Journal of Fluid Science and Technology

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1 Bulletin of the JSME Vol.9, No.3, 24 Journal of Fluid Science and Technology Promotion and control of turbulent mixing of hot and cold airflows in T-junction Takuya MATSUDA*, Masafumi HIROTA*, Hideo ASANO**, Shuichiro HORI***, Naoki MARUYAMA* and Akira NISHIMURA* *Department of Mechanical Engineering, Mie University 577 Kurimamachiya-cho, Tsu-shi, Mie , Japan **Thermal Systems Performance Development Division, DENSO CORPORATION - Showa-cho, Kariya-shi, Aichi , Japan ***Akashi Works, Kawasaki Heavy Industry - Kawasaki-cho, Akashi-shi, Hyogo , Japan Received 28 March 24 Abstract An experimental study was conducted on the promotion and control of turbulent mixing of hot and cold airflows in a rectangular channel with a T-junction, which simulated an HVAC unit for automobile air-conditioning system. A delta-wing row was installed on the bottom wall of the main channel before the T-junction to promote and control the turbulent thermal mixing. The mean temperature and velocity distributions were measured in several cross sections after the flow merging by thermocouples and PIV, respectively, and the flow in the mixing region was visually observed as well. The development of the thermal mixing layer was promoted effectively by delta wings and the degree of thermal mixing could be controlled by changing the angle of attack of wings. Longitudinal vortices produced by delta wings disappeared just after the merging of two flows, but high turbulence generated by the interaction of those vortices and the branch flow was maintained to further downstream cross sections. The proper orthogonal decomposition analysis was applied to the fluctuating concentration and the fluctuating velocity fields to extract the dominant spatial structures in the T-junction. It was suggested that longitudinal vortices with clockwise and counter-clockwise rotations were shed alternately just behind each delta wing. Key words: Turbulent mixing, Flow control, T-junction, HVAC, Delta wing, Experiment. Introduction Channels with T-junctions in which two flows with different velocities, temperatures, and/or concentrations are merged and mixed are seen in various thermo-fluids equipments such as combustion chamber, chemical reactor and piping system in power plants (Bruecker, 997, Wu, et al., 23, Ndombo and Howard, 2). The cross-flow type mixing T-junction is also found in the HVAC (Heating, Ventilating and Air-conditioning) unit used for an automobile air-conditioning system. Figure shows a cross-sectional view of the automobile HVAC unit, which contains a fan, an evaporator and a heater-core in a plastic housing (Kitada, et al., 2, Hirota, et al., 2). All air taken by the fan is once cooled by the evaporator and humidity is reduced as well, then a part of this cold air is heated by the heater-core. Temperatures of these hot and cold airflows are usually fixed due to the constraints of the refrigerant cycle for cooling and the engine coolant recirculation system for heating. Therefore, the temperature of air supplied to the cabin is controlled by mixing the hot and cold airflows at appropriate flow-rate ratios. In the mixing zone of the HVAC unit, hot and cold airflows impinge at nearly right angles as shown in Fig., and this flow configuration can be modeled by the turbulent thermal mixing of hot and cold airflows in a cross-flow type T-junction with rectangular cross sections. Nowadays, the downsizing of the HVAC unit is an important issue in the automobile A/C system, and it is also Paper No.4-55 [DOI:.299/jfst.24jfst42] 24 The Japan Society of Mechanical Engineers

2 Matsuda, Hirota, Asano, Hori, Maruyama and Nishimura, Journal of Fluid Science and Technology, Vol.9, No.3 (24) 2A = 2mm Top wall Y Z Cold flow U Y X H = 6mm V, v W, w Hot flow V V, v Bottom wall U, u Fig. Structure of HVAC unit for automobile B=3mm Fig. 2 Standard channel without mixing promoters X/B = h θ U, Tc Wing Y V, Th X H 2 d w Fig. 3 Example of tested delta-wing row (n = 5, d/w =.33).8B B Fig. 4 Test channel with the delta-wing row required that the temperature distribution in the cabin be controlled locally depending on the operation mode of the A/C system. Therefore, the promotion and control of turbulent mixing of hot and cold airflows are key subjects in the development of the HVAC unit. Active methods that need external power inputs, such as small jets, are quite effective to the mixing promotion/control of two flows (Bonnet, et al., 28, Hirota, et al., 28), but the passive methods without any external power inputs are required in the practical application to the HVAC unit for the automobile air-conditioning system. With these points as background, we conducted an experimental study on the promotion and control of turbulent mixing of hot and cold airflows in the T-junction with rectangular cross sections. We adopted a row of delta wings (Liou, et al., 2, Gentry and Jacobi, 22) as a promoter of the turbulent mixing of two flows considering feasibility to an actual HVAC unit, and tried to control the degree of mixing by changing the angle of attack of the wing row. In this paper, we at first show the characteristics of the velocity and temperature fields in a simple T-junction without any mixing promoters, and explain the problem in the promotion and control of the thermal mixing of two flows. Then, based on the results of the velocity and temperature measurements and flow visualization, we demonstrate the effectiveness of the delta wings as a mixing promoter/controller. Finally, the mechanism of mixing promotion and control by the delta wings is discussed based on the proper orthogonal decomposition analyses of the fluctuating fields. 