3.1. Time-Averaged Flow and Thermal Fields
The time-averaged flow and thermal fields obtained by the LES and RANS in a streamwise normal plane were compared with the experimental data of Burd et al. [34
] and Jung and Lee [11
]. As shown in Figure 2
, the film cooling effectiveness differed considerably with the turbulence model however, no significant difference was observed between the time-averaged flow and thermal fields. Therefore, the results of the RANS with the realizable k
model were compared with those of the experiments and LES as a representative case. When the orientation angle was 0°, a kidney vortex occurred symmetrically in the film cooling jet and both the LES and RANS predict this phenomenon well, as shown in Figure 3
The flow near the wall, which affected the heat transfer characteristics, indicated that the flow of the CRVP created a parallel flow moving along the wall. The two parallel flows collided at the symmetric plane z
= 0, and rose above the wall. In the experiment, the upward motion started to occur at approximately z
= 0.5, and the LES predicted this phenomenon well. In the RANS, the v
component was observed from approximately z
= 0.2, closer to the plane of symmetry than in the experimental data. In terms of the streamwise velocity distributions, as shown in Figure 3
b, both the LES and RANS exhibited distributions that were similar to the experimental data. Considering the central part of the film cooling jet (z
= 0, y
= 0.4) with a dimensionless velocity of 0.7 or less, indicated in blue, it can be noted that the area for the LES data is similar to that of the experiment however, the corresponding area for the RANS data is slightly larger, likely because the RANS predicts that the film cooling jet blocks the main flow more strongly than it actually does. According to the high-speed region marked in red, the LES prediction of the characteristics of the high velocity in the streamwise direction from the kidney vortex position is more similar to the experiment values than those obtained using the RANS.
The CFD data provided the velocity information below y
= 0.2, which could not be measured experimentally. Both the LES and RANS results indicated that the largest and smallest boundary layer thickness occurred at z
= 0, the plane of symmetry, and at approximately z
= 0.5, respectively. Therefore, the maximum heat transfer coefficient was expected to occur at approximately z
= 0.5. The maximum film cooling effectiveness was expected to occur on the plane of symmetry without a strong jet lift-off and this aspect could be confirmed considering the data presented in the next section. Figure 4
shows the structure of the vortex generated in the injectant in a streamwise normal plane in comparison with the experimental data. Since the orientation angle considered in the results shown in Figure 3
was 0°, a left and symmetrical vortex pair appeared. In contrast, when the compound angle was adopted, an asymmetric or single vortex flow occurred. The results obtained using a five-hole Pitot tube [10
] (Figure 4
a) or PIV [12
] (Figure 4
b) indicated that when the orientation angle was 15°, the counter-rotating vortex remained weak. For the orientation angle of 30° or 45°, the vortex became a single vortex. The particle image velocimetry (PIV) technique minimized the disturbance of the flow field pertaining to the sensor, however, the velocity near the wall could not be clarified because of the measurement method and its limitations.
For the simple angle at a blowing ratio of 0.5 (Figure 4
c), the CRVP was observed in both LES and RANS data, and the lift-off of the jet was predicted to a similar degree. Compared to the LES data, the upward flow predicted using the RANS was closer to the symmetry plane, the central temperature was higher, and the hot area marked in red was narrower. When the injection ratio reached 1.0 (Figure 4
d), the prediction of the lift-off of the jet of the LES was larger than that of the RANS. In addition, the LES results clearly indicate that the high-temperature region becomes mushroom-shaped owing to the influence of the CRVP.
When the compound angle was adopted, the flow patterns predicted through the LES and RANS at the blowing ratio of 0.5 (Figure 4
e) were different. In the LES result, the counter-rotating vortex remained weak however, in the RANS, the vortex changed to a single vortex. The point at which the upward flow started was predicted to be near z
= 0 and z
= 0.4 by the LES and RANS, respectively. Lee et al. [10
] reported that the CRVP changed to a single vortex at the orientation angle of 30° or more for a single jet. However, for the considered array jet, the transition to a single vortex was delayed at a low blowing ratio.
