous surface thickness decreased the superheat at ONB and increased CHF. Both effects reached an asymptote, after which increasing the thickness had no impact on superheat or CHF (Fig. 5.3). Chang and You [108] assume that a superheated liquid layer of thickness ~100 μm exists on the heated surface. They reason that if the surface is thinner than the superheated layer, the entire surface can be activated during nucleate boiling. If the surface is thicker than the superheated liquid layer, only the bottom portion of the surface will be activated. They denote surfaces as either microporous

82

5 Flow Boiling on a Porous Surface

or porous based on the surface thickness in relation to the superheated liquid layer thickness. Chang and You’s CHF results are consistent with those of El-Genk and Ali [20], who measured an increase in CHF with increasing surface thickness up to a limiting value followed by insensitivity of CHF to surface thickness. Trends in superheat, heat transfer coefficient, and CHF for pool boiling on microporous surfaces are also consistent with the limited data available for flow boiling on microporous surfaces [109, 113]. However, in studying flow boiling in a vertically oriented tube of 10.9 mm inner diameter, Sarwar et al. [113] varied the particle size and surface thickness independently. They found that Al2O3 particles of 1 μm diameter show little effect on the heat transfer behavior compared to that for the smooth surface. Based on SEM images, particles of this size create a second hard surface with little interstitial area. Particles of 10 μm diameter result in a ~25% increase in CHF over the smooth tube surface case. They also show that increasing the surface thickness in the range 20–50 μm for a fixed particle size of 10 μm increases CHF. The effect of the mass flux on flow boiling was investigated by Ammerman and You [109] in a single 2 mm × 2 mm microchannel and Sarwar et al. [113] in the tube described above. Both studies demonstrate that increasing the mass flux leads to an increase in CHF for boiling on both microporous and smooth surfaces. A linear increase for the microporous surfaces is noted by Sarwar et al. Chang and You [108] also measured pressure drop in their study. They report that the pressure drop is comparable for the microporous and smooth channels at lower mass flux and higher subcooling. At higher mass flux and lower subcooling, the pressure drop for the microporous surfaces is ~33% larger than that for the smooth channel at the highest mass flux and lowest value of subcooling.

5.2

Experimental Results: Water

Boiling heat transfer coefficients and pressure drop for water on each porous surface are shown in Figs. 5.4, 5.5, 5.6, and 5.7. Many of the trends discussed above for flow boiling of water on a smooth surface are also observed on the porous surfaces including the lack of superheat at ONB, boiling heat transfer coefficients shifted to the left for increasing mass flux and hydraulic diameter, and increased pressure drop for increasing mass flux and decreasing hydraulic diameter. The transition to CHF occurs at lower heat flux for lower mass flux and hydraulic diameter on the porous surfaces. Heat transfer behavior on the porous surface shows some pronounced differences compared to that on the smooth surface. On the smooth surface, the heat transfer coefficient increases with decreasing hydraulic diameter in the single-phase region. After ONB, the boiling curves were seen to almost collapse to one curve prior to the transition to CHF. On the porous surfaces, the heat transfer coefficient decreases dramatically with decreasing Dh in the single-phase region. After ONB some of the heat transfer coefficients trend toward each other, but all of the data for Dh = 200 μm

5.2 Experimental Results: Water

700 600

q"net [kW/m2]

500

b 24000

G [kg/m2s] Dh [mm] 150 350 550 200 500 1000

21000 18000

h [W/m2K]

a

83

15000

400

G [kg/m2s] Dh [mm] 150 350 550 200 500 1000

12000

300 200

9000 6000

100

3000

0 25

40

55

70 85 Tw [°C]

100

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130

0 25

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70 85 Tw [°C]

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115

130

–75

–60

–45

–30 –15 DT [°C]

0

15

30

–75

–60

–45

–30 –15 DT [°C]

0

15

30

Fig. 5.4 (a) Boiling curve and (b) heat transfer coefficient for water on Porous Surface 1, Ti = 30 ° C. ΔT = Tw - Tsat

b 18000

700 600

q"net [kW/m2]

500

G [kg/m2s] Dh [mm] 150 350 550 200 500 1000

15000 12000

h [W/m2K]

a

400 300 200

G [kg/m2s] Dh [mm] 150 350 550 200 500 1000

9000 6000 3000

100 0 25

40

55

70 85 Tw [°C]

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130

0 25

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70 85 Tw [°C]

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–60

–45

–30 –15 DT [°C]

0

15

30

–75

–60

–45

–30 –15 DT [°C]

0

15

30

Fig. 5.5 (a) Boiling curve and (b) heat transfer coefficient for water on Porous Surface 2, Ti = 30 ° C

with G = 150 kg/m2s and Dh = 500 μm shift to higher wall temperature and early transition to CHF. For Dh = 1000 μm, the heat transfer coefficient is so large that boiling is not achieved in this range of heat flux in some cases, and it is difficult to determine that the heat transfer coefficients would collapse for Dh = 500 and 1000 μm after ONB. In the larger gaps, the pressure drop is relatively insensitive to the presence of boiling. In the 200 μm gap, unlike single-phase flow on the smooth surface, the pressure drop increases prior to the initiation of boiling. This is especially pronounced for Surfaces 1 and 2, where in some cases the increase in pressure drop is as large as 200%. Surface 3 demonstrates an increase of the pressure drop in the singlephase region, but the increase is less dramatic for this surface.

84

b 16000

700 G [kg/m2s] Dh [mm] 150 350 550 200 500 1000

600

q"net [kW/m2]

500

12000 10000

400 300 200

Flow Boiling on a Porous Surface

G [kg/m2s] Dh [mm] 150 350 550 200 500 1000

14000

h [W/m2K]

a

5

8000 6000 4000

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2000

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55

70 85 Tw [°C]

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130

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70 85 Tw [°C]

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–30 –15 DT [°C]

0

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30

–75

–60

–45

–30 –15 DT [°C]

0

15

30

Fig. 5.6 (a) Boiling curve and (b) heat transfer coefficient for water on Porous Surface 3, Ti = 30 ° C

a 105

ΔP [kPa]

75

b 240 G [kg/m2s] Dh [μm] 150 350 550 200 500 1000

210 180 150

ΔP [kPa]

90

60

G [kg/m2s] Dh [μm] 150 350 550 200 500 1000

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c

240 210

ΔP [kPa]

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G [kg/m2s] Dh [μm] 150 350 550 200 500 1000

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70 85 Tw [°C]

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130

–75

–60

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–30 –15 ΔT [°C]

0

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Fig. 5.7 Pressure drop on (a) Porous Surface 1, (b) Porous Surface 2, and (c) Porous Surface 3. Ti = 30 °C

Experimental Results: Water

5.2

a

85

b

600 Smooth Surface

500

Porous Surface 1

500

Porous Surface 2 Porous Surface 3

q"net [kW/m2]

q"net [kW/m2]

Smooth Surface

600

Porous Surface 1 Porous Surface 2

400

700

Porous Surface 3

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q"net [kW/m2]

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Smooth Surface Porous Surface 1 Porous Surface 2 Porous Surface 3

400 300 200 100 0 25

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55

70 85 Tw [°C]

100

115

130

–75

–60

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–30 –15 DT [°C]

0

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30

Fig. 5.8 Boiling curves for water on smooth and porous surfaces, Dh = 500 μm, Ti = 30 °C. (a) to (c) are for G = 150, 350, and 550 kg/m2s, respectively

Comparisons of the smooth and porous surface heat transfer are shown in Figs. 5.8 and 5.9 as a function of mass flux. Porous Surface 1 exhibits a higher single-phase heat transfer coefficient at every mass flux. This corresponds to a shift of the boiling curve to lower wall temperatures. After ONB, the heat transfer coefficients for the smooth surface and Surface 1 collapse to one trend line. For G = 150 kg/m2s, both the smooth surface and Surface 1 transition to CHF. The boiling curves for Surfaces 2 and 3 follow the same trend as the smooth surface and Surface 1 for Tw < 55 °C. At higher wall temperature, the boiling data for Surfaces 2 and 3 shift to the right, with a corresponding decrease in the heat transfer coefficient and an earlier transition to CHF. This effect diminishes with increasing max flux. Boiling heat transfer as a function of Dh is shown in Figs. 5.10 and 5.11.

86

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a 10000

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Porous Surface 1

Porous Surface 1 Porous Surface 2 Porous Surface 3

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Flow Boiling on a Porous Surface

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Fig. 5.9 Heat transfer coefficient for water on smooth and porous surfaces, Dh = 500 μm, Ti = 30 °C. (a) to (c) are for G = 150, 350, and 550 kg/m2s, respectively

At the smallest gap size, the porous surfaces exhibit diminished heat transfer compared to that for the smooth surface. Transition to CHF occurs at a much lower heat flux than that for the smooth surface. As the gap size increases, the porous surfaces demonstrate increasing heat transfer with respect to the smooth surface. At Dh = 500 μm, Porous Surface 1 exhibits a larger heat transfer coefficient than the smooth surface. At Dh = 1000 μm, all three surfaces demonstrate increased heat transfer than the smooth surface. In general, Porous Surfaces 2 and 3 show similar heat transfer results, although boiling on Porous Surface 2 transitions to CHF earlier than Porous Surface 3. The pressure drop for each porous surface as a function of mass flux and hydraulic diameter are shown in Figs. 5.12 and 5.13, respectively. For Dh = 500 μm the pressure drop on Porous Surface 1 is almost equivalent to that for the smooth surface (Fig. 5.12). The pressure drop on Porous Surface 2 is almost always the largest measured, with the measured pressure drop being up to eight times larger

5.2

a

Experimental Results: Water

87

b

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Smooth Surface

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Porous Surface 2

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Porous Surface 3

q"net [kW/m2]

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Fig. 5.10 Boiling curves for water on smooth and porous surfaces, G = 350 kg/m2s, Ti = 30 °C. (a) to (c) are for Dh = 200, 500, and 1000 μm, respectively

than that for the smooth surface at the same wall temperature. Though the pressure drop for Porous Surface 1 is nearly equivalent to that for the smooth surface for Dh = 500, for the 200 and 1000 μm gaps the pressure drop is much larger for Surface 1 than the smooth surface. For flow over a porous surface, there are two ways that it can increase the pressure drop (or decrease momentum): (i) the presence of the porous surface increases the roughness of the wall, and (ii) flow at the pore scale serves as a sink of momentum from viscous and inertial losses in the porous structure. From the top views in Figs. 2.10, 2.11, and 2.12, Porous Surface 1 has a more packed structure and lower porosity than Surfaces 2 and 3. This results in Porous Surface 2 and 3 appearing as rougher structures to the flow over the wall. If one compares the side views, Porous Surface 2 has a more open pore structure, and Porous Surface 3 is more densely packed. Thus, Porous Surface 2 should have more flow through the surface than Porous Surface 3, increasing pressure loss at the pore scale for Porous Surface 2.