2. Experimental apparatus A schematic diagram of the standard test channel that has no mixing promoters is shown in Fig. 2. The vertical branch channel was joined to the horizontal main channel at right angles to form a T-junction. The specification of this channel was essentially the same as that used in our preceding study (Hirota, et al., 2) except that the second edge (edge in the downstream side) of the T-junction was planed off. We chamfered this second edge because high turbulence caused by the flow separation at this sharp edge was located below the thermal mixing layer, and did not contribute so much to the turbulent thermal mixing of two flows (Hirota, et al., 28). By chamfering this edge, the scale of the separation bubble was considerably reduced. Airflows in the main and branch channels were merged in the T-junction after flowing through heat exchangers, settling chambers and contraction flow nozzles. The height of the main channel H was 6 mm and the width 2A was 2 mm. The width of the branch was the same as that of the main channel (= 2A = 2 mm), and this is a geometric feature of the modeled HVAC unit. The X-way length of the [DOI:.299/jfst.24jfst42] 24 The Japan Society of Mechanical Engineers 2

3 Matsuda, Hirota, Asano, Hori, Maruyama and Nishimura, Journal of Fluid Science and Technology, Vol.9, No.3 (24) U/U.2. U/U u /U.2. u /U V/V.2. V/V v /V.2. v /V X/B (a) Main channel (on the Y-axis at X/B = -3) (b) Branch (on the X-axis at = -) Fig. 5 Distributions of inflow mean velocities and its turbulence intensities in the standard channel branch cross section B was 3 mm. The chamfered length of the second edge was 6 mm =.2B. The coordinate system is also shown in Fig. 2. In an actual HVAC unit, the exit of the mixing zone corresponds to the cross section at X/B = 2-3 of this test channel. It should be noted that, as shown in Fig., several ducts are connected to the HVAC unit in an actual automobile air-conditioning system. Therefore, the influences of those ducts, i.e., downstream conditions, on the mixing must be taken into account in the actual HVAC unit. In this study, however, we could not simulate the downstream conditions of the actual HVAC unit because they could be variously changed depending on the air-conditioning mode in the cabin. Therefore, the discussion in this paper is limited to the performance of the delta wings as mixing promoter/controller in a simple T-junction. The mean and fluctuating velocity components in the X, Y and Z directions are denoted as U, V, W, and u, v, w, respectively. Figure 3 shows an example of the delta-wing rows tested in this study. We tested several kinds of delta-wing rows with different wing number n, wing height h, wing base length w and wing clearance d. In this paper, however, the results obtained with the wing row with n = 5, h/h =.45 and d/w =.33 are mainly presented, which was the most effective as a mixing promoter among the tested wing rows. The vertical angle and the aspect ratio (Gentry and Jacobi, 22) of each delta wing was 37 and.33, respectively As shown in Fig. 4, it was installed on the bottom wall of the main channel before the T-junction. We expected that turbulence could be enhanced inside the thermal mixing layer by the interaction between longitudinal vortices generated behind the wings in the main flow and the branch flow that merged with it in the T-junction. This high turbulence might act effectively on the vertical development of the thermal mixing layer. Moreover, we also expected that the turbulence intensity and resulting turbulent mixing of two flows could be controlled by changing the angle of attack of the wing row. The installation position of the delta-wing row was optimized based on the mean temperature distributions measured in preliminary experiments, and it was determined as X/B = -2.8 on the bottom wall of the main channel. The angle of attack of wings was varied from to 7 at pitches, so the wings were inclined against the main flow. Experiments were conducted keeping the main-flow Reynolds number at which was defined based on the hydraulic diameter of the main channel D h and the bulk velocity in it before the mixing U. The bulk velocity of the branch flow V was determined so that the velocity ratio VR = V /U was.5 or., but the results obtained with VR =.5 are mainly reported in this paper. U was m/s, and V was m/s at VR =.5. Velocity distributions were measured by 2-D PIV under an isothermal condition. For statistical analyses, the mean velocity and turbulence intensities were calculated by an ensemble average of 5 instantaneous velocity fields. Figure 5 shows the distributions of inflow mean velocities and its turbulence intensities measured on the symmetric axes of the main channel (X/B = -3) and the branch ( = -) in the standard channel without delta wings. The mean velocities show uniform distributions in the regions of about 8 % on the symmetric axes in both channels, and the turbulence intensities are about 4% (main channel) and 2% (branch) in the corresponding regions. In the measurement of the mean temperature distributions, the bulk temperature of the branch flow was set at 6 C (= T h ) while the main flow was in room temperature (= T c = 2 25 ºC). The time-averaged local temperature distributions were measured by a thermocouple rake. In order to examine the behavior of the interface between two flows, the flow visualization was [DOI:.299/jfst.24jfst42] 24 The Japan Society of Mechanical Engineers 3