At a blowing ratio of 1.0 with the compound angle (Figure 4
f), the CRVP transformed to a single vortex. The main flow was entrained along the upward flow of the vortex and the hot region was crescent-like. This aspect was common between the LES and RANS however, the LES predicted a higher lift-off than that pertaining to the RANS and the starting point of the upward flow was predicted to be closer to the plane of symmetry.
shows a comparison of the boundary layer temperature obtained through the CFD techniques at a blowing ratio of 0.5 with the experimental data presented by Jung and Lee [11
] at three streamwise positions. At x
= 2.5 with a simple angle (Figure 5
a), the area of the high-temperature region (displayed in red) predicted by the LES was more similar to the experiment value. The RANS-predicted high-temperature region with a dimensionless temperature θ
of 0.5 or higher was smaller than that in the experiment. Even at the downstream position, x
= 5.0 (Figure 5
b), the RANS underpredicted the intensity of mixing with the main flow compared to that obtained in the LES.
In the experimental data, the lift-off was unclear at the upstream locations (Figure 5
a,b) because no data near the wall could be obtained through the cold wire measurement. At x
= 10, as shown in Figure 5
c, the center of the injectant appeared near y
= 0.5 and lift-off could be observed in this part. The LES predicted that the lift-off occurred more intensely than that in the experiment, whereas the RANS did not predict any lift-off.
When the compound angle was adopted, the thermal field became asymmetric. This change in the temperature distribution was well predicted by both the LES and RANS (Figure 5
d,f). However, in the case of the compound angle, the mixing characteristics could not be determined simply by considering the area of the hot part, as in the case of the simple angle. Nevertheless, the characteristics could be clarified considering the spacing of the isotherms. In particular, the isotherm spacing in the RANS was wider than that in the experiment.
At a blowing ratio of 0.5, the LES predicted a lift-off and the RANS did not. At x
= 5.0 (Figure 5
b), the point at which the highest temperature occurred was measured to be y
= 0.3, and the LES predicted the point as y
= 0.5. The RANS predicted that the highest temperature would occur near the wall even in the downstream location, x
When the blowing ratio reached 1.0, lift-off of the injectant occurred in the case of both the simple and compound angle injection (Figure 6
). In Figure 6
a, which shows the temperature distribution at x
= 2.5 for the simple angle, the area marked in red, pertaining to the CRVP, appeared to have an inverted heart shape. As shown in Figure 3
, the LES predicted the location of the upward flow near the wall, closer to that in the experiment, and the shape of the high-temperature region obtained using the LES was similar to that in the experiment as well.
As the film cooling jet flowed downstream, it mixed with the main flow, thereby reducing the dimensionless temperature and changing the shape of the temperature distribution. In the case of a simple angle injection, the isotherm shape became similar to a concentric circle as the jet flowed downstream and both the LES and RANS predicted this phenomenon (Figure 6
b,c). At x
= 10 (Figure 6
c), the maximum dimensionless temperature was approximately 0.4, observed at a height of approximately y
= 1, and both the LES and RANS predicted this phenomenon to a similar extent.
In the case of the compound angle, at a blowing ratio of 1.0, the CRVP changed to a single vortex, and the high-temperature region exhibited a crescent shape at x
= 2.5 (Figure 6
d). In the case of the compound angle injection, the LES predicted the lift-off of the injectant to be 10% higher than that in the experimental data, whereas the RANS prediction was similar to the experiment value. The temperature distributions at the downstream locations for the RANS data were more similar to the experiment than those in the LES (Figure 6
3.2. Adiabatic Film Cooling Effectiveness
For the local distributions of the adiabatic cooling effectiveness, the LES data and RANS results obtained using three turbulence models were compared with the experimental data presented by Jung and Lee [11
]. Figure 7
shows comparisons of the distributions at a blowing ratio of 0.5. In the case of both the simple and compound angles, the LES-obtained distribution was closer to that obtained experimentally than that of the RANS. In the upstream region within x
= 2, the realizable k
and RSM overpredicted the film cooling performance and thus a region with high effectiveness (red contour) appeared, which did not appear in the experimental data. The k
SST did not severely overpredict the film cooling effectiveness in the upstream region however, the diffusion in the downstream, compared with the other models, was predicted to be smaller than the experiment value.
