NUMERICAL AND EXPERIMENTAL INVESTIGATION OF SINGLE AND TWO-PHASE IMPINGING JET HEAT TRANSFER ZHENGQUAN LOU NATIONAL UNIVERSITY OF SINGAPORE 2007 NUMERICAL AND EXPERIMENTAL INVESTIGATION OF SINGLE AND TWO-PHASE IMPINGING JET HEAT TRANSFER ZHENGQUAN LOU (Bachelor, SJTU) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2007 Summary Impinging jet heat transfer is one of the flow techniques used to cool or heat the target surfaces by fluid impingement on them. It is widely used in industrial applications ranging from drying of textiles and films, metal sheet manufacturing, gas turbine cooling to electronic component cooling. With the rapid increase of the heat dissipation in electronic components, impinging jet technique becomes more important to cool the hot chip. The objective of the current research was to test the heat transfer performance of impinging jet system under various boundary conditions. In this study, both numerical and experimental methods were used to examine the single and two-phase problems. For the single phase heat transfer, the effects of different boundary conditions and various parameters, e.g. geometric parameters, Biot number, fin structure and presence of a baffle in the jet flow, on the heat transfer performance were studied using a Computational Fluid Dynamics (CFD) method. The parameters such as Nusselt number, thermal resistance and heat flux, were obtained to evaluate the heat transfer performance of the impinging jet system. For the two-phase problem, a mixture model, incorporated with User Defined Functions (UDFs), were used to simulate the process of heat transfer and mass transfer. The current study discussed the effects of superheat of target plate, sub-cooled working fluid and various inlet velocities on the two-phase heat transfer performance. Moreover, visualization of two-phase process was obtained. i Other than the simulation work, an experiment was set up to test the heat transfer performance of single and two-phase problems with water and FC-72 as the working fluids. The parameters, e.g. impingement orientation, jet width and inlet velocity, were examined in the experiment. The simulation results and experimental results were compared and a reasonable agreement was obtained. Finally, on the basis of the verified simulation model, more predictions of two-phase micro-scale impinging jet were carried out in view of its promising application in industry. This dissertation addresses the numerical and experimental investigation of single and two-phase impinging jet heat transfer. The goal of this study is to contribute to a more detailed investigation of effects of various parameters on impinging jet heat transfer so as to improve the design of the current impinging jet system. In the current investigation, the relationships between the local Nusselt number Nu x , average Nusselt number Nu m , jet width W , jet height H , H / W and Re have been generalized. Also, the effects of subcooled water temperature, inlet velocity and superheat temperature of target plate on the heat transfer performance have been obtained. Distributions of temperature contour, velocity contour, velocity vector and volume fraction of vapor are obtained. The effect of surface roughness on the two-phase impinging jet heat transfer has also been examined. A dielectric fluid FC-72 has tested and the comparison between FC-72 and water is carried out. The advantages of FC-72 in the industrial application are reported. ii Acknowledgements I would like to express my sincere gratitude to my supervisors, Professor Arun S. Mujumdar and Assoc. Professor Christopher Yap, for their tremendous support and patient guidance. I am deeply grateful for their critical and crucial suggestions and comments on my research work. I am forever indebted to them for guiding me in the research world of impinging jet heat transfer. I would like to thank the lab officer of Air-conditioning Lab, Mr. Sacadevan Raghavan for his kindness and enthusiastic help in the preparation of the experimental equipment. I would also like to extend my thanks to my friends, Mr. Huang Lixin, Mr. Wang Shijun, Mr. Wu Zhonghua, Mr. Wang Xiangqi and many others. I am greatly obliged to my parents for their continuous supports from childhood to now. Finally, I am also grateful to NUS for its financial support for my Ph. D program. Zhengquan Lou Singapore December 2006 iii Table of contents Summary……………………………………………………………………………….