88

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Porous Surface 1 Porous Surface 2

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Flow Boiling on a Porous Surface

Porous Surface 3

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Porous Surface 1 Porous Surface 3

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–45

–30 ΔT [°C]

Fig. 5.11 Heat transfer coefficient for water on smooth and porous surfaces, G = 350 kg/m2s, Ti = 30 °C. (a) to (c) are for Dh = 200, 500, and 1000 μm, respectively

5.3

Experimental Results: Dilute Emulsions

Boiling data and measured heat transfer coefficient as a function of ε and gap size on Surface 1 are shown in Fig. 5.14. For Dh = 200 μm, the emulsions exhibit decreased heat transfer coefficients compared to those for water, with a shift of the boiling curve to higher wall temperatures and transition to CHF at very low heat flux. For Dh = 500 μm, the 0.1% emulsion shows a slight shift of the boiling curve to the right below the boiling point of the continuous component. At ~100 °C, a further diminishment in heat transfer is seen as CHF is approached. For larger volume fraction, the boiling curve is shifted to even higher wall temperatures. It appears that CHF is independent of ε on Porous Surface 1. For Dh = 1000 μm, there is a shift in the boiling data to lower wall temperature for all volume fractions. However, the heat transfer coefficient for the emulsions is lower than that for water at the same

5.3 Experimental Results: Dilute Emulsions

a

89

b

30

60 Smooth Surface

Smooth Surface

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Porous Surface 1

Porous Surface 1 Porous Surface 2

Porous Surface 2

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Porous Surface 3

DP [kPa]

DP [kPa]

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DT [°C]

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Tw [°C]

Tw [°C]

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Porous Surface 1 Porous Surface 2

DP [kPa]

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Porous Surface 3

60 40 20 0 25

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–75 –60

–45

70 85 Tw [°C] –30

–15

100

115

130

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15

30

DT [°C]

Fig. 5.12 Pressure drop for water on smooth and porous surfaces, Dh = 500 μm, Ti = 30 °C. (a) to (c) are for G = 150, 350, and 550 kg/m2s, respectively

wall temperature, indicating that the difference in temperature between the wall and fluid is larger for the emulsions than water. The corresponding pressure drop for Porous Surface 1 is shown in Fig. 5.15. For the smallest gap, the pressure drop appears to be relatively insensitive to volume fraction of the disperse component, although CHF occurs so early in this gap that this conclusion is uncertain. For Dh = 500 and 1000 μm, the pressure drop increases with increasing volume fraction, and the emulsions demonstrate a larger increase in pressure drop after 100 °C than water. The effect of volume fraction on pressure drop diminishes with Dh > 500 μm. The boiling data and heat transfer coefficients for Porous Surface 2 are shown in Fig. 5.16. On this surface, the emulsions increase heat transfer coefficients for the majority of the experiments. The largest increases are seen for Dh = 200 μm, where the emulsions shift the boiling data to lower wall temperature, and the largest heat transfer coefficient is measured for ε = 1%. For this gap height, a large increase in

90

a

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Smooth Surface

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Porous Surface 1

Porous Surface 1 Porous Surface 2

Porous Surface 2

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Porous Surface 3

ΔP [kPa]

ΔP [kPa]

120 90

Porous Surface 3

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Flow Boiling on a Porous Surface

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–75 –60

–45

c

85

100

115

130

0

15

30

T [°C] w 15

30

–75 –60

–45

–30 –15 ΔT [°C]

14 Smooth Surface

12

Porous Surface 1 Porous Surface 2

10 ΔP [kPa]

Porous Surface 3

8 6 4 2 0 25

40

55

–75

–60

–45

70 Tw [°C]

85

100

115

–30

–15

0

15

ΔT [°C]

Fig. 5.13 Pressure drop for water on smooth and porous surfaces, G = 350 kg/m2s, Ti = 30 °C. (a) to (c) are for Dh = 200, 500, and 1000 μm, respectively

the heat transfer coefficient is seen after boiling of the disperse component commences for ε = 0.1%. For ε = 0.5, 1, and 2%, the increase in the heat transfer coefficient for 56 < Tw < 100 °C is more moderate, and the increased benefit compared to water with increasing wall temperature is primarily due to the decrease in the water heat transfer coefficient. A similar moderate increase in the heat transfer coefficient over this range of wall temperatures is seen for all volume fractions at Dh = 500 μm. The primary increase in heat transfer compared to that in water comes because of a diminished heat transfer coefficient with increasing wall temperature for water. For Dh = 1000 μm, the emulsions shift the boiling curve slightly to the left and result in slightly higher heat transfer coefficients with the largest heat transfer coefficients measured for ε = 2%.

Experimental Results: Dilute Emulsions

5.3

a

91

d 4800

250 H= 1% H= 2%

Water H= 0.1% H= 0.5%

Water H= 0.1% H= 0.5%

4000 3200

H= 1% H= 2%

h [W/m K]

2

q"net [kW/m ]

200

2

150

2400

100

1600

50

800 0

0 26

41

56

71

86

101

116

26

131

41

56

71

–30

b

–15

0

86

101

116

131

45

60

75

Tw [°C]

Tw [°C] 15 30 DT [°C]

45

60

–30

75

–15

0

15

30

DT [°C]

e

700

14000

H= 1% H= 2%

Water H= 0.1% H= 0.5%

600

10000 h [W/m K]

2

q"net [kW/m ]

500

8000

2

400 300

H= 1% H= 2%

Water H= 0.1% H= 0.5%

12000

6000

200

4000

100

2000

0

0 26

41

56

71

86

101

116

131

146

26

41

56

71

Tw [°C] –30

–15

0

15

86

101

116

131

146

30 45 DT [°C]

60

75

90

Tw [°C]

30 45 DT [°C]

60

75

90

–30

c

–15

0

15

f 700

18000 H= 1% H= 2%

Water H= 0.1% H= 0.5%

600

12000 h [W/m K]

2

q"net [kW/m ]

500

2

400

H= 1% H= 2%

Water H= 0.1% H= 0.5%

15000

300 200

9000 6000 3000

100

0

0 26

41

56

71

86

101

116

26

41

56

Tw [°C] –30

–15

0

15 DT [°C]

71

86

101

116

30

45

60

Tw [°C] 30

45

60

–30

–15

0

15 DT [°C]

Fig. 5.14 (a) to (c) Boiling curves and (d) to (f) heat transfer coefficient for emulsions on Porous Surface 1 with Dh = 200, 500, and 1000 μm. Ti = 30 °C, G = 350 kg/m2s.

92

60 50 ΔP [kPa]

b

70 Water H= 0.1% H= 0.5%

H= 1% H= 2%

20

40 30

Water H= 0.1% H= 0.5%

H= 1% H= 2%

15 10

20

5

10 0 26

Flow Boiling on a Porous Surface

30 25

ΔP [kPa]

a

5

0 41

56

71

86

101

116

131

26

41

56

71

86 101 Tw [°C]

116

131

146

45

60

75

–30

–15

0

15

30 45 ΔT [°C]

60

75

90

T [°C] w –30

–15

0

15 30 ΔT [°C]

c

18

12 ΔP [kPa]

H= 1% H= 2%

Water H= 0.1% H= 0.5%

15

9 6 3 0 26

41

56

71

86

101

116

30

45

60

T [°C] w –30

–15

0

15 ΔT [°C]

Fig. 5.15 Pressure drop for emulsions on Porous Surface 1, Ti = 30 °C, G = 350 kg/m2s. (a) to (c) are for Dh = 200, 500, and 1000 μm, respectively

The increase in heat transfer coefficient on Porous Surface 2 is likely a result of the open pore network on both the top and in the interior of the porous surface layer. This open pore network would allow FC-72 droplets to flow down into the porous structure and nucleate bubbles within the confined space there. After nucleation, the resulting vapor would also flow out of this porous structure more easily than in a structure that is more densely packed, either at the top of the surface (Porous Surface 1) or in the interior of the surface (Porous Surface 3).1 1 See Fig. 2.3 for the emulsion droplet distribution, Figs. 2.6, 2.7, and 2.8 for SEM images of the porous surfaces, and Table 2.2 for the porosity of each surface. Although the emulsions have an average droplet size of 10.7 μm, there are droplets as large as 25–30 μm present in the flow. For Porous Surface 1, there are a few pores of ~20 μm, but most of the surface is densely packed with pores 10 μm. In distinction, Porous Surface 2 has many pores of ~30 μm on the top and through the thickness, resulting in a more open structure throughout.

a

Experimental Results: Dilute Emulsions

d

250 200

q″net [kW/m2]

93

H= 1% H= 2%

Water H= 0.1% H= 0.5%

5600 Water H= 0.1% H= 0.5%

4800 4000 h [W/m2K]

5.3

150 100

H= 1% H= 2%

3200 2400 1600

50 0 26

800

41

56

71

86

101

116

0 26

131

41

56

71

–30

–15

0

15 30 ΔT [°C]

45

60

–30

75

b

116

131

–15

0

15 30 ΔT [°C]

45

60

75

101

116

131

45

60

75

9000

500

H= 1% H= 2%

Water H= 0.1% H= 0.5%

6000

400 300 200

H= 1% H= 2%

4500 3000 1500

100 0 26

Water H= 0.1% H= 0.5%

7500

h [W/m2K]

600

q″net [kW/m2]

101

e 700

41

56

71

86

101

116

0 26

131

41

56

71

–30

–15

0

86

Tw [°C]

Tw [°C] 15 30 ΔT [°C]

45

60

–30

75

c

–15

0

15 30 ΔT [°C]

f 700

500

18000 H= 1% H= 2%

Water H= 0.1% H= 0.5%

12000

400 300 200

9000 6000 3000

100 0 26

H= 1% H= 2%

Water H= 0.1% H= 0.5%

15000

h [W/m2K]

600 q″net [kW/m2]

86

Tw [°C]

Tw [°C]

0 41

56

71

86

101

116

26

41

56

Tw [°C] –30

–15

0

15 ΔT [°C]

71

86

101

116

30

45

60

Tw [°C] 30

45

60

–30

–15

0

15 ΔT [°C]

Fig. 5.16 (a) to (c) Boiling curves and (d) to (f) heat transfer coefficient for emulsions on Porous Surface 2 with Dh = 200, 500, and 1000 μm. Ti = 30 °C, G = 350 kg/m2s

94

a

5

b

150 Water H= 0.1% H= 0.5%

70

H= 1% H= 2%

Water H= 0.1% H= 0.5%

60 50

90

DP [kPa]

DP [kPa]

120

60

Flow Boiling on a Porous Surface

H= 1% H= 2%

40 30 20

30 10 0

0 26

41

56

71 86 Tw [°C]

101

116

131

26

41

56

71 86 Tw [°C]

101

116

131

–30

–15

0

15 30 DT [°C]

45

60

75

–30

–15

0

15 30 DT [°C]

45

60

75

c

21 18

DP [kPa]

15

H= 1% H= 2%

Water H= 0.1% H= 0.5%

12 9 6 3 0 26

41

56

71

86

101

116

30

45

60

Tw [°C] –30

–15

0

15 DT [°C]

Fig. 5.17 Pressure drop for emulsions on Porous Surface 2, Ti = 30 °C, G = 350 kg/m2s. (a) to (c) are for Dh = 200, 500, and 1000 μm, respectively

For a subset of the data on this surface, improved heat transfer and a decrease in the pressure drop are measured for boiling emulsions (Fig. 5.17). This is demonstrated for Dh = 200 and 500 μm, where the pressure drop measured for ε = 0.1% is significantly lower than that for water. For Dh = 200 μm, the pressure drop for ε = 1 and 2% are comparable to that for water. For Dh = 500 μm, the measured pressure drop for water is much higher than that for the emulsions over the full range of ε. At Dh = 1000 μm, where the heat transfer benefit is the lowest, the pressure drop for all emulsions is larger than that for water. At all gap sizes, the pressure drop increases with increasing ε greater than 0.1%. On Porous Surface 3 and Dh = 200 μm, the boiling data and heat transfer coefficient for ε = 0.5 and 1% are similar to those for water (Fig. 5.18a, d). For ε = 0.1%, the heat transfer coefficient is diminished compared to that for water. The 2% emulsion case shows a much higher heat transfer coefficient than water over the full range of wall temperatures. Thus, the heat transfer coefficient increases with increasing ε up to 2% at this gap size.

