CFD ANALYSIS OF TURBULENT THERMAL MIXING OF HOT AND COLD AIR IN AUTOMOBILE HVAC UNIT

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1 ISTP-6, 005, PRAGUE 6 TH INTERNATIONAL SYMPOSIUM ON TRANSPORT PHENOMENA CFD ANALYSIS OF TURBULENT THERMAL MIING OF HOT AND COLD AIR IN AUTOMOBILE HVAC UNIT Hideo Asano ((, Kazuhiko Suga (3, Masafumi Hirota (, Hiroshi Nakayama (, Shunsaku Hirayama ( and Yasuhiro Mizuno ( ( DENSO CORPORATION, Kariya , Japan. ( Nagoya University, Nagoya , Japan. (3 Toyota Central R & D Labs., Inc., Nagakute, Aichi 480-9, Japan. Corresponding author: hirota@mech.nagoya-u.ac.jp Phone: Fax: Keywords: Automobile air-conditioning, Turbulent thermal mixing, Planar shear layer, Second moment closure, heat flux model, Abstract The results of numerical simulations on turbulent flow and thermal mixing of hot and cold airflows in the HVAC unit used in automobile air-conditioning system are presented, and their reliability is examined by comparing them with experimental data. To simplify the problems, the thermal mixing in the HVAC unit has been modeled by the twodimensional planar turbulent mixing layer. Three turbulence models have been tested; namely, standard linear k-ε model, low-re cubic nonlinear k-ε model, and two-component-limit second moment closure (TCL SMC. For turbulent heat fluxes, prescribed turbulent Prandtl numbers are applied along with the k-ε models. TCL SMC is coupled with a generalized gradient diffusion hypothesis ( or its higher order version ( model. The results suggest that TCL SMC + ( model can predict the distributions of turbulent heat fluxes and mean temperature of the mixed flow successfully. Introduction Turbulent mixing of two flows with different velocities, temperatures and/or concentrations is encountered in many engineering applications, such as chemical reactor, piping system in power plant, combustion chamber, etc. One of the typical examples can be also found in the HVAC (Heating, Ventilating and Air- Conditioning unit used in the automobile airconditioning system []. Figure shows a schematic of the HVAC unit, in which a fan, an evaporator and a heater-core are packaged. In this unit, all air taken by the fan is once cooled down by the evaporator to reduce humidity, and a part of this cold air is heated by the heatercore. Then, hot and cold air is mixed at appropriate flow-rate ratios to control the air temperature blown into the compartment of an automobile. The temperature of the mixed airflow is determined by the flow-rate ratio of the hot and cold air, and it is controlled by the opening of the air-mix door that is settled between the evaporator and the heater-core. Thus it follows that, in the HVAC unit, the hot and cold airflows meet at various angles and various velocity ratios depending on the air temperature required in the automobile compartment. Nowadays it is strongly desired that the HVAC unit be designed virtually by making the most use of CAE to reduce the developing time. This digital engineering requires the numerical simulations of turbulent mixing of hot and cold airflows. At the present stage, however, the reliability of the calculated velocity and temperature distributions in the mixed airflow is not high enough to be directly applicable to the