4 Matsuda, Hirota, Asano, Hori, Maruyama and Nishimura, Journal of Fluid Science and Technology, Vol.9, No.3 (24) conducted as well in the flow-merging region. The branch flow was seeded by oil particles provided by a Laskin-nozzle type particle generator, and the interface between two flows visualized by a laser light sheet was captured by a digital high-speed video camera. The captured images were converted to the instantaneous concentration distributions. The dominant structures of the velocity and concentration fields were extracted by applying the proper orthogonal decomposition to the results obtained by PIV and the flow visualization. By a comparison of these results, we examine the mechanism of promotion and control of turbulent mixing of two flows by the delta-wing row. 3. Results and discussion 3. Temperature and velocity fields in the standard channel without mixing promoters At first, the characteristics of the velocity and mean temperature fields in the standard channel without mixing promoters are overviewed in this section, and based on them the problem and strategy for promoting the thermal mixing is explained. Distributions of the non-dimensional mean temperature (T-T c )/(T h -T c ) in half cross sections of the channel (Z/A > ) at X/B =,, 2 and 3 with the velocity ratio of VR =.5 are shown in Fig. 6. The mean temperature shows quite uniform distributions in the spanwise direction (Z-direction), and the development of the thermal mixing layer is quite slow. In particular, in the cross sections of X/B > 2 corresponding to the exit of the mixing zone of the HVAC unit, the upward development of the thermal mixing layer is relatively limited in comparison with the downward development. This limited development of the thermal mixing layer in the upward direction is closely related to the distribution of turbulence intensity v'/u, where v' is RMS of the fluctuating velocity component in the vertical (Y-axis) direction. Figure 7 shows the distributions of v'/u measured in the symmetric plane of Z/A = and the half cross section at X/B = of the standard channel. The red lines show the locations at which (T-T c )/(T h -T c ) =. (upper boundary of the thermal mixing layer) and (T-T c )/(T h -T c ) =.9 (lower boundary of the thermal mixing layer). The value of v' near the upper boundary is quite smaller than that near the lower boundary, and the location of the high turbulence intensity is below the thermal mixing layer in X/B >. In this channel geometry, the heat transfer between the hot and cold airflows is dominated by the turbulent heat flux vt and its main production term is expressed as v 2 T/Y. Therefore, the production of vt is quite small in the upper part of the thermal mixing layer (Hirota, et al, 28) and this causes such a limited development of the thermal mixing layer in the upward direction as observed in Fig (T-Tc)/(Th-Tc) Z/A.5 Z/A.5 Z/A.5 Z/A (a) X/B = (b) X/B = (c) X/B = 2 (d) X/B = 3 Fig. 6 Distributions of mean temperature (T-T c )/(T h -T c ) in the standard channel v /U/ X/B 4..5 Z/A Fig. 7 Distribution of turbulence intensity v'/u in Z/A= and X/B = in the standard channel [DOI:.299/jfst.24jfst42] 24 The Japan Society of Mechanical Engineers 4

5 Matsuda, Hirota, Asano, Hori, Maruyama and Nishimura, Journal of Fluid Science and Technology, Vol.9, No.3 (24) From these results in the standard channel, it is expected that the upward development of the thermal mixing layer can be promoted effectively if v is increased in its upper part. Among many options, we adopted a delta-wing row as a mixing promoter considering feasibility to an actual HVAC unit and potential to promote and control the mixing level of two flows. In a preliminary experiment, we measured mean velocity distributions downstream the delta-wing row installed in a straight duct, and confirmed that the wings produced the common-flow down longitudinal vortices with the apex leaning upstream and the common-flow up vortices with the apex leaning downstream. These results agreed with those reported by Zaman et al (994). Based on these results, we selected the wing arrangement with the apex leaning upstream ( = - 7 ) as described before, because we aimed for the interaction between the upward inflow from the branch and the downward flow generated by the wings to increase the gradient of V and promote the production of turbulence v. In the following, we show the characteristics of the temperature and velocity fields measured in the mixing T-junction with the delta-wing row, and demonstrate its effectiveness in promoting and controlling the turbulent thermal mixing of hot and cold airflows. 