5.3

a

Experimental Results: Dilute Emulsions

d

300 H= 1% H= 2%

Water H= 0.1% H= 0.5%

250 200

5000

150

H= 1% H= 2%

Water H= 0.1% H= 0.5%

4000 2 h [W/m K]

q"net [kW/m2]

95

3000 2000

100 1000

50

0

0 26

41

56

71

86

101

116

26

131

41

56

71

T [°C] w –30

b

0

15 30 DT [°C]

45

60

–30

75

e H= 1% H= 2%

Water H= 0.1% H= 0.5%

400 300

–15

0

15

30

45

60

75

8000

Water H= 0.1% H= 0.5%

H= 1% H= 2%

41

71

101

116

131

45

60

75

6000

2000

100

0 26

0 26

41

56

71

86

101

116

131

56

–30

–15

0

15 30 DT [°C]

45

60

–30

75

f

600

H= 1% H= 2%

0

15

30

14000

10000

400 300

8000 6000

200

4000

100

2000

0

H= 1% H= 2%

Water H= 0.1% H= 0.5%

12000

h [W/m2K]

500

–15

DT [°C]

700 Water H= 0.1% H= 0.5%

86

Tw [°C]

T [°C] w

q"net [kW/m2]

131

4000

200

c

116

12000 10000

h [W/m2K]

500

101

DT [°C]

700 600

q"net [kW/m2]

–15

86

Tw [°C]

0 26

41

56

71

86

101

116

26

41

56

T [°C] w –30

–15

0

15 DT [°C]

71

86

101

116

30

45

60

Tw [°C] 30

45

60

–30

–15

0

15 DT [°C]

Fig. 5.18 (a) to (c) Boiling curves and (d) to (f) heat transfer coefficient for emulsions on Porous Surface 3 with Dh = 200, 500, and 1000 μm. Ti = 30 °C, G = 350 kg/m2s

96

Flow Boiling on a Porous Surface

5

For Dh = 500 μm, the boiling curve and heat transfer coefficient are similar to water at low wall temperature for all volume fractions (Fig. 5.18b, e). For Tw > 80 ° C, the water shows a slight shift of the boiling data to higher wall temperature and a decrease in heat transfer coefficient. For this same range of wall temperature, the emulsions demonstrate a slightly increasing heat transfer coefficient with increasing wall temperature, but the primary benefit compared to water comes as a result of the diminished water heat transfer coefficient. For the 1000 μm gap, the boiling curves for water and all emulsions are similar (Fig. 5.18c). The heat transfer coefficient for water is slightly larger at lower Tw, but the heat transfer coefficient for the emulsions is slightly higher for Tw > 70 °C as a result of the increased coefficient for the emulsions as the disperse component boils (Fig. 5.18f). The pressure drop on Porous Surface 3 is shown in Fig. 5.19. For Dh = 200 and 1000 μm, the pressure drop is larger for the emulsions than for water at all ε. The pressure drop for ε = 2% in the 200 μm gap displays interesting behavior. Rather

a

b

420 360 300

30 Water H= 0.1% H= 0.5%

25 20 ΔP [kPa]

ΔP [kPa]

H= 1% H= 2%

Water H= 0.1% H= 0.5%

240 180

H= 1% H= 2%

15 10

120

5

60

0

0 26

41

56

71 86 Tw [°C]

101

116

131

26

41

56

71 86 Tw [°C]

101

116

131

-30

-15

0

15 30 ΔT [°C]

45

60

75

-30

-15

0

15 30 ΔT [°C]

45

60

75

c

12

8 ΔP [kPa]

H= 1% H= 2%

Water H= 0.1% H= 0.5%

10

6 4 2 0 26

41

56

71

86

101

116

30

45

60

T [°C] w

-30

-15

0

15 ΔT [°C]

Fig. 5.19 Pressure drop for emulsions on Porous Surface 3, Ti = 30 °C, G = 350 kg/m2s. (a) to (c) are for Dh = 200, 500, and 1000 μm, respectively

5.3

Experimental Results: Dilute Emulsions

97

than increasing steadily with increasing Tw, the pressure drop dramatically increases suddenly at Tw = 71 °C. Comparison with Fig. 5.18 shows that this coincides with a significant increase in heat transfer. The pressure drop for ε = 2% is also much greater than that for ε = 0.1, 0.5, or 1% at this gap size. For Dh = 500 μm, the pressure drop for ε = 0.1% is lower than for water, and ε = 0.5, 1, and 2% display equivalent or larger pressure drops than water. The pressure drop increases with increasing ε for every gap height. Comparisons of the heat transfer coefficients on the smooth and microporous surfaces are shown as a function of mass flux and gap size in Figs. 5.20 and 5.21. For the 500 μm gap size across the range of mass flux studied, Porous Surface 1 consistently has the highest heat transfer coefficients for boiling of water and the lowest heat transfer coefficients for boiling emulsions (Fig. 5.20). For G = 150 kg/m2s, the boiling curve for Surface 2 shifts to slightly lower wall temperature than that for Surface 3, but Surface 2 transitions to CHF at a slightly lower heat flux. At this mass flux, all three surfaces have a diminished heat transfer coefficient compared to that on the smooth surface. At G = 350 kg/m2s, Surfaces 2 and 3 show very similar heat transfer behavior. Up to Tw = 86 °C, all four surfaces have nearly equivalent boiling curves and heat transfer coefficients for the 1% emulsion. For Tw > 86 °C, Porous Surface 1 demonstrates a shift of the boiling curve to higher wall temperature, and the boiling curve for the smooth surface shifts to the left. For G = 550 kg/m2s and Tw < ~95 °C, the porous surfaces all show a higher heat transfer coefficient than the smooth surface. For Tw > ~95 °C, Porous Surface 1 and 3 shift to higher wall temperature with a greater shift occurring for Porous Surface 1; Porous Surface 2 and the smooth surface have approximately the same heat transfer coefficient and boiling curve. For Dh = 200 μm and G = 350 kg/m2s, the three porous surfaces all show diminished heat transfer with respect to the smooth surface for boiling of emulsions (Figs. 5.21a, d). Porous Surface 1 transitions to CHF at a very low heat flux and Surface 3 demonstrates a shift in the boiling curve to significantly higher wall temperatures. Porous Surface 2 and 3 transition to CHF at approximately the same heat flux. For Dh = 1000 μm, all three porous surfaces show increased heat transfer compared to the smooth surface. For Porous Surface 1, the boiling curve shifts to a much lower wall temperature. More moderate decreases in wall temperature are seen for Porous Surfaces 2 and 3, with a slightly larger decrease in Tw measured for Porous Surface 2. Thus, it appears that the porous surfaces have better heat transfer performance compared to that of the smooth surface with increasing gap size. At Dh = 1000 μm, the emulsions also provide better heat transfer coefficients than for water on every surface. The pressure drop for each surface is presented as a function of mass flux in Fig. 5.22 and gap size in Fig. 5.23. Similar to what is noted for boiling water on the porous surfaces, Porous Surface 2 consistently has the highest pressure drop in the emulsion boiling data set. At Dh = 500 μm, Porous Surfaces 1 and 3 display similar

98

a

5 Flow Boiling on a Porous Surface

d

600 Water

10000

Smooth Surface 1 Surface 2 Surface 3

400

h [W/m2K]

q"net [kW/m2]

500

12000

H=1%

300 200

Water

H=1%

56

71

Smooth Surface 1 Surface 2 Surface 3

8000 6000 4000

100

2000

0

0 26

41

56

71

86

101

116

131

41

26

T [°C] –30

–15

0

15 30 DT [°C]

45

60

75

b

–30

131

–15

0

15 30 DT [°C]

45

60

75

101

116

131

45

60

75

Smooth Surface 1 Surface 2 Surface 3

10000 h [W/m2K]

400

Water H=1%

12000

Smooth Surface 1 Surface 2 Surface 3

500 2 q"net [kW/m ]

116

14000 Water H=1%

600

300

8000 6000

200

4000

100

2000 0

0 26

41

56

71

86

101

116

26

131

41

56

71

–30

–15

0

15 30 DT [°C]

45

60

–30

75

f

700 Water H=1%

500

0

15 30 DT [°C]

18000 15000 12000

Smooth Surface 1 Surface 2 Surface 3

2

400 300 200

9000 6000 3000

100 0 26

–15

Water H=1%

Smooth Surface 1 Surface 2 Surface 3

h [W/m K]

600

41

56

71

86

101

116

131

146

0 26

41

56

71

T [°C] w –30

86

T [°C] w

Tw [°C]

q"net [kW/m2]

101

e 700

c

86

T [°C] w

w

–15

0

15

30 45 DT [°C]

86

101 116 131 146

T [°C] w 60

75

90

–30 –15

0

15

30 45 DT [°C]

60

75

90

Fig. 5.20 (a) to (c) Boiling curves and (d) to (f) heat transfer coefficient for water and 1% emulsions on smooth and microporous surfaces with G = 150, 350, and 550 kg/m2s, respectively. Ti = 30 °C, Dh = 500 μm

5.3 Experimental Results: Dilute Emulsions

d

400 350

250

Smooth Surface 1 Surface 2 Surface 3

8000 2

2

Water H=1% 10000

Smooth Surface 1 Surface 2 Surface 3

300 q"net [kW/m ]

12000

Water H=1%

h [W/m K]

a

99

200 150

6000 4000

100 2000

50 0

0 26

41

56

71

86

101

116

131

41

26

56

71

T [°C] –30

–15

0

15 30 DT [°C]

45

60

75

–30

116

131

–15

0

45

60

75

101

116

131

45

60

75

15 30 DT [°C]

e 700

14000 Water

600

H=1%

Smooth Surface 1 Surface 2 Surface 3

10000 h [W/m2K]

2

400

Water H=1%

12000

Smooth Surface 1 Surface 2 Surface 3

500 q"net [kW/m ]

101

w

b

300

8000 6000

200

4000

100

2000 0

0 26

41

56

71

86

101

116

26

131

41

56

71

–30

–15

0

86

T [°C] w

Tw [°C] 15 30 DT [°C]

45

60

–30

75

c

–15

0

15 30 DT [°C]

f 700

18000 Water H=1%

600

Water

15000

Smooth Surface 1 Surface 2 Surface 3

2

400 300 200

H=1%

Smooth Surface 1 Surface 2 Surface 3

12000 h [W/m2K]

