This is to certify that the thesis entitled COMPUTATIONAL STUDY OF HEAT AND MASS TRANSFER WITH PHASE CHANGE CONDENSATION AND EVAPORATION IN A DEVELOPING, TWO-DIMENSIONAL WALL JET VELOCITY AND TEMPERATURE FIELDS presented by R. Arman Dwiartono has been accepted towards fulfillment of the requirements for the MS. degree in Department of Mechanical @W/éw I Major Professor's Signature 8/20/2004 Date MSU is an Affirmative Action/Equal Opportunity Institution Engineering LIBRARY Michigan State University PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE DATE DUE DATE DUE 6/01 cJClRC/DateDuepGS—p. 15 COMPUTATIONAL STUDY OF HEAT AND MASS TRANSFER WITH PHASE CHANGE CONDENSATION AND EVAPORATION IN A DEVELOPING, Two- DIMENSIONAL WALL JET VELOCITY AND TEMPERATURE FIELDS By R. Arman Dwiartono A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Mechanical Engineering ’ 2004 ABSTRACT COMPUTATIONAL STUDY OF HEAT AND MASS TRANSFER WITH PHASE CHANGE CONDENSATION AND EVAPORATION IN A DEVELOPING, TWO-DIMENSIONAL WALL JET VELOCITY AND TEMPERATURE FIELDS By R. Arman Dwiartono One of the important aspects of this study is to predict condensation and evaporation during window defogging or defrosting that happens in certain temperatures. The safety issue to defrost or defog in a short period of time is a main concern in automotive industry to avoid any hazard that could happen to drivers. The government also regulates this safety issue. A 2—D steady state and transient computational simulation with phase change modeling with the implementation of User Defined Function were performed with FLUENT as the commercial code to be compared with the experimental study that was done previously. It was determined later that in predicting the window defogging, Sherwood Number plays as an important role. Results of this computational study were in good agreement with the experimental and other study regarding window defogging that was done previously. This study shows that computational simulation could be applied successfully to investigate condensation and evaporation for the window defogging or defrosting problem. To my parents, brother, and Eliza iii ACKNOWLEDGMENT I wish to express my deepest thanks to my graduate advisor, Dr. Craig Somerton, for his time, constant support and helpful advice throughout my entire program. He was always available whenever I needed his help. To my committee members, Bashar AbdulNour Ph.D., Paul Hoke Ph.D., and Dr. Andre Benard I would like to say my thanks to them, they also help me with their advice and assistance. They Spent their time to help and taught me with their knowledge and experience in this subject. This research will not be as useful without the previous experiment done by Dr. Paul Hoke, Mr. Qingtian Wang, Dr. Bashar AbdulNour, and few other peOple. lwould like to thank them for their valuable resources for this research. Dr. AbdulNour and Dr. Paul Hoke of Ford Motor Company have the confidence in me and continue to support me in the technical field to do this research during my program. Finally, I would like to thank my friends, family, and Eliza for their support to keep me going. They always gave me moral boost and kept my confidence high. iv TABLE OF CONTENTS List of Tablesvu List of Figures...... ............viii Nomenclaturex Introduction... 1 CHAPTER 1. Background investigation and review of literature... 2 1.1 BACKGROUND INVESTIGATION...................................................2 1.28ACKGROUNDEQUATIONS.............. 4 1.3 REVIEW OF LITERATURE.............. ........5 CHAPTER 2 Numerical methodology... ............9 21 DESCRIBING EQUATIONS AND BOUNDARY CONDITIONS ......9 2.1.1 WALL REGIONOSy< JHANDO l+§lvrp15+ml= 12 6 6T 6 6T {Ex—[kefl gTZh/JfflflefliJ'gike/f 57-2th v(r)efl]}+Sh (2.9) Where E is the total energy u2 E=h—-:—:-+—2— (2.10) For ideal gas, the boundary condition with j as the species for the enthalpy is: h: —Dw<¢,, —¢W) (2.31) Where, p = and D = ... 2.32 (314 ax ( ) One of the major inadequacies of the central differencing scheme is its inability to identify flow direction. The value of property (D at a west cell face is always influenced by both (hp and 6D,, in central differencing. In a strongly convective flow from west to east, the above treatment is unsuitable because the west cell face should receive much stronger influencing from node W than from node P. The upwind differencing (also known as “donor cell’) differencing scheme takes into account the flow directions when determining the value at a cell face. The convected value of (D at a cell face is taken to be equal to the value at the upstream node. In upwind, when the flow is in the positive direction, uW > 0, U. > 0 (FW > 0, F,, > 0), the scheme sets ,1 =¢W and II =11], (2.33) W The discretized equation then becomes _ _ _ _ ._ 2.34 The upwind differencing scheme utilizes consistent expressions to calculate fluxes through cell face; therefore it can be easily shown that the formulation is conservative. 24 2.4 MESH GENERATION Gambit is the software used to generate the mesh. Gambit allows us to decompose geometries for structured hex meshing or perform automated hex meshing with control over clustering. It has single interface for meshing geometry that bring together all FLUENT preprocessing in one environment. Later, the mesh was exported to FLUENT 2D version 6.0 and 6.1. In terms of the equations, realizable k-s is (r-ke) similar to standard k-e (s- ke), where k2 I1, = ,, _; (2.35) Unlike the standard k—s where the C], is a constant, in r-ke the Cu is C, = 1 U'k (2.36) A +A —— 0 3 8 Where A0 is 4.04, As is J3Cos¢ , and u‘ = \[SUSU + (290,! (2.37) O), is the mean rate of rotation tensor Viewed in the rotating reference frame with the angular velocity (0k. Previous works Show that r-ke gives better accuracy in predicting a variety of turbulent flows result than s-ke. 25 CHAPTER 3 STEADY STATE AND TRANSIENT SIMULATION 3.1 STEADY-STATE INITIAL CONDITIONS In order to run the iterations in Fluent, the following initial conditions