3.2 Mean temperature distributions in the channel with the delta-wing row Distributions of the non-dimensional mean temperature (T-T c )/(T h -T c ) measured in a half cross section of < Z/A < at X/B = 2 of the test channel with the delta-wing row are shown in Fig. 8. As described before, this streamwise location of the test channel corresponds to the exit of the mixing zone of an actual HVAC unit. The velocity ratio VR is.5. The angle of attack of the wings is changed from to 7, and the triangles shown at the bottom of each figure correspond to the locations of the delta wings. At =, the mean temperature shows an uneven distribution in the spanwise direction, and the thermal mixing layer near the trough of the wavy isotherms is thinner than that in the standard channel. This suggests that longitudinal vortices generated by the delta wings influence the temperature distribution in the mixing layer. As is increased, the thermal mixing layer becomes thicker and the spanwise unevenness of the temperature distribution is gradually relieved. The development of the thermal mixing layer was saturated in > 6. These results demonstrate that the delta-wing row works well as a mixing promoter and the thickness of the thermal mixing layer can be controlled by changing the angle of attack of the wings as expected. In an actual HVAC unit for the automobile air-conditioning system, the spanwise uniformity of the mean temperature distribution is desired to secure the comfortability of the cabin. As described above, the spanwise uniformity of the mean temperature distribution is improved as is increased. This mixing performance of the present delta-wing row is favorable to the HVAC unit (T-Tc)/(Th-Tc) Z/A.9.5 Z/A.9.5 Z/A.9.5 Z/A.9.5 Z/A.9.5 Z/A (a) = (b) = 3 (c) = 4 (d) = 5 (e) = 6 (f) = 7 Fig. 8 Variation of (T-T c )/(T h -T c ) with the angle of attack of the delta-wing row (X/B = 2) (T-Tc)/(Th-Tc) Z/A Z/A Z/A (a) X/B = -.5 (b) X/B = (c) X/B = (d) X/B = 2 Fig. 9 Variation of (T-T c )/(T h -T c ) in the streamwise direction ( = 6 ) Z/A [DOI:.299/jfst.24jfst42] 24 The Japan Society of Mechanical Engineers 5

6 Matsuda, Hirota, Asano, Hori, Maruyama and Nishimura, Journal of Fluid Science and Technology, Vol.9, No.3 (24) Figure 9 shows the streamwise evolution of the mean temperature field after the flow merging. The angle of attack is fixed at 6 and VR is.5. At X/B = -.5 in the flow-merging region, the isotherms shows a wavy characteristic and it is caused by the influence of longitudinal vortices generated by the delta wings. This spanwise non-uniformity of the mean temperature distribution is gradually reduced in further downstream locations, and a relatively uniform temperature distribution is obtained at X/B = 2 as described above. These results suggest that after the hot and cold airflows are merged in the T-junction heat is transported in both the Y- and Z-directions by turbulence. 3.3 Evaluation of mixing promotion and control with mixing parameter of temperature profile As described above, the delta-wing row adopted in this study can promote and control the mixing of two airflows. In order to evaluate quantitatively the performance of the delta-wing row as a mixing promoter and controller, we defined a non-dimensional mixing parameter of temperature profile. Figure illustrates the concept of this parameter. The blue lines in the figure show the spanwise-averaged non-dimensional mean temperature distribution measured in the T-unction with the delta-wing row, and it is denoted as T * m. The thickness of the thermal mixing layer W is defined as the difference of the Y-coordinates at which T * m =. (Y = Y. ) and T * m =.9 (Y = Y.9 ), i.e., W = Y. -Y.9. The violet line is the virtual dimensionless mean temperature distribution showing the state that the hot and cold airflows are not mixed at all. In this case, the mean temperature is assumed to change from T c to T h like a step function at the center of the thermal mixing layer. This discontinuous mean temperature distribution is denoted as T * um and expressed as follows. T um * Y Y Y Y.. W / 2 W / 2 () The red line shows the mean temperature distribution that is considered to be ideal for the automobile HVAC unit, in which T m * changes linearly from T m * =. to T m * =.9 in the thermal mixing layer and this mean temperature distribution T id * is expressed by the following equation..8 W Y Y. 9 T id *. 9 (2) Here, the area enclosed by T * m and T * um is denoted as S, and that enclosed by T * id and T * um is denoted as S 2 as shown by green areas in Fig.. They are expressed by the following equations. S Y. * Tum Y.9 T * m dy and S 2 Y. * Tum Y.9 T * id dy (3) From these parameters, we defined the mixing parameter of temperature profile M by the following equation. S S 2 Y. W/2 W W/2 W Y.9 T - T c T - T c T h -T c T h -T c Fig. Concept of the mixing parameter of temperature profile M [DOI:.299/jfst.24jfst42] 24 The Japan Society of Mechanical Engineers 6