500 q"net [kW/m ]

86

T [°C]

w

9000 6000 3000

100

0

0 26

41

56

71

86

101

116

26

41

56

T [°C] –30

–15

0

15 DT [°C]

71

86

101

116

30

45

60

T [°C]

w

w

30

45

60

–30

–15

0

15 DT [°C]

Fig. 5.21 (a) to (c) Boiling curves, and (d) to (f) heat transfer coefficient for water and 1% emulsions on smooth and microporous surfaces with Dh = 200, 500, and 1000 μm, respectively. Ti = 30 °C, G = 350 kg/m2s

100

a

5

b

30 Water H=1%

25

Water H=1% Smooth Surface 1 Surface 2 Surface 3

50 ΔP [kPa]

ΔP [kPa]

20

70 60

Smooth Surface 1 Surface 2 Surface 3

15 10

Flow Boiling on a Porous Surface

40 30 20

5

10

0

0 26

41

56

71

86

101

116

131

26

41

56

71

T [°C] w –30

–15

0

15

30

45

60

75

–30

–15

0

15

ΔT [°C]

c

86

101

116

131

45

60

75

T [°C] w 30

ΔT [°C]

120 Water H=1%

100

ΔP [kPa]

80

Smooth Surface 1 Surface 2 Surface 3

60 40 20 0 26

41

56

71

86

101

116

131

146

30 45 ΔT [°C]

60

75

90

T [°C] w

–30

–15

0

15

Fig. 5.22 Pressure drop for water and 1% emulsions on the smooth and microporous surfaces, Dh = 500 μm, Ti = 30 °C. (a) to (c) are for G = 150, 350, and 550 kg/m2s, respectively

pressure drop behavior over the range of mass flux tested (Fig. 5.22). For Dh = 200 μm, Porous Surface 3 has the highest pressure drop with a step increase displayed at Tw ~ 71 °C (Fig. 5.23a). This step increase is not coincident with an increase in heat transfer as occurred with the 2% emulsion on this surface. For Dh = 500 μm, Porous Surfaces 1 and 3 display a similar measured pressure drop (Fig. 5.23b) and that for Surface 1 is slightly higher in the 1000 μm gap (Fig. 5.23c).

a

Experimental Results: Dilute Emulsions

b

240 Water H=1%

210 180 ΔP [kPa]

101

150

Water H=1% Smooth Surface 1 Surface 2 Surface 3

50

120 90

40 30 20

60

10

30 0 26

70 60

Smooth Surface 1 Surface 2 Surface 3

ΔP [kPa]

5.3

41

56

71

86

101

116

0 26

131

41

56

71

–30

–15

0

15

101

116

131

45

60

75

w

30

45

60

–30

75

–15

0

ΔT [°C]

c

86

T [°C]

Tw [°C]

15 30 ΔT [°C]

20 Water H=1% Smooth Surface 1 Surface 2 Surface 3

ΔP [kPa]

16 12 8 4 0 26

41

56

71

86

101

116

30

45

60

Tw [°C] –30

–15

0

15 ΔT [°C]

Fig. 5.23 Pressure drop for water and 1% emulsions on the smooth and microporous surfaces, G = 350 kg/m2s, Ti = 30 °C. (a) to (c) are for Dh = 200, 500, and 1000 μm, respectively

Chapter 6

Physical Mechanisms and Correlation

For single-component, single-phase flow, the differential equations governing the fluid motion can be derived from mass and momentum balances on a differential fluid element. For Newtonian fluids, this approach leads to the Navier-Stokes equations. For most single-phase flows, fluid motion and energy can be decoupled such that the equations of motion can be solved for the fluid velocity, as well as density or pressure, and then these results can be inserted into the energy equation to determine energy or temperature. For multiphase flows, a similar approach can be applied to determine the equations of motion and energy. However, care must be taken to account for the interaction between phases and changes in mass, momentum, and energy for a given phase that arise due to the phase-change process, which leads to additional terms in the differential equations. Taking these additional terms into account, the mass, momentum, and energy equations for the kth phase are [120]
*  ∂ðαk ρk Þ þ ∇ ∙ α k ρk U k = Γ k |{z} ∂t
*  ∂ α k ρk U k ∂t

ð6:1Þ

1


* * * *  * þ ∇ ∙ αk ρk Uk Uk = Γk Ukj þ ∇ ∙ ðαk Tk Þ þ αk ρk b k þ Mk |fflffl{zfflffl} |fflfflfflfflfflffl{zfflfflfflfflfflffl} |fflfflffl{zfflfflffl} |{z} 2

3

4

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 B. M. Shadakofsky, F. A. Kulacki, Flow Boiling of a Dilute Emulsion In Smooth and Rough Microgaps, Mechanical Engineering Series, https://doi.org/10.1007/978-3-031-27773-3_6

ð6:2Þ

5

103

104

6

 αk ρk

∂ek * þ Uk  ∇ek ∂t



Physical Mechanisms and Correlation


 * * = αk Tk : ∇Uk - ∇  αk q k þ αk ρk Bk þ |fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl} |fflfflffl{zfflfflffl} 6




8

7

*  Ek þ Γk ekj - ek - Uk  Uk þ Ukj  Uk |{z} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl 2 ffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} 9

1*

*

*

ð6:3Þ

10

Similar to the single-component transport equations, the left sides of Eqs. (6.1)– (6.3) contain terms for the time rate of change and advection of mass, momentum, and internal energy, respectively. These equations govern transport for the kth phase and are scaled by the volume fraction αk. Although the time rate of change and advection terms are well known and standard, the source terms require elaboration. In Term 1, Γk represents the rate of production of phase k due to phase change. As Term 2 also involves this symbol, it is the rate of production of momentum for phase * k due to mass production from the jth phase. In this term, Ukj is the relative velocity between phases j and k. Term 3 is the sink of momentum due to traction, where Tk is the traction tensor. For most multiphase flows of engineering interest, the constituent fluids are Newtonian such that the components of the traction tensor are [121]
 * 2 Tij = - Pδij þ 2μSij þ μv - μ ∇ ∙ Uδij 3   1 ∂ui ∂uj þ Sij = 2 ∂xj ∂xi

ð6:4Þ ð6:5Þ

where δij is the Kronecker delta. The traction tensor includes the effect of pressure and viscosity. Term 4 represents the body force present on phase k. For most applications, the only body force is that due to gravity. (Additional body forces, e.g., electromagnetic forces, may be taken into account under special situations.) Term 5 accounts for the force on phase k due to interactions with other phases. In the energy equation, Term 6 represents the friction work done on phase k due to viscous effects. This term is frequently neglected in single-phase studies. Term 7 is the heat transfer done on phase k. It is common practice to rewrite the internal energy in terms of temperature so that Eq. (6.3) becomes a differential equation for * temperature of the kth phase. If this is done, the constitutive equation for q k in Term 7 is Fourier’s law of conduction. Terms 8 and 9 represent the work done on phase k due to body forces and interactions with other phases, respectively. Finally, as Term 10 involves Γk, this term accounts for the energy transferred to phase k via phase change. This term involves both internal energy and kinetic energy. These equations can be solved numerically using direct numerical simulation (DNS), large-eddy simulation (LES), or Reynolds-averaged Navier-Stokes (RANS) techniques. Any of these techniques can be a valuable tool for studying the boiling process. However, constitutive equations for the traction tensor, pressure and heat

6

Physical Mechanisms and Correlation

105

transfer, and models to describe the phase change process and interactions between phases must first be developed before any CFD technique can be applied. Ultimately, these models require an understanding of the physical mechanisms governing the boiling process. Such understanding can come from carefully studying the experimental results for trends and drawing conclusions based on these trends. Therefore, an explanation of some physical mechanisms that may be at play in the experimental results described in the previous chapters is given below. Based on these mechanisms, dimensionless numbers are also suggested for correlation of the data. To begin a discussion of possible mechanisms, consider the various factors that have been shown to affect boiling heat transfer in emulsions. Previous pool boiling experiments have demonstrated that the boiling process is affected by the fluids used in the emulsion, the mean droplet size or size distribution, and the emulsion volume fraction (see Sect. 4.1). The use of additives to stabilize the emulsion also has an impact on experimental results, but the effect of various additives is not yet clear, so this factor will not be included. Visualization experiments further indicate that boiling of the disperse component occurs at the heated surface and not in suspension, and these experiments suggest that droplets of the disperse component agglomerate on the surface to create a film. This is consistent with the results from this study, and it is assumed here that flow boiling of the disperse component also takes place at the wall. Our experimental results show that depending on the specific combination of volume fraction, mass flux, gap height, and heat flux, heat transfer is either impaired or improved compared to single-component heat transfer. Generally, heat transfer decreases for increasing mass flux, decreasing gap height, and increasing volume fraction. After the emulsion starts boiling, the heat transfer coefficient increases, though it can be lower than that for a single component flow at the same experimental conditions over a broad range of wall heat flux. These results suggest that at least two heat transfer mechanisms are taking place, one that decreases and one that increases heat transfer. Consider an emulsion of volume fraction ε flowing at a mass flux G in a gap of height H. To be consistent with the experimental results, the flow is fully developed and above a surface being heated from below with a constant heat flux, q″, which causes a thermal boundary layer to develop. Finally, consideration here is restricted to a smooth surface. When the disperse component has a greater density than the continuous component, droplets in the middle of the gap tend to settle toward the heated wall. As a droplet settles from a region of higher velocity to lower velocity, it experiences drag due to its velocity being higher than the local velocity. This drag force will decrease the inertia of the droplet, and the droplet will fall further toward the heated wall. As the droplet migrates toward the wall, it is possible that heating from the wall will cause rotation within the droplet resulting in a Magnus lift force upon the droplet [122]. Thus, whether an individual droplet comes into contact with the heated surface is determined by a balance of these forces. Note that these forces would also be present if the flow is not fully developed and a hydraulic boundary layer is growing. However, the magnitude of these forces may change, e.g., a larger drag

106

6

Fig. 6.1 Droplet deposition and release geometry

Physical Mechanisms and Correlation

Continuous component Disperse component, liquid

Disperse component, vapor

t Ao

Ae

Ao

force may be felt due to a greater difference between the droplet velocity and the local flow velocity as it enters the boundary layer. As droplets contact the surface, they can agglomerate and form a film over portions of it. In the film, the primary heat transfer mechanism is conduction. If the disperse component has a lower thermal conductivity than the continuous component as in the present investigation, the presence of this film will decrease heat transfer to the portion of the surface below the film. If the surface temperature is high enough to cause nucleation within the film, some of the disperse component will boil on the surface, and vapor bubbles will rise into the bulk of the flow. This will cause increased mixing in the flow, thereby increasing heat transfer. Thus, the overall impact on heat transfer is governed by the number of droplets deposited on the surface, nd; the surface area covered by the film, Ao; the number of droplets that boil on the surface, nb (or the amount of liquid volume released that would make up nb droplets); and the surface area, Ae, that is exposed to the bulk flow and can be cooled via mixing. This geometry is shown in Fig. 6.1. The droplets, bubbles, and film thickness are not to scale compared to the gap height in this figure. Because there are two coexisting heat transfer mechanisms, the overall heat transfer coefficient can be determined by superposition [123]. The two mechanisms affect different portions of the wall so the heat transfer coefficient for each must also be partitioned by the surface area for which it applies hA = hfilm Ao þ hmix Ae