…i Acknowledgements………………………………………………………… ……………iii Table of contents……………………………………………………………………… iv Nomenclature……………………………………………………………………………vi List of Figures………………………………………………………………………… .viii List of Tables…………………………………………………………………………….xii Publications arising from this thesis…………………………………………………… xiii Chapter Introduction…………………………………………………………….… 1.1 Background…………………………………………………………………… .…….1 1.2 Introduction of Impinging Jet Technique…………………………………… …….…9 1.3 Objectives ………………………………………………………………….… ……10 1.4 Scope……………………………………………………………….… ……11 Chapter Literature Review………….…….……….……………………….… .……13 2.1 Geometric effect ……………………………………………………………………14 2.2 Conjugate Heat Transfer……………………………………………….……… …16 2.3 Fin Structure……………………………………………………………….… … .…18 2.4 Effect of an Inserted Baffle ……………………………………………… …………21 2.5 Two-phase IJHT: Experimental Investigation……………………………… ………23 2.6 Two-phase IJHT: Numerical Investigation………………………………… .………27 Chapter Fundamentals of Single and Two-phase IJHT…………………… ……34 3.1 Description of the Basic Impinging Jet System………………………………………34 3.2 Modeling of Single-phase Simulation………………………………………… .……36 3.3 Fundamental Theory of Boiling Heat Transfer………………………………….……37 3.4 Models for Multiphase Flow and Heat Mass Transfer…………………… …………42 3.5 General Guidelines of Model Selection………………………………………………46 3.6 Conservation Equations and Other Equations……………………………… .………48 3.7 User-Defined-Functions……………………… …………………………… ………50 Chapter Effects of Geometric Parameters on Confined IJHT…………………… 52 4.1 Problem Description……………………………………………………….…………52 4.2 Calculation of Thermal Parameters ……………………………………….…………54 4.3 Results and Discussion……………………………………………………….………55 4.3.1 Effect of Jet Width W ………………………………………… ………….………56 4.3.2 Effect of Jet Height H ………………………………………………… .…………59 4.3.3 Effect of Jet Reynolds Number……………………………………………… ……61 4.3.4 Effect of Surface Roughness………………………………………………….……62 4.3.5 Effect of the Inlet Velocity Profile …………………………………………………65 4.4 Summary of Chapter… …………………………………………………………… .66 Chapter Conjugate Heat Transfer under a Confined IJ……………………………68 5.1 Problem Description………………………………………………………………… 68 5.2 Results and Discussion……………………………………………………………… 70 5.2.1 Relationship between Bi x , Bim and k p …………………… ………………………70 iv 5.2.2 Relationship between Bi x , Bim and Nu ………………………………………… 75 5.2.3 Selection of Target Plate…………………………………………….………… .…77 5.3 Summary of Chapter… …………………………………………………………… .77 Chapter Simulation of Laminar IJHT to Finned Heat Sinks………………………79 6.1 Problem Description………………………………………………………….………79 6.2 Results and Discussion……………………………………………………….………83 6.2.1 Effect of Fin Number……………………………………………………….………83 6.2.2 Effect of Fin Height H f ……………………………………………………………86 6.2.3 Effect of Fin-to-spacing Ratio W f / S f ………………………………….…………89 6.3 Summary of Chapter… …………………………………………………………… .92 Chapter Numerical Investigation of Baffle Effect on IJHT……………….… ……93 7.1Problem description …………………………………………………………….……93 7.1.2 Numerical Simulation………………………………………………………………94 7.1.3 Formulation of Parameters…………………………………………………………95 7.2. Results and Analysis…………………………………………………………………97 7.2.1 Orientation of Baffle……………………………………………………… ………97 7.2.2 Locations of Vertical Baffle……………………………………………… .……100 7.2.3 Locations of Horizontal Baffle……………………………………………………104 7.3. Summary of Chapter… ……………………………………………………………106 Chapter Numerical Simulation of Two-phase IJHT…………………….…………108 8.1 Problem Description…………………………………………………………………108 8.2 Results and Discussion………………………………………………………………111 8.2.1. Effect of Subcooling………………………………………………………………112 8.2.2. Effect of Inlet Velocity v ………………………………………………… .……114 8.2.3. Effect of Superheat Target Plate …………………………………………………119 8.2.5 Visualizations of the Volume Fractions of Vapor…………………………………124 8.2.6 Investigations of Micro-impinging Jet ……………………………………………128 8.2.7 Effect of Surface Roughness………………………………………………………133 8.3 Summary of Chapter… …………………………………………………………….136 Chapter Experimental Investigation of Single and Two-phase IJHT……….……137 9.1 Experiment Setup and Procedure……………………………………………………137 9.2 Uncertainty of measurement………………………………………………… .……140 9.3 Results and Discussion ………………………………………………………… .