7 Matsuda, Hirota, Asano, Hori, Maruyama and Nishimura, Journal of Fluid Science and Technology, Vol.9, No.3 (24) M h/h = S /S 2, W/H..8.6 S /S 2 W/H Standard º 2º 3º 4º 5º 6º 7º. Standard (a) Comparison of M for different wing height (b) Breakdown of M (h/h =.45) Fig. Variation of the mixing parameter of temperature profile for M S W (4) S H 2 S /S 2 means the deviation of the temperature distribution measured in the test channel from ideal one, and W/H is the dimensionless thickness of the thermal mixing layer. Thus, this parameter can evaluate quantitatively the performance of the delta-wing row from viewpoints of not only its ability to promote and control the mixing of two flows but also the appropriateness of the mean temperature distribution in the mixing layer for the HVAC unit. The variations of M to the angle of attack of the wings are shown in Fig.. The values of M obtained for three delta-wing rows with different height (h/h =.5,.3 and.45) are compared with that for the standard channel in Fig. (a). For all wing heights, M increases linearly as is increased. This result demonstrates again that the mixing of hot and cold airflows can be controlled by changing the angle of attack of the delta wings. At the same, larger value of M can be obtained with higher wings. The maximum M is attained with the wing row of h/h =.45 at = 7. We found that the mean temperature showed considerably non-uniform distributions in the spanwise direction with higher wings of h/h =.6. From these results, we decided that the delta-wing row with the height of h/h =.45 had the highest performance as a mixing promoter/controller among the wing rows tested in this study. The distributions of S /S 2 and W/H for h/h =.6 are shown in Fig. (b). The values of S /S 2 are nearly constant irrespective of, and W/H increases in proportion to. This result means that the mixing parameter of temperature profile defined in this paper mainly reflects the thickness of the thermal mixing layer. In this study, we measured the pressure difference P between the location upstream the delta-wing row (X/B = -6.) and the exit of the channel (X/B = 2) to evaluate the influence of the wings on the pressure loss. Since the confluent loss arose in the T-junction, P in the standard channel was 6. Pa and 3.5 Pa for VR =.5 and VR =, respectively. In the channel with the delta-wing row of h/h =.45, P increased as was increased and attained to 2.7 Pa (VR =.5) and 36.5 Pa (VR = ) at = 7º. These increases of P about 5 Pa are relatively small in comparison with the confluent loss, and would be within the permissible range in the application to the HVAC unit. 3.4 Mean velocity and turbulence intensity in the channel with the delta-wing row The streamwise evolution of the secondary flow mean velocity vectors measured at = 3 with the same wing row as Figs. 8 and 9 is shown in Fig. 2. The velocity ration VR is.5. In a half cross section at X/B = -2 that is located.8 B downstream the wing-row base, a pair of longitudinal vortices with a common-flow down (Liou, et al., 2, You, et al., 26) along the wing bisector is generated just downstream each wing. At X/B = - corresponding to the entrance of the flow-merging region, the downward flow is considerably weakened but a secondary flow pattern similar to that appeared at X/B = -2 is still observed. At X/B = -.5 in the middle of the flow-merging region, no longitudinal vortices are observed and high and low upward velocity regions are distributed alternately in the spanwise direction. The low upward velocity regions correspond to the common-flow down regions observed at X/B = -2 and -. This suggests that a vortex structure is broken in the flow-merging region by the overwhelming upward inflow from the branch, but the influence of the longitudinal vortices still remains in this region. Such footprints of the longitudinal vortices produced by the wings, however, disappear in further downstream cross sections of X/B >. [DOI:.299/jfst.24jfst42] 24 The Japan Society of Mechanical Engineers 7

8 Matsuda, Hirota, Asano, Hori, Maruyama and Nishimura, Journal of Fluid Science and Technology, Vol.9, No.3 (24) Z/A.5.5 Z/A Z/A.5 Z/A.5 Z/A.5.5 (a) X/B = -2 (b) X/B = - (c) X/B = -.5 (d) X/B = (e) X/B = Fig. 2 Streamwise evolution of the secondary flow mean velocity vectors ( = 3 ) Z/A.5.5 Z/A.5 Z/A Z/A.5.5 (f) X/B = 2 Z/A (a) X/B = -2 (b) X/B = - (c) X/B = -.5 (d) X/B = (e) X/B = Fig. 3 Streamwise evolution of the secondary flow mean velocity vectors ( = 6 ) Z/A Z/A.5 Z/A Z/A.2..5 Z/A Z/A..2.5 Z/A (a) X/B = -2 Z/A.5.5 Z/A Z/A..5 Z/A (f) X/B = Z/A..5 (f) X/B = Z/A (b) X/B = - (c) X/B = -.5 (d) X/B = (e) X/B = Fig. 5 Streamwise variation of the turbulence intensity v /U ( = 6 ) (a) X/B = Z/A.5.. (b) X/B = - (c) X/B = -.5 (d) X/B = (e) X/B = Fig. 4 Streamwise variation of the turbulence intensity v /U ( = 3 ) (a) X/B = (f) X/B = 2.2 Z/A v /U Z/A.5 Z/A...5 Z/A.5 Z/A (b) X/B = - (c) X/B = -.5 (d) X/B = (e) X/B = Fig. 6 Streamwise variation of the turbulence intensity w /U ( = 6 ).5 Z/A (f) X/B = 2 Figure 3 shows the secondary flow vectors at a larger angle of attack = 6. The vortex pattern is qualitatively similar to that observed at = 3, but the scale and intensity of vortices at X/B = -2 are larger than those at = 3 and the vortices are clearly observed at X/B = - as well. The influence of the longitudinal vortices on the velocity distributions, i.e., high and low upward velocity regions, is still observed at X/B = and disappears in X/B >. Next, the distributions of turbulence intensity v'/u, vertical velocity component, at = 3 are shown in Fig. 4. This fluctuating velocity component contributes to the turbulent transport of heat in the Y-direction, i.e., the upward development of the thermal mixing layer. At X/B = -2 just downstream the wing row, v' shows the local maximums in [DOI:.299/jfst.24jfst42] 24 The Japan Society of Mechanical Engineers 8