ð6:6Þ

where Ao is the area covered by the droplet film and Ae the area exposed to the emulsion. The heat transfer coefficient in the droplet film is determined by the thermal conductivity and the film thickness: hfilm =

kd t

ð6:7Þ

Droplet liquid conductivity, kd, is an order of magnitude lower than kc (see Appendix A), and consequently conduction through the droplet film limits total heat transfer. The heat transfer coefficient, hmix, accounts for heat transfer in the

6

Physical Mechanisms and Correlation

107

continuous component due to the bulk fluid flow and a component associated with additional mixing caused by vapor release at the heated surface. Areas Ao and Ae can be written in terms of the droplet diameter, d, nd, nb, and t Ao =

πnd d3 6t

Ae = Ai þ

ð6:8Þ

πnb d3 6t

ð6:9Þ

where Ae is the exposed area both initially not covered by the film and as a result of boiling and bubble release. It is expected that nd and nb are proportional to ε and dependent on various system and flow parameters, Dh, G, and μc. The film thickness, t, is proportional to d and possibly ε if the film is more than one droplet thick. Closure of a model of this form requires determination of the heat transfer coefficient hmix, as well as the effect that heat transfer and various flow parameters have on nd and nb. It is not the intent here to close this model but to gain an understanding of mechanisms to determine appropriate parameters for correlation of the emulsion data. It is shown below that the correlation developed based on these mechanisms fits the experimental data very well. These mechanisms suggest several system properties that can be used to correlate the emulsion boiling data: kd, d, Dh, μc, ρd/ρc, G, hfg, Cp,c, ε, q″, h. Though strict similitude may not hold in this system, these parameters suggest that seven dimensionless groups are necessary to correlate the data hDh kd ρd ρc

GDh μc GC p d kd

q00 Ghfgd d Dh

1 1þε

ð6:10Þ

The first three terms are similar to the Nusselt, Reynolds, and boiling numbers that are often used to correlate single- and two-phase convection data. However, the first and third terms use the thermal conductivity and latent heat of the disperse component, and the second term uses the viscosity of the continuous component. These terms do not use mixture properties because the properties of these specific components are deemed to be more important than each respective property for the other component. The form of the fourth term is chosen to account for ε appearing to have a large effect on the heat transfer results at low values and the effect diminishing asymptotically as ε increases. The fifth and sixth terms may be the most significant parameters in this group. The density ratio governs how many droplets contact the heated surface, and it can be expected that the heat transfer mechanisms may differ if the disperse component has a lower density than the continuous component. It is possible that in that case, boiling will be caused by superheated droplets coming into the thermal boundary layer, with nucleation occurring via a combination of interaction between

108

6 10000 8000 hmeasured [W/m2K]

Fig. 6.2 Comparison between the measured emulsion heat transfer coefficient and Eq. (6.11)

Physical Mechanisms and Correlation

6000 4000 2000 0 0

2000

4000

6000

hpredicted

[W/m2K]

8000

10000

neighboring droplets and bubbles. If boiling occurs at the wall in this case, droplet deposition may primarily be due to turbulence caused either by the boiling process or in the bulk flow if the flow is turbulent. The sixth term accounts for the sensible heat transfer to the continuous component advected from the surface compared to the conduction heat transfer through the film of droplets. When the smooth surface data is correlated based on these parameters, the following correlation results: h  - 1:48  00 0:84  
   - 2:37  GC p d 2:24 1 3:42 d GDh q kd = 0:0067 kd Dh Dh 1 þ ε μc Ghfg d ð6:11Þ Note that the correlation does not include the density ratio because only one combination of fluids was used in this study. This correlation fits the data very well, with 95.7% of the experimental data falling within ±10% of the predicted value (Fig. 6.2). It can be argued that the data fits the correlation so well because many parameters have been used, and one should expect to get a better fit with an increasing number of parameters. Various reasons account for the necessity of including all of these parameters, however. All of the properties used in the parameters are significant owing to the consideration of the physical mechanisms above. The p-value (the statistical parameter used to determine whether a given variable is significant in correlating data) for every parameter demonstrates that each has a strong correlation with the experimental data. Finally, it may be expected that the last two parameters in Eq. (6.10) would show the least correlation with the experimental data. Though these may be two of the most important parameters to include, each has only three values that appear in the data set, with additional minor variation due to the effect of

Physical Mechanisms and Correlation

Fig. 6.3 Comparison between the measured ratio of the emulsion and water heat transfer coefficients and Eq. (6.12)

109

0.75 0.5 [(h–h0)/h0]measured

6

0.25 0 –0.25 –0.5 –0.5

–0.25

0

0.25

0.5

0.75

[(h–h0)/h0]predicted

temperature on thermophysical properties. Their effect on the correlation was examined by neglecting them and correlating the data a second time. The resulting correlation fits the data considerably worse than Eq. (6.11). This correlation and additional correlations are given in Appendix C. The data can also be analyzed with respect to the heat transfer coefficient for water at the same wall temperature and experimental conditions to determine when the emulsions result in higher heat transfer. This data is correlated, resulting in  - 1:46  00 0:76  
   - 1:46  GCp d 1:73 h - h0 GDh q 1 4:15 d = 0:045 - 1 ð6:12Þ kd h0 μc Ghfg d Dh 1þε

The data shows more scatter with respect to Eq. (6.12), with 36.4% of the experimental data falling within ±15% of the predicted value and 58.7% within ±30% (Fig. 6.3). However, the correlation captures the trend of the experimental data. Although these correlations do a relatively good job of matching the data, it should be cautioned that they should not be used for design. As they represent only one combination of droplet diameter, disperse component, and continuous component, they are used to demonstrate the validity of these specific dimensionless parameters in correlating the emulsion boiling data. In Eqs. (6.11) and (6.12), the absolute volume fraction—rather than percentage—is used for ε. Disperse component properties are determined at the saturation temperature, and continuous component properties are determined at the film temperature.

Chapter 7

Conclusion

7.1

Flow Boiling on Smooth Surfaces

In flow boiling of water on the smooth surfaces, the heat transfer coefficient increases with increasing mass flux and decreasing gap size. After the onset of nucleate boiling (ONB) and prior to transition to the critical heat flux (CHF), the heat transfer coefficients collapse to one curve. CHF increases with increasing gap size and increasing mass flux. The effects of the liquid subcooling, wall heat flux, mass flux, and gap size on the two-phase heat transfer coefficient are correlated well using the Nusselt, Jakob, Reynolds, and boiling numbers, with 98% of the experimental data falling within ±30% of the Nusselt number predicted by Eq. (3.1). For boiling of emulsions on the smooth surface, increasing the volume fraction up to 0.1 or 0.5% enhances cooling in some cases, but increasing it further to 1 or 2% provides no additional benefit and decreases heat transfer in some experiments. The emulsion improves heat transfer compared to water for larger gap sizes and lower mass fluxes. With decreasing gap size and increasing mass flux, the presence of the emulsion progressively decreases heat transfer compared to water. In almost all experiments, the heat transfer coefficient for the emulsion increases with increasing wall temperature. Based on these observations, it is posited that two mechanisms for heat transfer exist when boiling emulsions, one that impairs and one that enhances heat transfer. The thermal conductivity of FC-72 is an order of magnitude lower than that of water, so if a film of the FC-72 disperse component covers a significant portion of the wall, heat transfer will be limited by conduction in this film. As the wall temperature increases, FC-72 on the wall will boil and release from the wall, thereby increasing the portion of the wall exposed to the bulk flow and increasing heat transfer to the exposed portion of the wall via enhanced mixing. Based on these mechanisms and the experimental observations, various flow and system parameters are identified as important to the heat transfer behavior. From © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 B. M. Shadakofsky, F. A. Kulacki, Flow Boiling of a Dilute Emulsion In Smooth and Rough Microgaps, Mechanical Engineering Series, https://doi.org/10.1007/978-3-031-27773-3_7

111

112

7 Conclusion

them seven nondimensional groups have been identified and used to correlate the emulsion heat transfer coefficient via multiple linear regression. Three of these terms are similar to the Nusselt, Reynolds, and boiling numbers and utilize properties of the disperse and continuous components, depending on which component is deemed to be more important for that parameter. The volume fraction in the form 1/(1 + ε), the ratio of disperse and continuous component densities, and the ratio of the droplet diameter to hydraulic diameter are also used. The final parameter used in the correlation is a new nondimensional number to account for the ratio of sensible heat advected from the wall and conduction in the film of the disperse component, GCpd/kd. Using these parameters, except for ρd/ρc, correlations are developed for the heat transfer coefficient and the augmentation ratio (h - h0)/h0, where h0 is the water heat transfer coefficient at the same experimental condition. A very good fit is obtained for the heat transfer coefficient, with 95.7% of the experimental data falling within ±10% of the correlation (Eq. (6.11)). For the heat transfer coefficient ratio, 58.7% of the experimental data falls within ±30% of the predicted value, though the correlation captures the trend of the data well. In Sect. 4.2 comparison is made between the results of this study and those of Janssen and Kulacki [78] and Morshed et al. [79] where there is crossover with the present data (Fig. 7.1a). The only data points that intersect here are those for water and ε = 1% in the 500 μm gap at G = 150 kg/m2s. It is noted that the data of [78] show increasing heat transfer for increasing ε up to 2% at G = 133 kg/m2s. This trend is not seen for that range of ε at G = 350 kg/m2s in this investigation. However, decreasing mass flux increases emulsion heat transfer, so it is possible that this trend would be captured by the correlation developed. A comparison between the heat transfer coefficients measured in [78] and that predicted by Eq. (6.11) is shown in Fig. 7.1b. Equation (6.11) predicts the data of Janssen and Kulacki [78] well, with the majority of the data falling within ±30% of the predicted value. For moderate heat fluxes, the measured and predicted coefficients compare very favorably. For ε = 1 and 2%, as the heat flux increases, Eq. (6.11) predicts consistently lower heat transfer coefficients than measured by Janssen and Kulacki.

7.2

Flow Boiling on Porous Surfaces

For flow boiling of water on porous surfaces, many of the trends seen for boiling on the smooth surface are also present. On the porous surfaces however, the singlephase heat transfer coefficient decreases with decreasing gap size, and the boiling curves do not collapse to one curve following ONB. The porous surfaces show enhanced heat transfer relative to that of the smooth surface with increasing mass flux and gap size. For Dh = 200 μm, the heat transfer coefficient is significantly reduced for each porous surface. The best heat transfer coefficient for the porous surfaces is consistently displayed on Porous Surface 1.