…143 9.3.1 Heat Transfer Results…………………………………………………………… .143 9.3.2 Orientation Effect of Impinging Jet System……………………………………….147 9.3.3 Effect of Jet Width……………………………………………………………… .154 9.3.4 Comparison between FC-72 and Water ………………………………………… .158 9.4 Summary of Chapter… …………………………………………………………….160 Chapter 10 Conclusions and Recommendations…………………………….………162 10.1 New Contributions…………………………………………… …………… ……164 10.2 Recommendations in the Future Work………………… …………………………164 References…………………………………………………… .……………….………166 Appendices……………………………………………… .…………………….……175 v Nomenclature Bottom surface area of the heat sink m2 Top surface area of the heat sink Local Biot number at the stagnation point Average Biot number Local Biot number Specific heat m2 J/kg•K f hm hx H Hf Friction factor Average convective heat transfer coefficient W/m2•K Local convective heat transfer Jet height Fin height W/m2•K mm mm kf Thermal conductivity of the working fluid W/m•K kp Thermal conductivity of the target plate W/m•K k fin lb L M Nu Nu e Nu m ΔP q qx Re Sf Thermal conductivity of the plate-fin W/m•K Baffle length Target plate length flow rate Nusselt number at the stagnation point Effective Nusselt number Average Nusselt number Pressure drop between inlet and outlet Heat flux Local heat flux Reynolds number Spacing between two adjacent fins mm mm ml/min Pa W/m2 W/m2 ρuW / μ mm T fin Average temperature of the plate-fin K Tw u W Wf Wall temperature the target plate Inlet jet velocity Jet width Fin width K m/s mm mm wb X Y Width of the baffle Horizontal distance to the axis Vertical distance to the target plate mm mm mm Ab At Bi0 Bim Bi x Cp vi Greek symbol α Impingement orientation δ Target plate thickness ρ Fluid density μ Dynamic viscosity υ Kinematic viscosity θ af Thermal resistance mm kg/m3 kg/m•s m2/s K/W Subscripts f Working fluid x Local w Wall m Mean (or average) Stagnation point vii List of figures Fig. 1.1 Heat transfer coefficient attainable with natural convection, single-phase liquid forced convection and boiling for different coolants. Fig. 1.2 A conventional design of an electronic cooling device by a heat sink Fig. 1.3 A typical configuration of a heat pipe Fig. 1.4 Geometric configuration of the micro-channel the heat transfer .5 Fig. 1.5 Geometric configuration of an impinging jet system Fig. 1.6 Thermal resistance for various cooling fluids .6 Fig. 1.7 Flow chart of the current investigation of impinging jet heat transfer……… 12 Fig. 2.1 Classification of impinging jet heat transfer in term of various parameters… .13 Fig. 3.1a Geometric configuration of an impinging jet system………………………… .35 Fig. 3.1b An impinging jet system with a scheme of its vortex structure……………… .35 Fig. 3.2 Rising air bubble in water. Left: x − Velocity versus time. Right: Shape and flow field at t = for D / h = 32 . The contour shown for α = 10 − 12, , and, − 10 −12 …… 44 Fig. 4.1 Schematic diagram of the impinging jet domain…………………………… .53 Fig. 4.2 Grid information of the right half computational domain the impinging jet system 54 Fig. 4.3 Distributions of surface temperature along the plate with H / W as a parameter ………………………………………………………………………….…… .57 Fig. 4.4 Distributions of local Nusselt numbers Nu x along the plate with H / W as a parameter ……………………………………………………………………………… .57 Fig. 4.5 Relationship between pressure drop and H / W .……………………………… 58 Fig. 4.6 Distributions of local Nusselt numbers Nu x along the plate with H / W as a parameter ……………………………………………………………………………… .59 Fig. 4.7 Relationship between the local Nusselt numbers Nu x and H / W at the stagnation area . …………………………………………………………………………………… 61 Fig. 4.8 Distributions of local Nusselt number Nu m along the plate with Re as parameter . ………………………………………………………………………………62 Fig. 4.9 Correlation between the average Nusselt number Nu m , Reynolds number Re and H / W .