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A STUDY OF HEAT TRANSFER IN NONBOILING TWOPHASE GASLIQUID FLOW IN PIPES FOR HORIZONTAL, SLIGHTLY INCLINED, AND VERTICAL ORIENTATIONS By CLEMENT CHIHWEI TANG Bachelor of Science in Mechanical Engineering Oklahoma State University Stillwater, Oklahoma 2000 Master of Science in Mechanical Engineering Oklahoma State University Stillwater, Oklahoma 2003 Submitted to the Faculty of the Graduate College of the Oklahoma State University in partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY May, 2011 ii A STUDY OF HEAT TRANSFER IN NONBOILING TWOPHASE GASLIQUID FLOW IN PIPES FOR HORIZONTAL, SLIGHTLY INCLINED, AND VERTICAL ORIENTATIONS Dissertation Approved: Dr. Afshin J. Ghajar Dissertation Adviser Dr. David G. Lilley Dr. Frank W. Chambers Dr. Martin S. High Outside Committee Member Dr. Mark E. Payton Dean of the Graduate College iii ACKNOWLEDGEMENTS I would like to express my most sincere gratitude to my advisor, Dr. Afshin. J. Ghajar, for his excellent guidance, consistent encouragement, and dedication to teaching and research; I am greatly indebted to him for his invaluable inspiration. I would also like to express my appreciation to Dr. David. G. Lilley, Dr. Frank. W. Chambers and Dr. Martin S. High for their willingness to serve as my committee members despite their busy schedules. Their helpful comments, guidance, and encouragements are invaluable. Furthermore, I would like to thank Wendell Cook and Melkamu Woldesemayat for their help in the laboratory. Special thanks to Wendell Cook for assisting me in designing and constructing the new experimental setup for twophase flow, as well as the experimental setup for miniand microtube flow. Although the scope of my thesis does not include using both of those experimental setups, I am nonetheless grateful for the opportunity to be a participant in both projects. Another colleague that deserves special thanks is Jaeyong Kim, who initially showed me the ins and outs of operating twophase flow experiments. In fact, the idea of constructing the new twophase flow experimental setup was conceived by him. At the moment of this writing, four M.S. theses have been produced out of the studies involving the new experimental setup for twophase flow. I have indeed reaped the benefits of his labor in the twophase flow laboratory. iv My gratitude extends to my parents, whose support and encouragement are priceless. Their prayers for me during the course of this study have brought many blessings into my life. Special gratitude and appreciation are expressed to my loving wife, Grissadee Rataree, for her unwavering love, patience and support. I also like to dedicate this work to my son, Jadon, whose youthful humor and insatiable curiosity are constant inspirations to me. Finally, and foremost, I thank the Lord Jesus Christ for establishing the work of my hands. v TABLE OF CONTENTS Chapter Page I. INTRODUCTION ...................................................................................................1 1.1 Basic Definitions in TwoPhase Flow ............................................................3 1.2 TwoPhase Flow Patterns ...............................................................................7 Flow Patterns in TwoPhase Horizontal Flow ............................................ 7 Flow Patterns in TwoPhase Vertical Flow ................................................ 9 1.3 Research Objectives .....................................................................................10 1.4 Broader Impact .............................................................................................12 1.5 Brief Outline of this Study ...........................................................................13 II. LITERATURE REVIEW ......................................................................................14 2.1 TwoPhase Flow Heat Transfer ....................................................................14 2.2 TwoPhase Flow Pattern Maps ....................................................................29 2.3 Void Fraction ................................................................................................33 2.4 Relationship of Pressure Drop and Heat Transfer ........................................38 2.5 Chapter Summary .........................................................................................41 III. DEVELOPMENT OF NONBOILING TWOPHASE HEAT TRANSFER CORRELATIONS .................................................................................................42 3.1 Development of a General NonBoiling TwoPhase Heat Transfer Correlation ....................................................................................................42 3.2 Flow Pattern Factor and Inclination Factor ..................................................45 Flow Pattern Factor ................................................................................... 45 Inclination Factor ...................................................................................... 47 3.3 General NonBoiling TwoPhase Heat Transfer Correlation .......................49 3.4 A Reynolds Analogy Approach for Heat Transfer Estimation in Non Boiling TwoPhase Pipe Flow ......................................................................51 Development of a Reynolds analogy Heat Transfer Correlation .............. 52 3.5 Chapter Summary .........................................................................................55 IV. EXPERIMENTAL SETUP AND PROCEDURES ...............................................56 4.1 Description of Current Experimental Setup .................................................56 Flow Loop ................................................................................................. 57 Supply of Working Fluids ......................................................................... 57 AirWater Mixing Section ........................................................................ 60 vi Chapter Page Calming and Observation Section ............................................................ 60 Heat Transfer Test Section........................................................................ 60 Heat Source ............................................................................................... 64 4.2 Instrumentation .............................................................................................64 Flow Rate Measurements .......................................................................... 64 Temperature Measurements ...................................................................... 65 Pressure Measurements ............................................................................. 65 Power Measurement.................................................................................. 65 Data Acquisition System........................................................................... 66 4.3 Experimental Procedures ..............................................................................67 StartUp Procedure.................................................................................... 68 Measurement Procedure............................................................................ 70 4.4 Data Reduction .............................................................................................73 4.5 Effects of Dissolved Air ...............................................................................76 4.6 Chapter Summary .........................................................................................78 V. EXPERIMENTAL RESULTS...............................................................................79 5.1 SinglePhase Flow Results ...........................................................................79 Frictional Pressure Drop in SinglePhase Flow ........................................ 80 SinglePhase Flow Heat Transfer Coefficient along the Pipe .................. 84 Heat Transfer in SinglePhase Flow ......................................................... 85 5.2 Flow Patterns and Flow Maps ......................................................................88 5.3 Heat Transfer in Horizontal and Slightly Upward Inclined Pipe Flows ....101 5.4 Influence of Pipe Inclination on Heat Transfer Coefficient .......................107 5.5 Chapter Summary .......................................................................................121 VI. COMPARISON OF TWOPHASE HEAT TRANSFER CORRELATIONS WITH EXPERIMENTAL RESULTS .................................................................122 6.1 The General TwoPhase Heat Transfer Correlation ...................................122 6.2 Comparison of the General Correlation with Experimental Results for Specific Pipe Orientations and GasLiquid Flows .....................................127 TwoPhase Flow in Horizontal and Slightly Inclined Pipes ................... 127 TwoPhase Flow in Vertical Pipe ........................................................... 135 Summary ................................................................................................. 140 6.3 Comparison of the General Correlation with All Experimental Data ........142 6.4 The Use of Different Void Fraction Correlations with the General Correlation ..................................................................................................146 Horizontal to Vertical Pipes Void Fraction Correlations ........................ 146 Horizontal Pipe Void Fraction Correlations ........................................... 147 Vertical Pipe Void Fraction Correlations ............................................... 149 6.5 Practical Illustrations of Using the General TwoPhase Heat Transfer Correlation ..................................................................................................151 Application for AirWater Flow in Horizontal Pipe ............................... 151 Application for Air and GasOil Flow in Vertical Pipe .......................... 154 vii Chapter Page Application for AirSilicone Flow in Vertical Pipe ................................ 157 6.6 The Reynolds Analogy TwoPhase Heat Transfer Correlation..................160 6.7 Assessment of the Exponents for the Reynolds Analogy Correlation .......164 6.8 Comparison of the Reynolds Analogy Correlation with All Experimental Data ......................................................................................165 6.9 Exponents of the Reynolds Analogy Correlation for Specific Pipe Orientations and GasLiquid Flows ...........................................................169 6.10 Performance of Other Correlations ............................................................173 6.11 Chapter Summary .......................................................................................176 VII. SUMMARY AND RECOMMENDATIONS......................................................177 7.1 Summary of Present Study .........................................................................177 7.2 Recommendations for Possible Future Study ............................................179 REFERENCES ................................................................................................................184 APPENDIX A ..................................................................................................................196 A.1 Friction Factor ............................................................................................197 A.2 Heat Transfer Coefficient ...........................................................................198 APPENDIX B ..................................................................................................................201 viii LIST OF TABLES Table Page 1. Experimental data sets used in the study by Kim et al. (1999) ..........................24 2. Heat transfer correlations chosen in the study by Kim et al. (1999) ..................25 3. Values of constants suggested for the various models and correlations summarized by Butterworth (1975) ...................................................................35 4. Summary of the deviations between measured and calculated friction factor using various correlations ........................................................................83 5. Summary of the deviations between measured and calculated Nusselt number using various correlations .....................................................................87 6. Summary of experimental conditions and measured twophase heat transfer data for horizontal and 2°, 5°, and 7° pipe inclinations ......................101 7. Summary of the conditions of experimental data used for comparison with the general twophase heat transfer correlation, Eq. (3.18) .............................125 8. Results of the predictions by Eq. (3.18) with specific leading coefficient and exponents for various pipe orientations and gasliquid flows ...................134 9. Results of the predictions by Eq. (6.15) for all 1156 experimental heat transfer data points with different gasliquid combinations and pipe inclinations .......................................................................................................145 10. Results predicted by the general twophase heat transfer correlation, Eq. (6.15), applied with various void fraction correlations compared with experimental results ..........................................................................................150 11. Summary of the conditions of experimental data used for comparison with the Reynolds analogy twophase heat transfer correlation, Eq. (3.27) ............162 12. Comparison of the predictions by Eq. (6.21) and all 916 experimental data points with different gasliquid combinations and pipe inclinations ...............168 13. Comparison of the predictions by Eq. (6.22) and all 916 experimental data points with different gasliquid combinations and pipe inclinations ...............171 ix Table Page 14. Comparison of the predictions by Eq. (6.21) versus Eq. (2.34) and Eq. (2.35) ................................................................................................................175 15. Comparison of capabilities between the current and new experimental setups ................................................................................................................180 x LIST OF FIGURES Figure Page 1. Schematic of flow patterns observed in horizontal gasliquid flow (adapted from Carey, 1992) .............................................................................8 2. Schematic of flow patterns observed in vertical gasliquid flow (adapted from Carey, 1992) ............................................................................................9 3. Flow map for vertical flow by Hewitt and Roberts (1969) ...............................29 4. Flow map for horizontal and near horizontal flow by Taitel and Dukler (1976) .............................................................................................................30 5. Flow map for horizontal airwater flow by Weisman et al. (1979) ..................31 6. Flow map for horizontal flow by Spedding and Nguyen (1980) ......................32 7. Gasliquid interface and wettedperimeter ........................................................46 8. Flow loop of the current experimental setup.....................................................58 9. Schematic of airwater mixing section ..............................................................61 10. Schematic of heat transfer test section ..............................................................62 11. Graphical user interface of the LabVIEW Virtual Instrument (VI) program ..........................................................................................................67 12. Startup procedure for twophase heat transfer and isothermal pressure drop experiments ............................................................................................69 13. Measurement procedure for twophase heat transfer and isothermal pressure drop experiments .............................................................................71 14. Nodal arrangement for finite difference solution (adapted from Ghajar and Kim, 2006) ..............................................................................................75 15. Comparison of measured and calculated singlephase friction factor ..............83 16. Variation of local Nusselt number along the heated test section for singlephase flow ...........................................................................................84 17. Comparison of measured and calculated singlephase heat transfer data .........87 xi Figure Page 18. Photographs of flow patterns for horizontal flow. ............................................89 19. Flow map of horizontal pipe with photographs of representative flow patterns ...........................................................................................................90 20. Change of flow pattern transition boundaries as pipe inclined upward from horizontal orientation ............................................................................91 21. Flow patterns data points from Barnea et al. (1980) plotted on the flow maps for horizontal and 2° inclined flows .....................................................93 22. Representative photographs of wavy flow patterns for horizontal, 2°, 5°, and 7° pipe inclinations (ReSG = 16000 and ReSL = 1500) .............................95 23. Representative photographs of slug flow patterns for horizontal, 2°, 5°, and 7° pipe inclinations (ReSG = 4000 and ReSL = 17000) .............................96 24. Representative photographs of annular flow patterns for horizontal, 2°, 5°, and 7° pipe inclinations (ReSG = 28000 and ReSL = 17000) ......................97 25. Flow maps for horizontal, 2°, 5°, and 7° inclined flows with distribution of heat transfer data collected ........................................................................99 26. Variation of twophase heat transfer coefficient with superficial liquid Reynolds number .........................................................................................103 27. Variation of twophase heat transfer coefficient with superficial gas Reynolds number .........................................................................................105 28. Influence of pipe inclination on twophase heat transfer coefficient for varying superficial gas and liquid Reynolds numbers .................................111 29. Variation of the twophase heat transfer coefficient (hTP, top) with the superficial gas Reynolds number for ReSL = 1500 and ReSL = 5000 ............117 30. Twophase heat transfer coefficient at circumferential locations of the pipe ...............................................................................................................119 31. Comparison of the predictions by Eq. (6.5) with all 196 experimental heat transfer data points for airwater flow in horizontal pipes ...................132 32. Comparison of the predictions by Eq. (6.6) with all 184 experimental heat transfer data points for airwater flow in 2° inclined pipes ..................132 33. Comparison of the predictions by Eq. (6.7) with all 184 experimental heat transfer data points for airwater flow in 5° inclined pipes ..................133 34. Comparison of the predictions by Eq. (6.8) with all 187 experimental heat transfer data points for airwater flow in 7° inclined pipes ..................133 xii Figure Page 35. Comparison of the predictions by Eq. (3.18) with all 405 experimental heat transfer data points for various gasliquid combinations in vertical pipes .............................................................................................................141 36. Comparison of the predictions by Eq. (6.15) with the entire experimental database (1156 data points) for various pipe inclinations and gasliquid combinations ................................................................................................144 37. Comparison of predictions by Eq. (6.21) and experimental twophase heat transfer coefficients for airwater flow in 0, 5, and 90° pipes ..............165 38. Comparison of predictions by Eq. (6.21) and experimental twophase heat transfer coefficients for various gasliquid flows in vertical pipe ........166 39. Comparison of predictions by Eq. (6.21) and experimental twophase heat transfer coefficients for all 916 data points ..........................................167 40. Comparison of predictions by Eq. (6.22) and experimental twophase heat transfer coefficients for various gasliquid flows in vertical pipe ........172 41. Comparison of predictions by Eq. (6.22) and experimental twophase heat transfer coefficients for all 916 data points ..........................................172 42. Schematic of isothermal flow test section .......................................................181 B1. Repeatability results of experimental heat transfer coefficient for airwater flow in horizontal and slightly inclined pipes ...................................202 xiii NOMENCLATURE A crosssectional area, m2 s A surface area, m2 Bo Bond number (see Eötvös number), dimensionless C constant leading coefficient, dimensionless 0 C twophase distribution coefficient, dimensionless c specific heat at constant pressure, kJ/kg·K f c Fanning friction factor, dimensionless D inside diameter of pipe, m h D hydraulic diameter, m o D outside diameter of pipe Eo Eötvös number ( ρ ρ 2 σ ) ( )gD L G = − , dimensionless F modified Froude number in Taitel and Dukler (1976) map, dimensionless P F flow pattern factor, dimensionless S F shape factor, dimensionless Fr Froude number ( u gD = 2 ), dimensionless b f bubble, plug, or slug frequency, s1 G mass flux or mass velocity, kg/s·m2 g gravitational acceleration, m/s2 xiv I inclination factor, dimensionless i electrical current, A h heat transfer coefficient, W/m2·K K slip ratio, dimensionless K wavy flow parameter in Taitel and Dukler (1976) map, dimensionless k thermal conductivity, W/m·K L length of test section, m b L bubble, plug, or slug length, m m& mass flow rate, kg/s TC@ST N Number of thermocouple at a thermocouple station ST N Number of thermocouple station Nu Nusselt number ( = hD k ), dimensionless Pr Prandtl number ( = cμ k ), dimensionless p pressure, Pa a p atmospheric pressure, Pa p pressure drop, Pa Q volumetric flow rate, m3/s q& heat transfer rate, W g q& heat generation rate, W q&′′ heat flux, W/m2 R electrical resistance, L L R liquid fraction or liquid holdup, dimensionless Re Reynolds number ( = ρuD μ ), dimensionless xv S circumference fraction in Kaminsky (1999) correlation, dimensionless L S wettedperimeter, m T dispersed bubble flow parameter in Taitel and Dukler (1976) map, dimensionless T temperature, °C u axial velocity, m/s b u bubble, plug, or slug velocity, m/s GM u drift velocity, m/s V voltage drop, V v specific volume, m3/kg w uncertainty, dimension varies with measured parameter X Martinelli parameter ( ( ) ( ) ) f ,SL f ,SG = ∂p ∂z ∂p ∂z , dimensionless x flow quality ( m m G = & & ), dimensionless Y inclination parameter in Taitel and Dukler (1976) map, dimensionless z axial coordinate Greek Symbols α void fraction, dimensionless ( ) L β R holdup dependent factor in Kaminsky (1999) correlation, dimensionless δ distance from a node to a control volume interface (see Figure 14), m ε roughness height of pipe wall, m μ dynamic viscosity, N·s/m2 ν slug frequency in Deshpande et al. (1991) correlation, s1 φ twophase multipliers, dimensionless xvi ϕ angle from the circumferential top of pipe, rad. γ electrical resistivity, L·m θ inclination angle of pipe or test section, deg. or rad. ρ density, kg/m3 σ surface tension, N/m 0 τ wall shear stress, N/m2 ψ ratio of heat transfer coefficients, dimensionless Superscripts m constant exponent, dimensionless n constant exponent, dimensionless p constant exponent, dimensionless q constant exponent, dimensionless r constant exponent, dimensionless Subscripts ATM atmosphere avg average B bulk btm bottom of pipe CAL calculated EXP experimental e node e (see Figure 14) eff effective xvii eq equilibrium state f frictional component G gas phase in inlet j index of thermocouple in the circumferential location k index of thermocouple station in the axial location L liquid phase m mixture n node n (see Figure 14) out outlet p node p (see Figure 14) SG superficial gas SL superficial liquid SYS system TP twophase top top of pipe W wall Wi inner wall Wo outer wall w node w (see Figure 14) Abbreviations A annular P plug xviii PS plug/slug S slug SB slug/bubbly SBA slug/bubbly/annular ST stratified W wavy WA wavy/annular WS wavy/slug 1 CHAPTER I INTRODUCTION In many industrial applications, such as the transport of oil and natural gas in pipelines and wellbores, the knowledge of nonboiling twophase, twocomponent (liquid and permanent gas) heat transfer is required. During the transport of twophase hydrocarbon fluids from an oil reservoir to the surface, temperature of the hydrocarbon fluids changes due to the difference in temperatures of the oil reservoir and the surface. The difference in temperature results in heat transfer between the hydrocarbon fluids and the earth surrounding the oil well. In such situation, the ability to estimate the flowing temperature profile is necessary to address several design problems in petroleum production engineering (Shiu and Beggs, 1980). In subsea oil and natural gas production, hydrocarbon fluids may exit the reservoir with a temperature of 75°C and flow in subsea surroundings of 4°C (Trevisan et al., 2006). As a result of the temperature difference between the reservoir and the surroundings, the knowledge of heat transfer is critical in the effort to prevent gas hydrate and wax deposition blockages (Furuholt, 1988). Wax deposition can cause severe problems including the reduction of inner pipe diameter causing blockage, increase in surface roughness of the pipe leading to restricted flow line pressure, decrease in 2 production, and various other mechanical problems (McClaflin and Whitfill, 1984). Here are some examples of the economical losses that caused by wax deposition blockages: (1) a direct cost of five million dollars in removing the blockage from a subsea pipeline, (2) a production downtime loss in 40 days costing 25 million dollars (Fogler, 2008), and (3) the cost of an oil platform abandonment by Lasmo Company (U.K.) that amounted to 100 million dollars (Singh et al., 2000). Schemes such as coilspring wire insert, twisted tape insert, and helical ribs have been used to promote turbulence in pipes for the purpose of enhancing heat transfer. Although such heat transfer enhancement schemes have been proven to be effective, they do come with drawbacks, such as fouling, increases in pressure drop, and even blockage. Celata et al. (1999) presented an approach to enhance heat transfer in pipe flow by injecting small amount of gas into the liquid flow to promote turbulence. In the experimental study performed by Celata et al. (1999), a uniformly heated vertical pipe was internally cooled by water, while heat transfer coefficients with and without air injection were measured. The introduction of a small air flow rate into the water flow resulted in increases of the heat transfer coefficient up to 20–40% for forcedconvection, and even larger heat transfer enhancement for mixedconvection (Celata et al., 1999). Twophase flow can occur in some situations related to the ongoing and planned space operations. In such situations, the knowledge of heat transfer characteristics is important for designing piping systems for space operations limited by size constraints (Fore et al., 1996). To investigate heat transfer mechanisms in twophase slug and annular flows under microgravity conditions, Fore et al. (1996, 1997) conducted heat 3 transfer measurements for airwater and air50% aqueous glycerin on broad of NASA’s ZeroG KC135 aircraft. Wang et al. (2004) investigated forced convection heat transfer on the shell side of a TEMAF horizontal heat exchanger using 60% aqueous glycerin and air mixture. Their work resulted in recommendation of correlations for twophase heat transfer coefficient in stratified, intermittent, and annular flows in shellandtube heat exchangers. Furthermore, since the mechanisms of heat transfer and mass transfer are analogous to one another, the knowledge of twophase heat transfer can be applicable to twophase mass transfer. In order to successfully apply the knowledge of twophase heat transfer to solve mass transfer problems, the appropriate parallels between the two mechanisms have to be first sorted out. Mass transfer in twophase flow can be found in many chemical processes. One conceivable application is predicting the rate of corrosion in pipes that transport twophase flow. In cases when chemical reactions between the pipe surface and the twophase fluids are heavily influenced by mass transfer, the ability to predict the mass transfer coefficient becomes very beneficial to engineers. Although twophase flow may occur in different types, such as gasliquid flow, gassolid flow, and liquidsolid flow, it should be noted that the focus of present study is on twophase gas and liquid pipe flow. 1.1 Basic Definitions in TwoPhase Flow In gasliquid twophase pipe flow, the gas and liquid are simultaneously in interaction with each other inside the pipe. As a result, two phase flow is generally more complicated to describe physically and mathematically than single phase pipe flow. Since 4 the flow conditions in a pipe vary with the pipe length, the pipe cross section, and time, the gasliquid flow is an extremely complex threedimensional transient problem involving two different fluid properties. The definitions in twophase flow presented here are that of onedimensional flow (the flow conditions in each phase only vary with distance along the tube) and it is perhaps the most important and common method developed for analyzing twophase pressure drop, void fraction, and heat transfer. The total mass flow rate (m& ) through the tube is equal to the sum of the mass flow rates of gas ( G m& ) and liquid ( L m& ): G L m& = m& + m& . (1.1) The flow quality ( x ), which is the ratio of the gas mass flow rate to the total mass flow rate, is defined as m m m m x G L & & & & = = 1− . (1.2) The mass flux (G ) or mass velocity is commonly defined as A m G & = . (1.3) where the total cross sectional area ( A ) is the sum of the cross sectional areas occupied by both gas and liquid phases ( G L A = A + A ). Void fraction (α ) is defined as the volume of space the gas phase occupies in a given two phase flow in a pipe, hence for a total pipe cross sectional area of A , the void fraction is A Aα = G , (1.4) and the liquid holdup is 5 A A R L L = 1−α = . (1.5) Many twophase flow correlations are based on a variable called superficial velocity. The superficial velocity of a fluid phase is defined as the velocity that the phase would exhibit as if it flows through the total cross section of the pipe alone. The superficial gas velocity ( SG u ) is defined as A Gx Q u G G SG = = ρ . (1.6) The actual gas velocity can be expressed as A Q u G G α = . (1.7) Likewise, the superficial liquid velocity ( SL u ) is defined as ( ) A G x Q u L L SL = − = ρ 1 , (1.8) and the actual liquid velocity is expressed as ( )A Q u L L −α = 1 . (1.9) The slip ratio ( K ) is defined as the ratio of the actual velocities between the phases, G L L G x x u u K ρ ρ α α − − = = 1 1 . (1.10) When the actual gas velocity is equal to the actual liquid velocity ( K = 1), there is noslip between phases, and this condition is commonly referred to as homogeneous twophase flow. 6 Twophase flow requires expressions for key physical properties, such as density and viscosity. In expressing such relations, preference should be given to those equations that satisfy the property values at 100% gas or liquid flow (Levy, 1999). The twophase density ( TP ρ ) may be expressed as ρ ρ ( α ) ρ α TP L G = 1− + , (1.11) and the twophase viscosity ( TP μ ) is μ μ ( α ) μ α TP L G = 1− + . (1.12) Reynolds number in twophase flow can be expressed in several ways. The most common expression is the superficial Reynolds number. The superficial gas Reynolds number ( SG Re ) is defined as G G G SG SG u D xGD Re μ μ ρ = = , (1.13) and superficial liquid Reynolds number ( SL Re ) is defined as L L L SL SL u D x GD μ μ ρ (1 ) Re − = = . (1.14) Occasionally, the in situ liquid phase Reynolds number ( L Re ) is preferred over the superficial liquid Reynolds number ( SL Re ). In such occasion, the in situ liquid phase Reynolds number ( L Re ) is defined as D u D m Re L L L L L L L μ π α μ ρ (1 ) 4 − = = & . (1.15) 7 1.2 TwoPhase Flow Patterns The gas and liquid phases in a twophase flow can exist in several distinct morphological flow patterns. Flow patterns in twophase flow are among the most important characteristics, since they strongly influence the hydrodynamics and transport processes of twophase flow. Pressure drop, flow stability, and heat and mass transfer are all influenced by flow patterns. Flow Patterns in TwoPhase Horizontal Flow The flow patterns that may occur in twophase flow inside horizontal round tubes are shown in Figure 1. One of the main differences between the flow patterns observed for horizontal flow and those for vertical flow is that there is a tendency for stratification of the flow in horizontal flow. Regardless of the flow pattern, the gas tends to migrate toward the top of the tube while the lower portion of the tube carries more of the liquid. The descriptions of the flow patterns are as follows: Bubbly flow: At very low quality (i.e., low G m& ), bubbly flow is often observed. Due to buoyancy, the bubbles mainly flow in the upper portion of the tube. Plug flow: Plug flow is formed when coalescence of small bubbles produces larger plugtype bubbles, which flow in the upper portion of the tube. Stratified flow: At low liquid and gas flow rates, stratified flow is often observed. Because of gravitational force, the liquid flows along the bottom of a horizontal tube. 8 Wavy flow: When gas flow rate is increased in the stratified flow regime, eventually the interface becomes unstable, whereupon the interface becomes wavy. This type of flow is categorized as wavy flow. Slug flow: Slug flow is characterized by large gas bubbles almost filling the tube and separated by slugs of liquid. Annular flow: Annular flow consists of an annular liquid film and of gas core. Figure 1. Schematic of flow patterns observed in horizontal gasliquid flow (adapted from Carey, 1992) 9 Flow Patterns in TwoPhase Vertical Flow The typical flow patterns observed in twophase flow inside a vertical round tube are illustrated in Figure 2. The descriptions of the flow patterns are as follows: Bubbly flow: The gas phase is approximately uniformly distributed in the form of discrete bubbles in a continuous liquid phase. Slug flow: The gas flows as large bulletshaped bubbles along with some smaller gas bubbles distributed throughout the liquid. Churn flow: Churn flow shows some similarity with slug flow. It is, however, much more chaotic, frothy and disordered. Wispy Annular flow: When both the liquid and gas flow rates are high, an annulartype flow is observed with heavy “wisps” of entrained liquid flowing in the gas core. Annular flow: The liquid flows partly as annular film near the tube wall and partly in the form of droplets distributed in the gas core. Figure 2. Schematic of flow patterns observed in vertical gasliquid flow (adapted from Carey, 1992) 10 1.3 Research Objectives The main objective of this research is to establish a fundamental understanding of heat transfer in nonboiling twophase pipe flow. The key processes that govern heat transfer in nonboiling twophase pipe flow are flow patterns, pressure drop, void fraction, and inclination effects. The fundamental understanding of heat transfer in nonboiling twophase pipe flow can be achieved in twofold; namely, qualitatively and quantitatively. All the experimental data to be collected for flow patterns, heat transfer, pressure drop, void fraction, and flow visualization provide valuable insights to describing the physics of heat transfer in nonboiling twophase pipe flow qualitatively. However, to be able to successfully and effectively quantify heat transfer in nonboiling twophase pipe flow, the development of a general heat transfer correlation or model that has the robustness to handle all major twophase flow patterns and inclination effects is necessary. Before one can successfully establish a fundamental understanding of heat transfer in nonboiling twophase pipe flow, the following questions need to be answered: 1) How do flow patterns change as the pipe is upwardly inclined from horizontal position? 2) How does heat transfer respond when the pipe is upwardly inclined from horizontal position? 3) How does the change of one flow pattern to another flow pattern influence the heat transfer? 4) Can pressure drop be used to accurately correlate heat transfer via the Reynolds analogy used in single phase flow? 11 To address these questions, the proposed study will provide experimental data, qualitative and quantitative physical insights into the key processes that govern heat transfer in nonboiling twophase pipe flow. Hence, the following is a list of primary tasks for the overall study: Task 1: Literature search on twophase pipe flow for flow patterns, nonboiling heat transfer, pressure drop, and void fraction prediction methodologies, experimental methodologies, and experimental data. Task 2: Based on heat transfer correlations available in the literature, develop a general heat transfer correlation that has the robustness to handle all major flow patterns and upward inclination effects. Explore the viability of developing a correlation using momentum and heat transfer (Reynolds) analogy. Task 3: Collect experimental data for flow patterns, pressure drop, and heat transfer at different pipe inclinations (0, 2, 5, and 7°). Task 4: Analyze the characteristics of the key processes that govern heat transfer in nonboiling twophase pipe flow from the experimental data. Task 5: Validate the developed correlation(s) with available experimental data, from measurements and other sources in the literature. Task 6: Document and present the research findings in the forms of published papers and doctoral dissertation as deliverables. 12 1.4 Broader Impact The results of this research will provide a fundamental understanding of nonboiling twophase pipe flow and heat transfer. The database of experimental results for flow patterns, pressure drop, and heat transfer, will be a significant milestone in the road map of scientific understanding for twophase flow. Presently available computational fluid dynamics (CFD) codes are generally inadequate to predict the hydrodynamic and transport processes of twophase flow. Thus, a complete and well collected database will be very valuable for CFD codes developers who seek to validate their models with experimental data. The impact of the experimental database is summarized as follows: Flow pattern data: Flow pattern data can be used for the development and validation of methodologies for predicting twophase flow patterns, whether they are semiempirical methods, graphical methods, or numerical methods. Flow pattern data can also be used to provide input into heat transfer and pressure drop models, since flow patterns strongly influence all the hydrodynamic and transport processes. Pressure drop data: Pressure drop data will be useful in the development and validation of numerical models and pressure drop correlations. Pressure drop data can be useful in the design of twophase flow system, for example in estimating the pumping power. Heat transfer data: Heat transfer data can be used to facilitate the development and validation of numerical models and heat transfer correlations. In addition, the results of this research will serve as a bridge for the fundamental understanding of twophase flow from conventional sized pipes to miniaturized channels. 13 Presently, researchers are refining the method for distinguishing between macrochannel and microchannel twophase flow and heat transfer. A comprehensive understanding of twophase pipe flow from the proposed study will be useful for distinguishing the similarities and differences of hydrodynamic and transport process behaviors in conventional sized pipes and microchannels. 1.5 Brief Outline of this Study The contents of this manuscript are geared towards the elements that support this proposal to conduct an extensive and systematic study of heat transfer in nonboiling twophase gasliquid pipe flow. Chapter II is devoted to the review of selected literature about twophase flow in the areas of heat transfer, flow pattern maps, void fraction and the relationship of pressure drop and heat transfer. In Chapter III, the development of the twophase nonboiling correlations is discussed. Chapter IV focuses on the experimental setup and procedures used in this study. Chapter V discusses the experimental results. Chapter VI presents the validation of the correlations developed in Chapter III. Finally in Chapter VII, the summary and remaining work are laid out. 14 CHAPTER II LITERATURE REVIEW For several decades, numerous investigators have studied the hydrodynamic and transport processes of twophase gasliquid pipe flow. The works of various investigators available in the literature are discussed here. In this chapter, the literature review is categorized into four sections. Section 2.1 focuses on twophase flow heat transfer. In Section 2.2, selected literature on twophase flow patterns are discussed. In Section 2.3, the focus is on void fraction, and Section 2.4 is on the relationship of pressure drop and heat transfer. 2.1 TwoPhase Flow Heat Transfer Johnson and AbouSabe (1952) measured static pressure drop and heat transfer for twophase airwater flow in a horizontal brass tube. The tube has an inner diameter of 25.4 mm and a length of 4.57 m. The experiments were conducted in the flow rate ranges of 7.56 to 113 kg/min for water and 0 to 1.51 kg/min for air. For heat transfer measurements, the test section was heated with uniform wall temperature. For twophase flow with low air rates, Johnson and AbouSabe (1952) observed considerable increases in the heat transfer coefficients. Using the measured heat transfer data, they developed a 15 twophase flow heat transfer correlation for different flow patterns in horizontal tube. Most of the heat transfer data predicted by their correlation were within ±15% agreement with their measured data. The correlation developed by Johnson and AbouSabe (1952) is expressed as 2 0.333 1/ 2 1/ 2 ( ) 1 0.006Re L SG L L TP R h h φ + = − , (2.1) where L h can be determined using 0 8 0 4 0 023 . L . L SG Nu = . Re Pr . King (1952) investigated the characteristics of pressure drop and heat transfer for twophase flow of an airwater mixture in a horizontal copper pipe with an inner diameter of 18.7 mm. King (1952) also observed increases in the average heat transfer coefficients for twophase flow with low gas flow rates, as similarly observed by Johnson and Abou Sabe (1952). King (1952) improved the correlation proposed by Johnson and AbouSabe (1952), by adjusting the constant and exponents of the correlation. The correlation improved by King (1952) is expressed as 2 0.32 1/ 2 0.52 ( ) 1 0.025 L SG L L TP Re R h h φ + = − , (2.2) where L h can be determined using 0 8 0 4 0 023 . L . L SG Nu = . Re Pr . Fried (1954) extended the study of Johnson and AbouSabe (1952) and investigated the characteristics of pressure drop and heat transfer for airwater flow in a horizontal pipe with an inner diameter of 18.7 mm. The experiments were conducted for flow rate ranges of 7.57 to 98.4 kg/min for water and 0.0693 to 1.56 kg/min for air. The 16 heat transfer measurements were conducted with uniform pipe wall temperature. The heat transfer data measured by Fried (1954) were correlated within ±30%. Johnson (1955) extended the work of Johnson and AbouSabe (1952) and measured pressure drop and heat transfer for twophase flow of airoil mixture in a steamheated horizontal pipe. The measurements by Johnson (1955) were conducted with the same experimental apparatus used by Johnson and AbouSabe (1952). Based on the measured results, Johnson (1955) observed that the heat transfer for airoil flow was significantly greater than that for airwater flow. Groothuis and Hendal (1959) measured heat transfer for airwater and airgasoil flows. The authors observed that the introduction of small amount of air at low liquid flow rates caused an increase in heat transfer rate, which was similarly observed by Johnson and AbouSabe (1952) as well as King (1952). The correlation developed by Groothuis and Hendal (1959) is expressed as 0.87 1/3 0.14 0.029 ( / ) TP TP L B W Nu = Re Pr μ μ , (2.3) for airwater flow, and 0.39 1/3 0.14 2.6 ( / ) TP TP L B W Nu = Re Pr μ μ , (2.4) for airgasoil flow. Knott et al. (1959) measured the heat transfer rate of twophase mixture of nitrogen gas and viscous oil. The measurements were conducted with uniform heat flux. In the bubbly region, the authors attributed the increase in the twophase heat transfer coefficient to the addition of gas phase, which effectively increased the mean velocity of the mixture. Based on their observations of the experimental results, they proposed a correlation for twophase heat transfer coefficient: 17 1/ 3 1 = + SL SG L TP u u h h , (2.5) where L h is determined from Sieder and Tate (1936) equation. Davis and David (1964) used a slip model to empirically correlate the convective heat transfer in the regions of annular and annularmist flow. The authors empirically determined that the slip ratio (uG / uL) to be a function of the gasliquid density ratio (ρG / ρL). From the slip model, the following correlation was developed: 0.4 0.28 0.87 0.060 L G L L TP Pr DGx Nu = ρ μ ρ . (2.6) Using the proposed correlation, the authors showed that experimental data were correlated generally to within an averaged absolute error of 17% for vapor mass fraction above 10%. Oliver and Wright (1964) experimentally studied gasliquid slug flow in horizontal tubes with a common inner diameter of 12.7 mm for two different tube lengths (1.22 and 1.31 m). The shorter tube was used for pressure drop measurements, while the longer tube was for heat transfer measurements. The study was conducted with both Newtonian and nonNewtonian fluids. The authors observed higher heat transfer in twophase slug flow in comparison with singlephase flow. The authors also observed the maximum heat transfer occurred when the liquid holdup was between 0.3 and 0.5. When developing their correlation, Oliver and Wright (1964) employed two assumptions: (1) the slug flow was ideal, in which both gas and liquid phases moved substantially at the same velocity, and (2) the liquid phase was the dominant phase in affecting both flow and heat transfer characteristics, while the gas phase remained an inert medium. The heat 18 transfer correlation for Newtonian fluids proposed by Oliver and Wright (1964) is expressed as = − L L TP L R R Nu Nu 1.2 0.2 0.36 , (2.7) where L Nu is determined by 1/3 0.14 ( ) 615 . 1 + = W B L G L L L D Pr A Q Q D Nu μ μ μ ρ . Hughmark (1965) proposed two heat transfer correlations for gasliquid slug flow in horizontal pipes: one for turbulent slug flow and another for laminar slug flow. The correlation for turbulent slug flow was developed from the momentumheat transfer analogy, where the friction factor was determined from measured pressure drop. The correlation for turbulent slug flow covered the liquid slug Reynolds number range from 26000 to 4.5×106. For laminar slug flow, Hughmark (1965) proposed the following correlation: 1/ 3 0.14 0.5 75 . 1 = − W B L L L L TP L R k L m c Nu R μ & μ . (2.8) When compared with the experimental results documented by Oliver and Wright (1964), the correlation for laminar slug flow predicted the experimental data with a mean absolute deviation of 8.4%. For laminar flow, the range of liquid slug Reynolds number was from 1600 to 4600. Pletcher and McManus (1968) measured pressure drop and heat transfer coefficient for horizontal airwater annular flow in a tube with an inner diameter of 25.4 mm. The test section had a length of 1.52 m and was heated electrically. The heated test section was located 2.67 m downstream of the liquid injection. Measurements were 19 conducted for water flow rate varied from 1.94 to 10.4 kg/min, air flow rate varied from 0.816 to 7.00 kg/min, and heat flux between 23.3 and 40.3 kW/m2. Significant circumferential variations of tube wall temperatures at low air flow rates were observed. In addition, the authors found that the measured pressure drop agreed relatively well with the Lockhart and Martinelli (1949) correlation, and the measured heat transfer coefficients correlated well with the ( )0.4 G L X m& m& term to within ±20%. Martin and Sims (1971) studied the forced convection heat transfer to water and airwater mixtures in a horizontal rectangular channel with air injected through a porous heated wall. They defined the main dependent variables in their study as heat transfer coefficient and flow pattern, while the main independent variables were the air injection rate through the porous heated wall and both superficial velocities of gas and liquid. With no air injection through the porous heated wall, the authors observed increase in heat transfer coefficient with increasing superficial gas velocity. The heat transfer correlation proposed by Martin and Sims (1971) for the case when the air injection rate through the porous heated wall was zero is expressed as 1/ 2 64 . 0 1 = + SL SG L TP u u h h (2.9) where L h is determined by the Sieder and Tate (1936) equation. The correlation predicted 88% of the measured data within ±20%. It should be noted that this study was conducted with rectangular channel, and the authors stated that their work was incomparable with the data for round tubes. Shah (1981) presented correlations for estimating heat transfer of permanent gasliquid mixtures in horizontal and vertical channels (both circular and noncircular). The 20 correlations showed good agreement with 672 heat transfer data points from various experimental studies. The various experimental studies compiled by Shah (1981) included a range of channel hydrodynamic diameter (4 to 70 mm), 10 gasliquid combinations, and a wide range of heat and mass flux. The comparisons between the correlations and experimental data had a rootmeansquare error of 15.5%, and 96% of the data points were predicted to within ±30%. The correlation of Shah (1981) for ReSL < 170 is expressed as 1/ 4 1 = + SL SG L TP u u h h , (for <170 SL Re ) (2.10) where L h is determined from 1/3 0.14 1.86[ ( )] ( ) L SL L B W Nu = Re Pr D L μ μ . For ReSL > 170, the author presented the correlations graphically, stating that they were “too complex to be expressed mathematically.” The correlations presented graphically are difficult to use as general purpose correlations, and the results estimated by the correlations are difficult to replicate. Shoham et al. (1982) performed measurements of heat transfer characteristics for twophase gasliquid slug flow in a horizontal pipe. The heated test section was made of a brass pipe with an inner diameter of 38.1 mm. With a length to diameter ratio (L/D) of 46.2, the heated test section was heated electrically. By attaching thermocouples circumferentially around the test section, local heat transfer coefficients were measured. The measurements were performed with water flow rate range from 27.2 to 96.1 kg/min and air flow rate range from 0.136 to 0.653 kg/min. Shoham et al. (1982) observed that heat transfer coefficients at the bottom of the pipe were consistently higher than those at the top of the pipe, by as much as a factor of 2. They also observed that in the regions 21 where gas phase was in contact with the pipe surface, the heat transfer coefficients dropped to very low values. This finding supports the assumption of Oliver and Wright (1964) that the liquid phase was the dominant phase in affecting heat transfer characteristics. The ratio of bottom to top heat transfer coefficient (hTP, btm / hTP, top) was lower at high liquid and low gas flow rates. At a fixed liquid flow rate, hTP, btm / hTP, top increased with increasing gas flow rate. Kago et al. (1986) experimentally investigated flow characteristics (pressure drop and liquid holdup) and heat transfer coefficient in a horizontal pipe with an inner diameter of 51.5 mm. With a length to diameter ratio (L/D) of 9.5, the heated section was made of copper pipe and it was heated electrically. The measurements were conducted for plug and slug flow patterns, and the viscosity of the liquid phase was varied from 0.8 to 55 mPa·s. The gasliquid mixture was made of air being mixed with water or aqueous solutions of carboxymethyl cellulose, for the purpose of controlling the liquid phase viscosity in the system. The authors reported that their pressure drop measurements agreed qualitatively with the study of Baker (1954). When compared with the Lockhart and Martinelli (1949) correlation, they showed that the correlation overpredicted their measured pressure drop data. Heat transfer coefficient was observed to increase with increasing liquid velocity and decreasing liquid viscosity. In addition, Kago et al. (1986) reported that the heat transfer coefficient was nearly independent of the gas velocity when uSG < 1 m/s. However, the heat transfer coefficient increased with increasing gas velocity for 1 < SG u < 10 m/s. From the experimental results, Kago et al. (1986) developed a heat transfer correlation for 3×102 < ReSL < 3×105, and it is expressed as 22 (0.021Re 4.5) Pr {1 0.3exp[ 0.5( 2) ]} 2 0.14 0.8 1/ 3 + − − = + L W L B TP L L Nu Fr μ μ , (2.11) where 1/ 2 Re = −L L SL L L R Du μ ρ and gD u Fr SL L = . Deshpande et al. (1991) performed heat transfer measurements for airwater plugslug flow in horizontal pipes with two different inner diameters (25.4 and 56.9 mm). The stainless steel test section was 1.7 m long and heated electrically. The measurements were conducted with water velocity ranged from 0.2 to 1.1 m/s and the air velocity was adjusted to as high as 3.6 m/s. According to this study, the twophase mixture velocity and slug frequency were two important factors that influenced the heat transfer coefficient at the top of the pipe (hTP, top). Deshpande et al. (1991) also observed that the heat transfer coefficients at the bottom of the pipe (hTP, btm) were always greater than those at the top of the pipe (hTP, top), which was similar to the finding of Shoham et al. (1982). In addition, they observed that as the superficial liquid velocity (uSL) increased, the (hTP, top / hTP, btm) ratio decreased due to increase in slug frequency. The authors presented correlations to estimate hTP, top, hTP, btm, and hTP, avg. When compared with the experimental data, 93.5% of the data points for hTP, btm and hTP, avg were within ±10% agreement, while 90% the data points for hTP, top were within ±15% agreement. The correlations developed by Deshpande et al. (1991) for hTP, top, hTP, btm, and hTP, avg are expressed as 0.3 0.83 0.4 , 1 . 0 Pr Re 023 . 0 = − m SL TP btm L L u u Nu , (2.12) 23 0.21 0.53 0.44 0.4 , Pr Re 93 . 1 = g u u u Nu SL m SL TP top m m ν , (2.13) 0.76 0.83 0.4 , Pr Re 023 . 0 = m SL TP avg m m u u Nu , (2.14) where L m L L Du Re μ ρ = , m m m m Du Re μ ρ = , m SL SG u = u + u , and 1 02 2 2 02 0 0434 . m m SL gD u D . u u . + ν = . Hetsroni et al. (1998a, b) investigated the heat transfer of plug flow for airwater mixture in horizontal and slightly inclined (2 and 5°) tube. The tube wall was heated electrically and the thermal profiles were observed using infrared thermographs. The heated test section had an inner diameter of 49.2 mm and a length to diameter ratio (L/D) of 3.6. Thermographs were obtained at axial locations of x/D = 0.45, 0.9, and 2.4. According to the authors’ analysis, superficial liquid velocity (uSL), bubble length (Lb), bubble velocity (ub), and bubble frequency (fb) were the main parameters that influenced heat transfer coefficient at the upper part of the tube. They also observed that the heat transfer coefficient for inclined tube to be much higher than that in horizontal tube. The heat transfer correlation proposed by Hetsroni et al. (1998a, b) is expressed as ϕ < 0.3 TP TP L h = 0.15(h ) + 0.85h ϕ , for 0.9 Fr 2.0 L < < 0.03 Fr 0.43 G < < (2.15) where ϕ ( ) TP h and L h are determined using 24 = + − b b b TP L L u f L (h ) h 0.40 0.54Fr exp 1.2 ϕ , 0 83 0 5 0 0155 . L . L L Nu = . Re Pr . Kim et al. (1999) conducted an extensive survey of twophase flow heat transfer correlations and experimental data that were available in the literature. In this survey, the authors identified 20 heat transfer correlations and seven sets of experimental data. The main purpose of this study was to check the validity of the correlations available in the literature. Table 1 shows the sources of the seven experimental data sets used by Kim et al. (1999) in their study. Table 2 shows the 20 correlations identified in the study. Among the correlations and experimental data identified by Kim et al. (1999), there were only six correlations and two sets of experimental data applicable for horizontal flow. The rest of the correlations and experimental data sets were for vertical flow. In addition, correlations for horizontal flow were mainly applicable to specific flow patterns. Kim et al. (1999) found no correlation and experimental data set that were applicable for inclined flow. Table 1. Experimental data sets used in the study by Kim et al. (1999) Source Orientation Fluids No. of data points Aggour (1978) Vertical Heliumwater 53 Aggour (1978) Vertical R12water 44 Vijay (1978) Vertical Airwater 139 Vijay (1978) Vertical Airglycerin 57 Rezkallah (1987) Vertical Airsilicone 162 King (1952) Horizontal Airwater 48 Pletcher (1966) Horizontal Airwater 21 25 Table 2. Heat transfer correlations chosen in the study by Kim et al. (1999) 26 Table 2. (continued) 27 Kaminsky (1999) surveyed the literature and proposed correlations for estimating twophase heat transfer coefficient in horizontal and vertical pipes. According to this study, the experimental data that were available in the literature were largely limited to pipes with small diameters, low operating pressures, and airwater systems. For laminar flow (ReSL < 2100), Kaminsky (1999) proposed a heat transfer correlation, which was a function of liquid holdup. The correlation is expressed as 1 3 , (R D / D) R h h L h L L L TP β = , for < 2100 SL Re (laminar) (2.16) For turbulent flow (ReSL > 2100), the author proposed a correlation that was derived from the momentumheat transfer analogy. A parameter called the circumference fraction (S) was also introduced to the correlation. The correlation for turbulent flow is expressed as 1/ 2 S h h L L TP =φ , for > 2100 SL Re (turbulent) (2.17) where L h is determined by the Sieder and Tate (1936) equation. When compared with experimental data, the results predicted by the correlation showed significant deviations for some of the horizontal flow cases. The author stated that the deviations were the results of having assumed S = 1 and large viscosity divergence between the viscosities evaluated at the bulk and at the pipe wall temperatures. In addition, there were very limited data for horizontal twophase flow, especially for the laminar flow (ReSL < 2100). Kim and Ghajar (2002) performed measurements of heat transfer coefficients for different flow patterns in a horizontal pipe. A total of 150 twophase flow heat transfer data points for various flow patterns were measured under uniform heat flux condition. The measurements were collected for superficial liquid Reynolds number ranged from 640 to 35500 and superficial gas Reynolds number ranged from 40 to 21200. 