7.2

Flow Boiling on Porous Surfaces

113

a 800 Janssen, Kulacki [107], ε=0.1% Janssen, Kulacki [107], ε=1% Janssen, Kulacki [107], ε=2% Morshed et al. [108], water Morshed et al. [108], ε=0.5% Morshed et al. [108], ε=1% This study, water This study, ε=1%

700

q"net [kW/m2]

600 500 400 300 200 100 0 25

55

40

70

85

100

115

130

145

160

Tw [°C]

b 10000 hmeasured [W/m2K]

+30% 8000 6000 −30% 4000 2000 0 0

2000

4000

6000

8000

10000

hpredicted [W/m2K]

Fig. 7.1 (a) Comparison of Dh = 500 μm, G = 150 kg/m2s emulsion boiling data to data in a 500 μm gap [78] and in a 672 μm gap [79]. (b) Heat transfer coefficient measured in [78] compared to that predicted by Eq. (6.11). The solid line represents equivalence between measured and predicted values

The pressure drop for the porous surfaces is generally greater than that for water on the smooth surface. The largest pressure drops are measured for Porous Surface 2. This is attributed to the increased roughness of the wall due to the large pores seen from the top view of the surface and increased momentum lost at the pore scale due to flow through the relatively open porous structure.

114

7

Conclusion

Boiling of emulsions on the porous surfaces shows a mixture of enhanced and degraded heat transfer. For Surface 1 with Dh = 200 and 500 μm, the heat transfer is lower for the emulsions than water. At Dh = 1000 μm, the boiling curves shift to lower Tw, but h is lower than that for water. For Porous Surface 2 the emulsions enhance heat transfer for the majority of the data set, and this is especially pronounced for smaller gaps. The emulsions also decrease the measured pressure drop on Porous Surface 2 for the cases where heat transfer is increased. Porous Surface 3 shows similar behavior for the emulsions and water for most of the data set. The increase in heat transfer on Porous Surface 2 is likely a result of the open pore network on both the top and interior of the porous surface. This open pore network would allow FC-72 droplets to flow down into the porous structure and nucleate bubbles within the confined space there. After nucleation, the resulting vapor would also flow out of this porous structure more easily than in a structure that is more densely packed, either at the top of the surface, e.g., Porous Surface 1, or in the interior of the surface, e.g., Porous Surface 3. The trends discussed for each surface are shown graphically for the mean heat transfer coefficient ratio (h - h0)/h0 in Figs. 7.2, 7.3, 7.4, and 7.5. These graphs demonstrate the regions where the emulsions provide enhanced or impaired heat transfer relative to water on each surface. It is important to note that the bars on the graphs do not correspond to uncertainty in the measured ratio. The lower bar and upper bar, respectively, represent the minimum and maximum measured ratios. For example, the bars shown for ε = 0.5% in Fig. 7.2c correspond to the maximum and minimum heat transfer coefficient ratio for the water and emulsion experiments compared in Fig. 4.16.

7.3

Summation

A map of all of the existing emulsion experiments is given in Fig. 7.6. The corresponding publications shown in the map are listed in Table 7.1. On this map, Dh → 1 corresponds to pool boiling. Almost all of the data points on the map correspond to individual experiments, with the exception of those of Morshed et al. [79], that represent 1–3 mass fluxes for one value of ε in their microchannels and microgap, and some data of Bulanov and Gasanov et al. obtained for pool boiling with multiple fluids at the same value of ε [65, 66, 68, 74, 81]. This investigation expands the existing database greatly by investigating the variation of volume fraction, mass flux, hydraulic diameter, and surface condition. From the trends in the experimental data and the existing experiments shown in Fig. 7.6, further investigation is warranted for lower volume fractions (ε < 0.5%) and larger gap sizes (Dh ~ 1 mm). Other areas of investigation that can be considered to increase understanding of boiling of emulsions and move closer toward their use

7.3 Summation

115 ε [%]

a 0.00

0.1

1

0.5

2

–0.05

(h–h0)/h0

–0.10

G=150

–0.15

G=350

–0.20

G=550

–0.25 –0.30 –0.35 –0.40

b 0.40 0.30 0.20 (h–h0)/h0

0.10 0.00

G=150

–0.10

G=350

–0.20

G=550

–0.30 –0.40 –0.50 0.1

0.5

ε [%]

1

2

c 0.60 0.50

(h–h0)/h0

0.40 0.30 G=150 0.20

G=350

0.10

G=550

0.00 –0.10 0.1

0.5

ε [%]

1

2

Fig. 7.2 Ratio of the emulsion heat transfer coefficient to that for water at the same wall temperature on the smooth surface. (a) to (c) are for Dh = 200, 500, and 1000 μm

116

7 Conclusion ε [%]

a 0.1

1

0.5

2

0 –0.05

(h–h0)/h0

–0.1 –0.15

G=150

–0.2

G=350

–0.25

G=550

–0.3 –0.35 –0.4 –0.45 –0.5

(a) ε [%]

b 0.1

1

0.5

2

0

(h–h0)/h0

–0.1 –0.2

G=150

–0.3

G=350 G=550

–0.4 –0.5 –0.6 –0.7

ε [%]

c 0.1

(h–h0)/h0

0 –0.05 –0.1 –0.15 –0.2 –0.25 –0.3 –0.35 –0.4 –0.45 –0.5

0.5

1

2

G=150 G=350 G=550

Fig. 7.3 Ratio of the emulsion heat transfer coefficient to that for water at the same wall temperature on Porous Surface 1. (a) to (c) are for Dh = 200, 500, and 1000 μm

7.3 Summation

a

117

0.7 0.6

(h–h0)/h0

0.5 0.4 0.3

G=150

0.2

G=350

0.1

G=550

0 –0.1 –0.2 0.1

1

0.5

2

ε [%]

b

0.6 0.5

(h–h0)/h0

0.4 0.3 G=150

0.2

G=350

0.1

G=550

0 –0.1 –0.2 0.1

1

0.5

2

ε [%]

(h–h0)/h0

c

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 –0.2

G=150 G=350 G=550

0.1

1

0.5

2

ε [%]

Fig. 7.4 Ratio of the emulsion heat transfer coefficient to that for water at the same wall temperature on Porous Surface 2. (a) to (c) are for Dh = 200, 500, and 1000 μm

118

7 Conclusion

a

0.7 0.6

(h–h0)/h0

0.5 0.4 0.3 0.2 0.1

G=150 G=350

0 –0.1 –0.2 –0.3

0.1

1

0.5

2

ε [%]

b

0.3 0.25

(h–h0)/h0

0.2 0.15 0.1 0.05

G=150

0 –0.05

G=350 G=550

–0.1 –0.15 –0.2 0.1

1

0.5

2

ε [%]

c

0.2 0.15

(h–h0)/h0

0.1 0.05 G=150 0

G=350 G=550

–0.05 –0.1 –0.15 0.1

1

0.5

2

ε [%]

Fig. 7.5 Ratio of the emulsion heat transfer coefficient to that for water at the same wall temperature on Porous Surface 3. (a) to (c) are for Dh = 200, 500, and 1000 μm

7.3

Summation

119

Mori et al. Roesle and Kulacki Morshed et al. G=66,130,264 kg/m2s

Ostrovskiy Bulanov, Skripov, Khmylnik G=27 kg/m2s Janssen, Kulacki G=133 kg/m2s

Bulanov, Gasanov et al. Gasanov, Bulanov G=12 kg/m2s Shadakofsky, Kulacki G=150,350,550 kg/m2s

Dh [mm]

∞

10

1

0.1

0.01 0.001

0.01

0.1

1

10

100

ε [%]

Fig. 7.6 Map of existing emulsion boiling experiments. The corresponding publications are listed in Table 7.1. Dh → 1 represents pool boiling results

in design are droplet-wall interactions for individual and multiple droplets via visualization and CFD, use of CFD for studying flow boiling of dilute emulsions, boiling of emulsions on structured walls where the wall structure is tailored to the droplet size, use of dilute emulsions in impingement heat transfer, and the effect of emulsion properties on CHF.

Fluids studied Various; sodium oleate, span 80, and tween 80 surfactants

Ether/glycerin

Water/PMS300

Water/R113, water/benzene, water/butyl alcohol

Water/PES-4, diethyl ether/ water

Paper Mori, Inui, and Komotori [58]

Bulanov, Skripov, and Shuravenko [124]

Bulanov, Skripov, and Khmyl’nin [65]

Ostrovskiy [59]

Bulanov, Skripov, and Khmylnik [76]

Table 7.1 Comparison of emulsion investigations

0–33% by weight

20–80%

0.8–3.2%

10%

Volume fractions studied 5–50%

Vertical 0.2 mm DIA platinum wire

Vertical 0.2 mm DIA platinum wire

Vertical 6 mm DIA stainless steel tube

8.4 mm inner DIA tube

40–99 °C

–

60 °C

Heater geometry Horizontal 0.2 mm DIA nickel wire

20 °C

Emulsion bulk/inlet temperature 100 °C

Notable results KF 96-in-water stabilized with tween 80 boils at higher Tw than with sodium oleate; KF 96/, dodecane/, and undecane/water emulsions boil at lower Tw than KF54-in-water; sudden foaming in the bulk fluid reported Boiling of 5 μm DIA droplets begin at Tw ~ 60 °C above Ts for ether; heat transfer coefficients ~ 3X higher compared to glycerin; fluctuations in heat transfer coefficient up to 30% of mean due to sequential sudden boiling and slow vaporization Researchers report no effect of ε; at 40 °C bulk temperature, emulsions boiled at Ts for water; at 99 °C, h decreases until (Tw T ) = 40 °C and increases thereafter; this is attributed to water vapor wetting the wire For all emulsions studied, the heat transfer coefficient is approximately equal to that of the lower Ts component irrespective of ε; some variability is seen in water-in-benzene emulsions, with heat transfer coefficient decreasing with increasing fraction of benzene For flow boiling of water-in-PES4 emulsions, boiling begins at TS for water; enhancement is measured up to ε = 33%, but experimental scatter may account for variation in 12, 20, and 33% data sets

120 7 Conclusion

Water/PES-5; sodium phosphate sodium hydroxide surfactants

Water/PES-5

Water/PES-5, Freon-113/ water, diethyl ether/water

Water/PES-5

Various; activated carbon, zeolites, and carbon surfactants

Various; activated carbon, zeolites, and surfactants

Bulanov, Skripov, Gasanov, and Baidakov [71]

Gasanov, Bulanov, and Baidakov [66]

Bulanov [69]

Bulanov and Gasanov [72]

Bulanov, Gasanov, and Turchaninova [125]

Bulanov and Gasanov [67]

0.05 and 0.1 mm DIA platinum wire

0.05 and 0.1 mm DIA platinum wire

–

Emulsion in contact with 125 °C flowing fluid

Vertical 0.05 and 0.1 mm DIA platinum wire

Vertical 0.1 mm DIA platinum wire

43.5–55 °C

30–65 °C

–

98 °C

20–72 °C

25–60 °C

0.1–8%

–

0.10%

0.001– 10%

1–10%

0.1–8%

Summation (continued)