9 Matsuda, Hirota, Asano, Hori, Maruyama and Nishimura, Journal of Fluid Science and Technology, Vol.9, No.3 (24).2.6 v'/u.2 v /U Standard channel v /U (T-Tc)/(Th-Tc).8 Channel with wings v /U (T-Tc)/(Th-Tc) Standard = 3 deg. = 6 deg Z/A.8 (T-Tc)/(Th-Tc) Fig. 7 Comparison of spanwise distributions of v'/u Fig. 8 Comparison of (T-T c )/(T h -T c ) and v'/u the regions between the wings. In the cross sections located further downstream, these large v' regions spread in both the spanwise and vertical directions. v' once decreases at X/B = - but increases to attain the maximum at X/B = -.5. This large v' is generated by the large velocity gradient V/ Z observed in Fig. 2(c), and it follows that the interaction between the longitudinal vortices generated in the main flow and the branch flow that enters the main channel produces high turbulence in the flow merging region. Then v' decreases gradually in the streamwise direction, but v' inside the mixing layer is much larger than that observed in the standard channel (Fig. 7) and the turbulent mixing of hot and cold airflows can be promoted effectively. The results of v'/u at = 6 are shown in Fig. 5. At X/B = -2, the local maximums of v'/u are observed not between the wings but at the locations just behind the wings. In the cross sections of X/B > -, the values of v'/u are generally larger than those at = 3. This increase of v' with larger brings about the promotion of the development of the thermal mixing layer as observed in Fig. 8. Figure 6 shows RMS of the fluctuating velocity component in the spanwise direction w'/u measured at = 6. The distributions of w' are qualitatively similar to those of v', but the values of w'/u are generally smaller than those of v'/u. This suggests that w' is mainly caused by the redistribution from v'. Similar to the v' distributions shown above, w'/u shows large values inside the thermal mixing layer. Thus, it is thought that heat is transported in the spanwise direction as well by w and consequently the mean temperature (T-T c )/(T h -T c ) shows relatively uniform distribution in the Z-direction at = 6 as observed in Figs. 8 and 9. Figure 7 compares spanwise distributions of v' measured at X/B = 2 on the line of =.5 in the standard channel and the channel with = 3 and = 6. It is again ascertained that the distribution of v' at = 6 is qualitatively similar to that at = 3, but the values are about 3% larger. This increase of v' contributes to further promotion of turbulent mixing with larger angle of attack of wings. Figure 8 shows a comparison of (T-T c )/(T h -T c ) and v'/u measured at X/B = 2 and Z/A =.4 in the standard channel and the channel with the delta-wing row of = 6. v' in the channel with the wings is much increased in the region corresponding to the upper part of the thermal mixing layer in the standard channel. It is understood that this increase of v' contributes to the promotion of turbulent heat transport in the Y-direction, i.e., the upward development of the thermal mixing layer. 3.5 Visualization of interface between two flows In order to examine the detailed structure of the interface between the main and branch flows, we made the flow visualization. Oil particles were seeded to the branch flow, and the interface of two flows visualized by a laser-light sheet was captured by the digital high-speed video camera. Figure 9 shows an example of snapshots captured in the cross section at X/B = with the angle of attack = 3 and VR =.5. The interface between the main and branch flow shows a relief structure, and the branch flow juts out into the main flow at the locations between the delta wings. From the observation of the time-series images, we found that the branch flow that enters the main flow was fluctuating widely in both the vertical and spanwise directions. These results show that the interface of the main and branch flows has complex three-dimensional unsteady characteristics. As described before, the time-averaged longitudinal vortices disappear in this cross section, but it is observed that footprints of the longitudinal vortices generated by the.2 [DOI:.299/jfst.24jfst42] 24 The Japan Society of Mechanical Engineers 9

10 Matsuda, Hirota, Asano, Hori, Maruyama and Nishimura, Journal of Fluid Science and Technology, Vol.9, No.3 (24) X/B= Z/A (T-T c )/(T h -T c ) C/C Fig. 9 Visualized flow (X/B =, = 3 ) Fig. 2 Comparison of C/C and (T-T c )/(T h -T c ) delta wings still remain in the instantaneous field. At a smaller angle of attack of =, a relief structure of the interface of two flows similar to that shown in Fig. 9 was also observed but its spanwise fluctuation was quite smaller than that observed at larger. In this study, we converted the results of the flow visualization into the concentration distributions by compensating the uneven distribution of the light intensity in the laser sheet. Figure 2 shows a comparison of distributions of the mean temperature (T-T c )/(T h -T c ) and mean concentration C/C measured in Z/A = at = 3, where C denotes the mean concentration of the branch flow. The mean concentration distribution was calculated by an ensemble average of 2 instantaneous concentration fields. The distributions of the mean concentration in the mixing layer agree well with those of the mean temperature. Therefore, we can assume that the instantaneous concentration field is similar to the instantaneous temperature field. Based on this assumption, we applied the proper orthogonal decomposition to the fluctuating velocity and concentration fields to extract a dominant structure that contributes to the turbulent mixing of the hot and cold airflows. 