2 Blower Evaporator Air-Mix Door Cold Air Cold Air Hot Air Heater Core Defroster Duct Foot Duct Face Duct Fig.. Conceptual illustration of HVAC unit design of the HVAC unit. This is because the velocity field of the mixed flow usually shows complex features, and the present turbulence models are not designed to predict it with sufficient accuracy. In addition to the problems of turbulence models, the modeling of the turbulent heat fluxes is also a key issue for improving the performance of numerical simulations of the turbulent thermal mixing encountered in the HVAC unit []. Detailed data on the flow and temperature fields in the HVAC unit are, however, quite scarce, and thus the suitability of turbulence and turbulent heat flux models for the simulation of thermal mixing process encountered in the HVAC unit has not been examined in detail yet. With these points as background, in this study, we have made numerical simulations on turbulent thermal mixing of hot and cold airflows in the HVAC unit, and examined their reliability by comparing the results with experimental data. The turbulent thermal mixing in HVAC unit has been modeled by the mixing of simple two parallel flows with different velocities and temperatures, i.e., twodimensional planar turbulent mixing layer, as shown in Fig.. We have tested three turbulence models for velocity field and they have been coupled with three turbulent heat flux models; the first turbulence model is the standard linear k-ε model and the second one is the low-reynoldsnumber cubic nonlinear k-ε model [], both of which have been coupled with prescribed turbulent Prandtl numbers for turbulent heat fluxes. The third turbulence model is the twocomponent-limit second moment closure (TCL SMC [3], which is coupled with a generalized gradient diffusion hypothesis ( [4] or its higher order version ( [5] for turbulent heat fluxes. TCL SMC is the latest version of the Reynolds stress transport model, and its usefulness has been confirmed for a few complex flows. The tested cases are, however, wall turbulence and its performance in the application to the mixing layer is not clarified yet. In this study, we compare the simulated results with measured ones [6], and evaluate the performance and suitability of these models in the application to the turbulent thermal mixing in the HVAC unit. Flow geometry As described above, in this study, the turbulent thermal mixing in the HVAC unit has been modeled by the two-dimensional planar turbulent mixing layer. Figure shows the schematic of the flow geometry. Cold airflow at T c = 30 C and hot airflow at T h = 80 C are mixed in the test section after flowing through the settling chambers, flow nozzles and developing regions. Each developing region has a cross section of 00 mm 97.5 mm, and the splitter plate that divides the hot and cold flows is 5 mm thick. The mixing section has a cross section of 00 mm 00 mm. These dimensions of the test channel were determined referring to the practical HVAC unit []. The velocity of the cold flow U c was kept at 4 m/s, and that of the hot flow U h was set at m/s and 4 m/s (velocity ratio r = U h = and, respectively. Under both velocity ratios, cold air flows in the upper half of the test channel and hot air flows in the lower half. It was confirmed that in the cold flow side a turbulent boundary layer about 5 mm thick was formed at the end of the splitter plate. The Reynolds number based on the momentum thickness of this boundary layer is about 380. Under these experimental conditions, the Richardson number is as small as , thus the influence of the buoyancy force is negligibly small. We confirmed that the velocity distribution measured under this non-isothermal condition agreed well with that obtained under the

3 CFD ANALYSIS OF TURBULENT THERMAL MIING OF HOT AND COLD AIR IN AUTOMOBILE HVAC UNIT Nozzle Cold air Uc, Tc Hot air Uh, Th enlarged view 5 Fig.. Test channel used in the experiment (-D mixing layer Fig. 3 Grid system used around the tip of the splitter plate isothermal condition. The coordinate system is also shown in Fig.. The mean and fluctuating velocity components in each direction are denoted as U, U and, u, respectively. T and t denote the mean and fluctuating temperatures. Details of the experiments are described in a reference [6]. In the numerical simulation, two-dimensional calculation has been made in this study. The exit of the calculation region is set at 000 mm downstream from the tip of the splitter plate to avoid the influence of the exit condition on the simulated flow field. In order to calculate the flow field just after the flow merging accurately, quite a fine grid system is formed around the tip of the splitter plate. Figure 3 shows the grid system near the splitter-plate tip used in the present numerical simulation. The number of the grid points has been changed from 5,000 to 5,000 depending on the turbulence models. The flow parameters measured at 35 mm upstream from the tip of the splitter plate have been used as the initial values of the numerical simulations Splitter plate 00 3 Turbulence models 3. Flow field Considering the computation time allowed in the practical design of HVAC unit, three kinds of RANS turbulence models for flow field have been tested in this study. The first model is the standard linear k-ε model that has been widely used in various engineering applications. The second model is the low-reynolds-number cubic nonlinear k-ε model []. This model can reproduce the anisotropy of turbulent stresses accurately and thus it is expected that the reliability of predictions of complex turbulent flows be improved. The third model is the two-component-limit second moment closure (TCL SMC [3]. This is the latest Reynolds stress transport model, and can predict the turbulence anisotropy more successfully than other models. Although its usefulness has been confirmed for a few complex flows, such as 3-D curved duct flow and turbulent obstacle flow, the tested cases are still limited to wall turbulence and its performance in the application to the free turbulence is not fully clarified yet. Recently, Suga applied this model to the turbulent mixing layer and obtained satisfactory results. Since these turbulence models need lengthy expressions, details of each turbulence model are not described in this paper: see the references for details of these models. 3. Turbulent heat fluxes The standard k-ε models and the low- Reynolds-number cubic nonlinear k-ε model adopted in this study have been combined with prescribed turbulent Prandtl numbers Pr t. This is the simplest way to express the turbulent heat fluxes. Pr t is assumed to be 0.9 for the low-re nonlinear k-ε model. Three values of Pr t, 0., and 0.9 are tested with the standard k-ε model to examine the influence of Pr t -values on the mean temperature distributions. As for TCL SMC, two turbulent heat flux models have been tested. One is a generalized gradient diffusion 3