Little effect found with surfactant use on heat transfer coefficient; heat transfer coefficient depends on ε to ~1% and is independent of ε thereafter; heat transfer coefficient increases with increasing Tw; nucleate boiling is observed up to Tw = 235 °C Boiling of 1–60 μm DIA droplets show that increasing volume fraction increases heat transfer coefficient for ε ≤ 1% and then has little effect thereafter; increasing volume fraction decreases temperature overshoot at boiling onset Analytical model developed for boiling emulsions valid for various concentration and droplet distributions; comparison is given to experimental results for assumed values of nucleation rate and characteristic droplet time Emulsion is brought into direct contact with a pool of hot fluid; nucleation rate of bubbles is measured; authors posit that bubbles are nucleating via homogeneous nucleation on small floccules followed by chain activation Authors provide tabulated values for h as a function of Tw for various experimental conditions, including emulsion fluids, temperature, volume fraction, use of surfactants, and storage time Activated carbon decreases superheat in water-in-PES5 and increases it in n-pentanein-glycerin; zeolites increase superheat in water-in-PES4; sodium hydrate and trisodium phosphate increase superheat in water-in-PES5

7.3 121

–

–

–

Roesle and Kulacki [60]

–

–

56–96 °C

–

FC-72/water, pentane/water, water/mineral oil

Roesle and Kulacki [83]

–

4–69%

147 °C

Heater geometry Vertical 0.05–0.2 mm DIA platinum wire

1%

Pentane/water

Bulanov, Gasanov, and Muratov [81]

Emulsion bulk/inlet temperature 36–60 °C

30 mm × 30 mm copper plate

FC-72/water

Roesle and Kulacki [77]

Volume fractions studied 1%

24–32 °C

Fluids studied Various

Paper Bulanov and Gasanov [126]

Table 7.1 (continued)

Notable results A short review of prior experimental results is provided regarding a boiling model and the effect of droplet size, use of adsorbents and use of surfactants Flow boiling experiments in 0.1 mm × 30 mm microgap conducted with 40 ≤ G ≤ 467 kg/m2-s; unsteady nature of experiments obscured heat transfer behavior; high volume of FC-72 inhibited heat transfer compared to pure water Nucleation of bubbles are assumed to occur via a shock wave that initiates chain activation; equations are derived for the wave amplitude at distance R from droplet and the critical volume required to initiate chain activation Bubble growth is modeled after initiation for a single droplet in a continuous liquid, including the effect of surface tension; the density ratio and droplet size impact bubble growth rate and frequency of oscillations Euler-Euler differential equations for flow and temperature are presented; bubble nucleation rates are determined via chain boiling, droplet wall contact, droplet-bubble collisions, and spontaneous nucleation mechanisms

122 7 Conclusion

Vertical wire

Horizontal 101 μm DIA copper wire

Horizontal 101 μm diameter copper wire

5 mm × 26 mm microchannel

22 °C

25 °C

25 °C

25 °C

0.1–10%

Water/VM-1S, n-pentane/ glycerol

FC-72/water, pentane/water

FC-72/water, pentane/water

FC-72/water

Bulanov and Gasanov [128]

Roesle and Kulacki [62]

Roesle and Kulacki [73]

Morshed, Paul, Fang, and Khan [79]

0.5–1%

0.1–1%

0.1–1%

–

–

–

Water/PES-5

Rozentsvaig and Strashinskii [127]

–

–

–

Water/PES-5

Rozentsvaig and Strashinskii [84]

Summation (continued)

The nucleation mechanism is modeled in two regimes of turbulent flow: Droplet diameters greater than or less than the Kolmogorov scale of turbulence; favorable comparison is shown with limited experimental data Bubble nucleation of droplets is modeled with 1 μm and 100 μm DIA based on resonance between the turbulent fluctuations and surface waves on the droplet; qualitative agreement found with experiments is posited Authors develop a model to determine superheat at onset of boiling; superheat is found to be dependent on ε-1/3, which fits data for water-in-VM1s and n-pentane-inglycerol data For FC72-in-water, increasing ε decreases temperature overshoot, the reverse is found for pentane-in-water; emulsions exhibited similar h versus (Tw - Ts) behavior as waterin-R113 and diethyl ether-in-water emulsions Visualization is correlated to heat transfer; bubbles form on the wire; bubble diameter decreases with increasing heat flux; bubble diameter suggests wetting of liquid on wire or coalescence of bubbles Experiments show increasing ε decreases single-phase heat transfer; no enhancement in two-phase heat transfer is measured; emulsions decrease axial temperature difference compared to water

7.3 123

Fluids studied Freon-11/water, pentane/ water, water/VM-1S

Water/PES-5, water/PMS300

Water/PES-5, water/PMS300, water/VM-1S

FC-72/water, pentane/water

Water/VO-1C

Paper Gasanov and Bulanov [68]

Rozentsvaig and Strashinskii [129]

Rozentsvaig and Strashinskii [130]

Roesle, Lunde, and Kulacki [131]

Gasanov and Bulanov [75]

Table 7.1 (continued)

0.1–1.5%

0.1–0.5%

0.001–2%

0.001–4%

Volume fractions studied 1–5%

Vertical 0.05 and 0.1 mm DIA platinum wire

Vertical 0.05 and 0.1 mm DIA platinum wire

Vertically oriented thin 1008 steel strip

16 mm diam. pipe, 0.1 mm DIA platinum wire

–

25 °C

24 °C

Heater geometry 0.05 and 0.1 mm DIA platinum wire

–

Emulsion bulk/inlet temperature 16 °C

Notable results Though Freon-11 has a lower Ts than pentane, it boils at higher Tw; two regimes of boiling are identified based on heat flux and fluid motion; analytical relation for the time required for bubble formation is presented Boiling is modeled as a linear combination of conduction in the viscous sublayer near a surface and latent heat exchange; comparison is made to experimental data, and two distinct curves are demonstrated based on ε Authors use the model from [129] to determine the Nusselt number based on Reynolds number and compare predictions to experimental data; data show regimes of transition and developed turbulent boiling In single-phase convection, the emulsions produce lower heat transfer coefficient than in water, decreasing with increasing ε; increasing ε decreases superheat; slightly larger superheats are measured for pentane-in-water than FC72-in-water emulsions For flow boiling at G = 12 kg/m2s, increasing droplet diameter shifts heat transfer coefficients to lower Tw; lower Tw is required to initiate boiling compared to pool boiling; increasing droplet diameter and ε decreases critical heat flux

124 7 Conclusion

–

–

Paraffinic base oil/water, naphthenic base oil/water

FC-72/water, pentane/water

Rozentsvaig and Strashinskii [132]

Rozentsvaig and Strashinskii [133]

Janssen and Kulacki [78]

0.1–2%

1–20%

0.5–4%

Pentane/water, pentane/ glycerin

Gasanov [74]

–

1 μm gap between AA 1100 and AA 5182 rings

30 mm × 30 mm flat plate

–

25 °C

0.1 mm DIA platinum wire

–

22 °C High-speed visualizations demonstrate pentane-in-water emulsions boil at wire surface; pentane-in-glycerin emulsions boil close to the kinetic limit of superheat, so some bubbles are formed in the thermal boundary layer Unit and similarity analysis is performed to demonstrate the importance of the weber and Euler numbers for droplet breakup; breakup is assumed to be dominated by turbulent kinetic energy Authors modeled the use of oil-in-water emulsions for cooling and decreasing friction of high temperature machining applications; they develop an expression for the critical temperature for minimization of friction as a function of ε For boiling of FC72-in-water at G = 100 kg/m2s, boiling initiates at superheats of ~20–30 °C; up to 60% increase in heat transfer coefficient over water is measured; pentane-in-water produces no enhancement over water

7.3 Summation 125

Appendices

A. Thermophysical Properties of FC-721 (Tables A1 and A2) Table A1 Properties for FC-72 at 1 atm and 25 °C MW [kg/kmol] Tsat [°C] Pv [kPa] hfg [kJ/kg] ρ [kg/m3] μ [Ns/m2] ν [m2/s] Cp [J/kgK] k [W/mK] σ [N/m] n

338 56 30.9 88 1680 64 × 10-5 0.38 × 10-6 1100 0.057 0.01 1.251

1

The properties of FC-72 are provided by 3M™ at https://multimedia.3m.com/mws/media/64892 O/fluorinert-electronic-liquid-fc-72.pdf

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 B. M. Shadakofsky, F. A. Kulacki, Flow Boiling of a Dilute Emulsion In Smooth and Rough Microgaps, Mechanical Engineering Series, https://doi.org/10.1007/978-3-031-27773-3

127

128

Appendices

Table A2 FC-72 properties as a function of temperature T [°C] 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

ρ [kg/m3] 1740 1727 1714 1701 1688 1675 1662 1649 1636 1623 1610 1596 1583 1570 1557

μ × 105 [Ns/m2] 92.2 82.9 77.1 71.4 65.8 62.0 58.2 54.4 52.3 48.7 46.7 43.9 41.2 39.3 37.4

Cp [J/kgK] 1014 1022 1030 1037 1045 1053 1061 1068 1076 1084 1092 1099 1107 1115 1123

k [W/mK] 0.060 0.059 0.059 0.058 0.058 0.057 0.057 0.056 0.056 0.055 0.055 0.054 0.053 0.053 0.052

B. Measured Mass Flux for Each Experiment All mass fluxes tabulated are in kg/m2s (Tables B1, B2, B3, and B4).

Table B1 Mass flux for each experiment performed on the smooth surface. The inlet temperature for all emulsion runs is 30 °C Smooth Surface

Water, Ti = 30 °C Water, Ti = 51 °C Water, Ti = 70 °C 0.1% emulsion 0.5% emulsion 1% emulsion 2% emulsion

Hydraulic diameter (μm) 200 167, 345, 555 164, 365, 566 173, 358, 560 348 341 160, 356, 546 343

500 149, 348, 543 163, 351, 549 159, 347, 558 359 345 159, 357, 541 359

1000 152, 347, 552 147, 354, 558 153, 357, 538 362 345 143, 345, 558 359

Appendices

129

Table B2 Mass flux for each experiment performed on Porous Surface 1. The inlet temperature for all runs is 30 °C Porous Surface 1

Water 0.1% emulsion 0.5% emulsion 1% emulsion 2% emulsion

Hydraulic diameter (μm) 200 161, 360, 555 357 348 162, 350, 547 349

500 156, 352, 546 360 349 156, 349, 559 341

1000 158, 351, 548 346 346 157, 359, 553 341

Table B3 Mass flux for each experiment performed on Porous Surface 2. The inlet temperature for all runs is 30 °C Porous Surface 2

Water 0.1% emulsion 0.5% emulsion 1% emulsion 2% emulsion

Hydraulic diameter (μm) 200 164, 346, 548 354 350 162, 354, 552 350

500 156, 349, 560 355 352 163, 355, 541 350

1000 154, 356, 560 354 354 163, 352, 550 352

Table B4 Mass flux for each experiment performed on Porous Surface 3. The inlet temperature for all runs is 30 °C Porous Surface 3

Water 0.1% emulsion 0.5% emulsion 1% emulsion 2% emulsion

Hydraulic diameter (μm) 200 163, 353, 550 344 351 159, 356 356

500 159, 344, 548 351 344 157, 350, 553 345

1000 162, 360, 551 345 345 157, 355, 561 345

C. Other Forms of Correlation From the physical mechanisms discussed in Chap. 6, the following system parameters are deemed to be important for correlating the emulsion boiling data: kd, d, Dh, μc, ρd/ρc, G, hfg, Cp,c, ε, q″, h. Based on these parameters, seven dimensionless groups for correlating the data are