28 Based on the experimental data, Kim and Ghajar (2002) developed a correlation for the overall heat transfer coefficient of twophase flow with different flow patterns in a horizontal pipe. The correlation developed by Kim and Ghajar (2002) is expressed as q L G p L G m n L TP x x C h h − − = + − μ μ α α α Pr Pr 1 1 1 (1 ) , (2.18) for slug and slug transition flow C = 2.86 , m = 0.42 , n = 0.35 , p = 0.66, and q = −0.72 for wavyannular flow C = 1.58 , m = 1.40 , n = 0.54 , p = −1.93, and q = −0.09 for wavy flow C = 27.89 , m = 3.10 , n = −4.44 , p = −9.65, and q = 1.56 where L h is determined by the Sieder and Tate (1936) equation. The proposed correlation predicted the experimental data with a rootmeansquare error of 12%. However, the correlation did not cover all observed flow patterns, such as stratified flow, annular flow, and bubbly flow. Ghajar and Kim (2005) developed a general heat transfer correlation based on the work by Kim et al. (2000). The correlation was validated with 408 experimental data points for 0°, 2°, 5°, and 7° inclinations over a wide range of flow patterns. To handle the effects of various flow patterns and inclination angles on the twophase heat transfer data with only one correlation, the flow pattern factor (FP) and the inclination factor (I) were developed. The correlation successfully predicted 90% of the experimental data within ±20%. At the current state of knowledge, the correlation developed by Ghajar and Kim (2005) may be considered the most robust in terms of handling various inclination and flow pattern effects. However, the correlation has not been validated for inclination angles above 7°. The correlation developed by Ghajar and Kim (2005) is expressed as = + TP P L h F h 1 where L h is determined by the Sieder and Tate (1936) equation. Hewitt and Roberts (1969) commonly recommended for flow pattern map, the vertical axis represented the superficial gas momentum flux and the horizontal axis represented the superfi Roberts (1969) map perform Figure 3. Flow map for vertical flow by Hewitt and Roberts (1969) 29 ( ) − − r q L G p L G n P P m I Pr Pr F F x x C μ 1 μ 1 2.2 TwoPhase Flow Pattern Maps introduced a flow pattern map twophase upward vertical flow (see Figure superficial liquid momentum flux. performed reasonably well for airwater and steamwater (2.19) that has been 3). On their . The Hewitt and flows. Taitel and Dukler transition boundaries of flow. Five dimensionless parameters were introduced to characterize the flow pattern boundaries. The theoretical flow patterns transi The five dimensionless parameters used in the SG Dg cos u F θ = 1 2 SL K = F Re , ( ( ) − ∂ ∂ = ρ ρ p z T L G ( ) ( ) ∂ ∂ ∂ ∂ = f , f , p z p z X ( ) ( ) L G p z g Y ∂ ∂ − = ρ ρ Figure 4. Flow map for horizontal 30 (1976) developed a comprehensive model five flow patterns in horizontal and near horizontal gas transition boundaries are shown in Taitel and Dukler (1976) map are given as L G G ρ ρ ρ − , ) 1 2 g cosθ SL , 1 2 SG SL , SG sinθ . and near horizontal flow by Taitel and mprehensive for determining gasliquid tion Figure 4. (2.20) (2.21) (2.22) (2.23) (2.24) Dukler (1976) Weisman et al. (1979) cm) and fluid properties patterns in horizontal pipes (see Figure 5) in terms of dimensionless correlations water flow, ϕ1 and ϕ2 are Figure 5. Flow map for horizontal 31 investigated the influences of pipe diameters (viscosity, density, and surface tension) on two pipes. From their flow pattern data, an overall fl ) uSG / ϕ1 and uSL / ϕ2 was established. Both for predicting the transition boundaries. For the case of air 1.0. airwater flow by Weisman et al (1.27 to 5.08 twophase flow flow pattern map ϕ1 and ϕ2 are airet al. (1979) Spedding and Nguyen (1980) flow data, for vertically downward horizontal flow showed the regions of slug flow, droplet flow, flow patterns within the main fl Figure 6. Flow map for horizontal flow by 32 provided flow pattern maps, based on to vertically upward flow. Their flow four main flow patterns (stratified fl and mixed flow). In additional, there were 13 flow patterns (see Figure 6). Spedding and Nguyen airwater w pattern map for flow, bubble and subdivisions of (1980) 33 2.3 Void Fraction Dukler et al. (1964) compared three void fraction correlations (Lockhart & Martinelli, 1949; Hoogendoorn, 1959; and Hughmark, 1962) with 706 refined void fraction data collected by Hogendoorn (1959). The 706 void fraction data of Hogendoorn (1959) were collected from test runs in 24.5, 50.8, 88.9, and 139.7 mm (1, 2, 3½ and 5½ in.) diameter pipes for horizontal flows. Using statistical methods, Dukler et al. (1964) concluded that the Hughmark (1962) correlation was able to perform better than the other two. Chisholm (1973) developed equations for determining void fraction (α ) and slip ratio ( K ). The equations can be expressed as 1 2 1 1 1 − − = + L G / m L x x ρ ρ ρ ρ α , (2.25) and 1 2 = m L K ρ ρ , (2.26) where m ρ is the homogeneous mixture density and is defined as m L G x x ρ ρ ρ + − = 1 1 . (2.27) Marcano (1973) compared six void fraction correlations (Lockhart & Martinelli, 1949; Hughmark, 1962; Dukler et al., 1969; Eaton et al., 1967; Guzhov et al., 1967; and Beggs, 1972) with 238 natural gaswater data from Eaton (1966) and 58 airwater data from Beggs (1972). Marcano (1973) concluded that the Eaton et al. (1967) and Beggs (1972) correlations performed well due to the fact that the data used for comparison were 34 the data from which these correlations are developed. The correlations of Dukler et al. (1969) and Lockhart and Martinelli (1949) were found to perform satisfactorily, while the other correlations performed unsatisfactorily. In addition, the correlations by Eaton et al. (1967), Guzhov et al. (1967), and Beggs (1972) were found to have better performance for void fraction less than 0.65. For void fraction greater than 0.9, none of the six correlations gave reasonable accuracy. Palmer (1975) compared three void fraction correlations (Flanigan, 1958; Guzhov et al., 1967; and Beggs, 1972) with 174 natural gaswater data. The 174 experimental data were collected from a 50.8 mm (2 in.) diameter pipe with three (4.2, 7.1 and 7.5°) uphill and three downhill (3.8, 4.3 and 6.3°) orientations. Palmer (1975) concluded that the correlation by Beggs (1972) performed well for uphill flow, and the correlation by Flanigan (1958) was the least accurate among the three. Butterworth (1975) summarized some of the well known empirical equations for void fraction (α ) and slip ratio ( K ) having the following forms: r G L q L G P x x C − = − μ μ ρ ρ α 1 α 1 , (2.28) and r G L q L G p L G x x C V V K − = = − − μ μ ρ ρ 1 1 1 . (2.29) The values of C, p, q, and r for the different correlations are given in Table 3: 35 Table 3. Values of constants suggested for the various models and correlations summarized by Butterworth (1975) Model or Correlation C p q r Homogeneous Model 1 1 1 0 Zivi (1964) model 1 1 0.67 0 Turner & Wallis (1965) model 1 0.72 0.40 0.08 Lockhart & Martinelli (1949) correlation 0.28 0.64 0.36 0.07 Thom (1964) correlation 1 1 0.89 0.18 Baroczy (1966) correlation 1 0.74 0.65 0.13 Mandhane et al. (1975) compared twelve void fraction correlations (Lockhart & Martinelli, 1949; Hoogendoorn, 1959; Levy, 1960; Hughmark, 1962; Scott, 1962; Hughmark, 1965; Eaton et al., 1967; Guzhov et al., 1967; Chawla, 1969; Dukler et al., 1969; Beggs, 1972; and Agrawal et al., 1973) using 2700 void fraction data collected at the University of Calgary. Comparing the twelve correlations with the flow pattern maps by Baker (1954), Hoogendoorn (1959), Govier and Aziz (1972), and Mandhane et al. (1974), it was concluded that the correlation by Hughmark (1962) predicted the bubble, elongated bubble flow in all the four flow pattern maps and the slug flow in all but the flow pattern map by Baker (1954). The Agrawal et al. (1973) correlation predicted the stratified flow in the Mandhane et al. (1974) and Baker (1954) flow pattern maps, while the Dukler et al. (1964) correlation predicted those of Hoogendoorn (1959) and Govier and Aziz (1972). The Beggs (1972) correlation predicted the dispersedbubble flow in the flow pattern maps by Mandhane et al. (1975), while the Hughmark (1962) correlation predicted those of Hoogendoorn (1959) and Govier and Aziz (1972). Mandhane et al. 36 (1975) concluded that none of the twelve correlations was able to give satisfactory prediction in the annular and annularmist flow. Papathanassiou (1983) came up with a void fraction spectrum graph by deducing the physically realistic range within which twophase flow exists for a set of operating conditions and specified fluid. The void fraction spectrum graph was used to compare four void fraction correlations (Lockhart & Martinelli, 1949; Hoogendoorn, 1959; Bankoff, 1960; and Hughmark, 1962). Papathanassiou (1983) concluded that at void fraction about 0.4, the Lockhart and Martinelli (1949) correlation was out of the physically realistic range. At void fraction of greater than 0.7, the correlation by Bankoff (1960) was found to be outside the realistic region. The disagreement between the void fraction correlations in the lower and upper extreme ranges of void fraction is explained by the fact that few experimental results at this range exist when the correlations were developed. Abdulmajeed (1996) collected 88 airkerosene void fraction data in a horizontal 50.8 mm (2 in.) diameter pipe and compared the data with 15 void fraction correlations. The 88 void fraction data were used in an effort to simplify the mechanistic model of Taitel and Dukler (1976) and develop a new void fraction correlation. The void fraction correlation developed by Abdulmajeed (1996) was able to predict void fraction in stratified, slug and annular flow, in contrast to the implicit Taitel and Dukler (1976) model which was specifically developed for stratified flow. Spedding (1997) extensively compared over 100 void fraction correlations with the experimental data collected by Spedding and his coworkers (1976, 1979, 1989, 1991, and 1993) for pipe diameters ranging from 26 to 95.3 mm. Spedding (1997) noted that no 37 single correlation could satisfactorily handle all flow regimes and angles of inclination. Different void fraction correlations were recommended specifically for various flow patterns and pipe orientations. Woldesemayat and Ghajar (2007) conducted a comprehensive review of 68 void fraction correlations and 2845 experimental data points for horizontal and upward inclined twophase pipe flow from various sources. Based on the findings of this extensive review, Woldesemayat and Ghajar (2007) recommended a general void fraction correlation that predicted 85.6% of the 2845 experimental data points within ±15%. The general void fraction correlation recommended by Woldesemayat and Ghajar (2007) will be validated with our experimental setup. 38 2.4 Relationship of Pressure Drop and Heat Transfer Several investigators have attempted to correlate pressure drop and heat transfer for twophase pipe flow. In this section, selected literature which documented the effort of relating pressure drop with heat transfer are considered. The parameters regularly found in the literature relating pressure drop with heat transfer are in the following forms: The twophase multipliers defined by Lockhart and Martinelli (1949) are expressed as f SL f TP L p z p z , 2 , ( ) ( ) ∂ ∂ ∂ ∂ φ = , (2.30) and f SG f TP G p z p z , 2 , ( ) ( ) ∂ ∂ ∂ ∂ φ = . (2.31) The Martinelli parameter is expressed as f SG f SL p z p z X , 2 , ( ) ( ) ∂ ∂ ∂ ∂ = . (2.32) The ratio of the twophase flow heat transfer coefficient ( TP h ) to the single phase liquid flow heat transfer coefficient ( L h ) is expressed as TP L h / h ψ 2 = . (2.33) Johnson and AbouSabe (1952) stated in their study that even though their pressure drop results were within ±30% agreement with the analysis of Lockhart and Martinelli (1949), there were significant secondary flow effects that they observed that were not accounted for by Lockhart and Martinelli (1949). Johnson and AbouSabe (1952) did not give clear explanations for the secondary flow effects, and suggested that 39 the flow patterns play a significant role. Johnson and AbouSabe (1952) correlated their experimental data for 2 2 L ψ φ versus X to within ±20%. King (1952) showed that with appropriate correction to allow for the change of momentum of the fluids, one could correlate the twophase nonisothermal pressure drop with heat transfer coefficient by means of the Martinelli parameter ( X ). King (1952) also proposed that 2 2 / L ψ φ as a function of X as a good correlation, which was very similar to the approach presented by Johnson and AbouSabe (1952). Fried (1954) extended the work of Johnson and AbouSabe (1952) and showed that the Martinelli correlation was in well agreement with his isothermal pressure drop data. Fried (1954) also found that the nonisothermal pressure drop was greater than the isothermal by as much as 55%. It was suggested that the difference was due to the change in kinetic energy. After compensating for the change in kinetic energy in the phases, Fried (1954) concluded that the Martinelli correlation was still applicable for nonisothermal flow. However, the compensation method that he used was not specified. Johnson (1955) also extended the work of Johnson and AbouSabe (1952) and measured heat transfer and static pressure drop for twophase twocomponent flow in a horizontal pipe. The pipe was made of copper and it was heated by steam. Correlations for heat transfer and nonisothermal pressure drop were compared with results from airoil and airwater flows. Hughmark (1965) used the analogy of momentumheat transfer (Reynolds analogy) to develop a heat transfer correlation for twophase turbulent slug flow in horizontal pipe. Using a very similar manner as the Reynolds analogy for single phase flow, the twophase flow heat transfer coefficient and the friction factor were related. The 40 correlation was tested with the experimental data from Johnson and AbouSabe (1952) and Johnson (1955). However, the size of the data was limited and the accuracy of the correlation was inconclusive. Pletcher and McManus (1968) found that for airwater annular flow in a horizontal tube, there was no significant difference between the nonisothermal pressure drop and the isothermal pressure drop. The experimental data were correlated by plotting TP L h /φ versus X and TP L h /φ versus 0.4 ( / ) G L X m& m& . The agreement between the measured and correlated data was within ±20%. Vijay et al. (1982) correlated the twophase flow heat transfer in a vertical tube by adopting and modifying the correlation for horizontal flow developed by Fried (1954). The correlation presented was expressed in a general form as q SL p TP L h / h C( ) Re ψ 2 = = φ 2 , (2.34) where C, p, and q are adjustable constants to address flow characteristics such as flow pattern. Vijay et al. (1982) tested the correlation with various flow patterns in vertical flow and found that C = 1.148, p = 0.454, and q = −0.020 would give a rootmeansquare deviation of 18%. Kaminsky (1999) developed a correlation for twophase flow heat transfer based on the momentum and heat transfer analogy. The correlation for > 2100 SL Re is expressed as TP L L ψ 2 h h S1/ 2φ = / = , (2.35) where the circumference fraction (S) was given as S =1 for all flow patterns (vertical) and slug and annular flows (horizontal), 41 1−α = S −sin(2π S) 2π for stratified flow (horizontal). It was reported that the correlation predicted the experimental data from various sources to within ±33%. 2.5 Chapter Summary Throughout this chapter, the literature on twophase heat transfer, flow pattern maps, void fractions, and the relationship of pressure drop and heat transfer are discussed. After reviewing the literature, it is clear that heat transfer data for twophase flow are limited, especially with the effects of inclination. Likewise, flow pattern maps for inclined twophase flow are virtually nonexistence. Although, there are many correlations and experimental data on void fraction available in the literature, it should be noted that very few studies have been reported whereby the investigators combined study of heat transfer, flow patterns, void fraction, and pressure drop in their work. 42 CHAPTER III DEVELOPMENT OF NONBOILING TWOPHASE HEAT TRANSFER CORRELATIONS In the preceding chapter, several nonboiling twophase heat transfer correlations available in the literature have been surveyed. From those correlations, common parameters were indentified and used for the development of two nonboiling twophase heat transfer correlations in this study. In this chapter, the development of two nonboiling twophase heat transfer correlations is discussed. The first correlation, which is referred to as a general nonboiling twophase heat transfer correlation, was developed based on the variables that influence the heat transfer in twophase pipe flow. The second correlation, which is referred to as a Reynolds analogy twophase heat transfer correlation, was developed based on the analogy of momentum and heat transfer. 3.1 Development of a General NonBoiling TwoPhase Heat Transfer Correlation The development of a general nonboiling twophase heat transfer correlation can be approached in a similar manner used for developing heat transfer correlation for single phase flow. For steadystate incompressible single phase flow in a pipe, the variables that 43 influence the heat transfer are k, c, u, ρ, μ, and D. With three reference dimensions (mass, length, and time), according to Buckingham pi theorem three dimensionless parameters can be defined: Nu = hD k , (3.1) Re = uρD μ , (3.2) and Pr = cμ k . (3.3) From the above three dimensionless parameters, the Nusselt number and its functional dependence can be expressed as Nu = f (Re,Pr). (3.4) Based on the functional expression for Nusselt number expressed in Eq. (3.4), an empirical correlation can be represented as a b CRe Pr k hD Nu = = or a b h = CRe Pr (3.5) where a, b, and C are constants to be determined from experimental data. In nonboiling twophase pipe flow, assuming incompressible phases, the twophase heat transfer is influenced by the phasic heat transfer coefficients: TP L G h C h C h 1 2 = + or L G L TP h h C C C h h 1 2 1 = 1+ . (3.6) Using the expression represented in Eq. (3.5), the above equation can be written as 44 b L G a SL SG L TP Pr Pr Re Re C C C h h = + 1 2 1 1 . (3.7) Substituting the definitions of superficial gas and liquid Reynolds numbers (ReSG and ReSL) into Eq. (3.7) yields b L G a SL L L SG G G L TP Pr Pr u D u D C C C h h = + ρ μ ρ μ 1 2 1 1 . (3.8) Also, using the definition of the mass flow rate for the gas and liquid phases, m u A G SG G & = ρ and m u A L SL L & = ρ , the following expression is obtained: x x u u m m SL L SG G L G − = = ρ 1 ρ & & . (3.9) Substituting Eq. (3.9) into Eq. (3.8) and rearranging yields d G L b L G a L TP Pr Pr x x C C C h h − = + μ μ 1 1 1 2 1 or − = + d G L b L G a TP L Pr Pr x x C C h C h μ μ 1 1 1 2 1 . (3.10) Equation (3.10) is an unrefined expression of the nonboiling twophase heat transfer correlation. In order to refine the nonboiling twophase heat transfer correlation, such that it is suitable for predicting heat transfer coefficients of flow with various flow patterns and pipe inclinations, additional parameters need to be introduced to Eq. (3.10). 45 3.2 Flow Pattern Factor and Inclination Factor Flow Pattern Factor In twophase flow, flow patterns play an important role and influence the hydrodynamics, which in turn influence the thermal aspect of the flow. For the twophase heat transfer correlation to effectively address the influence of flow patterns on the heat transfer coefficients, a parameter to represent the flow patterns need to be introduced. Taitel and Dukler (1976) developed a comprehensive model for describing transitions of flow patterns. In the model developed by Taitel and Dukler (1976), the transition boundary between the stratified and intermittent (slug, plug, and semislug flows) or annulardispersed regions can be represented in terms of a flow pattern map with a modified Froude number (F) versus the Martinelli parameter (X), see Figure 4 (p. 30). The modified Froude number (F) introduced by Taitel and Dukler (1976) can be expressed as ρ ρ θ ρ Dg cos u F G L G G − = or (ρ ρ ) θ ρ cos 2 L G G G Dg u F − = . (3.11) The introduction of the modified Froude number (F) by Taitel and Dukler (1976) as one of the parameters representing the transition boundary between flow pattern regions indicated that inertia and gravitational forces have significant influence on flow pattern transitions. When developing a parameter to represent the flow patterns in their twophase heat transfer correlation, Kim and Ghajar (2006) introduced the flow pattern factor, 2 , = D S F L eff P π . (3.12) 46 The flow pattern factor ( P F ) was represented as the square ratio of the effective wettedperimeter ( L eff S , ) to the circumference of a circular pipe (see Figure 7). Based on the Eq. (3.12), the flow pattern factor ( P F ) gives value approaching unity for flow pattern (e.g. plug or annular) that has effective wettedperimeter approximately the circumference of the pipe. With void fraction, inertia and gravitational forces as factors that influence flow patterns, the flow pattern factor can be expressed as α 2α (1 ) P S F = − + F . (3.13) The shape factor ( S F ), appears in Eq. (3.13), is in essence a normalized and modified Froude number: − − = − ( ) ( ) tan 2 2 1 L G G G L S g D u u F ρ ρ ρ π . (3.14) The shape factor ( S F ), is applicable for slip ratios (= ) ≥1 G L K u u , which is common in gasliquid flow, and represents the shape changes of the gasliquid interface by the force acting on the interface due to the relative momentum and gravity forces. Figure 7. Gasliquid interface and wettedperimeter (from Kim and Ghajar, 2006) 47 In vertical twophase flow, the effective wettedperimeter ( L eff S , ) is typically the circumference of the pipe (see Figure 2, p. 9). For a vertical pipe, the cosθ term in Eq. (3.14) is zero, rendering the shape factor ( S F ) as unity, and thus the flow pattern factor ( P F ) in Eq. (3.13) is unity as well. According to Eq. (3.12), the flow pattern factor ( P F ) is unity when the effective wettedperimeter ( L eff S , ) is equal to the circumference of the pipe. Also, in single phase liquid flow, the flow pattern factor ( P F ) is unity, since the void fraction is zero. Inclination Factor Ghajar and Kim (2005) proposed a parameter called the inclination factor ( I ) to account for the influence of inclination on twophase heat transfer coefficient. Due to the density difference between gas and liquid, the liquid phase is much more affected by the inclination effects. In inclined pipes, the inclination factor ( I ) proposed by Ghajar and Kim (2005) takes into account the gravitational and liquid inertia forces, which is expressed as 2 ( )sin 1 L SL L G u gD I ρ ρ −ρ θ = + . (3.15) When used with the twophase heat transfer correlation [see Eq. (2.19)], the inclination factor [see Eq. (3.15)] has contributed favorably to the heat transfer correlation to accurately predict experimental data (all data points within ±30%) for slightly inclined flow (2°, 5°, and 7°) with ReSL > 2000 (Ghajar and Kim, 2005; Tang and Ghajar, 2007) However, for flow in slightly inclined pipe and ReSL < 2000, the twophase heat transfer correlation [see Eq. (2.19)] along with the inclination factor [see Eq. (3.15)] 48 only predicted 75% of the experimental data points to within ±30% (Tang and Ghajar, 2007). Upon revisiting the twophase heat transfer correlation, Eq. (2.19), along with the equation for inclination factor, Eq. (3.15), Ghajar and Tang (2008a) realized that the correlation has not accounted for the surface tension force. Surface tension is a variable that can affect the hydrodynamics of gasliquid twophase flow, especially for cases with low liquid inertia force (low ReSL). For low liquid inertia twophase flow, as the balance between the inertia and gravitational forces change and rebalance, surface tension force plays an important role in the behavior of the gasliquid interface (Ghajar and Tang, 2008b; Ghajar and Tang, 2009; Ghajar and Tang, 2010). Rather than using Eq. (3.15) to represent the inclination factor, which has not accounted for surface tension force, it is sensible to include the surface tension when expressing the inclination factor. Although liquid inertia force is extremely important in twophase pipe flows, it has been accounted for during the development of the twophase heat transfer correlation (see Section 3.1). Taking the surface tension force into account, the expression for the inclination factor may therefore be represented as I = 1 + Eo sinθ , (3.16) where the Eötvös number (Eo) is defined as ( ) σ ρ ρ 2 gD Eo L G − = . (3.17) The Eötvös number (Eo), sometimes referred as Bond number (Bo), represents the hydrodynamic interaction between gravitational and surface tension forces that occurs in twophase flow. 49 3.3 General NonBoiling TwoPhase Heat Transfer Correlation The parameters that represent the influences of flow pattern and pipe inclination on twophase heat transfer have been developed in previous section (see Section 3.2). Having the flow pattern factor (FP) and the inclination factor (I) representing the influences of flow pattern and pipe inclination, the heat transfer correlation expressed in Eq. (3.10) can be refined as a general nonboiling twophase heat transfer correlation. The term “general” implies that the nonboiling twophase heat transfer correlation has the robustness of predicting heat transfer coefficients for twophase flow with various flow patterns, pipe inclinations, and gasliquid combinations. In addition, the general nonboiling twophase heat transfer correlation is developed to handle wide ranges of superficial gas and liquid Reynolds numbers (ReSG and ReSL). The nonboiling twophase heat transfer correlation developed in Section 3.1 is given in Eq. (3.10): − = + d G L b L G a TP L Pr Pr x x C C h C h μ μ 1 1 1 2 1 . (3.10) where C1 and C2 are parameters representing the influences of flow pattern and pipe inclination on the twophase heat transfer coefficient. With the flow pattern factor and inclination factor developed in Section 3.2, the expressions for C1 and C2/C1 can be represented such that P C ∝ F 1 and r m P P I F F C C − ∝ 1 1 2 , 50 where m and r are constant exponents. Applying the above representations for C1 and C2/C1 into the nonboiling twophase heat transfer correlation, Eq. (3.10), yields − − = + r q G L p L G n P P m TP P L I Pr Pr F F x x h F h C μ 1 μ 1 1 , (3.18) where the coefficient C and exponents m, n, p, q, and r are values to be determined from experimental data. The flow pattern factor ( P F ) and inclination factor ( I ) are evaluated using Eq. (3.13) and Eq. (3.16), respectively. In Eq. (3.18), the liquid phase heat transfer coefficient (hL) is evaluated using the Sieder and Tate (1936) correlations: For stratified flow (θ = 0°, ReSL < 2200 and ReSG < 10000), 1/ 3 0.14 1/ 3 1/ 3 1.86 W L L B L L L L D D k Pr Re h = μ μ ; (3.19) and for all other flow patterns, 0.14 4 / 5 1/ 3 0.027 W L L B L L L D k Pr Re h = μ μ . (3.20) Equations (3.19) and (3.20) are single phase heat transfer correlations proposed by Sieder and Tate (1936) for laminar and turbulent flows, respectively. For the in situ liquid phase Reynolds number (ReL) in Eq. (3.19) and Eq. (3.20), the following relationship is used rather than the superficial liquid Reynolds number: μ μ π ( α ) ρ − = = 1 4 D u D m Re L L L L L L L & . (1.15) 51 To evaluate the value of void fraction (α ) in the expressions for flow pattern factor ( P F ) [see Eq. (3.13)] and in situ liquid phase Reynolds number (ReL) [see Eq. (1.15)], the correlation developed by Woldesemayat and Ghajar (2007) is used: 1 0.25 2 1 ( ) ( ) 1 2.9 0.1 − − + = + 2 L ρ σ ρ ρ α ρ ρ L G SG SL SG SG C g C u u u u G L , (3.21) where ATM SYS p p C (1.22 1.22 sin ) 1 = + θ and (1 cos ) 2 C = D + θ . Note that the leading constant value of 2.9 in Eq. (3.21) carries a unit of m−0.25, and Eq. (3.21) should be used with SI units. Equation (3.18) is the general nonboiling twophase heat transfer correlation that has the robustness of predicting heat transfer coefficients for twophase pipe flow with various flow patterns, pipe inclinations, and gasliquid combinations. Since the values of C, m, n, p, q, and r are inferred from experimental measurements, Eq. (3.18) may be called an empirical correlation. The values of the leading coefficient (C) and the exponents (m, n, p, q, and r) can be varied specifically with the nature of the pipe inclination and gasliquid combinations to achieve higher level of accuracy. In order to determine the values of the leading coefficient (C) and the exponents (m, n, p, q, and r) experimental data measured in our twophase flow heat transfer laboratory as well as from other experimental studies were used. 3.4 A Reynolds Analogy Approach for Heat Transfer Estimation in NonBoiling Two Phase Pipe Flow The hydrodynamic and thermal conditions of nonboiling twophase flow are dependent upon the interaction between the two phases. Due to the complex nature of the 52 twophase gasliquid flow, the accessible heat transfer data and applicable correlations for nonboiling twophase flow are extremely limited in the literature. In most situations encountered by practicing engineers, direct heat transfer measurements for twophase flow are extremely difficult to perform. It is in such respect that mechanistic models for heat transfer estimation using, for example, analogy between friction factor and heat transfer can have appealing prospect. The concept of developing twophase heat transfer correlation based on the analogy of momentum and heat transfer has been explored by a few researchers (Fried, 1954; Vijay et al., 1982; Kaminsky, 1999). However, there are still many unanswered questions concerning the viability and robustness of a twophase heat transfer correlation developed based on the analogy of momentum and heat transfer. It is the goal of this study to explore the plausibility of using the Reynolds analogy to develop a mechanistic correlation to predict heat transfer coefficients for nonboiling twophase flow in pipes. Development of a Reynolds analogy Heat Transfer Correlation The development of a correlation to analogize momentum and heat transfer in nonboiling twophase pipe flow begins with the Reynolds analogy. The Reynolds analogy relates important parameters of momentum and thermal boundary layers in a simplistic form in terms of friction coefficient (cf), Nusselt number (Nu), Prandtl number (Pr), and Reynolds number (Re): 1 1 2 c = NuRe− Pr− f . (3.22) For flow inside pipes, the frictional pressure gradient is given as 2 0 4 2 = = − A m D c dz D dp f f & ρ τ . (3.23) 53 Combining both Eq. (3.22) and Eq. (3.23) yields the expression relating the heat transfer coefficient with the frictional pressure gradient: RePr dz dp m D A Nu f = − 2 2 4 & ρ . (3.24) Using the definitions for Nusselt number ( Nu ), Prandtl number ( Pr ), and Reynolds number ( Re ), Eq. (3.24) can be expressed in terms of the heat transfer coefficient ( h ) with the following expression: D A dz dp m c h f π ρ 2 = − & . (3.25) Adopting Eq. (3.25) for the use in nonboiling twophase pipe flow, the ratio of the heat transfer coefficient for the twophase flow ( TP h ) to the heat transfer coefficient for liquid singlephase flow ( L h ) becomes 2 , , L L L TP f L f TP L L TP L TP m m C dp dz dp dz m m C h h φ ρ ρ ρ ρ & & & & = = . (3.26) where C is a leading coefficient. To effectively represent twophase flow characteristics, the leading coefficient (C) would be a parameter that adequately represents certain hydrodynamic aspects of twophase flow. Note that the frictional pressure gradient ratio for the twophase flow to the liquid singlephase flow is recognized as the pressure drop multiplier ( 2 L φ ) defined by Lockhart and Martinelli (1949). In this study, the values for the twophase frictional pressure gradient, f TP dp dz , , are determined via experimental measurements, while the singlephase liquid frictional pressure gradients, f L dp dz , , are calculated using Eq. (3.23) with 54 f SL c = 16 / Re for ReSL < 2000, and the Blasius (1913) equation, 0.25 0.079/ f SL c = Re , for ReSL > 2000. In the development of their nonboiling twophase heat transfer correlation, Kim and Ghajar (2006) introduced a dimensionless parameter called the flow pattern factor (FP), see Eq. (3.13). The flow pattern factor accounts for the variety of flow patterns that can be found in twophase flow. The flow pattern factor takes into account parameters such as the void fraction, inertia and gravitational forces that influence flow patterns. Introducing the flow pattern factor (FP) as the leading coefficient of Eq. (3.26), and expressing each of the parameters in Eq. (3.26) as exponential functions, the Reynolds analogy heat transfer correlation takes on the following form: q L p L TP n m L P L TP m m F h h φ ρ ρ = & & . (3.27) The exponents in Eq. (3.27), m, n, p, and q, are constants to be determined for the experimental data. The mass flow rate (m& ) in Eq. (3.27) is the sum of the gas phase ( G m& ) and liquid phase ( L m& ) mass flow rates. The twophase density ( TP ρ ) is defined as the mass of twophase fluids per unit volume of the pipe and can be determined using TP G L ρ =αρ + (1−α)ρ . (3.28) The void fraction (α ) needed to calculate the twophase density in Eq. (3.28) is measured experimentally or estimated using void correlations recommended by Woldesemayat and Ghajar (2007). The singlephase liquid heat transfer coefficient ( L h ) is calculated using the Sieder and Tate (1936) correlation, Eq. (3.20). 