………………………………………………………………………………… .62 Fig. 4.10 Grid information of triangular, rectangular and sine roughness on the target plate . …………………………………………………………………………………….63 Fig. 4.11 Distributions of surface temperature along the rough target plate with Re = 80 . ……………………………………………………………………………………….63 Fig. 4.12 Comparison of local Nusselt numbers for different inlet velocity profiles . ….65 Fig. 5.1 Distributions of the surface temperature along the target plates for variable k p 71 Fig. 5.2 Distributions of heat flux q x along the target plate with variable k p ………… .71 Fig. 5.3 Distributions of the local Biot number Bi x for different material target plate . .72 viii Chapter 10 Conclusions and Recommendations Chapter 10 Conclusions and Recommendations This thesis presents numerical and experimental investigations of single and twophase impinging jet heat transfer under various operating conditions. Various parameter effects on the impinging jet heat transfer were tested numerically, e.g. geometric parameters, Biot number, fin structure and presence of a baffle in the jet flow. A simulation of two-phase problem was carried out using the mixture model in Fluent 6.2. For the single phase problem, the relationships between the local Nusselt number Nu x , average Nusselt number Nu m , jet width W , jet height H , H / W and Re have been generalized. Moreover, the effect of surface roughness on the single phase heat transfer performance has been obtained. Surface roughness generally deteriorate the single phase heat transfer performance due to the working fluid is trapped as recirculation eddies in the cavities of the rough plates. The conjugate heat transfer has been also studied numerically using different materials as the target plate. The correlations between the local and average Biot numbers and thermal conductivities of the target plates are generalized. Also, the relationships between the local and average Nusselt numbers and the average Biot number have been also obtained. Considering the factors such as the degree of temperature uniformity, average Nusselt number Nu m and industrial feasibility, the current prediction is valuable for the selection of the target plate in the impinging jet system. 162 Chapter 10 Conclusions and Recommendations For the single phase problem, the effect of a plate-fin heat sink has been studied with fin number, fin height, fin-to-spacing ratio as the parameters. Also, presence of a baffle in the flow region is studied with the changes of the baffle orientation, location and length. Average Nusselt number is obtained to evaluate the overall heat transfer performance. For the two-phase heat transfer, a mixture model, incorporated with UDFs, has been developed to simulate the boiling problem. In the current investigation, the effects of subcooled water temperature, inlet velocity and superheat temperature of target plate on the heat transfer performance have been obtained. Distributions of temperature contour, velocity contour, velocity vector and volume fraction of vapor are obtained. The effect of surface roughness on the two-phase impinging jet heat transfer has also been examined. The comparison between simulation and experimental results was carried out and the agreement is found to be good. On the basis of this verified simulation model, a prediction of two-phase micro-impinging jet heat transfer have been performed and it could be valuable for the design of micro-impinging jet system in industry. An experiment of impinging jet system has been set up to verify the simulation results. The effects of impinging orientation and jet width on impinging jet heat transfer were tested in the experiment. Moreover, both single phase and two-phase heat transfer were examined. For the single phase problem, the impinging orientation not affect the heat transfer performance significantly. However, for the two-phase problem, the impinging orientation affects the overall heat transfer performance greatly because of creation and movement of air and vapor bubbles. In addition, a range of the jet width W from 0.05 to 2.0 mm has been tested. From this investigation, it is found that small jet width can remove much higher heat flux that large jet width when the flow rate is kept 163 Chapter 10 Conclusions and Recommendations constant. Finally, a dielectric fluid FC-72 has tested and the comparison between FC-72 and water is carried out. The advantages of FC-72 in the industrial application are reported. 