3.6 Analyses of interface structure between two flows based on proper orthogonal decomposition The direct POD (Hilberg, et al., 994) used in this study is explained briefly here. In this study, instantaneous velocity or concentration was measured at M points in space and N points in time, i.e., a set of N snapshots. Here we define f(x, t) as a fluctuating velocity or concentration in a finite spatial domain S, and f(x, t) can be expanded into a finite series of M orthogonal eigenfunctions (k) (x) with time coefficients a (k) (t) as follows. f a M ( k ) ( k ), a ( t) Φ ( x k t x ) (5) ( k ) ( k ) ( t) f ( x, t) Φ ( x) dx (6) The eigenfunction (k) (x) that represents the spatial structure of the fluctuating field is obtained as a solution of the following equation. ( k ) (k) ( k ) R( x, x' ) Φ ( x' ) dx' Φ ( x) (7) S N R( x, x' ) f ( x, ti) f ( x', ti) (8) N i R(x, x ) is the two-point spatial correlation matrix, and (k) is the eigenvalue of the k th mode that is ordered in a decreasing order as () > (2) > (3) >. The superscript k denotes the eigenmode (k =, 2, 3, M). The total energy of f(x, t), which is denoted as E and defined below, is expressed as a sum of all the eigenvalues. E S f 2 M (k) x (9), t dx k [DOI:.299/jfst.24jfst42] 24 The Japan Society of Mechanical Engineers

11 Matsuda, Hirota, Asano, Hori, Maruyama and Nishimura, Journal of Fluid Science and Technology, Vol.9, No.3 (24) Z/A - Fig. 2 c()(x) at X/B = at = Z/A Fig. 22 v()(x) at X/B = -2 at = Z/A Fig. 23 c()(x) at X/B = at = Z/A Fig. 24 v()(x) at X/B = -2 at = 6 The contribution ratio of the k th mode to the total energy Ek is given as follows. M Ek ( k ) / ( k ) () k Thus, it follows that the structure expressed by the lower mode has a larger contribution to the total energy. This means that a dominant spatial structure of the fluctuating velocity or concentration field can be extracted by the eigenfunctions of lower modes. In the following, we show the results of the analyses that were applied to the fluctuating concentration c and the fluctuating velocity component in the vertical direction v. At first, we present the result of POD analysis applied to the fluctuating concentration c measured at X/B = (flow-merging region) at = 3 and VR =.5. Figure 2 shows the distribution of the eigenfunction of the first mode c()(x), which represents the most energetic spatial structure of the fluctuating concentration field in this cross section. The analysis was made in the region of. < <.4. The regions of positive and negative values are distributed alternately in the spanwise direction, and c()(x) shows antisymmetric distributions with respect to the bisector of each delta wing. That is, when c()(x) is negative on the right-hand side of one wing, it is positive on the left-hand side of that wing and vice versa. Next, the eigenfunction of the first mode for the fluctuating velocity component in the vertical direction v (denoted as v()(x)) obtained at X/B = -2 at = 3 is shown in Fig. 22. The distribution of v()(x) is qualitatively similar to that of c()(x). It is thought that this eigenfunction represents the instantaneous vortex structure that is generated by the delta-wing row. Figures 23 and 23 show the eigenfunctions c()(x) and v()(x) at = 6, respectively. They show qualitatively similar characteristics to those obtained at = 3, but the scale of each positive or negative value region is increased in comparison with that at = 3. Based on these results of POD analyses and flow visualization, the instantaneous structure of the interface between two flows and the turbulent mixing process can be illustrated as follows. Just behind the delta wing, longitudinal vortices with clockwise rotation and counter-clockwise rotation are shed from the wing periodically in > 3. These vortices are represented by the periodic distribution of the positive and negative regions of v()(x) observed in Figs. 22 and 24. The scale of these vortices increases as the angle of attack of the wings is increased. These longitudinal vortices are imposed upon the upward flow that enters the main channel from the branch in the flow-merging region. Thus, the instantaneous upward velocity in the flow-merging region changes in the spanwise direction, and high and low velocity regions interchange in time as observed in the flow visualization. The instantaneous concentration [DOI:.299/jfst.24jfst42] 24 The Japan Society of Mechanical Engineers