were inputted for the steady-state simulation: 1. Solver selected: Segregated (governing equations are solved sequentially) 0 Space: 2D 0 Velocity formulation: Absolute 0 Time: Steady o Gradient option: Cell-based o Viscous: realizable k-e 0 Near wall treatment: Enhanced wall treatment 2. Material selected: Water vapor (H20) mixture with all default density, cp, thermal conductivity, Viscosity, and molecular weight 3. Heated Plate: Temperature is set to 278.15 K (adjustable) 4. Inlet pressure: 0 Gauge total pressure: 0 Pa or constant velocity 1.6896 m/s 0 Temperature: 298.15 K (room temperature) . Direction specification method: Normal to boundary 0 Turbulence specification method: Intensity and hydraulic diameter - Turbulence intensity: 2.5% (measured in experiment) 26 - Hydraulic diameter: 0.284 m (calculated from real geometry) 5. Outlet Pressure: 0 Gauge pressure: -60 Pa 0 Backflow total temperature: 298.15 K o Backflow direction specification method: Normal to boundary 0 Turbulence direction specification method: Intensity and hydraulic diameter - Backflow turbulence intensity: 30% - Backflow hydraulic diameter: 0.42 m 6. Wall: Temperature is set to 278.15 K For the operating condition, the pressure is set to be 1 atrn (101325 Pa). This operating pressure, Pop, is important for incompressible ideal gas flow since it directly determines the density. The reference pressure location can also be specified, however when pressure boundaries are involved, the reference pressure location is ignored since it is no longer needed [10]. Fluent uses gauge pressure in calculation. When absolute pressure is needed, it can be obtained with: P =P +P (3.1) abs op The iteration was performed with energy equation selected. The simulation was done with second order upwind discretization to minimize numerical rounding error. The second order upwind proved to achieve better results when they are compared to the experimental data. 27 In order to investigate the mass transfer and condensation, a phase change UDF is also implemented as the initial condition before running the iteration. 3.2 STEADY-STATE RESULTS AND DISCUSSION The default boundary condition in FLUENT is the adiabatic wall, where the heat flux equals zero. Therefore, apart from the symmetry planes, the other parameters needed for this study are: Table 3.1. Initial Condition Inputted for Inlet and Outlet of the Model Port Total Press. Temp. Turbulent Intensity Hydraulic Dia. (m) 1P8) K) (‘D Inlet 0 298.15 2.5 0.284 Outlet -60 298.15 30 0.42 Temperature of the wall is set initially at 278.15 K, and temperature of the heated plate is also set at 278.15 K (adjustable). Results of these studies are represented through velocity, temperature, condensation, and evaporation fields Figures 3.1.1 to 3.10. 28 Figure 3.1.1. Flow Field (mls) of Air Region Figure 3.1.2. Zoom VIew of Flow Field (mls) of Air Region Figure 3.1.1 shows the contours of velocity after the simulation converged. The exact range of this velocity is from 0 mls to 15.658 mls. The more detail View of velocity contour along the thermally active plate is in Figure 3.1.2. As observed in the flow field of air region, the highest velocity occurs near the thermally active plate before decreasing along the bottom symmetry plane. The velocity distribution at the jet nozzle is nearly uniform. We see that the momentum of the jet is diffusing away from the thermally active wall as it flows through the chamber towards the outlet at the bottom. These results also show a small recirculation of the flow occurring on the left hand side of the Chamber. The principle of velocity measurements is based on convective heat transfer from a heated element to the surrounding flow. By passing an electric current through a thin metal wire, the wire temperature is higher than the ambient temperature. The velocity distribution of the flow field is of great interest in the wall jet study. For the study of the defogger flow, more attention needs to be paid in the developing region, since on the interior windshield surface of a vehicle it is in the developing region that the defogging effects need to be applied. Previous study shows that standard k—s model gives better predictions than realizable k-s model. However, the realizable k—e model is better in simulating the effect of the upstream contraction. As mentioned in Chapter 2, the design purpose of contraction is to provide an evenly distributed velocity profile at the jet nozzle. 30 12 ,0 7. AbdulNour1 st [4] j ,- Wang [9] I 8 I AbdulNouand [4] I x Wang(highiteration) [9] it Present work Veloclty (mls) O) 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Dimensionless Position at xlw = 7.62 Figure 3.2. Comparison of Velocity Magnitude with Previous Study Figure 3.2 shows the comparison of velocity magnitude at x/w = 7.62 with previous works by Wang [9] and AbdulNour [4]. As observed, the present work’s result is consistent with the previous numerical work. The velocity, as expected, is highest near the wall and decreases as we move away from the wall. The present’s work shows a velocity magnitude far from the wall to be higher compared to the previous studies. This may be due to a different laminar/turbulent transition point for each of the studies or over prediction of turbulent diffusion. 31 300 295 . =3 9 290 . 3 E g 235 . O .- _ _ J._ ..#W __. _ +x/w=1.59 28° . l+xlw=10.s +x/w=3.18 l+ W4 :15 “T X’W‘Z-PEJ 275 . - . e - a o 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Position (m) Figure 3.3. Temperature vs. Position at Different xlw Location In Figure 3.3, the air temperature is shown against positions at various xlw locations. When xlw = 0, the respective location is at the jet nozzle. Since the inlet temperature is at 298.15 K, and temperature at the thermally active plate is at 278.15 K, this has lowest temperature. However, this rises faster with respect to the position compared to other xlw locations. As xlw gets higher, the trend is Vice versa. As we move along the plate we see significant similarity in the temperature profile, indicating that one could imply a seIf-similarity approach to the problem. 