10.1 New Contributions 1) The effects of various parameters, e.g. jet width, jet height, Biot number, plate-fin heat sink and an embedded baffle, on single-phase impinging jet heat transfer have been studied. The current work has provided a study in the impinging jet system under particular operating conditions which are different with the studies in the literature; 2) The mixture model is adopted in Fluent 6.2 to simulate the two-phase impinging jet heat transfer. UDFs (User-Defined-Functions) are incorporated to the main model to simulate heat and mass transfer process. The effects of various parameters on the overall heat transfer performance have been discussed; 3) On the basis of the verified simulation model, a numerical investigation of microimpinging jet heat transfer has been carried out in view of its promising application in industry; 4) An experimental has been set up to test the thermal performance of single and twophase heat transfer using water and FC-72 as the working fluids. The simulation results and experimental results are compared and good agreements are obtained. 10.2 Recommendations in the Future Work 1) For the single phase impinging jet heat transfer, different types of impinging jet such as multiple round jets and declined jet could be further investigated. Also, effect of unsteady inlet velocity on the heat transfer performance can be investigated. 164 Chapter 10 Conclusions and Recommendations 2) For the two-phase problem, the simulation model could be improved further. Tracking the interface between vapor and water is still not so satisfactory. VOF model can be used to track the vapor-to-water interface. 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Heat Mass Transfer, Vol. 40, No. 17, pp. 4055-4059, 1997　 174 Appendices Appendices Relative (Slip) Velocity and the Drift Velocity The relative velocity (also referred to as the slip velocity) is defined as the velocity of a secondary phase ( p ) relative to the velocity of the primary phase ( q ): ρ ρ ρ v pq = v p − v q (1) The mass fraction for any phase ( k ) is defined as ck = α k ρk ρm (2) ρ The drift velocity and the relative velocity ( v qp ) are connected by the following expression: n ρ ρ ρ v dr , p = v pq − ∑ c k v qk (3) k =1 Fluent's mixture model makes use of an algebraic slip formulation. The basic assumption of the algebraic slip mixture model is that to prescribe an algebraic relation for the relative velocity, a local equilibrium between the phases should be reached over short spatial length scale. The form of the relative velocity is given by: τ p (ρ p − ρ m ) ρ ρ v pq = a f drag ρ p (4) where τ p is the particle relaxation time ρ p d p2 τp = 18μ q (5) ρ d is the diameter of the particles (or droplets or bubbles) of secondary phase p , a is the 175 Appendices secondary-phase particle's acceleration. The default drag function f drag is taken from Schiller and Naumann: f drag = + 0.15 Re 0.687 (Re ≤ 1000 ) (6) f drag = 0.0183 Re (Re ≤ 1000 ) (7) ρ and the acceleration a is of the form ρ ρ ρ ρ ρ ∂v m a = g − (v m ⋅ ∇ )v m − ∂t (8) The simplest algebraic slip formulation is the so-called drift flux model, in which the acceleration of the particle is given by gravity and/or a centrifugal force and the particulate relaxation time is modified to take into account the presence of other particles. In turbulent flows the relative velocity should contain a diffusion term due to the dispersion appearing in the momentum equation for the dispersed phase. Fluent adds this dispersion to the relative velocity: ( ρ p − ρ m )d p2 ρ v ρ v pq = a − m ∇α q 19 μ p f drag α pσ D (9) where ( vm ) is the mixture turbulent viscosity and ( σ D ) is a Prandtl dispersion coefficient. When solving a mixture multiphase calculation with slip velocity, formulations for the drag function can be directly prescribed. The available choices are: • Schiller-Naumann (the default formulation) • Morsi-Alexander • Symmetric • Constant • User-defined functions 176 Appendices In this simulation, an energy function for heat transfer, liquid and vapor functions for mass transfer were written in source code to solve heat and mass transfer process. Volume Fraction Equation for the Secondary Phases From the continuity equation for secondary phase p , the volume fraction equation for secondary phase p can be obtained: n ∂ (α p ρ p ) + ∇ ⋅ (α p ρ p vρm ) = −∇ ⋅ (α p ρ p vρdr , p ) + ∑ (m&qp − m&pq ) ∂t q =1 177 (10) [...]