12 Matsuda, Hirota, Asano, Hori, Maruyama and Nishimura, Journal of Fluid Science and Technology, Vol.9, No.3 (24) distribution reflects this tempo-spatial change of the instantaneous vertical velocity. As a result, the characteristic relief structure in the spanwise direction as observed in Fig. 9 and extracted as c () (x) in Figs. 2 and 23 is formed in the concentration field. Since the scale of the longitudinal vortices becomes larger as the angle of attack of the wings is increased, the mixing layer can grow at larger and the degree of the thermal mixing can be controlled by changing the angle of attack of the wing row. In smaller angle of attack, on the other hand, the spanwise fluctuation of the relief structure of the interface between two flows decreased in comparison with larger as described before. This suggests that the periodic shedding of vortices from the delta wing was suppressed and a pair of steady longitudinal vortices was generated behind the delta wing at low. 4. Conclusions An experimental study was made on the promotion and control of turbulent mixing of hot and cold airflows in a rectangular channel with a T-junction that simulated the mixing zone of HVAC unit for automobile air-conditioning system. A delta-wing row was installed on the bottom wall of the main channel before the flow merging. The mean temperature and velocity distributions were measured in several cross sections by thermocouples and PIV, respectively, and the flow in the mixing region was visually observed as well. The main results are summarized as follows. () The turbulent mixing of hot and cold airflows is promoted effectively by the delta-wing row installed at the bottom wall of the main channel upstream the flow-merging region. At a small angle of attack of the wings (), the mean temperature shows an uneven distribution in the spanwise direction. As is increased, the thermal mixing layer becomes thicker and the spanwise unevenness of the mean temperature distribution is gradually relieved. (2) The mixing parameter of temperature profile was defined to evaluate quantitatively the degree of mixing of the hot and cold airflows and appropriateness of the mean temperature distribution in the mixing layer for the HVAC unit. The mixing parameter of temperature profile increases almost linearly with respect to. This demonstrates that the turbulent thermal mixing of hot and cold airflows can be controlled by changing the angle of attack of the delta-wing row. (3) A pair of longitudinal vortices with a common-flow down along the wing bisector is produced just after each delta wing, but they are broken by the merging of two flows. High turbulence is also produced just downstream the delta wings. The fluctuating velocity component in the vertical direction v' once decreases in the streamwise direction but increases to attain the maximum in the flow-merging region. The region of large v' exists inside the thermal mixing layer and it can promote the turbulent mixing of hot and cold airflows. The values of v in the mixing layer increases as is increased. (4) The proper orthogonal decomposition analysis was applied to the fluctuating concentration c and the fluctuating velocity v. The eigenfunction of the first mode for c and that for v show similar distributions with positive and negative regions distributed alternately in the spanwise direction. This result suggests that longitudinal vortices with clock-wise and counter-clockwise rotations are shed alternately just behind each delta wing. Since the scale of those vortices becomes larger as is increased, the mixing layer can grow at larger and the thermal mixing can be controlled by changing the angle of attack of the wing row. References Bonnet, J.-P., Siauw, W. L., Bourgois S. and Tensi, J., Influence of a synthetic jet excitation on the development of a turbulent mixing layer. Int. J. Heat Fluid Flow, Vol. 29 (28), pp Bruecker, C., Study of the three-dimensional flow in a T-junction using a dual-scanning method for three-dimensional scanning-particle-image-velocimetry (3-D SPIV), Exp. Thermal Fluid Science, Vol. 4 (997), pp Gentry, M. C. and Jacobi, M. A., Heat transfer enhancement by delta-wing-generated tip vortices in flat-plate and developing channel flows. J. Heat Transfer, Vol. 24 (22), pp Hilberg, D., Lazik, W. and Fiedler, H. E., The application of classical POD and snapshot POD in a turbulent shear layer with periodic structures. Appl. Sci. Res., Vol. 53 (994), pp Hirota, M., Kuroki, M., Nakayama, H., Asano, H. and Hirayama, S., Promotion of turbulent thermal mixing of hot and cold airflows in T-junction, Flow Turbulence and Combustion, Vol. 8 (28), pp Hirota, M., Mohri, E., Asano, H. and Goto, H., Experimental study on turbulent mixing process in cross-flow type [DOI:.299/jfst.24jfst42] 24 The Japan Society of Mechanical Engineers 2

13 Matsuda, Hirota, Asano, Hori, Maruyama and Nishimura, Journal of Fluid Science and Technology, Vol.9, No.3 (24) T-junction. Int. J. Heat Fluid Flow, Vol. 3 (2), pp Kitada, M., Asano, H., Kanbara, M. and Akaike, S., Development of automotive air-conditioning system basic performance simulator: CFD technique development, JSAE Review, Vol. 2 (2), pp Liou, T.-M., Chen, C.-C. and Tsai, T.-W., Heat transfer and fluid flow in a square duct with 2 different shaped vortex generators. J. Heat Transfer, Vol. 22 (2), pp Ndombo, J.-M. and Howard, R. J. A., Large eddy simulation and the effect of the turbulent inlet conditions in the mixing Tee, Nuclear Engineering Design, Vol. 24 (2), pp Wu, H. L., Peng, X. F. and Chen, T. K., Influence of sleeve tube on the flow and heat transfer behavior at a T-junction, Int. J. Heat Mass Transfer, Vol. 46 (23), pp You, D., Wang, M., Mittal, R. and Moin, P., Large-eddy simulations of longitudinal vortices embedded in a turbulent boundary layer. AIAA Journal, Vol. 44 (26), pp Zaman, K. B. M. Q., Reeder, M. F. and Samimy, M., Control of an axisymmetric jet using vortex generators, Phys. Fluids, Vol. 6-2 (994), pp [DOI:.299/jfst.24jfst42] 24 The Japan Society of Mechanical Engineers 3