130

Appendices

hDh kd ρd ρc

GDh μc GC p d kd

q00 Ghfgd d Dh

ε ðC1Þ

The density ratio is not considered in this analysis because only one set of fluids is used in this study. The remaining dimensionless groups result in the correlation   - 2:31   - 1:41  00 0:81   GC p d 2:15 GDh q k d - 0:022 d h = 0:0068 ε kd Dh μc Ghfg d Dh

ðC2Þ

This correlation has 96.2% of the experimental data within ±10% of the predicted value. The ratio of the emulsion heat transfer coefficient to that for water at the same wall temperature and experimental condition can also be correlated as   - 1:37   - 1:34  00 0:72   GC p d 1:60 h - h0 d GDh q - 0:030 = 0:049ε - 1 ðC3Þ kd h0 μc Ghfg d Dh

This correlation has 37.0% of the experimental data within ±15% and 59.2% within ±30% of the predicted value. The experimental boiling data is compared to the predicted heat transfer coefficients in Fig. C1. With so many parameters being used in the correlation, a good fit may be simply due to the number of parameters. Although the p-value (a statistical parameter that demonstrates whether a given parameter correlates with the experimental data) for every nondimensional number shows the necessity of including each, the data can be correlated without the inclusion of some groups to view their significance. The last

b 0.75 [(h–h0)/h0]measured

hmeasured [W/m2K]

a 10000 8000 6000 4000 2000 0

0

2000 4000 6000 8000 10000 hpredicted

[W/m2K]

0.5 0.25 0 −0.25 −0.5 −0.5 −0.25

0

0.25

0.5

0.75

[(h–h0)/h0]predicted

Fig. C1 (a) Comparison between the measured emulsion heat transfer coefficient and that predicted by Eq. (C2). (b) Comparison between the measured ratio of the emulsion and water heat transfer coefficients and the ratio predicted by Eq. (C3). The solid line represents equivalence between the measured and predicted values

Appendices

b [(h–h0)/h0]measured

10000

hmeasured [W/m2K]

a

131

8000 6000 4000 2000 0 0

2000 4000 6000 8000 10000 hpredicted [W/m2K]

0.75 0.5 0.25 0 −0.25 −0.5 −0.5 −0.25

0

0.25

0.5

0.75

[(h–h0)/h0]predicted

Fig. C2 (a) Comparison between the measured emulsion heat transfer coefficient and that predicted by Eq. (C4). (b) Comparison between the measured ratio of the emulsion and water heat transfer coefficients and the ratio predicted by Eq. (C5). The solid line represents equivalence between the measured and predicted values

two groups in Eq. (C1) have only three values in the experimental data, aside from minor variation due to the effect of temperature on properties, so these two numbers can be neglected to view their significance. If this is done, the data are correlated by  0:96  00 0:51 q kd - 0:028 GDh ε Dh μc Ghfg d  0:16  00 0:36 h - h0 q - 0:045 GDh = 1:73ε -1 h0 μc Ghfg d h = 1:80

ðC4Þ ðC5Þ

Equation (C4) has 51.6% of the experimental data within ±15% and 87.5% within ±30% of the predicted value. Equation (C5) has 39.1% of the experimental data within ±30% of the predicted value. The experimentally measured heat transfer coefficients are plotted in comparison to the predicted values in Fig. C2. It is clear that it is necessary to include the last two nondimensional numbers in Eq. (C1). It is not clear that the boiling number is the correct parameter to account for the effect of the disperse component latent heat. It is possible that the ratio of the total sensible heat to the continuous component and the total latent heat to the disperse component would be a more appropriate nondimensional group to quantify these two effects. If this ratio is used, the resulting correlations are h ¼ 1:53

  - 0:28  0:97     ρc ð1 - εÞC p ðT w - T f Þ - 0:065 GC p d - 0:64 kd - 0:13 d GDh ε Dh Dh μc ρd εhfg d kd

ðC6Þ

132

Appendices

h - h0 h0



= 0:29ε

0:14

d Dh

 - 0:029  0:26     ρc ð1 - εÞC p ðT w - T f Þ 0:21 GC p d - 0:41 GDh ρd εhfg d kd μc

-1 ðC7Þ Equation (C6) has 81.5% of the experimental data within ±15% and 98.9% within ±30% of the predicted value. Equation (C7) has no data that falls within ±50%, with the average error being 77%. The measured heat transfer coefficient is plotted against the predicted values in Fig. C3. As such, the boiling number better predicts both the heat transfer coefficient and the ratio. Note that the exponent on ε in Eqs. (C2) and (C3) is very close to zero. This may suggest that the use of ε in the correlation is unnecessary. However, the p-value for ε also indicates that there is a strong correlation for ε in the experimental data. Therefore, this may also indicate that the form of the number used to include ε is incorrect. The necessity of using ε will first be explored by neglecting it from the correlation procedure. The results are   - 2:45   - 1:57  00 0:87   GC p d 2:35 kd d GDh q h = 0:0053 kd Dh Dh μc Ghfg d   - 1:55   - 1:56  00 0:80   GC p d 1:86 d h - h0 GDh q = 0:034 -1 Dh kd h0 μc Ghfg d

b

10000

ðC9Þ

0.75 0.5

8000

[(h–h0)/h0]measured

hmeasured [W/m2K]

a

ðC8Þ

6000 4000 2000

0.25 0 −0.25 −0.5 −0.75 −1

0 0

2000

4000

6000

hpredicted [W/m2K]

8000

10000

−1 −0.75 −0.5 −0.25

0

0.25 0.5 0.75

[(h–h0)/h0]predicted

Fig. C3 (a) Comparison between the measured emulsion heat transfer coefficient and that predicted by Eq. (C6). (b) Comparison between the measured ratio of the emulsion and water heat transfer coefficients and the ratio predicted by Eq. (C7). The solid line represents equivalence between the measured and predicted values

a 10000

b [(h–h0)/h0]measured

133

hmeasured [W/m2K]

Appendices

8000 6000 4000 2000 0 0

2000 4000 6000 8000 10000 hpredicted [W/m2K]

0.75 0.5 0.25 0 −0.25 −0.5 −0.5

−0.25

0

0.25

0.5

0.75

[(h–h0)/h0]predicted

Fig. C4 (a) Comparison between the measured emulsion heat transfer coefficient and that predicted by Eq. (C8). (b) Comparison between the measured ratio of the emulsion and water heat transfer coefficients and the ratio predicted by Eq. (C9). The solid line represents equivalence between the measured and predicted values

Equation (C8) fits 95.1% of the experimental data within ±10% of the predicted value. Eq. (C9) fits 31.5% of the data within ±15% and 58.7% within ±30% of the predicted value. The measured heat transfer coefficient is plotted against the predicted values in Fig. C4. It appears that the correlation is slightly worse when not including ε. The experimental results demonstrate that ε has a large effect on the heat transfer behavior at low values, but the effect asymptotically decreases as ε increases. This is consistent with a form of 1/ε. Therefore, let us use 1/(1 + ε) to capture this experimental trend and have the effect of ε go to 0 for ε → 0. The resulting correlations are h   - 2:37   - 1:48  00 0:84   GC p d 2:24 1 d GDh q kd = 0:0067 kd Dh ð1 þ εÞ3:42 Dh μc Ghfg d ðC10Þ h - h0 h0

  - 1:46   - 1:46  00 0:76   GC p d 1:73 1 d GDh q = 0:045 kd μc Ghfg d ð1 þ εÞ4:15 Dh -1

ðC11Þ

These correlations demonstrate a strong dependence on ε for small values of ε, consistent with the experimental results. Equation (C10) fits the experimental data very well, with 95.7% of the experimental data falling within ±10% of the predicted value; 36.4% of the experimental data falls within ±15%, and 58.7% falls within

134

b

8000 6000 4000

0.5 0.25 0

−0.25

2000 0

0.75

[(h–h0)/h0]measured

10000

hmeasured [W/m2K]

a

Appendices

0

2000 4000 6000 8000 10000 hpredicted [W/m2K]

−0.5 0 0.25 0.5 −0.5 −0.25 [(h–h0)/h0]predicted

0.75

Fig. C5 (a) Comparison between the measured emulsion heat transfer coefficient and that predicted by Eq. (C10). (b) Comparison between the measured ratio of the emulsion and water heat transfer coefficients and the ratio predicted by Eq. (C11). The solid line represents equivalence between the measured and predicted values

±30% of the values predicted by Eq. (C11). Equation (C11) does a good job of capturing the trends in the data (Fig. C5). Therefore, this is the final correlation form that is used.

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Index

B Boiling curve, 1, 3, 23, 28, 33–35, 44, 47–51, 67, 68, 70, 72, 74, 80–82, 85, 88, 90, 96, 97, 112, 114 Boiling mechanism, 1 Boiling regimes, 44

C Correlations, 1, 5, 39, 45, 103–109, 112, 130–134 Coupled flow, 29

D Dilute emulsions, 43–75, 88–100, 119 Dimensionless groups, 40, 107, 129, 130 Droplet size distribution, 48

E Emulsion preparation, 7, 9 Experimental method and apparatus, 29

F FC72-in-water, 44–46, 48, 50, 51, 54, 55, 123–125 Flow boiling, 1–5, 7, 25–75, 77, 82, 105, 111, 112, 119, 120, 122, 124

Flow boiling history, 1–5 Friction factor, 64

H Heat transfer, 1–5, 9, 25–35, 40, 41, 43–49, 51–57, 60, 63, 66–72, 74, 77, 80–83, 85, 86, 88–90, 92, 94, 96, 97, 100, 104–109, 111, 112, 114, 119–125, 130–133 Heat transfer coefficients, 2–5, 19, 27–31, 33, 35, 40, 41, 43–49, 52, 53, 55, 63, 66–72, 74, 80–83, 85, 86, 88–90, 92, 94, 96, 97, 105–107, 109, 111, 112, 114, 120, 121, 124, 125, 130–133 Heat transfer correlation, v, vi, 45, 107, 109, 112, 129–134

L Liquid droplet film, 106 Laminar flow, 9, 20, 66

M Microgaps, 4, 5, 9, 20, 25–75, 77, 114, 122 Microporous surface preparation, 79–82 Microporous surfaces, v, 5, 9, 77–82, 97, 100, 101

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 B. M. Shadakofsky, F. A. Kulacki, Flow Boiling of a Dilute Emulsion In Smooth and Rough Microgaps, Mechanical Engineering Series, https://doi.org/10.1007/978-3-031-27773-3

141

142 N Nusselt number, 21, 40, 42, 44, 111, 124

P Porosity, 11, 15, 77–79, 81, 87 Pressure drop, 32, 33, 36, 39, 67, 69, 73, 78, 82, 83, 86, 87, 89, 94, 96, 97, 100, 113, 114

Index S Scanning Electron Microscopy (SEM) images, 11–18, 82, 92 Smooth surface, 23, 79–83, 85–87, 97, 105, 108, 111–113, 128 Superposed heat transfer coefficients, 106

U Uncertainty, 1, 19, 20, 114 R Repeatability, 23