55 3.5 Chapter Summary The development of two nonboiling twophase heat transfer correlations is presented in this chapter. The general nonboiling twophase heat transfer correlation was developed using important variables that influence heat transfer in twophase pipe flow. The mechanistic twophase heat transfer was developed using the Reynolds analogy to analogize momentum and heat transfer in nonboiling twophase pipe flow. Discussions on the performances of the two heat transfer correlations are presented in Chapter VI. 56 CHAPTER IV EXPERIMENTAL SETUP AND PROCEDURES The experimental setup was constructed with the capability of systematically collecting heat transfer data for all major twophase flow patterns and also slightly upward inclined flow. In this chapter, the description of the experimental setup and its instrumentation are presented. In addition, experimental procedures that are used in this experimental study are discussed. Finally, the technique for data reduction is also presented. 4.1 Description of Current Experimental Setup In this section, the main components of the current experimental setup will be briefly described. The current experimental setup was constructed with the capability of using it to measure nonboiling twophase pressure drop and heat transfer, and conduct flow visualization for all major flow patterns and upward inclination angles from 0° (horizontal) to 7°. The design and construction of this experimental setup, as well as the calibration of measuring instruments, were documented by Durant (2003). 57 Flow Loop A schematic diagram of the flow loop for the current experimental setup is illustrated in Figure 8. The mixing section, the calming and observation section, and the stainless steel test section rest on top of an aluminum Ibeam. The aluminum Ibeam is supported by a pivoting mechanism that is attached to an electric jack. The Ibeam is approximately 9.1 m (30 ft) long and the pivoting mechanism could bring the Ibeam to an upward inclination of approximately 8°. Inclination angles were measured with a contractor’s anglemeasuring tool and with a more precise digital xy axis accelerometer. The minimum resolution of the digital accelerometer is 0.5°. Supply of Working Fluids The working fluids used in this study were air and distilled water. The reservoir used for storing the distilled water is a 208liter (55 gallon) polyethylene tank. A Bell & Gosset (Series 1535) coupled centrifugal pump (size 3545 D10) is used to pump the distilled water from the reservoir. The pump draws the distilled water from the reservoir through an AquaPure AP12T water filter and an ITT Standard (Model BCF 4063) one shell and twotube pass heat exchanger. The heat exchanger is used to remove heat added to the distilled water during the experiment as well as to maintain a constant inlet liquid temperature. The cooling fluid used by the heat exchanger is tap water taken directly from the wall tap. 58 Figure 8. Flow loop of the current experimental setup 59 From the heat exchanger, the distilled water flowed through a Micro Motion (Model CMF125) Coriolis flow meter. The Coriolis flow meter is connected to a Digital FieldMount (Model RFT9739) transmitter that conditions the flow information for the data acquisition system. After passing the Coriolis flow meter, the distilled water then passes through a 1in. twelve turn gate valve. The gate valve is used to regulate the amount of distilled water that is flowing into the mixing section. From the gate valve, the distilled water flows through a 25.4 mm (1 in.) I.D. hose, and then through a oneway check valve and into the airwater mixing section. Air is supplied from an IngersollRand T30 (Model 2545) air compressor. The air supplied from the air compressor is regulated by a Speedaire (Model 4ZM22) 12.7 mm (½ in.) regulator. The air is then cooled by passing through a copper coil submerged in a vessel of water from the wall tap. The same water from the wall tap that is used for cooling the distilled water is also used for cooling the air. This is to ensure that both air and distilled water have the same inlet temperature. The air is then filtered by a Speedaire (Model 4ZL49) 12.7 mm (½ in.) air filter to remove moisture from the air before the air flow rate is being measured. From the air filter, the air flows through a Micro Motion (Model CMF100) Coriolis flow meter that is connected to another Digital FieldMount (Model RFT9739) transmitter. After passing the Coriolis flow meter, the air then passes through a needle valve, which is used to regulate the amount of air flowing into the mixing section. From the needle valve, the air flows through a flexible hose, and then through a oneway check valve and into the airwater mixing section. 60 AirWater Mixing Section The airwater mixing section is attached upstream of the calming and observation section. A schematic of the airwater mixing section is illustrated in Figure 9. This type of mixer was successfully used in twophase flow experimental studies by Ewing et al. (1999) and Kim (2000). Air and distilled water are supplied through a 25.4 mm (1 in.) copper tee and are mixed in the mixing well. After the mixing well, the temperature of the airwater twophase flow is measured by an Omega TMQSS125U6 thermal probe. Next, the airwater twophase flow enters into the calming and observation section. Calming and Observation Section The 2.24 m (88 in.) long calming and observation section is made of clear polycarbonate pipe with an inner diameter of 25.4 mm (1 in.). This gives the calming and observation section a length to diameter ratio (L/D) of 88. Airwater twophase flow leaving the mixing section is allowed to calm and develop through the calming and observation section before entering the test section. The calming and observation section also serves as the section where flow visualization is conducted. Heat Transfer Test Section The heat transfer test section is made of a schedule 10S 316 stainless steel pipe with an inner diameter of 27.9 mm (1.097 in.) and an outer diameter of 33.4 mm (1.315 in.). The heat transfer test section is 2.64 m (104 in.) long, giving a length to diameter ratio (L/D) of about 95. A schematic of the heat transfer test section is illustrated in Figure 10 (p. 62). Along the bottom of the stainless steel pipe, there are eleven pressure taps equally spaced at 25.4 cm (10 in.) interval. 61 Figure 9. Schematic of airwater mixing section 62 Figure 10. Schematic of heat transfer test section 63 Along the test section, there are 10 thermocouple stations equally spaced at 25.4 cm (10 in.) interval. Each thermocouple station has four thermocouples attached circumferentially around the pipe surface. Figure 10 (p. 62) shows the circumferential locations of the thermocouples, with “A” at the top of the pipe, “B” at 90° from the top in the clockwise direction, “C” at the bottom of the pipe, and “D” at 90° from the bottom in the clockwise direction. Omega TTT30 copperconstantan insulated Ttype thermocouples are used with Omega EXPPT20TWSH extension wire to connect to the data acquisition system. The thermocouples are cemented on the outside surface of the stainless steel test section with Omegabond 101 epoxy. The Omegabond 101 epoxy has a thermal conductivity of 1.04 W/m·K (0.6 Btu/ft·h·°F) and an electrical resistivity of 1 × 1015 2·m (3.28 × 1015 2·ft). Both ends of the stainless steel test section are attached to two 12.7 cm × 17.8 cm × 0.64 cm (5 in. × 7 in. × ¼ in.) copper plates. The two copper plates are attached to the ends of the test section by means of silversoldering. Both copper plates are connected with 4 gauge insulated cables to a LINCOLNWELD SA750 arc welder, which provides power to heat the test section with uniform heat flux. Eleven pressure tap holes were drilled along the bottom of the test section (see Figure 10). The diameters of the holes are 1.73 mm (0.068 in.), and they are equally spaced at 25.4 cm (10 in.) intervals. The holes are located at the bottom of the stainless steel pipe in order to ensure that only water could get into the pressure measuring system. The pressure taps are connected to standard selftapping saddle valves with the tapping core removed. The system pressure is measured by an Omega PX242060G absolute 64 pressure transducer, while the pressure drop between the first and the last pressure taps is measured by a Validyne DP15 differential pressure transducer. Heat Source Uniform wall heat flux is supplied to the test section by running high amperage DC current through the stainless steel test section from the LINCOLNWELD SA750 arc welder. The minimum current supplied by the LINCOLNWELD SA750 arc welder is 300 A, which is too high for flow with ReSL < 2000 and may cause dryout and local boiling. To solve this issue, a Miller Maxtron 450 DC inverter arc welder is used to supply DC current through the stainless steel test section for flow with ReSL < 2000. The current supplied by the Miller Maxtron 450 can go as low as 5 A, which is safe for operating at very low ReSL flow. This makes the measurement of heat transfer data for all major flow patterns possible. 4.2 Instrumentation Flow Rate Measurements The air flow rate is measured by Micro Motion (Model CMF100) Coriolis flow meter, and the water flow rate is measured by Micro Motion (Model CMF125) Coriolis flow meter. Both Coriolis flow meters are connected to Digital FieldMount (Model RFT9739) transmitters. The signals from the Digital FieldMount transmitters are relayed to the data acquisition system for data recording. 65 Temperature Measurements Surface temperatures of the test section are measured with Omega TTT30 Ttype thermocouples cemented on the test section using Omegabond 101. Airwater mixture temperatures before and after the test section are measured with Omega TMQSS 125U6 thermocouple probes. Signals from the thermocouples and the thermocouple probes are relayed to the data acquisition system for data recording. The calibration of the thermocouples and thermocouple probes was reported in detail by Durant (2003). Pressure Measurements Pressure drop between the first and the last pressure taps is measured using Validyne DP15 differential pressure transducer. The Validyne DP15 differential pressure transducer is connected to a Validyne CD15 carrier demodulator. Output signals from the differential pressure transducer are sent to the carrier demodulator to be demodulated, amplified and filtered. Signals from the demodulator are then relayed to the data acquisition system for data recording. Power Measurement The voltage drop across the heated test section is measured by a HP 3468B digital multimeter. The current flowing through the test section is determined by measuring the voltage drop across a shunt attached to the copper plate at the downstream of the test section. Knowing the voltage drop and the resistance across the shunt, the current flowing through the test section can be determined. The voltage drop across the shunt is recorded by the data acquisition system and the corresponding current is determined. Knowing the voltage drop across the test section and the current through the test section, the heat flux 66 on the test section can be determined. Heat fluxes obtained from electrical input and thermal output are used to check for heat balance to assure the system is working correctly. Data Acquisition System A National Instruments data acquisition system is used for recording and storing the data measured during the experiment. An AC powered fourslot National Instruments SCXI 1000 Chassis houses the data acquisition system. The chasis provides a low noise environment for signal conditioning. There are three National Instruments SCXI control modules housed inside the chassis: two SCXI 1102/B/C modules and one SCXI 1125 module. From the three modules, input signals from 40 thermocouples, two thermocouple probes, volt and current meters, and flow meters are gathered and recorded. The graphical user interface used for the data acquisition is a customized LabVIEW Virtual Instrument (VI) program developed specifically for this experimental setup. Figure 11 illustrates the graphical user interface of the LabVIEW Virtual Instrument (VI) program used for the data acquisition. The LabVIEW Virtual Instrument (VI) graphical user interface provides users with the features to monitor and record data. Data such as inlet, outlet, surrounding, and test section surface temperatures, pressure drop, system pressure, air and water mass flow rates, superficial gas and liquid Reynolds numbers, and current supplied by the DC arc welder to the test section are displayed on the graphical user interface. With these features on the graphical user interface, users can monitor the recorded data and readily identify any anomaly during the course of an experiment. 67 Figure 11. Graphical user interface of the LabVIEW Virtual Instrument (VI) program 4.3 Experimental Procedures The process of acquiring accurate experimental data requires a consistent adherence to a set of defined experimental procedures. The purpose of adhering to the experimental procedures is to maintain the integrity and repeatability of the experimental data, and proper functioning of the equipments and experimental setup. The experimental procedures are categorized into startup procedure and measurement procedure. The start 68 up procedure lists several steps to initiate the experimental setup and prepare it for conducting the measurements. The measurement procedure lists several steps to acquire quality and accurate experimental data. StartUp Procedure The startup procedure is a process that includes several steps to prepare the experimental setup for measurement. The main function of this startup procedure is to ensure that the experimental setup is operating properly and safely before the process of acquiring experimental data. Figure 12 is a flow chart illustrating the steps involved in the startup procedure. The first step in the startup procedure is turning on all electrical instruments: Digital FieldMount RFT9739 transmitters for both Coriolis flow meters, Validyne CD15 carrier demodulator for the differential pressure transducer, and the National Instruments data acquisition system. Once the data acquisition system is turned on, the LabVIEW Virtual Instrument (VI) program is launched and readings of all the thermocouples are monitored to ensure they are the same with the surrounding temperature. This process of checking the thermocouples’ readings with the surrounding temperature provides an initial and quick indication whether the thermocouples are working properly. The second step in the startup procedure is checking the Speedaire air filter and the AquaPure water filter. This process of checking the air and water filters is to ensure their functionality, and to maintain periodic replacement of the old filters. Old, dirty, and worn filters not only unable to function properly, but also reduce the flow capabilities of the fluids to the test section. 69 Figure 12. Startup procedure for twophase heat transfer and isothermal pressure drop experiments 70 The third step in the startup procedure is turning on the tap water, which served as cooling fluid for the copper coil in the air line and the ITT Standard one shell and twotube pass heat exchanger in the water line. The tap water cooled the air and distilled water flowing into the test section such that both air and distilled water have same inlet temperature. The fourth step in the startup procedure is turning on the IngersollRand T30 air compressor and the Bell & Gosset centrifugal pump. With the air compressor and centrifugal pump turned on, air and water are supplied to the test section. The final step in the startup procedure is checking for leakage in the flow loop, and verifying the test section inclination angle. Having completed the steps in the startup procedure illustrated in Figure 12 (p. 69), the experimental setup is ready for measurement procedure. The startup procedure described here is also applicable for isothermal twophase pressure drop experiments. Measurement Procedure The measurement procedure is a process that includes several steps to successfully acquire experimental data. The function of the measurement procedure is to ensure the integrity and repeatability of the experimental data, while maintaining the functionality of the experimental setup. Figure 13 is a flow chart illustrating the individual steps of the measurement procedure. The first step in the measurement procedure is checking the welder cables connecting the DC arc welder with the copper plates attached to the stainless steel test section. This is a precautionary step to ensure all connections are safe and ready for the experiment. Poor condition of cables and improper connections between the DC arc welder and the test section could equipment damage, over Figure 13. Measurement procedure for two 71 result in short circuit, which could potentially cause heating, or fire hazard. twophase heat transfer and isothermal pressure drop experiments thermal 72 The second step in the measurement procedure is adjusting the air and water flow rates. The flow of air is regulated by a needle valve while the water is regulated by a gate valve. Using the Digital FieldMount transmitters, for the Coriolis flow meters, to monitor the air and water flow rates, the needle and gate valves are adjusted until the desired air and water flow rates are achieved. Once the desired air and water flow rates are set, the third step in the measurement procedure is to turn on the DC arc welder. With the DC arc welder turned on, the current is adjusted to the desired amperage to be supplied to the stainless steel test section. By running DC current through the stainless steel pipe, heat flux is supplied to the test section. The fourth step in the measurement procedure is to allow flow to achieve steady state condition. The flow is considered to have achieved steady state condition when each of the two thermocouple probes, which measure the inlet and outlet bulk temperatures, is indicating less than 0.5°C fluctuation for 5 minutes. The inlet and outlet bulk temperatures are monitored using the graphical user interface of the LabVIEW Virtual Instrument (VI) program illustrated in Figure 11 (p. 67). The thermocouples measuring the outer surface temperatures of the pipe are carefully monitored to avoid the temperature from rising beyond 60°C. This is to keep the flow strictly nonboiling and avoid the possibility of local boiling. Once the steady state is achieved, the process of acquiring experimental data can begin, which is the fifth step in the measurement procedure. Experimental data collected are air and water mass flow rates, inlet and outlet bulk temperatures, surface temperatures of the test section, pressure drop, and uniform heat flux supplied to the test section via the 73 current from the DC arc welder. The typical number of samples collected for each measurement run is a thousand samples. When the experimental data is recorded, the following step in the measurement procedure is to turn off the DC arc welder and allow the test section to cool to room temperature. Once the test section is cooled to room temperature, another measurement run can begin, as illustrated in Figure 13 (p. 71). The steps described for the measurement procedure is applicable for isothermal pressure drop measurements as well. As depicted in Figure 13, steps in the measurement procedure that are involved with using the DC arc welder are not observed, when conducting isothermal twophase pressure drop measurements and flow pattern observations. 4.4 Data Reduction For a uniform wall heat flux condition, the experiment involved the measurements of outside pipe wall surface temperatures at discrete locations (see Figure 10, p. 62), as well as the inlet and outlet bulk temperatures. The circumferential heat transfer coefficient was calculated based on the knowledge of the heat flux and surface temperature at the inside wall of the pipe. Due to the difficulty of measuring the inside wall temperatures, they are instead calculated from the measured outside wall temperatures and the heat generation within the pipe wall. The data reduction program developed by Ghajar and Kim (2006) was used for calculating the circumferential heat transfer coefficients and the inside wall temperatures from the outside wall temperatures measured at discrete locations along the uniformly heated pipe. 74 For the pipe wall, the numerical solution of the conduction equation used in the data reduction program has four assumptions: (1) steady state condition exists; (2) conduction occurs in circumferential and radial directions; (3) conduction in axial direction is negligible; and (4) both electrical resistivity and thermal conductivity in the pipe wall are functions of temperature. Figure 14 shows the nodal arrangement for the finite difference solution used by Ghajar and Kim (2006) for the pipe wall. The heat balance on a control volume of the pipe wall at a given node (p) can be expressed as g n e s w q& = q& + q& + q& + q& . (4.1) From Fourier’s law of heat conduction, the rate of heat conduction in a given direction n is dn dT q& = −kA . (4.2) Applying the finite difference formulation for a control volume on a segment of the pipe (see Figure 14) with nonuniform thermal conductivity, the heat rates for nodes n, e, s, and w can be written as ( ) n p n n n p n n A T T k k q − = + − − + 1 δ δ & , (4.3) ( ) e p e e e p e e A T T k k q − = + − − + 1 δ δ & , (4.4) ( ) s p s s s p s s A T T k k q − = + − − + 1 δ δ & , (4.5) 75 w ( p w ) w w p w w A T T k k q − = + − − + 1 δ δ & . (4.6) Figure 14. Nodal arrangement for finite difference solution (adapted from Ghajar and Kim, 2006) The heat generated ( g q& ) at the control volume is given by A z q i R i g & = 2 = 2γ . (4.7) Substituting Eqs. (4.3) to (4.7) into Eq. (4.1) yields the following equation: 1 1 ( ) − − = − − − − + − + s s s p s s p g n e w A k k T T q q q q δ δ & & & & . (4.8) Equation (4.8) is used for calculating the temperatures of the interior nodes. Once the local inside wall temperature ( Wi T ) is calculated by applying Eq. (4.8), the local heat transfer coefficient can be determined from the local inside wall heat flux ( Wi q&′′ ) and the local bulk fluid temperature ( B T ): 76 TC ST ST Wi k j B k Wi k j k j j N k N T T q h for 1, 2, , and 1,2, , ( ) ( ) ( ) @ , , , K K & = = − ′′ = . (4.9) where the subscripts j and k are the indexes of the thermocouple in the circumferential location and the thermocouple station in the axial location, respectively. The local bulk temperature is given as T T T T z L B k in out in k ( ) = + ( − ) . (4.10) The average local heat transfer coefficient at a given thermocouple station is B k N j Wi k j TC@ST N j Wi k j TC@ST k T T N q N h TC@ST TC@ST ( ) ( ) 1 ( ) 1 1 , 1 , − ′′ = Σ Σ = = & . (4.11) In twophase flow heat transfer, due to the existence of nonuniform local heat transfer coefficients, the calculation of overall heat transfer coefficient for the entire pipe becomes necessary. The overall heat transfer coefficient was calculated by integrating the average local heat transfer coefficient ( k h ) along the pipe length: Σ= = NST k TP EXP k k h z L h 1 , 1 . (4.12) 4.5 Effects of Dissolved Air Since air and water are mixed together in the mixing section (see Figure 9, p. 61) before flowing to the test section, the mixing of air and water will naturally result in dissolved air being present in the water. Thus, it is reasonable to question whether the dissolved air in the working fluid can affect the heat transfer. 77 In a study done by MüllerSteinhagen et al. (1988) to determine the effect of various dissolved gasses (He, N2, Ar, CO2, C3H8) in water and heptane on convective heat transfer and subcooled boiling heat transfer in an annulus with a heated core, they found that convective heat transfer is not affected by dissolved gasses in flow of water and of heptane. However, dissolved gasses in water and heptane brought enhancement to the subcooled boiling heat transfer coefficient, due to the process of desorption and evaporation (MüllerSteinhagen et al., 1988). Steinke and Kandlikar (2004) conducted an experimental investigation to study the effect of dissolved gases on heat transfer during the flow of water in a microchannel. Their experiment was conducted for water with three different dissolved oxygen contents: 1.8, 5.4, and 8.0 parts per million (ppm). They found that water with higher dissolved oxygen content (8.0 ppm) experienced a slight reduction in heat transfer after the boiling incipience wall temperature is achieved, when compared to water with lower dissolved oxygen content (1.8 and 5.4 ppm). For water with high dissolved oxygen content (8.0 ppm), desorption of the dissolved gas during nucleation formed an insulating layer of bubbles on the heated surface, thus causing a slight reduction in heat transfer. Nucleation was observed at a surface temperature of 90.5°C for water with 8.0 ppm of dissolved oxygen. Prior to nucleation, no noticeable difference in heat transfer was observed for the three different cases of dissolved oxygen in water. In a more recent study, Cioncolini et al. (2007) concluded that the dissolved air in water for subcooled and saturated boiling flow did not cause any systematic deviation from predictions by correlations derived for degassed liquids. Cioncolini et al. (2007) attributed the lack of influence by the dissolved air on subcooled and saturated boiling 78 heat transfer to the fact that water can only dissolve moderate amount of air. Similar conclusions were also drawn by Cioncolini et al. (2007) for convective heat transfer in singlephase degassing flow. MüllerSteinhagen et al. (1988), Steinke and Kandlikar (2004), and Cioncolini et al. (2007) indicated that the presence of dissolved air in water does not affect convective heat transfer. Since all experiments conducted in this study were forced convective heat transfer, and do not include boiling, it is therefore not unreasonable to assume that dissolved air in water will not cause any anomaly in the heat transfer results. In addition, for all the measurements conducted in the study, the outer surface temperatures of the pipe were kept below 60°C to avoid local boiling. From Henry’s law, the amount of air dissolved in water at 25°C and 1 atm is approximately 0.023 g/kg. In this study, it is conceivable that the mixing of air and water may result in slightly higher amount of dissolved air in water than the value determined from Henry’s law. 4.6 Chapter Summary The current experimental setup was constructed for systematic study of heat transfer in nonboiling twophase flow for horizontal and slightly inclined cases. The setup was capable to be used for collecting flow patterns, pressure drop, and heat transfer data for all major flow patterns and inclination angles from 0° (horizontal) to 7° upward inclined. The experimental data collected with this experimental setup is useful for the understanding of the fundamentals of nonboiling twophase flow heat transfer, as well as for the validation of the developed twophase heat transfer correlations. 79 CHAPTER V EXPERIMENTAL RESULTS In this chapter, the experimental results collected from the experimental setup are presented. The results include flow patterns and heat transfer data systematically collected for horizontal and slightly inclined twophase flow in pipes. Before experiments on the twophase flow were conducted, experimental data for singlephase flow was measured. The objective of conducting measurements for singlephase flow is to establish the viability of the experimental setup for conducting twophase flow experiments. 5.1 SinglePhase Flow Results In this section, results of singlephase liquid flow frictional pressure drop and heat transfer measurements conducted with the test section are discussed. The objective of conducting frictional pressure drop and heat transfer measurements for singlephase flow in the test section is to verify the performance and reliability of the experimental setup. The perception is that if the results, both frictional pressure drop and heat transfer, from singlephase flow measurements are in agreement with established correlations, then it is not unreasonable to hold the assumption that the experimental setup is applicable for twophase flow
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Title  Study of Heat Transfer in Nonboiling Twophase Gasliquid Flow in Pipes for Horizontal, Slightly Inclined, and Vertical Orientations 
Date  20110501 
Author  Tang, Clement Chihwei 
Keywords  experiment, flow pattern, heat transfer, pipe inclination, pressure drop, twophase flow 
Department  Mechanical Engineering 
Document Type  
Full Text Type  Open Access 
Abstract  The main objective of this research is to establish a fundamental understanding of heat transfer in nonboiling twophase pipe flow. The key processes that govern heat transfer in nonboiling twophase pipe flow are flow patterns, pressure drop, void fraction, and pipe orientation. The fundamental understanding of heat transfer in nonboiling twophase pipe flow can be achieved in twofold; namely, qualitatively and quantitatively. Experiments for measuring heat transfer coefficient and pressure drop in horizontal and slightly inclined pipes were conducted. All the experimental data collected for heat transfer and pressure drop provided valuable insights to describing the mechanisms of heat transfer in nonboiling twophase pipe flow qualitatively. However, to be able to successfully and effectively quantify heat transfer in nonboiling twophase pipe flow, the development of heat transfer correlations that have the robustness to handle all major twophase flow patterns and inclination effects become necessary. From the observation of the experimental results, two correlations for heat transfer in twophase flow have been formulated: one is a general heat transfer correlation; another is a Reynolds analogy heat transfer correlation. Both correlations were compared with experimental results measured from horizontal, slightly inclined, and vertical pipes for various gasliquid flows. The experimental results were compiled from different independent sources with different experimental facilities. The general twophase heat transfer correlation was compared with 1156 experimental data points, while the Reynolds analogy correlation were compared with 916 experimental data points. The predicted results from both correlations with the experimental results showed satisfactory agreement. The general and Reynolds analogy heat transfer correlations predicted 93 and 89%, respectively, of the data points within �30%. The results of the comparisons with experimental data showed the robustness and capability of both correlations to adequately predict nonboiling twophase flow heat transfer for various flow patterns, pipe orientations, and gasliquid combinations. Both correlations also characterized the important physical parameters that influence heat transfer in nonboiling twophase flow. 