In the simple angle case (Figure 7
a), the CFD techniques predicted that the film cooling lasted longer than that in the experiment in the downstream region after x
= 10. Moreover, the CFD results indicated that the spread of the film cooling effect between the holes was delayed downstream compared to that in the experiment. This phenomenon likely occurred because of the influence of the smaller prediction of the CFD for the mixing of the main flow and injectant and the inability to impose artificial perfect insulation similar to that in the CFD in the experiments. By observing the film cooling effectiveness around the hole, which could not be obtained experimentally, the effectiveness around the rim could be attributed to the presence of the horseshoe vortex clearly highlighted in the LES.
In the case of the compound angle (Figure 7
b), the region with a high film cooling effectiveness spread widely and alleviated the degradation in the film cooling performance during the downstream flow. These characteristics were better predicted by the LES than by the RANS. The k
SST and RSM predicted that a region with low film cooling effectiveness would occur as the main flow was introduced to the surface with the downward flow of the main vortex generated in the film cooling jet in the downstream near the hole. This phenomenon was only slightly reflected in the LES and experiment. Khojasteh et al. [35
] reported that the reattachment of the cooling jet occurred at approximately x
= 1.5 in the simple angle case. Although this phenomenon was not clearly visible at M
= 0.5, it could be noted in the experimental results for M
= 1.0, as shown in Figure 8
Reattachment occurred in both the simple and compound angle cases and was more evident in the simple angle case. In the case of the simple angle, the area with high film cooling effectiveness due to the reattachment of the injectant could be observed only in the LES among the CFD results (Figure 8
a). The RANS results indicated that the film cooling effectiveness increased after x
= 5 however, this phenomenon was likely the effect of diffusion by mixing with the main flow rather than the reattachment. As shown in Figure 6
, after x
= 2.5, the height of the center of the injectant did not decrease even when the injectant moved downstream. In the case of the composite angle, both the LES and RANS predicted the occurrence of reattachment. Among the turbulence models, the realizable k
model obtained the distribution most similar to that in the experiment. At the blowing ratio of 1.0, the CFD techniques predicted film cooling effectiveness to be lower than that in the experiment and consequently, the distribution shown in Figure 8
involves more blue regions. Overall, the difference in the experimental data and simulation results was greater for the compound angle than for the simple angle.
To examine the film cooling performance between the holes and film cooling characteristics in the spanwise direction in the composite angle case, Figure 9
shows the spanwise variation of the film cooling effectiveness at x
= 2.5. The LES predicted the spanwise diffusion of the film cooling effectiveness better than the RANS. When the blowing ratio increased (Figure 9
c,d), the CFD techniques could not predict the spanwise spread accurately. Among the turbulence models, the k
SST and RSM obtained the best predictions for the film cooling performance at the blowing ratio of 0.5 and 1.0, respectively. In the case of the simple angle, the realizable k
and RSM could not predict the lift-off, and therefore, the centerline film cooling effectiveness was severely overestimated immediately downstream of the hole. The k
SST predicted the lift-off well at M
= 0.5, albeit incorrectly at M
= 1.0, corresponding to the largest difference from the experimental values. All the turbulence models predicted the lift-off more effectively in the case of the composite angle injection than the simple angle injection cases.