32 0. 050 0.054 0.050 0.047 0. 043 0.040 0. 056 , , 0.032 0.025 0.022 0.018 0.014 0.011 01!)? 0.034 0.(IJO Figure 3.4.1. Concentration Field (kg/m3) in Air Region 0050 0.054 0.050 0.017 = i 0.043 0.040 0.000 0.029 ‘ 0.025 0.022 0.010 0.014 0.011 0.007 0.004 0.000 Figure 3.4.2. Zoom Vrew of Concentration Field (kg/m3) in Air Region 33 Figures 3.4.1 and 3.4.2 shows the concentration field in the air region. Similar to flow field of the air region, the peak concentration decreases as the flow moves downstream along the thermally active plate. This is due to the removal of water vapor due to condensation. As expected most of the variation in concentration occurs in the air region close to the thermally active plate. Around the middle of the Chamber, there is a recirculation flow field with diminished concentration potential. 2.00 A 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00 0.000 0.003 0.006 0.009 0.012 0.015 0.018 0.021 a Hoke [1] T} — 95% CI Exp. , —-— -95% Cl Exp. 5 . -—-Present Work I ate (9/111in Condensation R Concentration Potential (kglm’t3) Figure 3.5.1. Comparison of Condensation Rate with Experimental Data 34 2.00 1 .80 - 1 .60 - 1.40 r 1.20 ~ 1.00 ~ 0.80 — 0.60 — 0.40 - I 0.20 r 0.00 .m ...—..h—w e “Abd DINO—LFfilj I AbdulNour [4] _ -:Ere_-°>§01W.9rk Condensation Rate (glmln) 4 g 1_ 0.000 0.002 0.004 0.006 0.000 0.010 0.012 0.014 0.016 0.018 0.020 Concentration Potential (kglm‘3) Figure 3.5.2. Comparison of Condensation Rate with Previous Computational Results The comparison of experimental results with 95% confidential intervals and the present work is presented in Figure 3.5.1. Figure 3.5.2 shows the comparison of previous computational work with the present study. Results are presented as the condensation rate versus the concentration potential. The experimental results were provided by Hoke [1], while the numerical steady-state condensation was provided by AbdulNour et al. [5]. The numerical steady-state condensation results were calculated using FLUENT 5.0 with a User Defined Function (UDF). All the results Show similar trend and range. Agreement between the computations and the experimental data (Figure 3.5.1) are fairly good, although the computation results of the present study show a somewhat smaller condensation rate. Comparisons of the results of the present study with the previous computations by AbdulNour [4] are quite good. 35 ate (glmln) I I Mass Transfer R 0 OJ i—JEEDOTGtiOn— I I I—l— Condensation JI , 0 L_.-.___ _ g -_ _ _ f ,_ .*_-._I-..- ._ - . .----- _ _ _ -_..I__S S $ 0.009 0.012 0.015 0.018 Concentration Potential (kglm‘3) 0 0.003 0.006 0.021 Figure 3.6. Comparison of Condensation and Evaporation at Liquid Layer Interface Results for evaporation have also been generated. A comparison between condensation and evaporation rates can be seen in Fig. 3.6, where the evaporation rate is slightly higher rate than the condensation rate. To obtain condensation results, the inlet temperature is set higher than the thermally active plate, while for evaporation rate the setup is reversed. One might assume that the mass transfer rate should be the same for the same concentration potential whether there is condensation or evaporation. However that is not the case based on Figure 3.6. 36 I 1.75 . +301 corEJaiorT _ i +with Diffusion 1-5 : flogeflwjngmfiusigni 1.25 0.75 . 0.5 Condensation Rate (glmln 0.25 _I _L 0 0.003 0.006 0.009 0.012 0.015 0.018 0.021 Concentration Potential (kg/mt‘3) _1_ A Figure 3.7. Condensation Rates Due to Diffusion and Convection Since the condensation rate includes both diffusive and convective components, it is of interest to see how both modes contribute to the total condensation rate. This is shown in Figure 3.7. It appears that each modes contributes nearly equally to the total condensation rate, with the convective mode having a slightly greater contribution. It is clear that only including the diffusive components, as it normally done, would lead to a significant under prediction in the mass transfer. 37 5250 FO-Conden—Satio; 450° ‘ iii/apostle 8 .D 3750 - 5 z 3000 r 3 CE) 2250 ~ 3 1 m 500 - 750 ~ 0 I I I r I u 0 1000 2000 3000 4000 5000 6000 7000 8000 Reynolds Number Figure 3.8. Local Shenrvood Number vs. Local Reynolds Number Figure 3.8 shows the plot of local Shenrvood Number against local Reynolds Number for both condensation and evaporation. They have been defined as Re, = ”/e'x (3.2) V Sh, = E (3.3) D As observed, for evaporation results, the Sherwood Number versus local Reynolds Number is higher than for the condensation results. This phenomenon could be the result of that the evaporation rate for current model is slightly higher than the condensation rate. The local Reynolds Number of a flow strongly 38 influences the velocity boundary layer characteristics and hence is of great importance in determining transfer coefficients. Reynolds Number is also the key parameter for determining whether flow is laminar or turbulent. The Sherwood Number can be used for future study to determine species transfer by means of correlations with windshield defogging or defrosting. With the evidence provided above that demonstrates the ability of the computational model to predict experimental results, the steady state results can be used to develop a prediction of window defogging. A mass balance on the liquid layer gives KA :17? - _ p v (3.4) pr The initial water layer thickness of 60 is not a constant mass transfer coefficient, and the liquid layer temperature is Changing by finite difference approximation. We find that 5(r)=5(r-xn_K:Pv At (3.5) I In order to use these results for predictive modeling, it will be useful to know the average mass transfer coefficient in terms of the jet velocity, or in dimensionless form the average Sherwood number Sh 2 avg (3.6) In terms of jet Reynolds Number Re = ujetw (3'7) jet v 39 These results from the computational model are shown in Figure 3.9 3000 r _*_W___*# 17::ENEEWEAQI 2500 ~ 2000 1500 » 1 000 Sherwood Number 500 I O i _L 4 4 0 1 500 3000 4500 6000 7500 Reynolds Number Figure 3.9. Sherwood Number vs. Reynolds Number Figure 3.10 shows the plot of the liquid layer thickness versus time at different jet Reynolds Number for evaporation. Initially, the boundary layer thickness is set at 5x106. For steady state time, it takes between 24 to 43 seconds before the liquid layer thickness reduces to zero. We ran the test at different Reynolds Number by varying the velocity, as higher velocity means higher Reynolds Number. As expected, the plot shows linear lines and all the results have similar trend for different Reynolds Number. 