... conjugate heat transfer under a confined impinging jet" , International Journal of Thermal Sciences, submitted Z.Q Lou, C Yap and A.S Mujumdar, "Numerical Investigation of Baffle Effect on Micro -Impinging Jet Heat Transfer" , International Journal of Thermal Sciences, Submitted, 2005 Z.Q Lou, C Yap and A.S Mujumdar, "Numerical Investigation of Two- phase Impinging Jet Heat Transfer" , Journal of Applied... rapid increase of heat dissipation rate required by electronic components, single phase heat transfer will eventually not be sufficient to meet the demand Thus, two- phase heat transfer (boiling heat transfer) has become a topic receiving increasing attention of major interest in the electronic cooling field Compared with single phase heat transfer, twophase heat transfer can increase the heat transfer effectiveness... geometry of the target plate is a key factor which affects the heat transfer effectiveness of the impinging jet system A target plate using a finned heat sink under an impinging jet affects heat transfer performance significantly Therefore, an investigation of fin design under an impinging jet is worthy of a further study Many experimental and numerical investigations of a heat sink under an impinging jet. .. Visualizations of the single and two- phase heat transfer for the +45° inclined impingement …………………………………………………………………………….151 Fig 9.12 Visualizations of the single and two- phase heat transfer for the sideways impingement…………………………………………………………………………… 153 Fig 9.13 Visualizations of the single and two- phase heat transfer for the upward impingement …………………………………………………………………………….154 Fig 9.14a Comparison of heat fluxes... roughness, impinging orientation, fin structure, an inserted baffle etc On the basis of the verified simulation model, a numerical investigation of the micro -impinging jet was also carried out 1.4 Scope In the current investigation, the study was mainly focused on the single and twophase impinging jet heat transfer Both numerical and experimental investigations were carried out For the single phase problem,... laminar impinging jet heat transfer to finned heat sink" ,Proceedings of ASME:2005 Summer Heat Transfer Conference 2005, Published on CD/Presented, San Francisco, USA Z.Q Lou, C Yap and A.S Mujumdar, "Experimental Investigation of Single Phase and Boiling Heat Transfer of Pure Water Under a Micro -impinging Jet Heat Transfer" ECI Conference on Boiling, Spoleto 7-12 May 2006 Z.Q Lou, C Yap and A.S Mujumdar,... developed to simulate two- phase problem in the impinging jet system 1.3 Objectives The main objective of the current studies was to examine the heat transfer performance in the impinging jet system under various operating conditions In this study, both numerical and experimental methods were used to examine the single and two- phase problems For the single phase heat transfer, the effects of different operating... Mujumdar and C Yap, "Effects of geometric parameters on confined impinging jet heat transfer" , Journal of Applied Thermal Engineering, Vol 25, No 17-18, Dec 2005, pp 2687-2697 Z.Q Lou, C Yap and A.S Mujumdar, "A Numerical Study of a Heat Sink Fin under a Laminar Impinging Jet" , Journal of Electronic Packaging, 2006 (Accepted) Z.Q Lou, C Yap and A.S Mujumdar, "Numerical investigation of laminar impinging jet. .. focused mainly on the air jets with jet width on the order of several millimeters However, more compact configurations and higher heat transfer performance are demanded because of the rapid increase of heat flux dissipation rates A micro -impinging jet of a dielectric fluid FC-72 is examined experimentally in the current study A few investigations of micro -impinging jet heat transfer were reported in... investigation of IJHTis presented Fig 1.7 11 Chapter 1 Introduction Fig 1.7 Flow chart of the current investigation of the impinging jet heat transfer 12 Chapter 2 Literature Review Chapter 2 Literature Review In this chapter, a brief overview of previous investigations on impinging jet heat transfer is presented Here, the review is classified by related research topics Classifications of impinging jet heat transfer . of single and two-phase impinging jet heat transfer. The goal of this study is to contribute to a more detailed investigation of effects of various parameters on impinging jet heat transfer so. NUMERICAL AND EXPERIMENTAL INVESTIGATION OF SINGLE AND TWO-PHASE IMPINGING JET HEAT TRANSFER ZHENGQUAN LOU NATIONAL UNIVERSITY OF SINGAPORE. USA Z.Q. Lou, C. Yap and A.S. Mujumdar, " ;Experimental Investigation of Single Phase and Boiling Heat Transfer of Pure Water Under a Micro -impinging Jet Heat Transfer& quot; ECI Conference