Note  Dissertation 
Rights  © Oklahoma Agricultural and Mechanical Board of Regents 
Transcript  A STUDY OF HEAT TRANSFER IN NONBOILING TWOPHASE GASLIQUID FLOW IN PIPES FOR HORIZONTAL, SLIGHTLY INCLINED, AND VERTICAL ORIENTATIONS By CLEMENT CHIHWEI TANG Bachelor of Science in Mechanical Engineering Oklahoma State University Stillwater, Oklahoma 2000 Master of Science in Mechanical Engineering Oklahoma State University Stillwater, Oklahoma 2003 Submitted to the Faculty of the Graduate College of the Oklahoma State University in partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY May, 2011 ii A STUDY OF HEAT TRANSFER IN NONBOILING TWOPHASE GASLIQUID FLOW IN PIPES FOR HORIZONTAL, SLIGHTLY INCLINED, AND VERTICAL ORIENTATIONS Dissertation Approved: Dr. Afshin J. Ghajar Dissertation Adviser Dr. David G. Lilley Dr. Frank W. Chambers Dr. Martin S. High Outside Committee Member Dr. Mark E. Payton Dean of the Graduate College iii ACKNOWLEDGEMENTS I would like to express my most sincere gratitude to my advisor, Dr. Afshin. J. Ghajar, for his excellent guidance, consistent encouragement, and dedication to teaching and research; I am greatly indebted to him for his invaluable inspiration. I would also like to express my appreciation to Dr. David. G. Lilley, Dr. Frank. W. Chambers and Dr. Martin S. High for their willingness to serve as my committee members despite their busy schedules. Their helpful comments, guidance, and encouragements are invaluable. Furthermore, I would like to thank Wendell Cook and Melkamu Woldesemayat for their help in the laboratory. Special thanks to Wendell Cook for assisting me in designing and constructing the new experimental setup for twophase flow, as well as the experimental setup for miniand microtube flow. Although the scope of my thesis does not include using both of those experimental setups, I am nonetheless grateful for the opportunity to be a participant in both projects. Another colleague that deserves special thanks is Jaeyong Kim, who initially showed me the ins and outs of operating twophase flow experiments. In fact, the idea of constructing the new twophase flow experimental setup was conceived by him. At the moment of this writing, four M.S. theses have been produced out of the studies involving the new experimental setup for twophase flow. I have indeed reaped the benefits of his labor in the twophase flow laboratory. iv My gratitude extends to my parents, whose support and encouragement are priceless. Their prayers for me during the course of this study have brought many blessings into my life. Special gratitude and appreciation are expressed to my loving wife, Grissadee Rataree, for her unwavering love, patience and support. I also like to dedicate this work to my son, Jadon, whose youthful humor and insatiable curiosity are constant inspirations to me. Finally, and foremost, I thank the Lord Jesus Christ for establishing the work of my hands. v TABLE OF CONTENTS Chapter Page I. INTRODUCTION ...................................................................................................1 1.1 Basic Definitions in TwoPhase Flow ............................................................3 1.2 TwoPhase Flow Patterns ...............................................................................7 Flow Patterns in TwoPhase Horizontal Flow ............................................ 7 Flow Patterns in TwoPhase Vertical Flow ................................................ 9 1.3 Research Objectives .....................................................................................10 1.4 Broader Impact .............................................................................................12 1.5 Brief Outline of this Study ...........................................................................13 II. LITERATURE REVIEW ......................................................................................14 2.1 TwoPhase Flow Heat Transfer ....................................................................14 2.2 TwoPhase Flow Pattern Maps ....................................................................29 2.3 Void Fraction ................................................................................................33 2.4 Relationship of Pressure Drop and Heat Transfer ........................................38 2.5 Chapter Summary .........................................................................................41 III. DEVELOPMENT OF NONBOILING TWOPHASE HEAT TRANSFER CORRELATIONS .................................................................................................42 3.1 Development of a General NonBoiling TwoPhase Heat Transfer Correlation ....................................................................................................42 3.2 Flow Pattern Factor and Inclination Factor ..................................................45 Flow Pattern Factor ................................................................................... 45 Inclination Factor ...................................................................................... 47 3.3 General NonBoiling TwoPhase Heat Transfer Correlation .......................49 3.4 A Reynolds Analogy Approach for Heat Transfer Estimation in Non Boiling TwoPhase Pipe Flow ......................................................................51 Development of a Reynolds analogy Heat Transfer Correlation .............. 52 3.5 Chapter Summary .........................................................................................55 IV. EXPERIMENTAL SETUP AND PROCEDURES ...............................................56 4.1 Description of Current Experimental Setup .................................................56 Flow Loop ................................................................................................. 57 Supply of Working Fluids ......................................................................... 57 AirWater Mixing Section ........................................................................ 60 vi Chapter Page Calming and Observation Section ............................................................ 60 Heat Transfer Test Section........................................................................ 60 Heat Source ............................................................................................... 64 4.2 Instrumentation .............................................................................................64 Flow Rate Measurements .......................................................................... 64 Temperature Measurements ...................................................................... 65 Pressure Measurements ............................................................................. 65 Power Measurement.................................................................................. 65 Data Acquisition System........................................................................... 66 4.3 Experimental Procedures ..............................................................................67 StartUp Procedure.................................................................................... 68 Measurement Procedure............................................................................ 70 4.4 Data Reduction .............................................................................................73 4.5 Effects of Dissolved Air ...............................................................................76 4.6 Chapter Summary .........................................................................................78 V. EXPERIMENTAL RESULTS...............................................................................79 5.1 SinglePhase Flow Results ...........................................................................79 Frictional Pressure Drop in SinglePhase Flow ........................................ 80 SinglePhase Flow Heat Transfer Coefficient along the Pipe .................. 84 Heat Transfer in SinglePhase Flow ......................................................... 85 5.2 Flow Patterns and Flow Maps ......................................................................88 5.3 Heat Transfer in Horizontal and Slightly Upward Inclined Pipe Flows ....101 5.4 Influence of Pipe Inclination on Heat Transfer Coefficient .......................107 5.5 Chapter Summary .......................................................................................121 VI. COMPARISON OF TWOPHASE HEAT TRANSFER CORRELATIONS WITH EXPERIMENTAL RESULTS .................................................................122 6.1 The General TwoPhase Heat Transfer Correlation ...................................122 6.2 Comparison of the General Correlation with Experimental Results for Specific Pipe Orientations and GasLiquid Flows .....................................127 TwoPhase Flow in Horizontal and Slightly Inclined Pipes ................... 127 TwoPhase Flow in Vertical Pipe ........................................................... 135 Summary ................................................................................................. 140 6.3 Comparison of the General Correlation with All Experimental Data ........142 6.4 The Use of Different Void Fraction Correlations with the General Correlation ..................................................................................................146 Horizontal to Vertical Pipes Void Fraction Correlations ........................ 146 Horizontal Pipe Void Fraction Correlations ........................................... 147 Vertical Pipe Void Fraction Correlations ............................................... 149 6.5 Practical Illustrations of Using the General TwoPhase Heat Transfer Correlation ..................................................................................................151 Application for AirWater Flow in Horizontal Pipe ............................... 151 Application for Air and GasOil Flow in Vertical Pipe .......................... 154 vii Chapter Page Application for AirSilicone Flow in Vertical Pipe ................................ 157 6.6 The Reynolds Analogy TwoPhase Heat Transfer Correlation..................160 6.7 Assessment of the Exponents for the Reynolds Analogy Correlation .......164 6.8 Comparison of the Reynolds Analogy Correlation with All Experimental Data ......................................................................................165 6.9 Exponents of the Reynolds Analogy Correlation for Specific Pipe Orientations and GasLiquid Flows ...........................................................169 6.10 Performance of Other Correlations ............................................................173 6.11 Chapter Summary .......................................................................................176 VII. SUMMARY AND RECOMMENDATIONS......................................................177 7.1 Summary of Present Study .........................................................................177 7.2 Recommendations for Possible Future Study ............................................179 REFERENCES ................................................................................................................184 APPENDIX A ..................................................................................................................196 A.1 Friction Factor ............................................................................................197 A.2 Heat Transfer Coefficient ...........................................................................198 APPENDIX B ..................................................................................................................201 viii LIST OF TABLES Table Page 1. Experimental data sets used in the study by Kim et al. (1999) ..........................24 2. Heat transfer correlations chosen in the study by Kim et al. (1999) ..................25 3. Values of constants suggested for the various models and correlations summarized by Butterworth (1975) ...................................................................35 4. Summary of the deviations between measured and calculated friction factor using various correlations ........................................................................83 5. Summary of the deviations between measured and calculated Nusselt number using various correlations .....................................................................87 6. Summary of experimental conditions and measured twophase heat transfer data for horizontal and 2°, 5°, and 7° pipe inclinations ......................101 7. Summary of the conditions of experimental data used for comparison with the general twophase heat transfer correlation, Eq. (3.18) .............................125 8. Results of the predictions by Eq. (3.18) with specific leading coefficient and exponents for various pipe orientations and gasliquid flows ...................134 9. Results of the predictions by Eq. (6.15) for all 1156 experimental heat transfer data points with different gasliquid combinations and pipe inclinations .......................................................................................................145 10. Results predicted by the general twophase heat transfer correlation, Eq. (6.15), applied with various void fraction correlations compared with experimental results ..........................................................................................150 11. Summary of the conditions of experimental data used for comparison with the Reynolds analogy twophase heat transfer correlation, Eq. (3.27) ............162 12. Comparison of the predictions by Eq. (6.21) and all 916 experimental data points with different gasliquid combinations and pipe inclinations ...............168 13. Comparison of the predictions by Eq. (6.22) and all 916 experimental data points with different gasliquid combinations and pipe inclinations ...............171 ix Table Page 14. Comparison of the predictions by Eq. (6.21) versus Eq. (2.34) and Eq. (2.35) ................................................................................................................175 15. Comparison of capabilities between the current and new experimental setups ................................................................................................................180 x LIST OF FIGURES Figure Page 1. Schematic of flow patterns observed in horizontal gasliquid flow (adapted from Carey, 1992) .............................................................................8 2. Schematic of flow patterns observed in vertical gasliquid flow (adapted from Carey, 1992) ............................................................................................9 3. Flow map for vertical flow by Hewitt and Roberts (1969) ...............................29 4. Flow map for horizontal and near horizontal flow by Taitel and Dukler (1976) .............................................................................................................30 5. Flow map for horizontal airwater flow by Weisman et al. (1979) ..................31 6. Flow map for horizontal flow by Spedding and Nguyen (1980) ......................32 7. Gasliquid interface and wettedperimeter ........................................................46 8. Flow loop of the current experimental setup.....................................................58 9. Schematic of airwater mixing section ..............................................................61 10. Schematic of heat transfer test section ..............................................................62 11. Graphical user interface of the LabVIEW Virtual Instrument (VI) program ..........................................................................................................67 12. Startup procedure for twophase heat transfer and isothermal pressure drop experiments ............................................................................................69 13. Measurement procedure for twophase heat transfer and isothermal pressure drop experiments .............................................................................71 14. Nodal arrangement for finite difference solution (adapted from Ghajar and Kim, 2006) ..............................................................................................75 15. Comparison of measured and calculated singlephase friction factor ..............83 16. Variation of local Nusselt number along the heated test section for singlephase flow ...........................................................................................84 17. Comparison of measured and calculated singlephase heat transfer data .........87 xi Figure Page 18. Photographs of flow patterns for horizontal flow. ............................................89 19. Flow map of horizontal pipe with photographs of representative flow patterns ...........................................................................................................90 20. Change of flow pattern transition boundaries as pipe inclined upward from horizontal orientation ............................................................................91 21. Flow patterns data points from Barnea et al. (1980) plotted on the flow maps for horizontal and 2° inclined flows .....................................................93 22. Representative photographs of wavy flow patterns for horizontal, 2°, 5°, and 7° pipe inclinations (ReSG = 16000 and ReSL = 1500) .............................95 23. Representative photographs of slug flow patterns for horizontal, 2°, 5°, and 7° pipe inclinations (ReSG = 4000 and ReSL = 17000) .............................96 24. Representative photographs of annular flow patterns for horizontal, 2°, 5°, and 7° pipe inclinations (ReSG = 28000 and ReSL = 17000) ......................97 25. Flow maps for horizontal, 2°, 5°, and 7° inclined flows with distribution of heat transfer data collected ........................................................................99 26. Variation of twophase heat transfer coefficient with superficial liquid Reynolds number .........................................................................................103 27. Variation of twophase heat transfer coefficient with superficial gas Reynolds number .........................................................................................105 28. Influence of pipe inclination on twophase heat transfer coefficient for varying superficial gas and liquid Reynolds numbers .................................111 29. Variation of the twophase heat transfer coefficient (hTP, top) with the superficial gas Reynolds number for ReSL = 1500 and ReSL = 5000 ............117 30. Twophase heat transfer coefficient at circumferential locations of the pipe ...............................................................................................................119 31. Comparison of the predictions by Eq. (6.5) with all 196 experimental heat transfer data points for airwater flow in horizontal pipes ...................132 32. Comparison of the predictions by Eq. (6.6) with all 184 experimental heat transfer data points for airwater flow in 2° inclined pipes ..................132 33. Comparison of the predictions by Eq. (6.7) with all 184 experimental heat transfer data points for airwater flow in 5° inclined pipes ..................133 34. Comparison of the predictions by Eq. (6.8) with all 187 experimental heat transfer data points for airwater flow in 7° inclined pipes ..................133 xii Figure Page 35. Comparison of the predictions by Eq. (3.18) with all 405 experimental heat transfer data points for various gasliquid combinations in vertical pipes .............................................................................................................141 36. Comparison of the predictions by Eq. (6.15) with the entire experimental database (1156 data points) for various pipe inclinations and gasliquid combinations ................................................................................................144 37. Comparison of predictions by Eq. (6.21) and experimental twophase heat transfer coefficients for airwater flow in 0, 5, and 90° pipes ..............165 38. Comparison of predictions by Eq. (6.21) and experimental twophase heat transfer coefficients for various gasliquid flows in vertical pipe ........166 39. Comparison of predictions by Eq. (6.21) and experimental twophase heat transfer coefficients for all 916 data points ..........................................167 40. Comparison of predictions by Eq. (6.22) and experimental twophase heat transfer coefficients for various gasliquid flows in vertical pipe ........172 41. Comparison of predictions by Eq. (6.22) and experimental twophase heat transfer coefficients for all 916 data points ..........................................172 42. Schematic of isothermal flow test section .......................................................181 B1. Repeatability results of experimental heat transfer coefficient for airwater flow in horizontal and slightly inclined pipes ...................................202 xiii NOMENCLATURE A crosssectional area, m2 s A surface area, m2 Bo Bond number (see Eötvös number), dimensionless C constant leading coefficient, dimensionless 0 C twophase distribution coefficient, dimensionless c specific heat at constant pressure, kJ/kg·K f c Fanning friction factor, dimensionless D inside diameter of pipe, m h D hydraulic diameter, m o D outside diameter of pipe Eo Eötvös number ( ρ ρ 2 σ ) ( )gD L G = − , dimensionless F modified Froude number in Taitel and Dukler (1976) map, dimensionless P F flow pattern factor, dimensionless S F shape factor, dimensionless Fr Froude number ( u gD = 2 ), dimensionless b f bubble, plug, or slug frequency, s1 G mass flux or mass velocity, kg/s·m2 g gravitational acceleration, m/s2 xiv I inclination factor, dimensionless i electrical current, A h heat transfer coefficient, W/m2·K K slip ratio, dimensionless K wavy flow parameter in Taitel and Dukler (1976) map, dimensionless k thermal conductivity, W/m·K L length of test section, m b L bubble, plug, or slug length, m m& mass flow rate, kg/s TC@ST N Number of thermocouple at a thermocouple station ST N Number of thermocouple station Nu Nusselt number ( = hD k ), dimensionless Pr Prandtl number ( = cμ k ), dimensionless p pressure, Pa a p atmospheric pressure, Pa p pressure drop, Pa Q volumetric flow rate, m3/s q& heat transfer rate, W g q& heat generation rate, W q&′′ heat flux, W/m2 R electrical resistance, L L R liquid fraction or liquid holdup, dimensionless Re Reynolds number ( = ρuD μ ), dimensionless xv S circumference fraction in Kaminsky (1999) correlation, dimensionless L S wettedperimeter, m T dispersed bubble flow parameter in Taitel and Dukler (1976) map, dimensionless T temperature, °C u axial velocity, m/s b u bubble, plug, or slug velocity, m/s GM u drift velocity, m/s V voltage drop, V v specific volume, m3/kg w uncertainty, dimension varies with measured parameter X Martinelli parameter ( ( ) ( ) ) f ,SL f ,SG = ∂p ∂z ∂p ∂z , dimensionless x flow quality ( m m G = & & ), dimensionless Y inclination parameter in Taitel and Dukler (1976) map, dimensionless z axial coordinate Greek Symbols α void fraction, dimensionless ( ) L β R holdup dependent factor in Kaminsky (1999) correlation, dimensionless δ distance from a node to a control volume interface (see Figure 14), m ε roughness height of pipe wall, m μ dynamic viscosity, N·s/m2 ν slug frequency in Deshpande et al. (1991) correlation, s1 φ twophase multipliers, dimensionless xvi ϕ angle from the circumferential top of pipe, rad. γ electrical resistivity, L·m θ inclination angle of pipe or test section, deg. or rad. ρ density, kg/m3 σ surface tension, N/m 0 τ wall shear stress, N/m2 ψ ratio of heat transfer coefficients, dimensionless Superscripts m constant exponent, dimensionless n constant exponent, dimensionless p constant exponent, dimensionless q constant exponent, dimensionless r constant exponent, dimensionless Subscripts ATM atmosphere avg average B bulk btm bottom of pipe CAL calculated EXP experimental e node e (see Figure 14) eff effective xvii eq equilibrium state f frictional component G gas phase in inlet j index of thermocouple in the circumferential location k index of thermocouple station in the axial location L liquid phase m mixture n node n (see Figure 14) out outlet p node p (see Figure 14) SG superficial gas SL superficial liquid SYS system TP twophase top top of pipe W wall Wi inner wall Wo outer wall w node w (see Figure 14) Abbreviations A annular P plug xviii PS plug/slug S slug SB slug/bubbly SBA slug/bubbly/annular ST stratified W wavy WA wavy/annular WS wavy/slug 1 CHAPTER I INTRODUCTION In many industrial applications, such as the transport of oil and natural gas in pipelines and wellbores, the knowledge of nonboiling twophase, twocomponent (liquid and permanent gas) heat transfer is required. During the transport of twophase hydrocarbon fluids from an oil reservoir to the surface, temperature of the hydrocarbon fluids changes due to the difference in temperatures of the oil reservoir and the surface. The difference in temperature results in heat transfer between the hydrocarbon fluids and the earth surrounding the oil well. In such situation, the ability to estimate the flowing temperature profile is necessary to address several design problems in petroleum production engineering (Shiu and Beggs, 1980). In subsea oil and natural gas production, hydrocarbon fluids may exit the reservoir with a temperature of 75°C and flow in subsea surroundings of 4°C (Trevisan et al., 2006). As a result of the temperature difference between the reservoir and the surroundings, the knowledge of heat transfer is critical in the effort to prevent gas hydrate and wax deposition blockages (Furuholt, 1988). Wax deposition can cause severe problems including the reduction of inner pipe diameter causing blockage, increase in surface roughness of the pipe leading to restricted flow line pressure, decrease in 2 production, and various other mechanical problems (McClaflin and Whitfill, 1984). Here are some examples of the economical losses that caused by wax deposition blockages: (1) a direct cost of five million dollars in removing the blockage from a subsea pipeline, (2) a production downtime loss in 40 days costing 25 million dollars (Fogler, 2008), and (3) the cost of an oil platform abandonment by Lasmo Company (U.K.) that amounted to 100 million dollars (Singh et al., 2000). Schemes such as coilspring wire insert, twisted tape insert, and helical ribs have been used to promote turbulence in pipes for the purpose of enhancing heat transfer. Although such heat transfer enhancement schemes have been proven to be effective, they do come with drawbacks, such as fouling, increases in pressure drop, and even blockage. Celata et al. (1999) presented an approach to enhance heat transfer in pipe flow by injecting small amount of gas into the liquid flow to promote turbulence. In the experimental study performed by Celata et al. (1999), a uniformly heated vertical pipe was internally cooled by water, while heat transfer coefficients with and without air injection were measured. The introduction of a small air flow rate into the water flow resulted in increases of the heat transfer coefficient up to 20–40% for forcedconvection, and even larger heat transfer enhancement for mixedconvection (Celata et al., 1999). Twophase flow can occur in some situations related to the ongoing and planned space operations. In such situations, the knowledge of heat transfer characteristics is important for designing piping systems for space operations limited by size constraints (Fore et al., 1996). To investigate heat transfer mechanisms in twophase slug and annular flows under microgravity conditions, Fore et al. (1996, 1997) conducted heat 3 transfer measurements for airwater and air50% aqueous glycerin on broad of NASA’s ZeroG KC135 aircraft. Wang et al. (2004) investigated forced convection heat transfer on the shell side of a TEMAF horizontal heat exchanger using 60% aqueous glycerin and air mixture. Their work resulted in recommendation of correlations for twophase heat transfer coefficient in stratified, intermittent, and annular flows in shellandtube heat exchangers. Furthermore, since the mechanisms of heat transfer and mass transfer are analogous to one another, the knowledge of twophase heat transfer can be applicable to twophase mass transfer. In order to successfully apply the knowledge of twophase heat transfer to solve mass transfer problems, the appropriate parallels between the two mechanisms have to be first sorted out. Mass transfer in twophase flow can be found in many chemical processes. One conceivable application is predicting the rate of corrosion in pipes that transport twophase flow. In cases when chemical reactions between the pipe surface and the twophase fluids are heavily influenced by mass transfer, the ability to predict the mass transfer coefficient becomes very beneficial to engineers. Although twophase flow may occur in different types, such as gasliquid flow, gassolid flow, and liquidsolid flow, it should be noted that the focus of present study is on twophase gas and liquid pipe flow. 1.1 Basic Definitions in TwoPhase Flow In gasliquid twophase pipe flow, the gas and liquid are simultaneously in interaction with each other inside the pipe. As a result, two phase flow is generally more complicated to describe physically and mathematically than single phase pipe flow. Since 4 the flow conditions in a pipe vary with the pipe length, the pipe cross section, and time, the gasliquid flow is an extremely complex threedimensional transient problem involving two different fluid properties. The definitions in twophase flow presented here are that of onedimensional flow (the flow conditions in each phase only vary with distance along the tube) and it is perhaps the most important and common method developed for analyzing twophase pressure drop, void fraction, and heat transfer. The total mass flow rate (m& ) through the tube is equal to the sum of the mass flow rates of gas ( G m& ) and liquid ( L m& ): G L m& = m& + m& . (1.1) The flow quality ( x ), which is the ratio of the gas mass flow rate to the total mass flow rate, is defined as m m m m x G L & & & & = = 1− . (1.2) The mass flux (G ) or mass velocity is commonly defined as A m G & = . (1.3) where the total cross sectional area ( A ) is the sum of the cross sectional areas occupied