4 hypothesis ( model [4], and the other is its high-order version (. These models are expressed as follows [5]. Pr t model: ν t Θ uiθ = ( Pr x model: Θ uiθ = cθ τ uiu j, x t i j k τ = ( ε model: Θ uiθ = cθ kτ ( σ ij + α ij (3 x uiu j uiul ulu j σ il = cσ + cσ (4 k k u lu j u jul α = Ω + Ω ij cα τ il li (5 k k U U i j Ω ij = (6 x j xi See the reference for details of the model coefficients [5]. In general, Pr t model cannot predict the turbulent heat fluxes reasonably in complex turbulent flows that have mean temperature and velocity gradients in multiple directions. In other words, this model cannot reproduce the streamwise turbulent heat flux under the fully developed thermal condition. This is because Pr t model assumes that turbulent heat flux in the i -direction u i t is generated only by the contribution of the mean temperature gradient in the i -direction, although u i t is generated by the mean temperature gradients not only in the i - direction but also in the j -directions (i j. heat flux model is generally successful in the computation of complex thermal field. It is, however, known that cannot predict the streamwise heat flux component reasonably well [5] though it is much better than Pr t. The high order version of mode, i.e., model, was developed by expanding with extra terms including a quadratic product of the Reynolds stress tensor to improve the j performance of the model. It is more effective to predict the streamwise turbulent heat flux. In general, the streamwise turbulent heat flux does not exert important influences on the mean temperature distribution in a fully developed flow. The flow in a practical HVAC unit is, however, so complex accompanied by frequent changes of its direction that the streamwise turbulent heat flux can become as important as transverse one to predict the mean temperature distribution. Since the performance of the -type heat flux models relies on the accuracy of the predicted turbulence anisotropy, and have been coupled with TCL SMC in this study. 4 Results and discussion In this paper, the results obtained with k-ε models coupled with Pr t are presented at first. Then the results of TCL SMC + ( models are shown and their performance on the prediction of thermal field in the plane turbulent mixing layer is examined in detail. 4. Flow field with k-ε models Figure 4 shows the distributions of the streamwise mean velocity U (left and the turbulent shear stress u (right obtained at the velocity ratio r = U h =. The solid line shows the results calculated by the standard (STD k-ε model, and the broken line shows those by low-reynolds-number nonlinear (LRN k-ε model. The experimental results are shown by open symbols. In this paper, the results obtained at three streamwise locations, =,.0 and.0, are presented, where D denotes a half of the side length of the mixing cross section (= 00 mm. These locations have been determined considering the size of practical HVAC units, at which the flow does not attain the self-similar state [7]. As shown in Fig. 4, the distributions of U obtained by model agree well with those by model at all, and these simulated results are in good agreement with experimental ones at all. The distributions of u are also successfully reproduced by these k-ε models, although their peak values are 4

5 CFD ANALYSIS OF TURBULENT THERMAL MIING OF HOT AND COLD AIR IN AUTOMOBILE HVAC UNIT = =.0 = U = =.0 =.0-0 Fig. 4. Mean velocity and turbulent shear stress distributions predicted by k-ε models (r = = r = =.0 = U Fig. 5. Mean velocity and turbulent shear stress distributions predicted by k-ε models (r = somewhat underpredicted at =. These results suggest that, at r =, the model as well as the model is good enough for predicting the flow field in the planar turbulent mixing layer. At the velocity ratio of r = shown in Fig. 5, however, the reliability of the simulated results becomes much lower than that for r =. From the U distributions shown in Fig. 5 (left, it is found that the thickness of the mixing layer is overpredicted with model and that the recovery of the velocity deficit region at =.0 is delayed in both k-ε models. As for u distributions, model generally overpredicts the experimental results, and the locations of the peak values are not well predicted by both models. As a whole, the reliability of the results obtained by model is lower than that of model under the velocity ratio of r = u *00 = =.0 =.0 r = u *00 4. Thermal field with k-ε + Pr t models At first, we show the results of the thermal fields calculated with a prescribed turbulent Prandtl number of 0.9; the flow field is calculated with two k-ε models. The results at r = are presented in Fig. 6; distributions of mean temperature (T, streamwise turbulent heat flux (T h and transverse turbulent heat flux u (T h are shown from the top of this figure. The transverse component of turbulent heat flux u t, which dominates the heat transport in the mixing layer, is underpredicted over all. Moreover, the streamwise component t, which is in almost the same level as u t in the experiment, is nearly zero in the simulations. As a result of such underpredictions of the turbulent heat fluxes, the simulation with Pr t = 0.9 tends to underpredict the development of the thermal mixing layer. The difference between the measured mean temperature and calculated one becomes larger in the region further downstream from the origin of the mixing layer. Quite similar results are obtained at r = shown in Fig. 7 and the difference between the experimental results and numerical ones is increased in comparison with the case of r =. It is thought that such an underprediction of u t as observed above can be improved by assuming smaller turbulent Prandtl number. Hence, in this study, we made the calculations with three turbulent Prantdl numbers of Pr t = 0., and 0.9. In these calculations, the standard k-ε model has been coupled with Pr t, because the reliability of the flow field predicted by model is higher than that of LRN k- ε model. Figures 8 and 9 show the results for r = and, respectively. At r =, the reliability of u t prediction is much improved with the turbulent Prandtl number of. In free turbulence, Pr t is often assumed to be in the range of 5-0.7: the result of r = supports this assumption about Pr t -value. On the other hand, at r =, the reliability of u t prediction is not improved so much by decreasing Pr t. This suggests that Pr t changes depending on the velocity field even in the relatively simple planar thermal mixing layer. 5