40 i—o-TRE é 1323.24 l+ Re = 2451.94 ; Re = 3775.22 ‘-*- Re = 4663.9 + Re = 5578.74 I:- 86: 67191? I I l l it; M ii .--- .-- .-- -V ----l Thickness (m) Time (s) Figure 3.10. Liquid Layer Thickness vs. Time at Different Reynolds Number The assumption of a constant mass transfer coefficient can be investigated by conducting a transient analysis with FLUENT as is done in the next section. 3.3 UNSTEADY-STATE INITIAL CONDITION Since defogging in real automotive world is not as simple as the steady state computational, one must cany out the experimental and computational testing of defogging or defrosting. Previous study provides experimental data that could be used for extensive modeling and prediction of condensation and evaporation for the transient study. 41 For unsteady-state simulation, the initial condition is similar to what the steady—state simulation are, except that the time is set to unsteady time. The unsteady formulation used is the second-order implicit to obtain more accurate results. The segregated solver makes it possible to solve the governing equations separately. Since the physical properties are assumed to be constant, for the unsteady—state simulation, few different steps were taken to obtain the simulation results. The initial step taken is selecting flow and turbulent equations, while deselecting the energy equation and the user-defined scalar, in performing the velocity simulation. This step was done until the velocity become converged. During this study, this step becomes converged after 475 iterations. Once the velocity converged, the second step is to select the energy equation and the user-defined scalar, while deselecting the flow equation in performing the temperature simulation. These two steps were also taken to save some simulation time. For the steady-state simulation, these steps were not used since the running time is not as long, and the equations were not as complicated as the unsteady-state simulation. In unsteady-state simulation, there exist a temperature dependent of air at a given pressure, which is the maximum amount of moisture the air can hold. At this point, the air is saturated, and the relative humidity is considered 100%. Any further drop in temperature or addition of moisture results in condensation of water vapor into liquid water in order to keep the thermodynamic equilibrium. The 42 dew point temperature is defined as the temperature at which condensation begins if the air is cooled at constant pressure. As mixture colds at this constant pressure, the partial pressure of vapor remains constant until the temperature drops below the dew point. For the unsteady-state simulation, User Defined Function (UDF) [9] was modified in a C program, compiled, and implemented in FLUENT to get the information needed for the mass flux. This UDF also contain the source term needed for the unsteady-state simulation. All operations for the UDF were done Via the “deflne_adjust” function in the UDF. All the “define_adjust” functions were used at the beginning of every iteration. Appendix A and Appendix B shows the UDF used for current transient study. The UDF in Appendix B is similar to that in Appendix A, however it does not contain the mass source of the model. The use of this UDF is to run a simple transient run, hence it will not take as long time to run the computational as UDF with the mass source. However, the accuracy of the result is also less than by using the UDF with mass source. In both UDF, adjustment of vapor mass fraction is made in the Define_Ad/'ust function named as spec _grad. For comparison, local saturation mass fraction of water vapor is stored in user—defined scalar (UDS) in FLUENT. The purpose of storing the flow variables into a user-defined scalar is to get the relative derivatives of the variables that cannot be returned directly by the solver to the UDF but are necessary to specify the source terms needed in the governing equations. 43 The formula needed to calculate such Reynolds Number, Sherwood Number, condensation rate, evaporation rate, etc should be inputted manually under “Define” pull down menu in FLUENT followed by the Custom Field Function selection. All this extra formula is used for the purpose of post— processing results. 3.4 UNSTEADY-STATE RESULTS AND DISCUSSION For the mass transfer simulation, an ideal gas mixture of vapor and air is set in FLUENT. The mass diffusivity, D, of the vapor in the mixture is assumed to be a constant at 2.28x10‘5 mzls. The inlet mainstream mass fraction (1)... corresponding to the relative humidity It)... can be calculated through the absolute humidity, (0. The relationship between absolute humidity and relative humidity is O.622¢P (0 = #L (3.3) sat The inlet mass fraction can be calculated from (t) °° ° (3.4) 00 Ha) w The local mass transfer coefficient of vapor along the thermally active plate is of interest of mass transfer, which is defined as J h ——-—W—— (3.5) m pw #200 where JW is the mass flux at the wall, pW is the mass concentration at the wall, and p... is the mass concentration along the main stream. 