by both gas and liquid phases ( G L A = A + A ). Void fraction (α ) is defined as the volume of space the gas phase occupies in a given two phase flow in a pipe, hence for a total pipe cross sectional area of A , the void fraction is A Aα = G , (1.4) and the liquid holdup is 5 A A R L L = 1−α = . (1.5) Many twophase flow correlations are based on a variable called superficial velocity. The superficial velocity of a fluid phase is defined as the velocity that the phase would exhibit as if it flows through the total cross section of the pipe alone. The superficial gas velocity ( SG u ) is defined as A Gx Q u G G SG = = ρ . (1.6) The actual gas velocity can be expressed as A Q u G G α = . (1.7) Likewise, the superficial liquid velocity ( SL u ) is defined as ( ) A G x Q u L L SL = − = ρ 1 , (1.8) and the actual liquid velocity is expressed as ( )A Q u L L −α = 1 . (1.9) The slip ratio ( K ) is defined as the ratio of the actual velocities between the phases, G L L G x x u u K ρ ρ α α − − = = 1 1 . (1.10) When the actual gas velocity is equal to the actual liquid velocity ( K = 1), there is noslip between phases, and this condition is commonly referred to as homogeneous twophase flow. 6 Twophase flow requires expressions for key physical properties, such as density and viscosity. In expressing such relations, preference should be given to those equations that satisfy the property values at 100% gas or liquid flow (Levy, 1999). The twophase density ( TP ρ ) may be expressed as ρ ρ ( α ) ρ α TP L G = 1− + , (1.11) and the twophase viscosity ( TP μ ) is μ μ ( α ) μ α TP L G = 1− + . (1.12) Reynolds number in twophase flow can be expressed in several ways. The most common expression is the superficial Reynolds number. The superficial gas Reynolds number ( SG Re ) is defined as G G G SG SG u D xGD Re μ μ ρ = = , (1.13) and superficial liquid Reynolds number ( SL Re ) is defined as L L L SL SL u D x GD μ μ ρ (1 ) Re − = = . (1.14) Occasionally, the in situ liquid phase Reynolds number ( L Re ) is preferred over the superficial liquid Reynolds number ( SL Re ). In such occasion, the in situ liquid phase Reynolds number ( L Re ) is defined as D u D m Re L L L L L L L μ π α μ ρ (1 ) 4 − = = & . (1.15) 7 1.2 TwoPhase Flow Patterns The gas and liquid phases in a twophase flow can exist in several distinct morphological flow patterns. Flow patterns in twophase flow are among the most important characteristics, since they strongly influence the hydrodynamics and transport processes of twophase flow. Pressure drop, flow stability, and heat and mass transfer are all influenced by flow patterns. Flow Patterns in TwoPhase Horizontal Flow The flow patterns that may occur in twophase flow inside horizontal round tubes are shown in Figure 1. One of the main differences between the flow patterns observed for horizontal flow and those for vertical flow is that there is a tendency for stratification of the flow in horizontal flow. Regardless of the flow pattern, the gas tends to migrate toward the top of the tube while the lower portion of the tube carries more of the liquid. The descriptions of the flow patterns are as follows: Bubbly flow: At very low quality (i.e., low G m& ), bubbly flow is often observed. Due to buoyancy, the bubbles mainly flow in the upper portion of the tube. Plug flow: Plug flow is formed when coalescence of small bubbles produces larger plugtype bubbles, which flow in the upper portion of the tube. Stratified flow: At low liquid and gas flow rates, stratified flow is often observed. Because of gravitational force, the liquid flows along the bottom of a horizontal tube. 8 Wavy flow: When gas flow rate is increased in the stratified flow regime, eventually the interface becomes unstable, whereupon the interface becomes wavy. This type of flow is categorized as wavy flow. Slug flow: Slug flow is characterized by large gas bubbles almost filling the tube and separated by slugs of liquid. Annular flow: Annular flow consists of an annular liquid film and of gas core. Figure 1. Schematic of flow patterns observed in horizontal gasliquid flow (adapted from Carey, 1992) 9 Flow Patterns in TwoPhase Vertical Flow The typical flow patterns observed in twophase flow inside a vertical round tube are illustrated in Figure 2. The descriptions of the flow patterns are as follows: Bubbly flow: The gas phase is approximately uniformly distributed in the form of discrete bubbles in a continuous liquid phase. Slug flow: The gas flows as large bulletshaped bubbles along with some smaller gas bubbles distributed throughout the liquid. Churn flow: Churn flow shows some similarity with slug flow. It is, however, much more chaotic, frothy and disordered. Wispy Annular flow: When both the liquid and gas flow rates are high, an annulartype flow is observed with heavy “wisps” of entrained liquid flowing in the gas core. Annular flow: The liquid flows partly as annular film near the tube wall and partly in the form of droplets distributed in the gas core. Figure 2. Schematic of flow patterns observed in vertical gasliquid flow (adapted from Carey, 1992) 10 1.3 Research Objectives The main objective of this research is to establish a fundamental understanding of heat transfer in nonboiling twophase pipe flow. The key processes that govern heat transfer in nonboiling twophase pipe flow are flow patterns, pressure drop, void fraction, and inclination effects. The fundamental understanding of heat transfer in nonboiling twophase pipe flow can be achieved in twofold; namely, qualitatively and quantitatively. All the experimental data to be collected for flow patterns, heat transfer, pressure drop, void fraction, and flow visualization provide valuable insights to describing the physics of heat transfer in nonboiling twophase pipe flow qualitatively. However, to be able to successfully and effectively quantify heat transfer in nonboiling twophase pipe flow, the development of a general heat transfer correlation or model that has the robustness to handle all major twophase flow patterns and inclination effects is necessary. Before one can successfully establish a fundamental understanding of heat transfer in nonboiling twophase pipe flow, the following questions need to be answered: 1) How do flow patterns change as the pipe is upwardly inclined from horizontal position? 2) How does heat transfer respond when the pipe is upwardly inclined from horizontal position? 3) How does the change of one flow pattern to another flow pattern influence the heat transfer? 4) Can pressure drop be used to accurately correlate heat transfer via the Reynolds analogy used in single phase flow? 11 To address these questions, the proposed study will provide experimental data, qualitative and quantitative physical insights into the key processes that govern heat transfer in nonboiling twophase pipe flow. Hence, the following is a list of primary tasks for the overall study: Task 1: Literature search on twophase pipe flow for flow patterns, nonboiling heat transfer, pressure drop, and void fraction prediction methodologies, experimental methodologies, and experimental data. Task 2: Based on heat transfer correlations available in the literature, develop a general heat transfer correlation that has the robustness to handle all major flow patterns and upward inclination effects. Explore the viability of developing a correlation using momentum and heat transfer (Reynolds) analogy. Task 3: Collect experimental data for flow patterns, pressure drop, and heat transfer at different pipe inclinations (0, 2, 5, and 7°). Task 4: Analyze the characteristics of the key processes that govern heat transfer in nonboiling twophase pipe flow from the experimental data. Task 5: Validate the developed correlation(s) with available experimental data, from measurements and other sources in the literature. Task 6: Document and present the research findings in the forms of published papers and doctoral dissertation as deliverables. 12 1.4 Broader Impact The results of this research will provide a fundamental understanding of nonboiling twophase pipe flow and heat transfer. The database of experimental results for flow patterns, pressure drop, and heat transfer, will be a significant milestone in the road map of scientific understanding for twophase flow. Presently available computational fluid dynamics (CFD) codes are generally inadequate to predict the hydrodynamic and transport processes of twophase flow. Thus, a complete and well collected database will be very valuable for CFD codes developers who seek to validate their models with experimental data. The impact of the experimental database is summarized as follows: Flow pattern data: Flow pattern data can be used for the development and validation of methodologies for predicting twophase flow patterns, whether they are semiempirical methods, graphical methods, or numerical methods. Flow pattern data can also be used to provide input into heat transfer and pressure drop models, since flow patterns strongly influence all the hydrodynamic and transport processes. Pressure drop data: Pressure drop data will be useful in the development and validation of numerical models and pressure drop correlations. Pressure drop data can be useful in the design of twophase flow system, for example in estimating the pumping power. Heat transfer data: Heat transfer data can be used to facilitate the development and validation of numerical models and heat transfer correlations. In addition, the results of this research will serve as a bridge for the fundamental understanding of twophase flow from conventional sized pipes to miniaturized channels. 13 Presently, researchers are refining the method for distinguishing between macrochannel and microchannel twophase flow and heat transfer. A comprehensive understanding of twophase pipe flow from the proposed study will be useful for distinguishing the similarities and differences of hydrodynamic and transport process behaviors in conventional sized pipes and microchannels. 1.5 Brief Outline of this Study The contents of this manuscript are geared towards the elements that support this proposal to conduct an extensive and systematic study of heat transfer in nonboiling twophase gasliquid pipe flow. Chapter II is devoted to the review of selected literature about twophase flow in the areas of heat transfer, flow pattern maps, void fraction and the relationship of pressure drop and heat transfer. In Chapter III, the development of the twophase nonboiling correlations is discussed. Chapter IV focuses on the experimental setup and procedures used in this study. Chapter V discusses the experimental results. Chapter VI presents the validation of the correlations developed in Chapter III. Finally in Chapter VII, the summary and remaining work are laid out. 14 CHAPTER II LITERATURE REVIEW For several decades, numerous investigators have studied the hydrodynamic and transport processes of twophase gasliquid pipe flow. The works of various investigators available in the literature are discussed here. In this chapter, the literature review is categorized into four sections. Section 2.1 focuses on twophase flow heat transfer. In Section 2.2, selected literature on twophase flow patterns are discussed. In Section 2.3, the focus is on void fraction, and Section 2.4 is on the relationship of pressure drop and heat transfer. 2.1 TwoPhase Flow Heat Transfer Johnson and AbouSabe (1952) measured static pressure drop and heat transfer for twophase airwater flow in a horizontal brass tube. The tube has an inner diameter of 25.4 mm and a length of 4.57 m. The experiments were conducted in the flow rate ranges of 7.56 to 113 kg/min for water and 0 to 1.51 kg/min for air. For heat transfer measurements, the test section was heated with uniform wall temperature. For twophase flow with low air rates, Johnson and AbouSabe (1952) observed considerable increases in the heat transfer coefficients. Using the measured heat transfer data, they developed a 15 twophase flow heat transfer correlation for different flow patterns in horizontal tube. Most of the heat transfer data predicted by their correlation were within ±15% agreement with their measured data. The correlation developed by Johnson and AbouSabe (1952) is expressed as 2 0.333 1/ 2 1/ 2 ( ) 1 0.006Re L SG L L TP R h h φ + = − , (2.1) where L h can be determined using 0 8 0 4 0 023 . L . L SG Nu = . Re Pr . King (1952) investigated the characteristics of pressure drop and heat transfer for twophase flow of an airwater mixture in a horizontal copper pipe with an inner diameter of 18.7 mm. King (1952) also observed increases in the average heat transfer coefficients for twophase flow with low gas flow rates, as similarly observed by Johnson and Abou Sabe (1952). King (1952) improved the correlation proposed by Johnson and AbouSabe (1952), by adjusting the constant and exponents of the correlation. The correlation improved by King (1952) is expressed as 2 0.32 1/ 2 0.52 ( ) 1 0.025 L SG L L TP Re R h h φ + = − , (2.2) where L h can be determined using 0 8 0 4 0 023 . L . L SG Nu = . Re Pr . Fried (1954) extended the study of Johnson and AbouSabe (1952) and investigated the characteristics of pressure drop and heat transfer for airwater flow in a horizontal pipe with an inner diameter of 18.7 mm. The experiments were conducted for flow rate ranges of 7.57 to 98.4 kg/min for water and 0.0693 to 1.56 kg/min for air. The 16 heat transfer measurements were conducted with uniform pipe wall temperature. The heat transfer data measured by Fried (1954) were correlated within ±30%. Johnson (1955) extended the work of Johnson and AbouSabe (1952) and measured pressure drop and heat transfer for twophase flow of airoil mixture in a steamheated horizontal pipe. The measurements by Johnson (1955) were conducted with the same experimental apparatus used by Johnson and AbouSabe (1952). Based on the measured results, Johnson (1955) observed that the heat transfer for airoil flow was significantly greater than that for airwater flow. Groothuis and Hendal (1959) measured heat transfer for airwater and airgasoil flows. The authors observed that the introduction of small amount of air at low liquid flow rates caused an increase in heat transfer rate, which was similarly observed by Johnson and AbouSabe (1952) as well as King (1952). The correlation developed by Groothuis and Hendal (1959) is expressed as 0.87 1/3 0.14 0.029 ( / ) TP TP L B W Nu = Re Pr μ μ , (2.3) for airwater flow, and 0.39 1/3 0.14 2.6 ( / ) TP TP L B W Nu = Re Pr μ μ , (2.4) for airgasoil flow. Knott et al. (1959) measured the heat transfer rate of twophase mixture of nitrogen gas and viscous oil. The measurements were conducted with uniform heat flux. In the bubbly region, the authors attributed the increase in the twophase heat transfer coefficient to the addition of gas phase, which effectively increased the mean velocity of the mixture. Based on their observations of the experimental results, they proposed a correlation for twophase heat transfer coefficient: 17 1/ 3 1 = + SL SG L TP u u h h , (2.5) where L h is determined from Sieder and Tate (1936) equation. Davis and David (1964) used a slip model to empirically correlate the convective heat transfer in the regions of annular and annularmist flow. The authors empirically determined that the slip ratio (uG / uL) to be a function of the gasliquid density ratio (ρG / ρL). From the slip model, the following correlation was developed: 0.4 0.28 0.87 0.060 L G L L TP Pr DGx Nu = ρ μ ρ . (2.6) Using the proposed correlation, the authors showed that experimental data were correlated generally to within an averaged absolute error of 17% for vapor mass fraction above 10%. Oliver and Wright (1964) experimentally studied gasliquid slug flow in horizontal tubes with a common inner diameter of 12.7 mm for two different tube lengths (1.22 and 1.31 m). The shorter tube was used for pressure drop measurements, while the longer tube was for heat transfer measurements. The study was conducted with both Newtonian and nonNewtonian fluids. The authors observed higher heat transfer in twophase slug flow in comparison with singlephase flow. The authors also observed the maximum heat transfer occurred when the liquid holdup was between 0.3 and 0.5. When developing their correlation, Oliver and Wright (1964) employed two assumptions: (1) the slug flow was ideal, in which both gas and liquid phases moved substantially at the same velocity, and (2) the liquid phase was the dominant phase in affecting both flow and heat transfer characteristics, while the gas phase remained an inert medium. The heat 18 transfer correlation for Newtonian fluids proposed by Oliver and Wright (1964) is expressed as = − L L TP L R R Nu Nu 1.2 0.2 0.36 , (2.7) where L Nu is determined by 1/3 0.14 ( ) 615 . 1 + = W B L G L L L D Pr A Q Q D Nu μ μ μ ρ . Hughmark (1965) proposed two heat transfer correlations for gasliquid slug flow in horizontal pipes: one for turbulent slug flow and another for laminar slug flow. The correlation for turbulent slug flow was developed from the momentumheat transfer analogy, where the friction factor was determined from measured pressure drop. The correlation for turbulent slug flow covered the liquid slug Reynolds number range from 26000 to 4.5×106. For laminar slug flow, Hughmark (1965) proposed the following correlation: 1/ 3 0.14 0.5 75 . 1 = − W B L L L L TP L R k L m c Nu R μ & μ . (2.8) When compared with the experimental results documented by Oliver and Wright (1964), the correlation for laminar slug flow predicted the experimental data with a mean absolute deviation of 8.4%. For laminar flow, the range of liquid slug Reynolds number was from 1600 to 4600. Pletcher and McManus (1968) measured pressure drop and heat transfer coefficient for horizontal airwater annular flow in a tube with an inner diameter of 25.4 mm. The test section had a length of 1.52 m and was heated electrically. The heated test section was located 2.67 m downstream of the liquid injection. Measurements were 19 conducted for water flow rate varied from 1.94 to 10.4 kg/min, air flow rate varied from 0.816 to 7.00 kg/min, and heat flux between 23.3 and 40.3 kW/m2. Significant circumferential variations of tube wall temperatures at low air flow rates were observed. In addition, the authors found that the measured pressure drop agreed relatively well with the Lockhart and Martinelli (1949) correlation, and the measured heat transfer coefficients correlated well with the ( )0.4 G L X m& m& term to within ±20%. Martin and Sims (1971) studied the forced convection heat transfer to water and airwater mixtures in a horizontal rectangular channel with air injected through a porous heated wall. They defined the main dependent variables in their study as heat transfer coefficient and flow pattern, while the main independent variables were the air injection rate through the porous heated wall and both superficial velocities of gas and liquid. With no air injection through the porous heated wall, the authors observed increase in heat transfer coefficient with increasing superficial gas velocity. The heat transfer correlation proposed by Martin and Sims (1971) for the case when the air injection rate through the porous heated wall was zero is expressed as 1/ 2 64 . 0 1 = + SL SG L TP u u h h (2.9) where L h is determined by the Sieder and Tate (1936) equation. The correlation predicted 88% of the measured data within ±20%. It should be noted that this study was conducted with rectangular channel, and the authors stated that their work was incomparable with the data for round tubes. Shah (1981) presented correlations for estimating heat transfer of permanent gasliquid mixtures in horizontal and vertical channels (both circular and noncircular). The 20 correlations showed good agreement with 672 heat transfer data points from various experimental studies. The various experimental studies compiled by Shah (1981) included a range of channel hydrodynamic diameter (4 to 70 mm), 10 gasliquid combinations, and a wide range of heat and mass flux. The comparisons between the correlations and experimental data had a rootmeansquare error of 15.5%, and 96% of the data points were predicted to within ±30%. The correlation of Shah (1981) for ReSL < 170 is expressed as 1/ 4 1 = + SL SG L TP u u h h , (for <170 SL Re ) (2.10) where L h is determined from 1/3 0.14 1.86[ ( )] ( ) L SL L B W Nu = Re Pr D L μ μ . For ReSL > 170, the author presented the correlations graphically, stating that they were “too complex to be expressed mathematically.” The correlations presented graphically are difficult to use as general purpose correlations, and the results estimated by the correlations are difficult to replicate. Shoham et al. (1982) performed measurements of heat transfer characteristics for twophase gasliquid slug flow in a horizontal pipe. The heated test section was made of a brass pipe with an inner diameter of 38.1 mm. With a length to diameter ratio (L/D) of 46.2, the heated test section was heated electrically. By attaching thermocouples circumferentially around the test section, local heat transfer coefficients were measured. The measurements were performed with water flow rate range from 27.2 to 96.1 kg/min and air flow rate range from 0.136 to 0.653 kg/min. Shoham et al. (1982) observed that heat transfer coefficients at the bottom of the pipe were consistently higher than those at the top of the pipe, by as much as a factor of 2. They also observed that in the regions 21 where gas phase was in contact with the pipe surface, the heat transfer coefficients dropped to very low values. This finding supports the assumption of Oliver and Wright (1964) that the liquid phase was the dominant phase in affecting heat transfer characteristics. The ratio of bottom to top heat transfer coefficient (hTP, btm / hTP, top) was lower at high liquid and low gas flow rates. At a fixed liquid flow rate, hTP, btm / hTP, top increased with increasing gas flow rate. Kago et al. (1986) experimentally investigated flow characteristics (pressure drop and liquid holdup) and heat transfer coefficient in a horizontal pipe with an inner diameter of 51.5 mm. With a length to diameter ratio (L/D) of 9.5, the heated section was made of copper pipe and it was heated electrically. The measurements were conducted for plug and slug flow patterns, and the viscosity of the liquid phase was varied from 0.8 to 55 mPa·s. The gasliquid mixture was made of air being mixed with water or aqueous solutions of carboxymethyl cellulose, for the purpose of controlling the liquid phase viscosity in the system. The authors reported that their pressure drop measurements agreed qualitatively with the study of Baker (1954). When compared with the Lockhart and Martinelli (1949) correlation, they showed that the correlation overpredicted their measured pressure drop data. Heat transfer coefficient was observed to increase with increasing liquid velocity and decreasing liquid viscosity. In addition, Kago et al. (1986) reported that the heat transfer coefficient was nearly independent of the gas velocity when uSG < 1 m/s. However, the heat transfer coefficient increased with increasing gas velocity for 1 < SG u < 10 m/s. From the experimental results, Kago et al. (1986) developed a heat transfer correlation for 3×102 < ReSL < 3×105, and it is expressed as 22 (0.021Re 4.5) Pr {1 0.3exp[ 0.5( 2) ]} 2 0.14 0.8 1/ 3 + − − = + L W L B TP L L Nu Fr μ μ , (2.11) where 1/ 2 Re = −L L SL L L R Du μ ρ and gD u Fr SL L = . Deshpande et al. (1991) performed heat transfer measurements for airwater plugslug flow in horizontal pipes with two different inner diameters (25.4 and 56.9 mm). The stainless steel test section was 1.7 m long and heated electrically. The measurements were conducted with water velocity ranged from 0.2 to 1.1 m/s and the air velocity was adjusted to as high as 3.6 m/s. According to this study, the twophase mixture velocity and slug frequency were two important factors that influenced the heat transfer coefficient at the top of the pipe (hTP, top). Deshpande et al. (1991) also observed that the heat transfer coefficients at the bottom of the pipe (hTP, btm) were always greater than those at the top of the pipe (hTP, top), which was similar to the finding of Shoham et al. (1982). In addition, they observed that as the superficial liquid velocity (uSL) increased, the (hTP, top / hTP, btm) ratio decreased due to increase in slug frequency. The authors presented correlations to estimate hTP, top, hTP, btm, and hTP, avg. When compared with the experimental data, 93.5% of the data points for hTP, btm and hTP, avg were within ±10% agreement, while 90% the data points for hTP, top were within ±15% agreement. The correlations developed by Deshpande et al. (1991) for hTP, top, hTP, btm, and hTP, avg are expressed as 0.3 0.83 0.4 , 1 . 0 Pr Re 023 . 0 = − m SL TP btm L L u u Nu , (2.12) 23 0.21 0.53 0.44 0.4 , Pr Re 93 . 1 = g u u u Nu SL m SL TP top m m ν , (2.13) 0.76 0.83 0.4 , Pr Re 023 . 0 = m SL TP avg m m u u Nu , (2.14) where L m L L Du Re μ ρ = , m m m m Du Re μ ρ = , m SL SG u = u + u , and 1 02 2 2 02 0 0434 . m m SL gD u D . u u . + ν = . Hetsroni et al. (1998a, b) investigated the heat transfer of plug flow for airwater mixture in horizontal and slightly inclined (2 and 5°) tube. The tube wall was heated electrically and the thermal profiles were observed using infrared thermographs. The heated test section had an inner diameter of 49.2 mm and a length to diameter ratio (L/D) of 3.6. Thermographs were obtained at axial locations of x/D = 0.45, 0.9, and 2.4. According to the authors’ analysis, superficial liquid velocity (uSL), bubble length (Lb), bubble velocity (ub), and bubble frequency (fb) were the main parameters that influenced heat transfer coefficient at the upper part of the tube. They also observed that the heat transfer coefficient for inclined tube to be much higher than that in horizontal tube. The heat transfer correlation proposed by Hetsroni et al. (1998a, b) is expressed as ϕ < 0.3 TP TP L h = 0.15(h ) + 0.85h ϕ , for 0.9 Fr 2.0 L < < 0.03 Fr 0.43 G < < (2.15) where ϕ ( ) TP h and L h are determined using 24 = + − b b b TP L L u f L (h ) h 0.40 0.54Fr exp 1.2 ϕ , 0 83 0 5 0 0155 . L . L L Nu = . Re Pr . Kim et al. (1999) conducted an extensive survey of twophase flow heat transfer correlations and experimental data that were available in the literature. In this survey, the authors identified 20 heat transfer correlations and seven sets of experimental data. The main purpose of this study was to check the validity of the correlations available in the literature. Table 1 shows the sources of the seven experimental data sets used by Kim et al. (1999) in their study. Table 2 shows the 20 correlations identified in the study. Among the correlations and experimental data identified by Kim et al. (1999), there were only six correlations and two sets of experimental data applicable for horizontal flow. The rest of the correlations and experimental data sets were for vertical flow. In addition, correlations for horizontal flow were mainly applicable to specific flow patterns. Kim et al. (1999) found no correlation and experimental data set that were applicable for inclined flow. Table 1. Experimental data sets used in the study by Kim et al. (1999) Source Orientation Fluids No. of data points Aggour (1978) Vertical Heliumwater 53 Aggour (1978) Vertical R12water 44 Vijay (1978) Vertical Airwater 139 Vijay (1978) Vertical Airglycerin 57 Rezkallah (1987) Vertical Airsilicone 162 King (1952) Horizontal Airwater 48 Pletcher (1966) Horizontal Airwater 21 25 Table 2. Heat transfer correlations chosen in the study by Kim et al. (1999) 26 Table 2. (continued) 27 Kaminsky (1999) surveyed the literature and proposed correlations for estimating twophase heat transfer coefficient in horizontal and vertical pipes. According to this study, the experimental data that were available in the literature were largely limited to pipes with small diameters, low operating pressures, and airwater systems. For laminar flow (ReSL < 2100), Kaminsky (1999) proposed a heat transfer correlation, which was a function of liquid holdup. The correlation is expressed as 1 3 , (R D / D) R h h L h L L L TP β = , for < 2100 SL Re (laminar) (2.16) For turbulent flow (ReSL > 2100), the author proposed a correlation that was derived from the momentumheat transfer analogy. A parameter called the circumference fraction (S) was also introduced to the correlation. The correlation for turbulent flow is expressed as 1/ 2 S h h L L TP =φ , for > 2100 SL Re (turbulent) (2.17) where L h is determined by the Sieder and Tate (1936) equation. When compared with experimental data, the results predicted by the correlation showed significant deviations for some of the horizontal flow cases. The author stated that the deviations were the results of having assumed S = 1 and large viscosity divergence between the viscosities evaluated at the bulk and at the pipe wall temperatures. In addition, there were very limited data for horizontal twophase flow, especially for the laminar flow (ReSL < 2100). Kim and Ghajar (2002) performed measurements of heat transfer coefficients for different flow patterns in a horizontal pipe. A total of 150 twophase flow heat transfer data points for various flow patterns were measured under uniform heat flux condition. The measurements were collected for superficial liquid Reynolds number ranged from 640 to 35500 and superficial gas Reynolds number ranged from 40 to 21200. 