6 = =.0 =.0 = r = =.0 =.0 = Prt= =.0 =.0 = r = Prt= =.0 = (T = =.0 = (T = =.0 =.0 r = (T = =.0 = (T = =.0 =.0 r = = =.0 =.0 = =.0 =.0 r = Prt= = =.0 =.0.0 Prt= = =.0 =.0 r = u u Fig. 6. Thermal field Fig. 7. Thermal field by Pr t model (r = by Pr t model (r = From the results described above, it is thought that the reliability of u t prediction may be improved by giving the Pr t distributions with some appropriate functions. As for the streamwise component t, however, Pr t given by functions cannot improve the reliability of the simulated result because the streamwise temperature gradient T/, to which t is assumed to be proportional, is almost zero in the present thermal mixing layer. In order to examine the reason for such complex t distributions as obtained in the measurement, Prt= Prt= u u Fig. 8. Thermal field Fig. 9. Thermal field with different Pr t with different Pr t (r = (r = the production terms in the transport equation of t have been evaluated based on the experimental data. Figure 0 shows the distributions of each term of t production, which is expressed as follows, measured at = [6]. P T D = uu U T A, c P U ut D B = c U T U D P C = ut (7 U T c 6

7 CFD ANALYSIS OF TURBULENT THERMAL MIING OF HOT AND COLD AIR IN AUTOMOBILE HVAC UNIT = TCL =.0 =.0 = =.0 =.0 TCL (a r = U u *00 Fig.. Mean velocity and turbulent shear stress distributions predicted by TCL SMC (r = = r = TCL =.0 =.0 = =.0 =.0 TCL (b r = Fig. 0. Production of t It is found that the distributions of the sum of these production terms are qualitatively similar to those of t shown above. In particular, the contributions of P A and P C, both of which include the gradient of mean quantity in the transverse ( direction, are much larger than that of P B. The term including T/ was smaller than P B and its contribution to t production was negligible. From these results, it follows that the influences of U / and T/ must be included to reproduce reasonably the complex distributions of t. This is a reason for the selection of -type turbulent heat flux models to calculate the thermal field of the present mixing layer. 4.3 Results of calculation with TCL SMC + ( models In this section, the results of the velocity and temperature fields calculated by TCL SMC + ( models are compared with the experimental data. Figure shows the distributions of U and u calculated for r = with TCL SMC. The calculated results agree U u *00 Fig.. Mean velocity and turbulent shear stress distributions predicted by TCL SMC (r = well with the experimental ones, although a slight delay of the recovery of the velocity deficit region is observed in U distributions. Figure shows the results for r =. The difference between the calculated distributions of u and measured ones is increased in comparison with that for r = ; in particular, u is underpredicted in a downstream region. From a comparison of Fig. with Fig. 5, however, it is understood that the reliability of the flow field calculated by TCL SMC is improved in comparison with the k-ε models. Thus, it follows that the difference between the numerical results of the thermal field shown below and those shown in Figs. 6-9 reflects the performance of both the turbulence model and turbulent heat flux model. Next, the thermal field is examined. Similar to Figs. 6-9, the distributions of the mean temperature, turbulent heat fluxes t and u t are compared with the experimental results. Figure 3 shows the results at r =. The values of t 7