44 The mass flux itself can be obtained with the following formula Jw=_ DP?) (3.6) 6y yzo Where D is the mass diffusivity, p is the mixture density of the wall, and <1) is the mass fraction of the vapor. For unsteady-state simulation, the result of the flow field, as expected, is similar to the steady-state simulation. The maximum velocity is slightly lower compared to the steady state velocity. However, the results of transient run are still within 95% confidence interval of previous experimental data. Hence this slight difference could be neglected. This difference could also be a cause of hysteresis. Velocity contour for the unsteady-state simulation is presented in Figure 3.11.1, with the zoom View presented in Figure 3.11.2. 45 14 13 , 11 10 9.1 . _ 8.2 ' 7.3 6.4 . 5.5 4.6 , 3.7 "I 2.7 t: 1.8 0.91 FIGURE 3.11.1. Velocity Flow Field after 5 Seconds In Unsteady-Simulation 0.91 FIGURE 3.11.2. Zoom \erw of Velocity Flow Field after 5 Seconds 46 (a. Q . Comparing Figures 3.11.1, 3.11.2 with steady state flow field of air region, Figures 3.1.1, and 3.1.2, the flow field is very similar. Notice that the maximum flow field of air region for the steady-state simulation is slightly higher, but not by much. This higher phenomenon could be caused that in unsteady—simulation, the simulation was done in two steps, by doing the velocity and turbulence first until it reaches steady state, followed by doing the energy flow. In the volumetric transient model, the same thin film is adopted similar to the 2—D steady state model. The liquid film on the wall has little influence on the velocity field and heat transfer. The impermeable surface model is still assumed valid at the interface between the liquid film and the gaseous air—vapor mixture. The computation starts from the interface where the mass fraction is saturated. The main difference of transient model with the steady-state model is the possible formation of liquid droplets in the volume of the flow that is now considered. Before, the thermodynamic equilibrium is only maintained on the wall surface. In transient, the water will condense into liquid droplets to keep local thermodynamic equilibrium in the volume of the flow. When the condensation or evaporation occurs, there will be latent heat released, which will affect the temperature distribution. Also, there will be a loss of mass in the gaseous phase as the water vapor condenses out into the liquid phase. 47 6.00E-06 5.00E-06 4.00E—06 3.00E-06 Condensation thickness (m 8 a”: O O I." I.“ 0.00E+00 I 06 - 06 - Le— Transient]J 50 100 150 Time (s) 200 250 Figure 3.12.1 . Present Study of Condensation Thickness vs. Time 12 10 I Condensate Thickness (pm ) O) I I l l l 'L —e— #10241: 0 +xlw=11, z/w=0 7* ___2£’W_=12_._2/W_=_° Error bars represent the 95% confidence band derived from the calibration experiment 50 100 150 Time ( sec ) 200 250 Figure 3.12.2. Condensation Thickness vs. Time from Previous Study 48 Figure 3.12.1, and 3.12.2 shows the results of condensation thickness versus time from present and previous study respectively. The result of the previous study is obtained from AbdulNour [11]. The present study result shows agreement with the previous study result. Although the numbers of condensation thickness are not exactly the same, the results of the present study are still within 95% confidence bar of the previous study. As expected, condensation thickness for this study should increase linearly, if not almost linearly as time increases during transient mn. Though for each xlw the condensation thickness is varying, the plot should show similar trend as seen in Figure 3.12.2. Condensation Rate (gls) A Time (s) Figure 3.13.1. Mass Flow Rate vs. Time at xlw = 1.59 49 Figure 3.13.1 above shows the plot mass flow rate against time step at xlw = 1.59. For the transient experiment, each time step is set at 0.25 second for the first four time steps and at increment of one second after that. The maximum iteration per-time step is set at 20. The condensation flow rate after 1 second looks like a straight line, however in the actual data, the flow rate is still increasing in slower rate compared to the first 4 time steps. The flow rate after five seconds become steady state, hence it will just show a straight line. Each xlw location shows similar trend as Figure 3.13.1. However, each xlw has different mass flow rate. The combination plot for the mass flow rate in each xlw is shown in Figure 3.13.2. 7.5 7 ... 6.5 - re 3’ a? » a . To' 5 _ m 4.5 - .5 4 “ ‘5; 3.3 - 5 25 — '2 2 ( ...; xlw-:0 'Lx/w-T —1.59 ‘ 8 1'5 +x/w=4.45 —x—x/w=3.18 1 l +x/w=7.62 +x/w=10.s 0.5 l -- - _ -___1__ _ - 0 l 1 L 1 I 1 I 1 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 Time (s) C Figure 3.13.2. Mass F low Rate Vs. Time for Different xlw 50 The plot of mass flow rate is obtained from the transient condensation experiment instead of the evaporation run. The plot of each xlw in Figure 3.13.2 after 1 second looks like straight line, however each line actually shows an increasing trend similar to Figure 3.13.1. As observed, as xlw increases, the mass flow rate is also higher with the exception of xlw = 0 where the mass flow rate is higher than the mass flow rate at xlw = 7.62. This could be a result that at xlw = 0, it is located at the jet nozzle of the model, where the area is smaller than the inlet velocity that causes pressure rise, hence resulting in a high flow rate. 88.448 8 E 88.446 3 2 88.444 1, 8 88.442 E 2 a, 88.44 8 0 88.438 » .l 88.438 0 1 2 3 4 5 6 Time (s) Figure 3.14.1. Local Shenrvood Number vs. Time at xlw = 3.18 51 160 140 V : = 3 , , #7 :/ , l 7 = 7 K 1 3 ‘—+—x/w=0 +x/w=1.59 g 120 l :+flw=3.18 +x/w=4_45[ 3 i+xlw=782 +x/w=10.8; z 100 x x x _ , g ) Razz. 13 )‘z x 4,; ... x 8 80 a a i A - E 5 60 - I—I—H—I—I 8 4o 0 ¢ Ar : % ¢ 4 20 0 Time (s) Figure 3.14.2. Local Sherwood Number vs. Time at Different x/w Figure 3.14.1 presents the Local Reynolds Number versus time at xlw = 3.18. The plot shows that local Sherwood Number is decreasing as time increases. The Sherwood Number will keep decreases as time continues to increase, although the decreasing rate will get slower after certain amount of time. For this transient study, the ShenNood Number is only obtained for some period of time. The importance of Sherwood Number for this study is to predict the window condensation or evaporation for the automotive industry. If the Sherwood Number of this computational study is in agreement with the experimental study done previously, then in the future the experimental test could be minimized, if 52 not scrapped, means that minimize the cost of the study by just doing computer simulation. For all local Shenlvood Number versus time for different xlw is presented in Figure 3.14.2. Sherwood Number for each xlw is actually decreasing similar to Figure 3.14.1. The plot in Figure 3.14.2 looks like straight line just because the dimensioning in Microsoft Excel when all local Sherwood Number is plotted in one graph. Results of Sherwood Number versus time in Figure 3.14.2 are internally consistent and in agreement to the experiment results of [1]. 