28 Based on the experimental data, Kim and Ghajar (2002) developed a correlation for the overall heat transfer coefficient of twophase flow with different flow patterns in a horizontal pipe. The correlation developed by Kim and Ghajar (2002) is expressed as q L G p L G m n L TP x x C h h − − = + − μ μ α α α Pr Pr 1 1 1 (1 ) , (2.18) for slug and slug transition flow C = 2.86 , m = 0.42 , n = 0.35 , p = 0.66, and q = −0.72 for wavyannular flow C = 1.58 , m = 1.40 , n = 0.54 , p = −1.93, and q = −0.09 for wavy flow C = 27.89 , m = 3.10 , n = −4.44 , p = −9.65, and q = 1.56 where L h is determined by the Sieder and Tate (1936) equation. The proposed correlation predicted the experimental data with a rootmeansquare error of 12%. However, the correlation did not cover all observed flow patterns, such as stratified flow, annular flow, and bubbly flow. Ghajar and Kim (2005) developed a general heat transfer correlation based on the work by Kim et al. (2000). The correlation was validated with 408 experimental data points for 0°, 2°, 5°, and 7° inclinations over a wide range of flow patterns. To handle the effects of various flow patterns and inclination angles on the twophase heat transfer data with only one correlation, the flow pattern factor (FP) and the inclination factor (I) were developed. The correlation successfully predicted 90% of the experimental data within ±20%. At the current state of knowledge, the correlation developed by Ghajar and Kim (2005) may be considered the most robust in terms of handling various inclination and flow pattern effects. However, the correlation has not been validated for inclination angles above 7°. The correlation developed by Ghajar and Kim (2005) is expressed as = + TP P L h F h 1 where L h is determined by the Sieder and Tate (1936) equation. Hewitt and Roberts (1969) commonly recommended for flow pattern map, the vertical axis represented the superficial gas momentum flux and the horizontal axis represented the superfi Roberts (1969) map perform Figure 3. Flow map for vertical flow by Hewitt and Roberts (1969) 29 ( ) − − r q L G p L G n P P m I Pr Pr F F x x C μ 1 μ 1 2.2 TwoPhase Flow Pattern Maps introduced a flow pattern map twophase upward vertical flow (see Figure superficial liquid momentum flux. performed reasonably well for airwater and steamwater (2.19) that has been 3). On their . The Hewitt and flows. Taitel and Dukler transition boundaries of flow. Five dimensionless parameters were introduced to characterize the flow pattern boundaries. The theoretical flow patterns transi The five dimensionless parameters used in the SG Dg cos u F θ = 1 2 SL K = F Re , ( ( ) − ∂ ∂ = ρ ρ p z T L G ( ) ( ) ∂ ∂ ∂ ∂ = f , f , p z p z X ( ) ( ) L G p z g Y ∂ ∂ − = ρ ρ Figure 4. Flow map for horizontal 30 (1976) developed a comprehensive model five flow patterns in horizontal and near horizontal gas transition boundaries are shown in Taitel and Dukler (1976) map are given as L G G ρ ρ ρ − , ) 1 2 g cosθ SL , 1 2 SG SL , SG sinθ . and near horizontal flow by Taitel and mprehensive for determining gasliquid tion Figure 4. (2.20) (2.21) (2.22) (2.23) (2.24) Dukler (1976) Weisman et al. (1979) cm) and fluid properties patterns in horizontal pipes (see Figure 5) in terms of dimensionless correlations water flow, ϕ1 and ϕ2 are Figure 5. Flow map for horizontal 31 investigated the influences of pipe diameters (viscosity, density, and surface tension) on two pipes. From their flow pattern data, an overall fl ) uSG / ϕ1 and uSL / ϕ2 was established. Both for predicting the transition boundaries. For the case of air 1.0. airwater flow by Weisman et al (1.27 to 5.08 twophase flow flow pattern map ϕ1 and ϕ2 are airet al. (1979) Spedding and Nguyen (1980) flow data, for vertically downward horizontal flow showed the regions of slug flow, droplet flow, flow patterns within the main fl Figure 6. Flow map for horizontal flow by 32 provided flow pattern maps, based on to vertically upward flow. Their flow four main flow patterns (stratified fl and mixed flow). In additional, there were 13 flow patterns (see Figure 6). Spedding and Nguyen airwater w pattern map for flow, bubble and subdivisions of (1980) 33 2.3 Void Fraction Dukler et al. (1964) compared three void fraction correlations (Lockhart & Martinelli, 1949; Hoogendoorn, 1959; and Hughmark, 1962) with 706 refined void fraction data collected by Hogendoorn (1959). The 706 void fraction data of Hogendoorn (1959) were collected from test runs in 24.5, 50.8, 88.9, and 139.7 mm (1, 2, 3½ and 5½ in.) diameter pipes for horizontal flows. Using statistical methods, Dukler et al. (1964) concluded that the Hughmark (1962) correlation was able to perform better than the other two. Chisholm (1973) developed equations for determining void fraction (α ) and slip ratio ( K ). The equations can be expressed as 1 2 1 1 1 − − = + L G / m L x x ρ ρ ρ ρ α , (2.25) and 1 2 = m L K ρ ρ , (2.26) where m ρ is the homogeneous mixture density and is defined as m L G x x ρ ρ ρ + − = 1 1 . (2.27) Marcano (1973) compared six void fraction correlations (Lockhart & Martinelli, 1949; Hughmark, 1962; Dukler et al., 1969; Eaton et al., 1967; Guzhov et al., 1967; and Beggs, 1972) with 238 natural gaswater data from Eaton (1966) and 58 airwater data from Beggs (1972). Marcano (1973) concluded that the Eaton et al. (1967) and Beggs (1972) correlations performed well due to the fact that the data used for comparison were 34 the data from which these correlations are developed. The correlations of Dukler et al. (1969) and Lockhart and Martinelli (1949) were found to perform satisfactorily, while the other correlations performed unsatisfactorily. In addition, the correlations by Eaton et al. (1967), Guzhov et al. (1967), and Beggs (1972) were found to have better performance for void fraction less than 0.65. For void fraction greater than 0.9, none of the six correlations gave reasonable accuracy. Palmer (1975) compared three void fraction correlations (Flanigan, 1958; Guzhov et al., 1967; and Beggs, 1972) with 174 natural gaswater data. The 174 experimental data were collected from a 50.8 mm (2 in.) diameter pipe with three (4.2, 7.1 and 7.5°) uphill and three downhill (3.8, 4.3 and 6.3°) orientations. Palmer (1975) concluded that the correlation by Beggs (1972) performed well for uphill flow, and the correlation by Flanigan (1958) was the least accurate among the three. Butterworth (1975) summarized some of the well known empirical equations for void fraction (α ) and slip ratio ( K ) having the following forms: r G L q L G P x x C − = − μ μ ρ ρ α 1 α 1 , (2.28) and r G L q L G p L G x x C V V K − = = − − μ μ ρ ρ 1 1 1 . (2.29) The values of C, p, q, and r for the different correlations are given in Table 3: 35 Table 3. Values of constants suggested for the various models and correlations summarized by Butterworth (1975) Model or Correlation C p q r Homogeneous Model 1 1 1 0 Zivi (1964) model 1 1 0.67 0 Turner & Wallis (1965) model 1 0.72 0.40 0.08 Lockhart & Martinelli (1949) correlation 0.28 0.64 0.36 0.07 Thom (1964) correlation 1 1 0.89 0.18 Baroczy (1966) correlation 1 0.74 0.65 0.13 Mandhane et al. (1975) compared twelve void fraction correlations (Lockhart & Martinelli, 1949; Hoogendoorn, 1959; Levy, 1960; Hughmark, 1962; Scott, 1962; Hughmark, 1965; Eaton et al., 1967; Guzhov et al., 1967; Chawla, 1969; Dukler et al., 1969; Beggs, 1972; and Agrawal et al., 1973) using 2700 void fraction data collected at the University of Calgary. Comparing the twelve correlations with the flow pattern maps by Baker (1954), Hoogendoorn (1959), Govier and Aziz (1972), and Mandhane et al. (1974), it was concluded that the correlation by Hughmark (1962) predicted the bubble, elongated bubble flow in all the four flow pattern maps and the slug flow in all but the flow pattern map by Baker (1954). The Agrawal et al. (1973) correlation predicted the stratified flow in the Mandhane et al. (1974) and Baker (1954) flow pattern maps, while the Dukler et al. (1964) correlation predicted those of Hoogendoorn (1959) and Govier and Aziz (1972). The Beggs (1972) correlation predicted the dispersedbubble flow in the flow pattern maps by Mandhane et al. (1975), while the Hughmark (1962) correlation predicted those of Hoogendoorn (1959) and Govier and Aziz (1972). Mandhane et al. 36 (1975) concluded that none of the twelve correlations was able to give satisfactory prediction in the annular and annularmist flow. Papathanassiou (1983) came up with a void fraction spectrum graph by deducing the physically realistic range within which twophase flow exists for a set of operating conditions and specified fluid. The void fraction spectrum graph was used to compare four void fraction correlations (Lockhart & Martinelli, 1949; Hoogendoorn, 1959; Bankoff, 1960; and Hughmark, 1962). Papathanassiou (1983) concluded that at void fraction about 0.4, the Lockhart and Martinelli (1949) correlation was out of the physically realistic range. At void fraction of greater than 0.7, the correlation by Bankoff (1960) was found to be outside the realistic region. The disagreement between the void fraction correlations in the lower and upper extreme ranges of void fraction is explained by the fact that few experimental results at this range exist when the correlations were developed. Abdulmajeed (1996) collected 88 airkerosene void fraction data in a horizontal 50.8 mm (2 in.) diameter pipe and compared the data with 15 void fraction correlations. The 88 void fraction data were used in an effort to simplify the mechanistic model of Taitel and Dukler (1976) and develop a new void fraction correlation. The void fraction correlation developed by Abdulmajeed (1996) was able to predict void fraction in stratified, slug and annular flow, in contrast to the implicit Taitel and Dukler (1976) model which was specifically developed for stratified flow. Spedding (1997) extensively compared over 100 void fraction correlations with the experimental data collected by Spedding and his coworkers (1976, 1979, 1989, 1991, and 1993) for pipe diameters ranging from 26 to 95.3 mm. Spedding (1997) noted that no 37 single correlation could satisfactorily handle all flow regimes and angles of inclination. Different void fraction correlations were recommended specifically for various flow patterns and pipe orientations. Woldesemayat and Ghajar (2007) conducted a comprehensive review of 68 void fraction correlations and 2845 experimental data points for horizontal and upward inclined twophase pipe flow from various sources. Based on the findings of this extensive review, Woldesemayat and Ghajar (2007) recommended a general void fraction correlation that predicted 85.6% of the 2845 experimental data points within ±15%. The general void fraction correlation recommended by Woldesemayat and Ghajar (2007) will be validated with our experimental setup. 38 2.4 Relationship of Pressure Drop and Heat Transfer Several investigators have attempted to correlate pressure drop and heat transfer for twophase pipe flow. In this section, selected literature which documented the effort of relating pressure drop with heat transfer are considered. The parameters regularly found in the literature relating pressure drop with heat transfer are in the following forms: The twophase multipliers defined by Lockhart and Martinelli (1949) are expressed as f SL f TP L p z p z , 2 , ( ) ( ) ∂ ∂ ∂ ∂ φ = , (2.30) and f SG f TP G p z p z , 2 , ( ) ( ) ∂ ∂ ∂ ∂ φ = . (2.31) The Martinelli parameter is expressed as f SG f SL p z p z X , 2 , ( ) ( ) ∂ ∂ ∂ ∂ = . (2.32) The ratio of the twophase flow heat transfer coefficient ( TP h ) to the single phase liquid flow heat transfer coefficient ( L h ) is expressed as TP L h / h ψ 2 = . (2.33) Johnson and AbouSabe (1952) stated in their study that even though their pressure drop results were within ±30% agreement with the analysis of Lockhart and Martinelli (1949), there were significant secondary flow effects that they observed that were not accounted for by Lockhart and Martinelli (1949). Johnson and AbouSabe (1952) did not give clear explanations for the secondary flow effects, and suggested that 39 the flow patterns play a significant role. Johnson and AbouSabe (1952) correlated their experimental data for 2 2 L ψ φ versus X to within ±20%. King (1952) showed that with appropriate correction to allow for the change of momentum of the fluids, one could correlate the twophase nonisothermal pressure drop with heat transfer coefficient by means of the Martinelli parameter ( X ). King (1952) also proposed that 2 2 / L ψ φ as a function of X as a good correlation, which was very similar to the approach presented by Johnson and AbouSabe (1952). Fried (1954) extended the work of Johnson and AbouSabe (1952) and showed that the Martinelli correlation was in well agreement with his isothermal pressure drop data. Fried (1954) also found that the nonisothermal pressure drop was greater than the isothermal by as much as 55%. It was suggested that the difference was due to the change in kinetic energy. After compensating for the change in kinetic energy in the phases, Fried (1954) concluded that the Martinelli correlation was still applicable for nonisothermal flow. However, the compensation method that he used was not specified. Johnson (1955) also extended the work of Johnson and AbouSabe (1952) and measured heat transfer and static pressure drop for twophase twocomponent flow in a horizontal pipe. The pipe was made of copper and it was heated by steam. Correlations for heat transfer and nonisothermal pressure drop were compared with results from airoil and airwater flows. Hughmark (1965) used the analogy of momentumheat transfer (Reynolds analogy) to develop a heat transfer correlation for twophase turbulent slug flow in horizontal pipe. Using a very similar manner as the Reynolds analogy for single phase flow, the twophase flow heat transfer coefficient and the friction factor were related. The 40 correlation was tested with the experimental data from Johnson and AbouSabe (1952) and Johnson (1955). However, the size of the data was limited and the accuracy of the correlation was inconclusive. Pletcher and McManus (1968) found that for airwater annular flow in a horizontal tube, there was no significant difference between the nonisothermal pressure drop and the isothermal pressure drop. The experimental data were correlated by plotting TP L h /φ versus X and TP L h /φ versus 0.4 ( / ) G L X m& m& . The agreement between the measured and correlated data was within ±20%. Vijay et al. (1982) correlated the twophase flow heat transfer in a vertical tube by adopting and modifying the correlation for horizontal flow developed by Fried (1954). The correlation presented was expressed in a general form as q SL p TP L h / h C( ) Re ψ 2 = = φ 2 , (2.34) where C, p, and q are adjustable constants to address flow characteristics such as flow pattern. Vijay et al. (1982) tested the correlation with various flow patterns in vertical flow and found that C = 1.148, p = 0.454, and q = −0.020 would give a rootmeansquare deviation of 18%. Kaminsky (1999) developed a correlation for twophase flow heat transfer based on the momentum and heat transfer analogy. The correlation for > 2100 SL Re is expressed as TP L L ψ 2 h h S1/ 2φ = / = , (2.35) where the circumference fraction (S) was given as S =1 for all flow patterns (vertical) and slug and annular flows (horizontal), 41 1−α = S −sin(2π S) 2π for stratified flow (horizontal). It was reported that the correlation predicted the experimental data from various sources to within ±33%. 2.5 Chapter Summary Throughout this chapter, the literature on twophase heat transfer, flow pattern maps, void fractions, and the relationship of pressure drop and heat transfer are discussed. After reviewing the literature, it is clear that heat transfer data for twophase flow are limited, especially with the effects of inclination. Likewise, flow pattern maps for inclined twophase flow are virtually nonexistence. Although, there are many correlations and experimental data on void fraction available in the literature, it should be noted that very few studies have been reported whereby the investigators combined study of heat transfer, flow patterns, void fraction, and pressure drop in their work. 42 CHAPTER III DEVELOPMENT OF NONBOILING TWOPHASE HEAT TRANSFER CORRELATIONS In the preceding chapter, several nonboiling twophase heat transfer correlations available in the literature have been surveyed. From those correlations, common parameters were indentified and used for the development of two nonboiling twophase heat transfer correlations in this study. In this chapter, the development of two nonboiling twophase heat transfer correlations is discussed. The first correlation, which is referred to as a general nonboiling twophase heat transfer correlation, was developed based on the variables that influence the heat transfer in twophase pipe flow. The second correlation, which is referred to as a Reynolds analogy twophase heat transfer correlation, was developed based on the analogy of momentum and heat transfer. 3.1 Development of a General NonBoiling TwoPhase Heat Transfer Correlation The development of a general nonboiling twophase heat transfer correlation can be approached in a similar manner used for developing heat transfer correlation for single phase flow. For steadystate incompressible single phase flow in a pipe, the variables that 43 influence the heat transfer are k, c, u, ρ, μ, and D. With three reference dimensions (mass, length, and time), according to Buckingham pi theorem three dimensionless parameters can be defined: Nu = hD k , (3.1) Re = uρD μ , (3.2) and Pr = cμ k . (3.3) From the above three dimensionless parameters, the Nusselt number and its functional dependence can be expressed as Nu = f (Re,Pr). (3.4) Based on the functional expression for Nusselt number expressed in Eq. (3.4), an empirical correlation can be represented as a b CRe Pr k hD Nu = = or a b h = CRe Pr (3.5) where a, b, and C are constants to be determined from experimental data. In nonboiling twophase pipe flow, assuming incompressible phases, the twophase heat transfer is influenced by the phasic heat transfer coefficients: TP L G h C h C h 1 2 = + or L G L TP h h C C C h h 1 2 1 = 1+ . (3.6) Using the expression represented in Eq. (3.5), the above equation can be written as 44 b L G a SL SG L TP Pr Pr Re Re C C C h h = + 1 2 1 1 . (3.7) Substituting the definitions of superficial gas and liquid Reynolds numbers (ReSG and ReSL) into Eq. (3.7) yields b L G a SL L L SG G G L TP Pr Pr u D u D C C C h h = + ρ μ ρ μ 1 2 1 1 . (3.8) Also, using the definition of the mass flow rate for the gas and liquid phases, m u A G SG G & = ρ and m u A L SL L & = ρ , the following expression is obtained: x x u u m m SL L SG G L G − = = ρ 1 ρ & & . (3.9) Substituting Eq. (3.9) into Eq. (3.8) and rearranging yields d G L b L G a L TP Pr Pr x x C C C h h − = + μ μ 1 1 1 2 1 or − = + d G L b L G a TP L Pr Pr x x C C h C h μ μ 1 1 1 2 1 . (3.10) Equation (3.10) is an unrefined expression of the nonboiling twophase heat transfer correlation. In order to refine the nonboiling twophase heat transfer correlation, such that it is suitable for predicting heat transfer coefficients of flow with various flow patterns and pipe inclinations, additional parameters need to be introduced to Eq. (3.10). 45 3.2 Flow Pattern Factor and Inclination Factor Flow Pattern Factor In twophase flow, flow patterns play an important role and influence the hydrodynamics, which in turn influence the thermal aspect of the flow. For the twophase heat transfer correlation to effectively address the influence of flow patterns on the heat transfer coefficients, a parameter to represent the flow patterns need to be introduced. Taitel and Dukler (1976) developed a comprehensive model for describing transitions of flow patterns. In the model developed by Taitel and Dukler (1976), the transition boundary between the stratified and intermittent (slug, plug, and semislug flows) or annulardispersed regions can be represented in terms of a flow pattern map with a modified Froude number (F) versus the Martinelli parameter (X), see Figure 4 (p. 30). The modified Froude number (F) introduced by Taitel and Dukler (1976) can be expressed as ρ ρ θ ρ Dg cos u F G L G G − = or (ρ ρ ) θ ρ cos 2 L G G G Dg u F − = . (3.11) The introduction of the modified Froude number (F) by Taitel and Dukler (1976) as one of the parameters representing the transition boundary between flow pattern regions indicated that inertia and gravitational forces have significant influence on flow pattern transitions. When developing a parameter to represent the flow patterns in their twophase heat transfer correlation, Kim and Ghajar (2006) introduced the flow pattern factor, 2 , = D S F L eff P π . (3.12) 46 The flow pattern factor ( P F ) was represented as the square ratio of the effective wettedperimeter ( L eff S , ) to the circumference of a circular pipe (see Figure 7). Based on the Eq. (3.12), the flow pattern factor ( P F ) gives value approaching unity for flow pattern (e.g. plug or annular) that has effective wettedperimeter approximately the circumference of the pipe. With void fraction, inertia and gravitational forces as factors that influence flow patterns, the flow pattern factor can be expressed as α 2α (1 ) P S F = − + F . (3.13) The shape factor ( S F ), appears in Eq. (3.13), is in essence a normalized and modified Froude number: − − = − ( ) ( ) tan 2 2 1 L G G G L S g D u u F ρ ρ ρ π . (3.14) The shape factor ( S F ), is applicable for slip ratios (= ) ≥1 G L K u u , which is common in gasliquid flow, and represents the shape changes of the gasliquid interface by the force acting on the interface due to the relative momentum and gravity forces. Figure 7. Gasliquid interface and wettedperimeter (from Kim and Ghajar, 2006) 47 In vertical twophase flow, the effective wettedperimeter ( L eff S , ) is typically the circumference of the pipe (see Figure 2, p. 9). For a vertical pipe, the cosθ term in Eq. (3.14) is zero, rendering the shape factor ( S F ) as unity, and thus the flow pattern factor ( P F ) in Eq. (3.13) is unity as well. According to Eq. (3.12), the flow pattern factor ( P F ) is unity when the effective wettedperimeter ( L eff S , ) is equal to the circumference of the pipe. Also, in single phase liquid flow, the flow pattern factor ( P F ) is unity, since the void fraction is zero. Inclination Factor Ghajar and Kim (2005) proposed a parameter called the inclination factor ( I ) to account for the influence of inclination on twophase heat transfer coefficient. Due to the density difference between gas and liquid, the liquid phase is much more affected by the inclination effects. In inclined pipes, the inclination factor ( I ) proposed by Ghajar and Kim (2005) takes into account the gravitational and liquid inertia forces, which is expressed as 2 ( )sin 1 L SL L G u gD I ρ ρ −ρ θ = + . (3.15) When used with the twophase heat transfer correlation [see Eq. (2.19)], the inclination factor [see Eq. (3.15)] has contributed favorably to the heat transfer correlation to accurately predict experimental data (all data points within ±30%) for slightly inclined flow (2°, 5°, and 7°) with ReSL > 2000 (Ghajar and Kim, 2005; Tang and Ghajar, 2007) However, for flow in slightly inclined pipe and ReSL < 2000, the twophase heat transfer correlation [see Eq. (2.19)] along with the inclination factor [see Eq. (3.15)] 48 only predicted 75% of the experimental data points to within ±30% (Tang and Ghajar, 2007). Upon revisiting the twophase heat transfer correlation, Eq. (2.19), along with the equation for inclination factor, Eq. (3.15), Ghajar and Tang (2008a) realized that the correlation has not accounted for the surface tension force. Surface tension is a variable that can affect the hydrodynamics of gasliquid twophase flow, especially for cases with low liquid inertia force (low ReSL). For low liquid inertia twophase flow, as the balance between the inertia and gravitational forces change and rebalance, surface tension force plays an important role in the behavior of the gasliquid interface (Ghajar and Tang, 2008b; Ghajar and Tang, 2009; Ghajar and Tang, 2010). Rather than using Eq. (3.15) to represent the inclination factor, which has not accounted for surface tension force, it is sensible to include the surface tension when expressing the inclination factor. Although liquid inertia force is extremely important in twophase pipe flows, it has been accounted for during the development of the twophase heat transfer correlation (see Section 3.1). Taking the surface tension force into account, the expression for the inclination factor may therefore be represented as I = 1 + Eo sinθ , (3.16) where the Eötvös number (Eo) is defined as ( ) σ ρ ρ 2 gD Eo L G − = . (3.17) The Eötvös number (Eo), sometimes referred as Bond number (Bo), represents the hydrodynamic interaction between gravitational and surface tension forces that occurs in twophase flow. 49 3.3 General NonBoiling TwoPhase Heat Transfer Correlation The parameters that represent the influences of flow pattern and pipe inclination on twophase heat transfer have been developed in previous section (see Section 3.2). Having the flow pattern factor (FP) and the inclination factor (I) representing the influences of flow pattern and pipe inclination, the heat transfer correlation expressed in Eq. (3.10) can be refined as a general nonboiling twophase heat transfer correlation. The term “general” implies that the nonboiling twophase heat transfer correlation has the robustness of predicting heat transfer coefficients for twophase flow with various flow patterns, pipe inclinations, and gasliquid combinations. In addition, the general nonboiling twophase heat transfer correlation is developed to handle wide ranges of superficial gas and liquid Reynolds numbers (ReSG and ReSL). The nonboiling twophase heat transfer correlation developed in Section 3.1 is given in Eq. (3.10): − = + d G L b L G a TP L Pr Pr x x C C h C h μ μ 1 1 1 2 1 . (3.10) where C1 and C2 are parameters representing the influences of flow pattern and pipe inclination on the twophase heat transfer coefficient. With the flow pattern factor and inclination factor developed in Section 3.2, the expressions for C1 and C2/C1 can be represented such that P C ∝ F 1 and r m P P I F F C C − ∝ 1 1 2 , 50 where m and r are constant exponents. Applying the above representations for C1 and C2/C1 into the nonboiling twophase heat transfer correlation, Eq. (3.10), yields − − = + r q G L p L G n P P m TP P L I Pr Pr F F x x h F h C μ 1 μ 1 1 , (3.18) where the coefficient C and exponents m, n, p, q, and r are values to be determined from experimental data. The flow pattern factor ( P F ) and inclination factor ( I ) are evaluated using Eq. (3.13) and Eq. (3.16), respectively. In Eq. (3.18), the liquid phase heat transfer coefficient (hL) is evaluated using the Sieder and Tate (1936) correlations: For stratified flow (θ = 0°, ReSL < 2200 and ReSG < 10000), 1/ 3 0.14 1/ 3 1/ 3 1.86 W L L B L L L L D D k Pr Re h = μ μ ; (3.19) and for all other flow patterns, 0.14 4 / 5 1/ 3 0.027 W L L B L L L D k Pr Re h = μ μ . (3.20) Equations (3.19) and (3.20) are single phase heat transfer correlations proposed by Sieder and Tate (1936) for laminar and turbulent flows, respectively. For the in situ liquid phase Reynolds number (ReL) in Eq. (3.19) and Eq. (3.20), the following relationship is used rather than the superficial liquid Reynolds number: μ μ π ( α ) ρ − = = 1 4 D u D m Re L L L L L L L & . (1.15) 51 To evaluate the value of void fraction (α ) in the expressions for flow pattern factor ( P F ) [see Eq. (3.13)] and in situ liquid phase Reynolds number (ReL) [see Eq. (1.15)], the correlation developed by Woldesemayat and Ghajar (2007) is used: 1 0.25 2 1 ( ) ( ) 1 2.9 0.1 − − + = + 2 L ρ σ ρ ρ α ρ ρ L G SG SL SG SG C g C u u u u G L , (3.21) where ATM SYS p p C (1.22 1.22 sin ) 1 = + θ and (1 cos ) 2 C = D + θ . Note that the leading constant value of 2.9 in Eq. (3.21) carries a unit of m−0.25, and Eq. (3.21) should be used with SI units. Equation (3.18) is the general nonboiling twophase heat transfer correlation that has the robustness of predicting heat transfer coefficients for twophase pipe flow with various flow patterns, pipe inclinations, and gasliquid combinations. Since the values of C, m, n, p, q, and r are inferred from experimental measurements, Eq. (3.18) may be called an empirical correlation. The values of the leading coefficient (C) and the exponents (m, n, p, q, and r) can be varied specifically with the nature of the pipe inclination and gasliquid combinations to achieve higher level of accuracy. In order to determine the values of the leading coefficient (C) and the exponents (m, n, p, q, and r) experimental data measured in our twophase flow heat transfer laboratory as well as from other experimental studies were used. 3.4 A Reynolds Analogy Approach for Heat Transfer Estimation in NonBoiling Two Phase Pipe Flow The hydrodynamic and thermal conditions of nonboiling twophase flow are dependent upon the interaction between the two phases. Due to the complex nature of the 52 twophase gasliquid flow, the accessible heat transfer data and applicable correlations for nonboiling twophase flow are extremely limited in the literature. In most situations encountered by practicing engineers, direct heat transfer measurements for twophase flow are extremely difficult to perform. It is in such respect that mechanistic models for heat transfer estimation using, for example, analogy between friction factor and heat transfer can have appealing prospect. The concept of developing twophase heat transfer correlation based on the analogy of momentum and heat transfer has been explored by a few researchers (Fried, 1954; Vijay et al., 1982; Kaminsky, 1999). However, there are still many unanswered questions concerning the viability and robustness of a twophase heat transfer correlation developed based on the analogy of momentum and heat transfer. It is the goal of this study to explore the plausibility of using the Reynolds analogy to develop a mechanistic correlation to predict heat transfer coefficients for nonboiling twophase flow in pipes. Development of a Reynolds analogy Heat Transfer Correlation The development of a correlation to analogize momentum and heat transfer in nonboiling twophase pipe flow begins with the Reynolds analogy. The Reynolds analogy relates important parameters of momentum and thermal boundary layers in a simplistic form in terms of friction coefficient (cf), Nusselt number (Nu), Prandtl number (Pr), and Reynolds number (Re): 1 1 2 c = NuRe− Pr− f . (3.22) For flow inside pipes, the frictional pressure gradient is given as 2 0 4 2 = = − A m D c dz D dp f f & ρ τ . (3.23) 53 Combining both Eq. (3.22) and Eq. (3.23) yields the expression relating the heat transfer coefficient with the frictional pressure gradient: RePr dz dp m D A Nu f = − 2 2 4 & ρ . (3.24) Using the definitions for Nusselt number ( Nu ), Prandtl number ( Pr ), and Reynolds number ( Re ), Eq. (3.24) can be expressed in terms of the heat transfer coefficient ( h ) with the following expression: D A dz dp m c h f π ρ 2 = − & . (3.25) Adopting Eq. (3.25) for the use in nonboiling twophase pipe flow, the ratio of the heat transfer coefficient for the twophase flow ( TP h ) to the heat transfer coefficient for liquid singlephase flow ( L h ) becomes 2 , , L L L TP f L f TP L L TP L TP m m C dp dz dp dz m m C h h φ ρ ρ ρ ρ & & & & = = . (3.26) where C is a leading coefficient. To effectively represent twophase flow characteristics, the leading coefficient (C) would be a parameter that adequately represents certain hydrodynamic aspects of twophase flow. Note that the frictional pressure gradient ratio for the twophase flow to the liquid singlephase flow is recognized as the pressure drop multiplier ( 2 L φ ) defined by Lockhart and Martinelli (1949). In this study, the values for the twophase frictional pressure gradient, f TP dp dz , , are determined via experimental measurements, while the singlephase liquid frictional pressure gradients, f L dp dz , , are calculated using Eq. (3.23) with 54 f SL c = 16 / Re for ReSL < 2000, and the Blasius (1913) equation, 0.25 0.079/ f SL c = Re , for ReSL > 2000. In the development of their nonboiling twophase heat transfer correlation, Kim and Ghajar (2006) introduced a dimensionless parameter called the flow pattern factor (FP), see Eq. (3.13). The flow pattern factor accounts for the variety of flow patterns that can be found in twophase flow. The flow pattern factor takes into account parameters such as the void fraction, inertia and gravitational forces that influence flow patterns. Introducing the flow pattern factor (FP) as the leading coefficient of Eq. (3.26), and expressing each of the parameters in Eq. (3.26) as exponential functions, the Reynolds analogy heat transfer correlation takes on the following form: q L p L TP n m L P L TP m m F h h φ ρ ρ = & & . (3.27) The exponents in Eq. (3.27), m, n, p, and q, are constants to be determined for the experimental data. The mass flow rate (m& ) in Eq. (3.27) is the sum of the gas phase ( G m& ) and liquid phase ( L m& ) mass flow rates. The twophase density ( TP ρ ) is defined as the mass of twophase fluids per unit volume of the pipe and can be determined using TP G L ρ =αρ + (1−α)ρ . (3.28) The void fraction (α ) needed to calculate the twophase density in Eq. (3.28) is measured experimentally or estimated using void correlations recommended by Woldesemayat and Ghajar (2007). The singlephase liquid heat transfer coefficient ( L h ) is calculated using the Sieder and Tate (1936) correlation, Eq. (3.20). 