3.3. Turbulence Statistics and Instantaneous Flow Fields
shows the turbulence intensity for each component obtained by the LES, in comparison with the experiment of Burd et al. [34
]. As the RANS severely underpredicted the turbulence intensity, the maximum values of all the components for the three models did not exceed 10% and thus did not appear within the contour range in Figure 10
. In the simple injection angle (β
= 0°) case, at M
= 1.0, the LES-obtained distribution was similar to that in the experiment under the same geometry and blowing ratio. Compared with that in Figure 3
, the turbulence intensity of all the components was high in the part in which upward flow occurred in the CRVP.
The three components exhibit a difference in the turbulence intensity below y/D = 0.2, which could not be measured experimentally. The urms and wrms components not blocked by the wall appeared high along the wall, whereas the vrms component converged to zero at the wall. In the case of the compound angle (β = 30°), the overall trend was similar to that of the simple angle. However, the CRVP changed to a single vortex and consequently, the contours became asymmetric, and the distribution moved in the +z direction.
At the blowing ratio of 0.5, the overall distributions appeared to be smaller than those at M
= 1.0 (Figure 10
d,f). Under the orientation angle of 30°, the movement in the z
direction was smaller than that at the blowing ratio of 1.0. The urms
component was larger than that when the blowing ratio was 1.0 near the wall.
shows the temperature fluctuations. The RANS predicted extremely small temperature fluctuations to be fitted within the contour range, and thus, only the LES results are shown in the figure. θrms
was large in the region surrounding the area with large velocity fluctuation, as shown in Figure 10
. In the same range of the contours, when β
= 0°, the value was slightly higher than that when β
= 30°. This finding supports the result of the high film cooling effectiveness under a compound angle as the injectant flowed downstream.
shows the isosurface of the second invariant of the velocity gradient tensor, which is known to reflect the vortex [36
]. A horseshoe vortex, Kelvin–Helmholtz vortex, hanging vortex, rear vortex, and hairpin vortex could be observed in all the cases. The CRVP could be observed in the simple angle case, and at the blowing ratio of 1.0 (Figure 12
c), the Kelvin-Helmholtz vortex appeared to be stronger with narrow intervals than that at the blowing ratio of 0.5 (Figure 12
In the case of the compound angle (Figure 12
b,d), the horseshoe vortex became asymmetric and the intensity of the Kelvin–Helmholtz vortex weakened. A single vortex was observed, with more complex vortices generated on the windward side. The vortical structures between the blowing ratios of 0.5 and 1.0 did not exhibit a distinct difference, and at the blowing ratio of 1.0, the injectant moved further in the spanwise direction.
shows the instantaneous temperature field at the wall obtained through the LES. t
* is the dimensionless time defined by the main flow velocity and diameter of the hole, such that t
* = 1 is the time that the main flow covers a distance equivalent to the hole diameter.
As the adiabatic condition was imposed on the wall, the instantaneous temperature field exhibited the instantaneous adiabatic film cooling effectiveness. When the blowing ratio was 0.5, the injectant flowed along the wall and traces of the injectant, indicated in light green on the contour, extended from the hole to the downstream region (Figure 13
a,b). When the blowing ratio reached 1.0, lift-off and reattachment occurred intermittently. As shown in Figure 13
c, when t
* = 2, traces of the injectant appeared from the hole however, when t
* = 4, the traces were eliminated owing to the influence of the near wall vortices, such as the rear vortex shown in Figure 12
In the case of the simple angle (Figure 13
a,c), the film cooling appeared around the rim of the hole due to the influence of the horseshoe vortex and hanging vortex. Under a compound angle, the film cooling effectiveness was reduced around the leeward side of the rim (Figure 13
b) or eliminated (Figure 13
d). This phenomenon was attributed to the main flow being entrained in the shear layer sweeps while the CRVP changed to a single vortex. In the case of the simple angle injection at the blowing ratio of 1.0, most of the insulating film was eliminated after x
= 10 (Figure 13
c) however, in the case of the compound injection angle, the injectant flowed along the wall and maintained the insulating film (Figure 13