Mixing ventilation flow in an enclosure driven by a transitional wall jet

Confined Flows

Underlying Flow Regime 4-20

Evaluation

Comparison of CFD calculations with experiments

The results of the steady RANS CFD simulations are compared with the measurement results from the PIV measurements. Figure 7 shows the dimensionless streamwise velocities (U/U_M) along vertical lines at three locations in the vertical center plane (z/L = 0.5) of the enclosure; x/L = 0.2; x/L = 0.5 and x/L = 0.8, for a slot Reynolds number of ≈ 1,000. Note that the results at x/L = 0.2 (Fig. 7a) are provided for the smaller region of interest, i.e. ROI2, while the other results are provided for the total vertical cross-section, i.e. ROI1.

Figure 7a shows that a top-hat profile is present at x/L = 0.2 in both the measurements and simulation results, and that the agreement between the predictions of the CFD models and the experimental results is very good; only RSM starts deviating below y/L = 0.82. Please note that in contrast to Figure 5, no top-hat profile is visible in Fig. 7c, which is due to the too low measurement resolution for ROI1 to capture the large velocity gradients in the boundary layer and shear layer. Figure 7d shows that the low-Reynolds number version of the k-ε model by Chang et al. (1995) provides the best agreement with the experimental results with respect to the location of maximum velocity, and thus with respect to the location of detachment of the wall jet. The worst overall agreement is present for the RSM model and SST model, especially with respect to the prediction of the location of maximum velocity and of jet detachment.

Figure 7: (a-c) Comparison of PIV results in ROI1 with CFD simulation results for Re ≈ 1,000: (a) U/U_M at x/L = 0.2 (ROI2). (b) Locations of x/L = 0.2, 0.5 and 0.8. (c) U/U_M at x/L = 0.5; (d) U/U_M at x/L = 0.8. Figure modified from van Hooff et al. (2013).

Velocity vector fields in the vertical center plane for Re ≈ 1,000 are shown in Figure 8. The vector fields illustrate the difference in location of jet detachment from the top surface. The detachment point as predicted by the low-Reynolds number version of the k-ε model shows the best agreement with the experimentally obtained location. The location of jet detachment is predicted to be too far upstream by the SST k-ω and RSM models, as indicated in the discussion on Figure 7 above. Figure 8 also depicts the center point of the large recirculation cell, as obtained from the experiments (Fig. 8a), and as obtained from the CFD simulations (Fig. 8b-d). Again, the best agreement is shown by the low-Reynolds k-ε model.

Figure 8: Time-averaged velocity vector fields in the vertical center plane for Re ≈ 1,000. (a) PIV measurements; (b) LR k-ε; (c) SST k-ω; (d) RSM. ● = measured center of the large recirculation zone, ○ = computed center of large recirculation zone. Figure from van Hooff et al. (2013).

Figure 9 shows the turbulent kinetic energy profiles along two vertical lines, obtained from the PIV measurements in ROI2 and the CFD simulations. Since the 2D PIV measurements only provided the velocity components in two out of three directions (streamwise and vertical), the third component (lateral; w) was unknown. Therefore, to be able to calculate the turbulent kinetic energy, the correlation between the normal stresses in a 2D wall jet, as described by Nielsen (1990), was used:

{w_{RMS}\approx {\sqrt {0.8}}\ u_{RMS}}\qquad (7)

At x/L = 0.2, the best agreement is obtained by the RSM model, while at x/L = 0.5 the best agreement is obtained with the SST k-ω model. However, it must be noted that all RANS models strongly underpredict the values of k in the inner region (boundary layer) of the wall jet (around y/L = 0.99 at x/L = 0.2 and around y/L = 0.94 at x/L = 0/5). Especially at x/L = 0.2 the RANS models do not seem to be able to capture the local increase in turbulent kinetic energy near the top surface (onset to more turbulent flow). Although all RANS models are low-Re number models, i.e. they solve the flow until the wall, they were not developed to model the transition from laminar to turbulent flow and this can be regarded as one of the main potential reasons for the observed discrepancies between experiments and CFD in the boundary layer.

Figure 9: Comparison of measured turbulent kinetic energy k and values obtained from CFD simulations for Re ≈ 1,000: (a) k at x/L = 0.2; (b) k at x/L = 0.5. Figure modified from van Hooff et al. (2013).

Figure 10 shows the dimensionless streamwise velocities (U/U_M) along vertical lines at three locations in the vertical center plane (z/L = 0.5) of the enclosure; x/L = 0.2; x/L = 0.5 and x/L = 0.8, for a slot Reynolds number of ≈ 2,500. At x/L = 0.5 and x/L = 0.8, the best agreement is again obtained by the low-Reynolds number version of the k-ε model by Chang et al. (1995) (Fig. 10c,d). Again, the worst agreement with respect to the prediction of the location of maximum velocity and of jet detachment is obtained with RSM and SST models; both models predict the location of jet detachment to be too far upstream.

Figure 10: (a-c) Comparison of PIV results in ROI1 with CFD simulation results for Re ≈ 2,500: (a) U/U_M at x/L = 0.2 (ROI2); (b) Locations of x/L = 0.2, 0.5 and 0.8. (c) U/U_M at x/L = 0.5; (d) U/U_M at x/L = 0.8. Figure modified from van Hooff et al. (2013).

The velocity vector fields in the vertical center plane for Re ≈ 2,500 are shown in Figure 11. The vector fields illustrate the difference in location of jet detachment from the top surface, with the early detachment as predicted by RSM and SST. Comparison of Figure 8 and Figure 11 shows the dependence of the location of detachment on the Reynolds number; increasing Reynolds numbers increase the distance from the inlet to the location of jet detachment. This tendency is captured by all RANS models as well. In addition, comparison of Figure 8 with Figure 11 shows that the differences between the experimentally obtained center of the large recirculation cell and the numerically obtained locations are smaller for higher Reynolds numbers, which is most visible when looking at the vector fields obtained with the RSM model.

Figure 11: (a-c) Time-averaged velocity vector fields in the vertical center plane for Re ≈ 2,500. (a) PIV measurements; (b) LR k-ε; (c) SST k-ω; (d) RSM. ● = measured center of the large recirculation zone, ○ = computed center of large recirculation zone.

Contributed by: T. van Hooff — Eindhoven University of Technology