2558 ““5“ 2557 . ifltatfintl 2556 l 2555 ~ 2554 - Reynolds Number N 01 01 OD 2552 2551 . —L . 5* . 1 Time (s) Figure 3.15. Reynolds Number vs. Time Figure 3.15 presents the plot of Reynolds Number versus time step during a transient run. As mentioned before, each time step is set at one seconds, and 53 the maximum iteration per-time step is set at 20. As expected, the Reynolds Number is showing a decreasing trend as time step increases, however the decreasing rate will slow down after certain amount of time. The trend of Figure 3.15 is in agreement with the experimental results [1]. Transient computational provides more complex calculation compared to the steady state experiment. In running the iteration it is more complicated since one need to reach steady state first with the velocity and turbulence equation (475 iterations) before running the energy equation to obtained the results expected. With the unsteady time, accurate source term by using UDF is needed in order to nm the iteration and not receiving error messages in FLUENT during the iteration run. With the help of F LUENT Support during this study, acceptable results are obtained for the importance of future studies. From the standpoint of formulation, source terms used are considered to be highly non-linear with respect to the flow variables solved in the governing equations, which make the equations more difficult to solve. The current algorithm of FLUENT is not exactly open to the users, makes it more difficult for user to find out the compatibility of the non-linearity source terms. 54 CHAPTER 4 CONCLUSIONS AND FUTURE WORK 4.1 CONCLUSIONS . This study shows that a computational simulation can be applied successfully in order to investigate condensation and evaporation phenomena with excellent comparison to results from previous studies. 0 Results of this computational study establish a tool appropriate for the development of defogging analysis. o It is believed that the volumetric phase change model is in ready stage with theoretical analysis of the model and the source terms to handle the transient problem. . The transient results are also in agreement with previous studies results. Thus a computational study could be done instead of an experimental study, significantly reducing costs. . Implementation of the UDF into the CFD software package FLUENT is critical in running the transient case, although it is not simple, and could be improved with technical support from F LUENT, Inc. 55 4.2 FUTURE WORK During the development of the study, the author developed several suggestions for future possible improvement. They are summarized below One of the shortcomings in the transient study is that the phase change only assumed to be occurred on the wall surface. If further study is done in this part, the author believes more accurate results could be obtained by incorporating moving boundary for the liquid layer. Numerically, the limits on velocity, temperature, and vapor concentration conditions in order for the key assumption of the model to hold needs to be further investigated to improve the accuracy of the results. Further investigation of compatibility between the algorithm of the code and the highly nonlinear source terms would also be of interest. More parameters could be investigated for the transient run, e.g. varying the velocity, temperature, concentration potential, and other basic initial conditions to capture all possible condition of window defogging or defrosting in the real world. Impact of flow transition from laminar to turbulent flow might be an interest for future study subject, since it will have some effect in the calculation accuracy of the model. Wrth the development of FLUENT software, there is always room for improvement for the transient study in predicting window defogging or defrosting with or without UDF. 56 The liquid layer set for current study is adiabatic. More sophisticated model for liquid layer with the effect of the outside part of the windshield could be an interest for future study. Further experimental test could be done with different Reynolds Number by using the valid Sherwood Number obtained in current study. Though this may change the geometry of the model. 57 APPENDICES 58 APPENDIX A USER DEFINED FUNCTION FOR THE VOLUMETRIC PHASE CHANGE MODEL #include "udf.h" #include "sg.h" #deflne L 2400.0e3 I" latent heat of water [J/kg] */ #define b L*18 / 8314.4 #define a b I (273.15 + 100.) DEF lNE_ADJUST(spec_grad, domain) { Thread *t; cell_t c; face_t f; float MLFS; l* saturation mole fraction */ float MSFS; /* saturation mass fraction */ float UVPR; I‘ x velocity of vapor *l float WPR; l“ y velocity of vapor *l thread_loop_c (t,domain) begin_c_loop_all (c,t) MLFS = exp(a - b / C_T(c,t)); f” equation (4.23) */ MSFS = (MLFS * 18129.) I (1. - MLFS * (1. - 18./29.)); /* equation (4.24) */ if (C_Yl(c,t,0) > MSFS) C_Yl(c,t,0) = MSFS; if (C_Yl(c,t,0) <= 0.0) C_Yl(c,t,0) = 1.0e-12; /* adjust the mass fraction of vapor if its is higher than the saturation value. */ if (NULL != THREAD_STORAGE(t,SV_UDS_I(3)) && NULL != THREAD_STORAGE(t,SV_UDS_I(0))) { 59 C_UDSl(c,t,3) = MSFS; C_UDSl(c,t,0) = C_Yl(c,t,0); } end_c_loop_all (c,t) thread_loop_f (t,domain) if (NULL 1: THREAD_STORAGE(t,SV_UDS_l(3)) && NULL 1: THREAD_STORAGE(t,SV_UDS_I(0))) { begin_f_loop (f,t) { float FMLFS = exp(a - b / F_T(f,t)); float FMSFS = (FMLFS * 18./29.)