55 3.5 Chapter Summary The development of two nonboiling twophase heat transfer correlations is presented in this chapter. The general nonboiling twophase heat transfer correlation was developed using important variables that influence heat transfer in twophase pipe flow. The mechanistic twophase heat transfer was developed using the Reynolds analogy to analogize momentum and heat transfer in nonboiling twophase pipe flow. Discussions on the performances of the two heat transfer correlations are presented in Chapter VI. 56 CHAPTER IV EXPERIMENTAL SETUP AND PROCEDURES The experimental setup was constructed with the capability of systematically collecting heat transfer data for all major twophase flow patterns and also slightly upward inclined flow. In this chapter, the description of the experimental setup and its instrumentation are presented. In addition, experimental procedures that are used in this experimental study are discussed. Finally, the technique for data reduction is also presented. 4.1 Description of Current Experimental Setup In this section, the main components of the current experimental setup will be briefly described. The current experimental setup was constructed with the capability of using it to measure nonboiling twophase pressure drop and heat transfer, and conduct flow visualization for all major flow patterns and upward inclination angles from 0° (horizontal) to 7°. The design and construction of this experimental setup, as well as the calibration of measuring instruments, were documented by Durant (2003). 57 Flow Loop A schematic diagram of the flow loop for the current experimental setup is illustrated in Figure 8. The mixing section, the calming and observation section, and the stainless steel test section rest on top of an aluminum Ibeam. The aluminum Ibeam is supported by a pivoting mechanism that is attached to an electric jack. The Ibeam is approximately 9.1 m (30 ft) long and the pivoting mechanism could bring the Ibeam to an upward inclination of approximately 8°. Inclination angles were measured with a contractor’s anglemeasuring tool and with a more precise digital xy axis accelerometer. The minimum resolution of the digital accelerometer is 0.5°. Supply of Working Fluids The working fluids used in this study were air and distilled water. The reservoir used for storing the distilled water is a 208liter (55 gallon) polyethylene tank. A Bell & Gosset (Series 1535) coupled centrifugal pump (size 3545 D10) is used to pump the distilled water from the reservoir. The pump draws the distilled water from the reservoir through an AquaPure AP12T water filter and an ITT Standard (Model BCF 4063) one shell and twotube pass heat exchanger. The heat exchanger is used to remove heat added to the distilled water during the experiment as well as to maintain a constant inlet liquid temperature. The cooling fluid used by the heat exchanger is tap water taken directly from the wall tap. 58 Figure 8. Flow loop of the current experimental setup 59 From the heat exchanger, the distilled water flowed through a Micro Motion (Model CMF125) Coriolis flow meter. The Coriolis flow meter is connected to a Digital FieldMount (Model RFT9739) transmitter that conditions the flow information for the data acquisition system. After passing the Coriolis flow meter, the distilled water then passes through a 1in. twelve turn gate valve. The gate valve is used to regulate the amount of distilled water that is flowing into the mixing section. From the gate valve, the distilled water flows through a 25.4 mm (1 in.) I.D. hose, and then through a oneway check valve and into the airwater mixing section. Air is supplied from an IngersollRand T30 (Model 2545) air compressor. The air supplied from the air compressor is regulated by a Speedaire (Model 4ZM22) 12.7 mm (½ in.) regulator. The air is then cooled by passing through a copper coil submerged in a vessel of water from the wall tap. The same water from the wall tap that is used for cooling the distilled water is also used for cooling the air. This is to ensure that both air and distilled water have the same inlet temperature. The air is then filtered by a Speedaire (Model 4ZL49) 12.7 mm (½ in.) air filter to remove moisture from the air before the air flow rate is being measured. From the air filter, the air flows through a Micro Motion (Model CMF100) Coriolis flow meter that is connected to another Digital FieldMount (Model RFT9739) transmitter. After passing the Coriolis flow meter, the air then passes through a needle valve, which is used to regulate the amount of air flowing into the mixing section. From the needle valve, the air flows through a flexible hose, and then through a oneway check valve and into the airwater mixing section. 60 AirWater Mixing Section The airwater mixing section is attached upstream of the calming and observation section. A schematic of the airwater mixing section is illustrated in Figure 9. This type of mixer was successfully used in twophase flow experimental studies by Ewing et al. (1999) and Kim (2000). Air and distilled water are supplied through a 25.4 mm (1 in.) copper tee and are mixed in the mixing well. After the mixing well, the temperature of the airwater twophase flow is measured by an Omega TMQSS125U6 thermal probe. Next, the airwater twophase flow enters into the calming and observation section. Calming and Observation Section The 2.24 m (88 in.) long calming and observation section is made of clear polycarbonate pipe with an inner diameter of 25.4 mm (1 in.). This gives the calming and observation section a length to diameter ratio (L/D) of 88. Airwater twophase flow leaving the mixing section is allowed to calm and develop through the calming and observation section before entering the test section. The calming and observation section also serves as the section where flow visualization is conducted. Heat Transfer Test Section The heat transfer test section is made of a schedule 10S 316 stainless steel pipe with an inner diameter of 27.9 mm (1.097 in.) and an outer diameter of 33.4 mm (1.315 in.). The heat transfer test section is 2.64 m (104 in.) long, giving a length to diameter ratio (L/D) of about 95. A schematic of the heat transfer test section is illustrated in Figure 10 (p. 62). Along the bottom of the stainless steel pipe, there are eleven pressure taps equally spaced at 25.4 cm (10 in.) interval. 61 Figure 9. Schematic of airwater mixing section 62 Figure 10. Schematic of heat transfer test section 63 Along the test section, there are 10 thermocouple stations equally spaced at 25.4 cm (10 in.) interval. Each thermocouple station has four thermocouples attached circumferentially around the pipe surface. Figure 10 (p. 62) shows the circumferential locations of the thermocouples, with “A” at the top of the pipe, “B” at 90° from the top in the clockwise direction, “C” at the bottom of the pipe, and “D” at 90° from the bottom in the clockwise direction. Omega TTT30 copperconstantan insulated Ttype thermocouples are used with Omega EXPPT20TWSH extension wire to connect to the data acquisition system. The thermocouples are cemented on the outside surface of the stainless steel test section with Omegabond 101 epoxy. The Omegabond 101 epoxy has a thermal conductivity of 1.04 W/m·K (0.6 Btu/ft·h·°F) and an electrical resistivity of 1 × 1015 2·m (3.28 × 1015 2·ft). Both ends of the stainless steel test section are attached to two 12.7 cm × 17.8 cm × 0.64 cm (5 in. × 7 in. × ¼ in.) copper plates. The two copper plates are attached to the ends of the test section by means of silversoldering. Both copper plates are connected with 4 gauge insulated cables to a LINCOLNWELD SA750 arc welder, which provides power to heat the test section with uniform heat flux. Eleven pressure tap holes were drilled along the bottom of the test section (see Figure 10). The diameters of the holes are 1.73 mm (0.068 in.), and they are equally spaced at 25.4 cm (10 in.) intervals. The holes are located at the bottom of the stainless steel pipe in order to ensure that only water could get into the pressure measuring system. The pressure taps are connected to standard selftapping saddle valves with the tapping core removed. The system pressure is measured by an Omega PX242060G absolute 64 pressure transducer, while the pressure drop between the first and the last pressure taps is measured by a Validyne DP15 differential pressure transducer. Heat Source Uniform wall heat flux is supplied to the test section by running high amperage DC current through the stainless steel test section from the LINCOLNWELD SA750 arc welder. The minimum current supplied by the LINCOLNWELD SA750 arc welder is 300 A, which is too high for flow with ReSL < 2000 and may cause dryout and local boiling. To solve this issue, a Miller Maxtron 450 DC inverter arc welder is used to supply DC current through the stainless steel test section for flow with ReSL < 2000. The current supplied by the Miller Maxtron 450 can go as low as 5 A, which is safe for operating at very low ReSL flow. This makes the measurement of heat transfer data for all major flow patterns possible. 4.2 Instrumentation Flow Rate Measurements The air flow rate is measured by Micro Motion (Model CMF100) Coriolis flow meter, and the water flow rate is measured by Micro Motion (Model CMF125) Coriolis flow meter. Both Coriolis flow meters are connected to Digital FieldMount (Model RFT9739) transmitters. The signals from the Digital FieldMount transmitters are relayed to the data acquisition system for data recording. 65 Temperature Measurements Surface temperatures of the test section are measured with Omega TTT30 Ttype thermocouples cemented on the test section using Omegabond 101. Airwater mixture temperatures before and after the test section are measured with Omega TMQSS 125U6 thermocouple probes. Signals from the thermocouples and the thermocouple probes are relayed to the data acquisition system for data recording. The calibration of the thermocouples and thermocouple probes was reported in detail by Durant (2003). Pressure Measurements Pressure drop between the first and the last pressure taps is measured using Validyne DP15 differential pressure transducer. The Validyne DP15 differential pressure transducer is connected to a Validyne CD15 carrier demodulator. Output signals from the differential pressure transducer are sent to the carrier demodulator to be demodulated, amplified and filtered. Signals from the demodulator are then relayed to the data acquisition system for data recording. Power Measurement The voltage drop across the heated test section is measured by a HP 3468B digital multimeter. The current flowing through the test section is determined by measuring the voltage drop across a shunt attached to the copper plate at the downstream of the test section. Knowing the voltage drop and the resistance across the shunt, the current flowing through the test section can be determined. The voltage drop across the shunt is recorded by the data acquisition system and the corresponding current is determined. Knowing the voltage drop across the test section and the current through the test section, the heat flux 66 on the test section can be determined. Heat fluxes obtained from electrical input and thermal output are used to check for heat balance to assure the system is working correctly. Data Acquisition System A National Instruments data acquisition system is used for recording and storing the data measured during the experiment. An AC powered fourslot National Instruments SCXI 1000 Chassis houses the data acquisition system. The chasis provides a low noise environment for signal conditioning. There are three National Instruments SCXI control modules housed inside the chassis: two SCXI 1102/B/C modules and one SCXI 1125 module. From the three modules, input signals from 40 thermocouples, two thermocouple probes, volt and current meters, and flow meters are gathered and recorded. The graphical user interface used for the data acquisition is a customized LabVIEW Virtual Instrument (VI) program developed specifically for this experimental setup. Figure 11 illustrates the graphical user interface of the LabVIEW Virtual Instrument (VI) program used for the data acquisition. The LabVIEW Virtual Instrument (VI) graphical user interface provides users with the features to monitor and record data. Data such as inlet, outlet, surrounding, and test section surface temperatures, pressure drop, system pressure, air and water mass flow rates, superficial gas and liquid Reynolds numbers, and current supplied by the DC arc welder to the test section are displayed on the graphical user interface. With these features on the graphical user interface, users can monitor the recorded data and readily identify any anomaly during the course of an experiment. 67 Figure 11. Graphical user interface of the LabVIEW Virtual Instrument (VI) program 4.3 Experimental Procedures The process of acquiring accurate experimental data requires a consistent adherence to a set of defined experimental procedures. The purpose of adhering to the experimental procedures is to maintain the integrity and repeatability of the experimental data, and proper functioning of the equipments and experimental setup. The experimental procedures are categorized into startup procedure and measurement procedure. The start 68 up procedure lists several steps to initiate the experimental setup and prepare it for conducting the measurements. The measurement procedure lists several steps to acquire quality and accurate experimental data. StartUp Procedure The startup procedure is a process that includes several steps to prepare the experimental setup for measurement. The main function of this startup procedure is to ensure that the experimental setup is operating properly and safely before the process of acquiring experimental data. Figure 12 is a flow chart illustrating the steps involved in the startup procedure. The first step in the startup procedure is turning on all electrical instruments: Digital FieldMount RFT9739 transmitters for both Coriolis flow meters, Validyne CD15 carrier demodulator for the differential pressure transducer, and the National Instruments data acquisition system. Once the data acquisition system is turned on, the LabVIEW Virtual Instrument (VI) program is launched and readings of all the thermocouples are monitored to ensure they are the same with the surrounding temperature. This process of checking the thermocouples’ readings with the surrounding temperature provides an initial and quick indication whether the thermocouples are working properly. The second step in the startup procedure is checking the Speedaire air filter and the AquaPure water filter. This process of checking the air and water filters is to ensure their functionality, and to maintain periodic replacement of the old filters. Old, dirty, and worn filters not only unable to function properly, but also reduce the flow capabilities of the fluids to the test section. 69 Figure 12. Startup procedure for twophase heat transfer and isothermal pressure drop experiments 70 The third step in the startup procedure is turning on the tap water, which served as cooling fluid for the copper coil in the air line and the ITT Standard one shell and twotube pass heat exchanger in the water line. The tap water cooled the air and distilled water flowing into the test section such that both air and distilled water have same inlet temperature. The fourth step in the startup procedure is turning on the IngersollRand T30 air compressor and the Bell & Gosset centrifugal pump. With the air compressor and centrifugal pump turned on, air and water are supplied to the test section. The final step in the startup procedure is checking for leakage in the flow loop, and verifying the test section inclination angle. Having completed the steps in the startup procedure illustrated in Figure 12 (p. 69), the experimental setup is ready for measurement procedure. The startup procedure described here is also applicable for isothermal twophase pressure drop experiments. Measurement Procedure The measurement procedure is a process that includes several steps to successfully acquire experimental data. The function of the measurement procedure is to ensure the integrity and repeatability of the experimental data, while maintaining the functionality of the experimental setup. Figure 13 is a flow chart illustrating the individual steps of the measurement procedure. The first step in the measurement procedure is checking the welder cables connecting the DC arc welder with the copper plates attached to the stainless steel test section. This is a precautionary step to ensure all connections are safe and ready for the experiment. Poor condition of cables and improper connections between the DC arc welder and the test section could equipment damage, over Figure 13. Measurement procedure for two 71 result in short circuit, which could potentially cause heating, or fire hazard. twophase heat transfer and isothermal pressure drop experiments thermal 72 The second step in the measurement procedure is adjusting the air and water flow rates. The flow of air is regulated by a needle valve while the water is regulated by a gate valve. Using the Digital FieldMount transmitters, for the Coriolis flow meters, to monitor the air and water flow rates, the needle and gate valves are adjusted until the desired air and water flow rates are achieved. Once the desired air and water flow rates are set, the third step in the measurement procedure is to turn on the DC arc welder. With the DC arc welder turned on, the current is adjusted to the desired amperage to be supplied to the stainless steel test section. By running DC current through the stainless steel pipe, heat flux is supplied to the test section. The fourth step in the measurement procedure is to allow flow to achieve steady state condition. The flow is considered to have achieved steady state condition when each of the two thermocouple probes, which measure the inlet and outlet bulk temperatures, is indicating less than 0.5°C fluctuation for 5 minutes. The inlet and outlet bulk temperatures are monitored using the graphical user interface of the LabVIEW Virtual Instrument (VI) program illustrated in Figure 11 (p. 67). The thermocouples measuring the outer surface temperatures of the pipe are carefully monitored to avoid the temperature from rising beyond 60°C. This is to keep the flow strictly nonboiling and avoid the possibility of local boiling. Once the steady state is achieved, the process of acquiring experimental data can begin, which is the fifth step in the measurement procedure. Experimental data collected are air and water mass flow rates, inlet and outlet bulk temperatures, surface temperatures of the test section, pressure drop, and uniform heat flux supplied to the test section via the 73 current from the DC arc welder. The typical number of samples collected for each measurement run is a thousand samples. When the experimental data is recorded, the following step in the measurement procedure is to turn off the DC arc welder and allow the test section to cool to room temperature. Once the test section is cooled to room temperature, another measurement run can begin, as illustrated in Figure 13 (p. 71). The steps described for the measurement procedure is applicable for isothermal pressure drop measurements as well. As depicted in Figure 13, steps in the measurement procedure that are involved with using the DC arc welder are not observed, when conducting isothermal twophase pressure drop measurements and flow pattern observations. 4.4 Data Reduction For a uniform wall heat flux condition, the experiment involved the measurements of outside pipe wall surface temperatures at discrete locations (see Figure 10, p. 62), as well as the inlet and outlet bulk temperatures. The circumferential heat transfer coefficient was calculated based on the knowledge of the heat flux and surface temperature at the inside wall of the pipe. Due to the difficulty of measuring the inside wall temperatures, they are instead calculated from the measured outside wall temperatures and the heat generation within the pipe wall. The data reduction program developed by Ghajar and Kim (2006) was used for calculating the circumferential heat transfer coefficients and the inside wall temperatures from the outside wall temperatures measured at discrete locations along the uniformly heated pipe. 74 For the pipe wall, the numerical solution of the conduction equation used in the data reduction program has four assumptions: (1) steady state condition exists; (2) conduction occurs in circumferential and radial directions; (3) conduction in axial direction is negligible; and (4) both electrical resistivity and thermal conductivity in the pipe wall are functions of temperature. Figure 14 shows the nodal arrangement for the finite difference solution used by Ghajar and Kim (2006) for the pipe wall. The heat balance on a control volume of the pipe wall at a given node (p) can be expressed as g n e s w q& = q& + q& + q& + q& . (4.1) From Fourier’s law of heat conduction, the rate of heat conduction in a given direction n is dn dT q& = −kA . (4.2) Applying the finite difference formulation for a control volume on a segment of the pipe (see Figure 14) with nonuniform thermal conductivity, the heat rates for nodes n, e, s, and w can be written as ( ) n p n n n p n n A T T k k q − = + − − + 1 δ δ & , (4.3) ( ) e p e e e p e e A T T k k q − = + − − + 1 δ δ & , (4.4) ( ) s p s s s p s s A T T k k q − = + − − + 1 δ δ & , (4.5) 75 w ( p w ) w w p w w A T T k k q − = + − − + 1 δ δ & . (4.6) Figure 14. Nodal arrangement for finite difference solution (adapted from Ghajar and Kim, 2006) The heat generated ( g q& ) at the control volume is given by A z q i R i g & = 2 = 2γ . (4.7) Substituting Eqs. (4.3) to (4.7) into Eq. (4.1) yields the following equation: 1 1 ( ) − − = − − − − + − + s s s p s s p g n e w A k k T T q q q q δ δ & & & & . (4.8) Equation (4.8) is used for calculating the temperatures of the interior nodes. Once the local inside wall temperature ( Wi T ) is calculated by applying Eq. (4.8), the local heat transfer coefficient can be determined from the local inside wall heat flux ( Wi q&′′ ) and the local bulk fluid temperature ( B T ): 76 TC ST ST Wi k j B k Wi k j k j j N k N T T q h for 1, 2, , and 1,2, , ( ) ( ) ( ) @ , , , K K & = = − ′′ = . (4.9) where the subscripts j and k are the indexes of the thermocouple in the circumferential location and the thermocouple station in the axial location, respectively. The local bulk temperature is given as T T T T z L B k in out in k ( ) = + ( − ) . (4.10) The average local heat transfer coefficient at a given thermocouple station is B k N j Wi k j TC@ST N j Wi k j TC@ST k T T N q N h TC@ST TC@ST ( ) ( ) 1 ( ) 1 1 , 1 , − ′′ = Σ Σ = = & . (4.11) In twophase flow heat transfer, due to the existence of nonuniform local heat transfer coefficients, the calculation of overall heat transfer coefficient for the entire pipe becomes necessary. The overall heat transfer coefficient was calculated by integrating the average local heat transfer coefficient ( k h ) along the pipe length: Σ= = NST k TP EXP k k h z L h 1 , 1 . (4.12) 4.5 Effects of Dissolved Air Since air and water are mixed together in the mixing section (see Figure 9, p. 61) before flowing to the test section, the mixing of air and water will naturally result in dissolved air being present in the water. Thus, it is reasonable to question whether the dissolved air in the working fluid can affect the heat transfer. 77 In a study done by MüllerSteinhagen et al. (1988) to determine the effect of various dissolved gasses (He, N2, Ar, CO2, C3H8) in water and heptane on convective heat transfer and subcooled boiling heat transfer in an annulus with a heated core, they found that convective heat transfer is not affected by dissolved gasses in flow of water and of heptane. However, dissolved gasses in water and heptane brought enhancement to the subcooled boiling heat transfer coefficient, due to the process of desorption and evaporation (MüllerSteinhagen et al., 1988). Steinke and Kandlikar (2004) conducted an experimental investigation to study the effect of dissolved gases on heat transfer during the flow of water in a microchannel. Their experiment was conducted for water with three different dissolved oxygen contents: 1.8, 5.4, and 8.0 parts per million (ppm). They found that water with higher dissolved oxygen content (8.0 ppm) experienced a slight reduction in heat transfer after the boiling incipience wall temperature is achieved, when compared to water with lower dissolved oxygen content (1.8 and 5.4 ppm). For water with high dissolved oxygen content (8.0 ppm), desorption of the dissolved gas during nucleation formed an insulating layer of bubbles on the heated surface, thus causing a slight reduction in heat transfer. Nucleation was observed at a surface temperature of 90.5°C for water with 8.0 ppm of dissolved oxygen. Prior to nucleation, no noticeable difference in heat transfer was observed for the three different cases of dissolved oxygen in water. In a more recent study, Cioncolini et al. (2007) concluded that the dissolved air in water for subcooled and saturated boiling flow did not cause any systematic deviation from predictions by correlations derived for degassed liquids. Cioncolini et al. (2007) attributed the lack of influence by the dissolved air on subcooled and saturated boiling 78 heat transfer to the fact that water can only dissolve moderate amount of air. Similar conclusions were also drawn by Cioncolini et al. (2007) for convective heat transfer in singlephase degassing flow. MüllerSteinhagen et al. (1988), Steinke and Kandlikar (2004), and Cioncolini et al. (2007) indicated that the presence of dissolved air in water does not affect convective heat transfer. Since all experiments conducted in this study were forced convective heat transfer, and do not include boiling, it is therefore not unreasonable to assume that dissolved air in water will not cause any anomaly in the heat transfer results. In addition, for all the measurements conducted in the study, the outer surface temperatures of the pipe were kept below 60°C to avoid local boiling. From Henry’s law, the amount of air dissolved in water at 25°C and 1 atm is approximately 0.023 g/kg. In this study, it is conceivable that the mixing of air and water may result in slightly higher amount of dissolved air in water than the value determined from Henry’s law. 4.6 Chapter Summary The current experimental setup was constructed for systematic study of heat transfer in nonboiling twophase flow for horizontal and slightly inclined cases. The setup was capable to be used for collecting flow patterns, pressure drop, and heat transfer data for all major flow patterns and inclination angles from 0° (horizontal) to 7° upward inclined. The experimental data collected with this experimental setup is useful for the understanding of the fundamentals of nonboiling twophase flow heat transfer, as well as for the validation of the developed twophase heat transfer correlations. 79 CHAPTER V EXPERIMENTAL RESULTS In this chapter, the experimental results collected from the experimental setup are presented. The results include flow patterns and heat transfer data systematically collected for horizontal and slightly inclined twophase flow in pipes. Before experiments on the twophase flow were conducted, experimental data for singlephase flow was measured. The objective of conducting measurements for singlephase flow is to establish the viability of the experimental setup for conducting twophase flow experiments. 5.1 SinglePhase Flow Results In this section, results of singlephase liquid flow frictional pressure drop and heat transfer measurements conducted with the test section are discussed. The objective of conducting frictional pressure drop and heat transfer measurements for singlephase flow in the test section is to verify the performance and reliability of the experimental setup. The perception is that if the results, both frictional pressure drop and heat transfer, from singlephase flow measurements are in agreement with established correlations, then it is not unreasonable to hold the assumption that the experimental setup is applicable for twophase flow 



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