8 = =.0 = (T (T = =.0 = = =.0 =.0 = r = =.0 = u u Fig. 3. Thermal field Fig. 4. Thermal field by ( model by ( model (r = (r = calculated with are slightly smaller than the experimental results at =, but they agree well with the measured values in a further downstream region. The higher-order version of, i.e.,, generally overpredicts t. These results show that model can predict the t distribution far more successfully than Pr t model. This is because -type turbulent heat flux model can incorporate the contribution of T/ into the formulation of t. As to u t, the difference = r = =.0 =.0 = =.0 =.0 r = between and is quite smaller than that for t. Both models underpredict the values of u t near the origin of the mixing layer, but the difference between the measured and calculated values becomes smaller in the downstream region. The reliability of u t calculated by and models is higher than that obtained with the prescribed Pr t model. As a result of such improvement in the calculation of turbulent heat fluxes, the distributions of the mean temperature at r =, shown at the top of Fig. 3, are more successfully reproduced by ( models than the Pr t model. Figure 4 shows the results at r =. Although the qualitative features of t distributions are well captured by both type models, generally overpredicts t as is the case with r = while underpredicts it. On the other hand, u t is underpredicted by both -type models in the region of > ; the disagreement between the experimental and numerical results is increased than the case of r =. This tendency is similar to that calculated with k-ε + Pr t models, but as a whole ( models can reproduce the distributions of u t with higher accuracy than the prescribed Pr t model. Similar to the case of r =, the reliability of the mean temperature distributions predicted by ( models is improved in comparison with the Pr t model, although the difference between measured and calculated values is somewhat increased in comparison with that for r =. Here it should be noted that the TCL SMC and ( models tested in this study were originally developed to the prediction of turbulent heat transfer in complex wall shear flows such as 3-D curved duct [5]. Thus, the model coefficients were optimized referring to the experimental data or DNS results in those flows. In the present study, the original models are used without any modifications. Since the characteristics of the present flow geometry are quite different from those of the wall turbulence, the performance of the predictions may be improved by adjusting the model coefficients to the mixing layer. In the numerical simulations 8

9 CFD ANALYSIS OF TURBULENT THERMAL MIING OF HOT AND COLD AIR IN AUTOMOBILE HVAC UNIT of turbulent thermal mixing in the HVAC unit, another important point is the computation time. It should be noted that the CPU time needed to attain the final result by TCL SMC + model was about three times as long as that for standard k-ε + Pr t model; this is within the scope of practical use. 4 Conclusions The numerical simulations of turbulent thermal mixing in a planar shear layer have been conducted, which simulates the mixing of hot and cold airflows in the HVAC unit used for automobile air-conditioning system. We have tested three turbulence models: standard k-ε model, low-re nonlinear k-ε model and TCL SMC. The first two k-ε models have been coupled with prescribed Pr t, and TCL SMC has been combined with model and its higher-order version for turbulent heat fluxes. By optimizing the Pr t -values, the k-ε + Pr t models can predict the distributions of u t with a sufficient accuracy at r =, but the reliability of u t prediction becomes lower at r =. The Pr t model cannot reproduce the t distributions in principle, and the reliability of the predicted mean temperature distributions is insufficient. TCL SMC + ( models can reasonably reproduce the turbulent heat fluxes and successfully predict the mean temperature distributions in the mixing layer. These results suggest that TCL SMC + ( models have high potential to the prediction of turbulent thermal mixing encountered in the HVAC unit for automobiles. [5] Suga, K. Predicting Turbulence and Heat Transfer in 3-D Curved Ducts by Near-Wall Second Moment Closures, Int. J. Heat Mass Transfer, Vol. 46, pp. 6 73, 003. [6] Asano, H., Hirota, M., Nakayama, H., Mizuno, Y. and Hirayama, S. Turbulent Thermal Mixing of Hot and Cold Air in Planar Shear Layer (Thermal Mixing in Automobile HVAC Unit, Proc. 6th World Conf. Exp. Heat Transfer, Fluid Mech., Thermodynamics, 3-a-3, Matsushima, Japan, 005 (in CD-ROM. [7] Abdul Asim, M. and Sadrul Islam, A. K. M. Plane Mixing Layers from Parallel and Non-Parallel Merging of Two Streams, Exp. in Fluids, Vol. 34, pp. 0-6, 003. References [] Kitada, M., Asano, H., Kanbara, M. and Akaike, S. Development of Automotive Air-Conditioning System Basic Performance Simulator: CFD Technique Development. JSAE Review, Vol., pp. 9-96, 000. [] Craft, T.J., Launder, B.E. and Suga, K. Development and Application of a Cubic Eddy-Viscosity Model of Turbulence. Int. J. Heat Fluid Flow, Vol. 7, pp. 08-5, 996. [3] Suga, K. Modeling Pressure-Transport for Turbulent Wake Flows. Proc. Turbulence Shear Flow Phenomena-3, Sendai, Japan, pp , 003. [4] Daly, B.J. and Harlow, F.H. Transport equation in turbulence. Phys. Fluid, Vol. 3, pp ,