/ (1. - FMLFS * (1. - 18./29.)); F_UDSl(f,t,3) = FMSFS; F_UDSl(f,t,0) = F_Yl(f,t,0); } end_f_loop (f,t) } thread_loop_c (t,domain) if (NULL != THREAD_STORAGE(t,SV_UDS_|(0)) && NULL != T_STORAGE_R_NV(t,SV_UDS|_G(0))) { begin_c_loop_all (c,t) float diff_eff = 2.88e-5 + (C_MU_T(c,t)l0.7); UVPR = C_U(c,t) - diff_eff * C_UDSl_G(c,t,0)[0]/C_UDS|(c,t,0); WPR = C_V(c,t) - diff_eff * C_UDSI_G(c,t,0)[1]/C_UDSl(c,t,0); C_UDSl(c,t,1) = C_R(c,t) * C_UDSl(c,t,0) *uva; C_UDSl(c,t,2) = C_R(c,t) * C_UDS|(c,t,0) * WPR; } end_c_loop_all (c,t) 6O } } thread_loop_f (t,domain) /* assign face value with way (1) *l { if (NULL l= THREAD_STORAGE(t,SV_UDS_|(0)) && NULL != THREAD_STORAGE(t,SV_UDS_I(1)) && NULL != THREAD_STORAGE(t,SV_UDS_l(2))) { begin_f_loop (f,t) { cell_t cell = F_CO(f,t); Thread *c_thread = THREAD_T0(t); if (NULL != T_STORAGE_R_NV(c_thread,SV_UDS|_G(0))) { F_UDSl(f,t,1) = C_UDSl(cell,c_thread,1); F_UDSl(f,t,2) = C_UDSl(cell,c_thread,2); } } end_f_loop (f,t) } } DEFINE_PROFILE(plate_mf, t, position) /* specify saturation mass fraction at the boundary */ face_t f; begin_f_loop (f,t) { float FMLFS = exp(a - b I F_T(f,t)); F_PROFILE(f,t,position) = (FMLFS * 18.]29.)/ (1. - FMLFS * (1. - 18129)); } end_f_loop (f,t) } DEF INE_SOURCE(mass_src, c, t, dS, eqn) . * /* source term of continuity and concentration equatron / { float source; 61 if (NULL r= T_STORAGE_R_NV(t,SV_UDSI_G(1)) && NULL 1: T_STORAGE_R_NV(t,SV_UDSI_G(2)) && NULL 1: THREAD_STORAGE(t,SV_UDS_l(0)) && NULL 1: THREAD_STORAGE(t,SV_UDS_l(3))) if (C_UDSl(c,t,O) < C_UDSl(c,t,3)) source = 0.; else source = C_UDSl_G(c,t,1)[0] + C_UDSl_G(c,t,2)[1]; /* equation (4.34) */ dSleqnl=0; return source; } DEFINE_SOURCE(energy_src, c, t, dS, eqn) /* source term for energy equation */ { float source; if (NULL != T_STORAGE_R_NV(t,SV_UDSI_G(1)) && NULL l= T_STORAGE_R_NV(t,SV_UDS|_G(2)) && NULL l= THREAD_STORAGE(t,SV_UDS_I(0)) && NULL != THREAD_STORAGE(t,SV_UDS_I(3))) { if (C_UDSl(c,t,O) < C_UDSl(c,t,3)) source = 0.; else source = -L * (C_UDSl_G(c,t,1)[0] + C_UDSl_G(c,t,2)[1j); } dS[eqn]=0; return source; } 62 APPENDIX B USER DEFINED FUNCTION FOR THE VOLUMETRIC PHASE CHANGE MODEL (WITHOUT MASS SOURCE) #include "udf.h" #include "sg.h" #define L 2400.0e3 /* latent heat of water [J/kg] */ #define b L*18 / 8314.4 #define a b I (273.15 + 100.) DEFINE_ADJUST(spec_grad, domain) { Thread *t; face_t f; float MLFS; /* saturation mole fraction */ float MSFS; l* saturation mass fraction */ float UVPR; /* x velocity of vapor */ float WPR; /* y velocity of vapor */ thread_loop_c (t,domain) begin_c_loop_all (c,t) MLFS = exp(a - b / C_T(c,t)); /* equation (4.23) */ MSFS = (MLFS *18./29.)/(1.- MLFS * (1. - 18./29.)); /* equation (4.24) */ if (C_Yl(c,t,0) > MSFS) C_Yl(c,t,0) = MSFS; if (C_Yl(c,t,0) <= 0.0) C_Yl(c,t,0) = 1.0e-12; /* adjust the mass fraction of vapor if its is higher than the saturation value. *I if (NULL != THREAD_STORAGE(t,SV_UDS_I(3)) && NULL I= THREAD_STORAGE(t,SV_UDS_I(0))) { 63 C_UDSl(c,t,3) = MSFS; C_UDSl(c,t,O) = C_Yl(c,t,0); } } end_c_loop_all (c,t) thread_loop_f (t,domain) if (NULL 1: THREAD_STORAGE(t,SV_UDS_l(3)) 88 NULL 1: THREAD_STORAGE(t,SV_UDS_I(0))) { begin_f_loop (f,t) { float FMLFS = exp(a - b / F_T(f,t)); float FMSFS = (FMLFS * 18129.) I (1. - FMLFS *(1.-18./29.)); F_UDSl(f,t,3) = FMSFS; F_UDSl(f,t,O) = F_Yl(f,t,0); } end_f_loop (f,t) } thread_loop_c (t,domain) 'rf (NULL != THREAD_STORAGE(t,SV_UDS_I(0)) && NULL != T_STORAGE_R_NV(t,SV_UDSI_G(0))) { begin_c_loop_all (c,t) float diff_eff = 2.88e-5 1- (C_MU_T(c,t)l0.7); UVPR = C_U(c,t) - diff_eff * C_UDSI_G(c,t,0)[0]/C_UDSI(c,t,0); WPR = C_V(c,t) - diff_eff * C_UDSl_G(c,t,0)[1]IC_UDSl(c,t,0); C_UDSl(c,t,1) = C_R(c,t) * C_UDSl(c,t,O) * UVPR; C_UDSl(c,t,2) = C_R(c,t) * C_UDSl(c,t,O) * WPR; } end_c_loop_all (c,t) .64 } } thread_loop_f (t,domain) l‘ assign face value with way (1) *l { if (NULL l= THREAD_STORAGE(t,SV_UDS_l(0)) && NULL != THREAD_STORAGE(t,SV_UDS_I(1)) && NULL != THREAD_STORAGE(t,SV_UDS_I(2))) { begin_f_loop (f,t) { cell_t cell = F_CO(f,t); Thread *c_thread = THREAD_T0(t); 1r (NULL 1= T_STORAGE_R_NV(c_thread,SV_UDSl_G(0))) F_UDSl(f,t,1) = C_UDSl(cell,c_thread,1); F_UDSl(f,t,2) = C_UDSl(cell,c_thread,2); } } end_f_loop (f,t) } } } DEF INE_PROF lLE(plate_mf, t, position) /* specify saturation mass fraction at the boundary */ face_t f; begin_f_loop (f,t) { float FMLF S = exp(a - b I F_T(f,t)); F_PROFILE(f,t,position) = (FMLFS * 18129.)! (1. - FMLFS * (1. - 18/29.»; } end_f_loop (f,t) } DEFINE_SOURCE(energy_src, c, t, dS, eqn) l* source term for energy equation *I { float source; 65 if (NULL 1: T_STORAGE_R_NV(t,SV_UDSl_G(1)) 88 NULL 1= T_STORAGE_R_NV(t,SV_UDSI__G(2)) 88 NULL 1= THREAD_STORAGE(t,SV_UDS_I(0)) 88 NULL 1= THREAD_STORAGE(t,SV_UDS_I(3))) if (C_UDSl(c,t,O) < C_UDSl(c,t,3)) source = 0.; else source = -L * (C_UDSl_G(c,t,1)[0] + C_UDSl_G(c,t,2)[11); } dSleqnl=0; return source; } 66 Residuals —continuity r—x-vclocity -—y-velocity ~—energy *cpsilon APPENDIX C RESIDUAL PLOT OF 2-D STEADY STATE RUN Ie+UB 3 -l 16+UB 1 le+U4 1 15+02 1 le-UI 1 18-05 1 W M 19-0231\“_\ . L ' ‘ “M. ‘EW “JR 18-08 I I I I I I ' I T I l I I I I ' I ' I 111 211 311 411 511 811 Iterations 67 APPENDIX D COMPUTATIONAL RESULTS Table D1. Condensation Rate with Onl Diffusion Aconcentration M Imin , 0.0044192 0.279067 0.00476326 0.286247 0.00514243 0.295807 0.00560799 0.307826 0.00615095 0.322712 0.00675215 0.341049 0.00744845 0.362481 0.0082635 0.39361 0.00921561 0.436279 0.0103052 0.488144 0.0115558 0.552178 0.0130065 0.628601 0.0146356 0.730184 0.0164875 0.864014 0.0185547 1.01902 Table 0.2. Condensation Rate with Only Convection Aconcentration M (glmirg 0.0044192 0.096576 0.00476326 0.104663 0.00514243 0.114017 0.00560799 0.125301 0.00615095 0.1376 0.00675215 0.158679 0.00744845 0.191277 0.0082635 0.225842 0.00921561 0.264279 0.0103052 0.309194 0.01 15558 0.373768 0.0130065 0.466739 0.0146356 0.561326 0.0164875 0.657306 0.0185547 0.76371 Table 0.3. Condensation Rate with Convection and Diffusion Aconcentration M (97min) 0.0044192 0.479285 68 0.00476326 0.491614 0.00514243 0.508035 0.00560799 0.528677 0.00615095 0.554242 0.00675215 0.585735 0.00744845 0.622543 0.0082635 0.676006 0.00921561 0.749288 0.0103052 0.838363 0.0115558 0.948339 0.0130065 1.07959 0.0146356 1 .25405 0.0164875 1.4839 0.0185547 1.75012 Table D.4. Reynolds and Sherwood Number for Condensation Reynolds Sherwoo 920.4194 3950.16 1490.928 3981.3 2120.237 2650.97 2760.184 1304.03 4250.244 592.781 5440.826 469.35 Table 0.5. Reynolds and Sherwood Number for Evaporation Reynolds herwood 1323.24 4973.98 2451.94 4896.83 3775.22 3017.72 4663.9 1469.95 5578.74 646.939 6710.73 466.2579 Table D.6. Reynolds Number for Transient Time (3) Re # 2557.474 2555.223 2553.944 2552.483 2551.953 2551.858 monsoon-s Table DJ. Liquid Layer Thickness vs. Time for Different Reynolds Number Re=1323.24 0 0.000 5.00E-06 69 5 4.337 4.34E-06 10 3.344 3.34E-06 15 2.197 2.20E—06 20 9.657 9.66E-07 25 4.765 4.77E-07 30 2.566 2.57E-07 35 9.654 9.65E—08 40 5.674 5.67E-08 45 2.902 2.90E-08 50 1.241 1 .24E-08 55 0.936 9.36E-09 60 0.750 7.50E-09 64 0.000 0.00E+00 Re=2451 .94 0 0.000 5.00E-06 5 3.686 3.69E-06 10 2.842 2.84E-06 15 1.867 1.87506 20 8.208 8.21 E-07 25 4.051 4.05E-07 30 2.181 2.18E-07 35 8.206 8.21E-08 40 4.823 4.82E-08 45 2.466 2.47E-08 50 1 .055 1 .05E—08 55 0.795 7.95E-09 60 0.000 0.00E+00 Re=3775.22 0 0.000 5.00E-06 5 3.252 3.25E-06 10 2.508 2.51E-06 15 1 .648 1 .65E—06 20 7.243 7.24E-07 25 3.574 3.57E-07 30 1 .924 1 .92E-O7 35 7.241 7.24E-08 40 4.256 4.26E-08 45 2.176 2.18E-08 50 0.931 9.31 E-09 7O 55 0.702 7.02E-09 56 0.000 0.00E+00 Re=4663.90 0 0.000 5.00E-06 5 2.819 2.82E-06 10 2.173 2.17E-06 15 1 .428 1 .43E-06 20 6.277 6.28E-07 25 3.098 3.10E-07 30 1 .668 1 .67E-07 35 6.275 6.28E—08 40 3.688 3.69E-08 45 1.886 1.89E—08 50 0.807 8.07E-09 52 0.000 0.00E+00 Re=5578.74 0 0.000 5.00E-06 5 2.385 2.39E—06 10 1 .839 1 .84E-06 15 1.208 1.21 E-06 20 5.311 5.31E-07 25 2.621 2.62E-07 30 1.411 1.41 E-07 35 5.310 5.31E-08 40 3.121 3.12E-09 45 1 .596 1 .60E-09 46 0.000 0.00E+00 Re=671 0.73 0 0.000 5.00E-06 5 1 .951 1 .95E-06 10 1.505 1.50E-06 15 7.243 7.24E-07 20 2.144 2.14E-07 25 1.155 1.15E-07 30 4.344 4.34E-08 35 2.553 2.55E—08 40 1.306 1.31E-08 42 0.000 0.00E+00 71 BIBLIOGRAPHY 72 Bibliography [1] Hoke, P. B. (2001 ). Experimental Study of Heat Transfer and Phase Change Condensation in 8 Developing, Two-Dimensional Wall Jet Flow Field with an lsotherrnal Boundary Condition, Thesis for PhD. Degree, Department of Mechanical Engineering, Michigan State University [2] Launder, B. E. and Rodi, W. (1981). The Turbulent Wall Jet, Prog. Aerospace Sci., Vol. 19, pp. 81-128. [3] Legay-Desesquelles, F. and Prunet-Foch, B. (1986). Heat and Mass Transfer with Condensation in Laminar and Turbulent Boundary Layers along a Flat Plate, Int. J. Heat Mass Transfer, Vol. 29, No 1, pp. 95—105. [4] AbdulNour, B. S. (1998). CFD Simulation of a Model Wall Jet Flow for Defogging and Defrosting, Project Report Corporation. Visteon, Michigan. [5] AbdulNour, R. S., VWllenborg, K., McGrath, J. J., Foss, J. F., AbdulNour, B. S. (2000). Measurement of the Convection Heat Transfer Coefficient for a Planar Wall Jet: Uniform Temperature and Uniform Heat Flux Boundary Conditions, Exper. Therm. Fluid Sci., Vol. 22, No. 3, pp. 123-131. [6] Peterson, P. F. (2000). Diffusion Layer Modeling for Condensation with Multi- Components Non-Condensable Gases, Journal of Heat Transfer Trans. ASME, Vol. 122, No.4, pp. 716-720. [7] Siow, E. C., Orrnistion, S. J., Soliman, H. M. (2002). Fully Coupled Solution of a Two-Phase Model for Laminar Film Condensation of Vapor-Gas Mixtures in Horizontal Channels, lnt. J. Heat and Mass Transfer, Vol. 45, No. 18, pp. 3689- 3702. [8] Hassan, M. 8., Petitjean, C., Deffieux, J. C., Gilotte, P. (1999). Windshield Defogging Simulation with Comparison to Test Data, Society of Automotive Engineers, Inc., Valeo Therrnique Habitacle. [9] Wang, Qingtian (1999). Numerical Simulations of 8 Developing Turbulent Wall Jet Along a Then'nally Active Surface, Thesis for Master Degree, Department of Mechanical Engineering, Michigan State University. [10] FLUENT Incorporated (2001). FLUENT 6 User’s Guide. [11] AbdulNour, B. S. (2000). Prediction of Fogging and Demisting, Project Presentation. Visteon Corporation, Michigan. 73 [12] AbdulNour, B. S. (1998). Numerical Simulation of Vehicle Defroster Flow Field, Automotive Climate Control, SAE Publication SP-1347, SAE Paper No. 980285, pp.9-14. [13] Cengel, Y. A. and Boles, M. A. (1989). Thermodynamics - An Engineering Approach, McGraw-Hill, Inc. [14] Eriksson, J. G., Kartsson, R. l. and Persson, J. (1998). An Experimental Study of aTwo-Dimensional Plane Turbulent Wall Jet, Experiments in Fluids 25, pp. 50-60. [15] Mills, A. F. (1999). Basic Heat and Mass TraLnsfer, 2"GI Edition, Prentice Hall, Inc., New Jersey. [16] lncorpera, F. P., and Dewitt, D. P. (1996). Fundamentals of Heat and Mass Transfer, 4th Edition, John Wiley and Sons, New York. [17] Anderson, D. A., Tannehill, J. C., and Pletcher, R. H. (1984). Computational Fluid Mechanicsang Heat Transfer, Taylor and Francis, Washington DC. [18] Versteeg, H. K., Malalasekera, W. (1995). An lntrgdgction to Computational Fluid _D_ynamicsLThe Finite Volume Methg, John VVrley and Sons, New York. [19] Hoke, P. B., Wang, Q., McGrath, J. J., AbdulNour, B. S. (1999). Experimental and Numerical Study of a Condensing Flow in a Developing Wall Jet, Turbulent Shear Flow Phenomena - 1 Conference, Santa Barbara CA, pp. 391—396. [20] Goldstein, R. J., and Cho, H. H. (1995). A Review of Mass-Transfer Measurements Using Naphthalene Sublimation, Experimental Thermal and Fluid Science, Vol. 10, lss. 4, pp. 416 - 434. [21] Goldstein, R. J. (1996). Fluid Mechanics Measurement 2"d Edition, Taylor and Francis, Washington DC. 74