CFD correlation at representative ride height

The CFD simulations for the isolated wing have completely been updated compared to Mahon’s work. Changes have been made to the CAD geometry, the grid technique and to the domain (see section 2.4). All simulations have been performed with a steady RANS solver, in accordance with industry standards. This saves a considerable amount of computational time compared to unsteady simulations and is an acceptable compromise considering that most of the flow is attached. The computational solutions have first been correlated to the experimental results at one typical ride height, which combines characteristics of the wing in free flow and in ground effect conditions. The results of these simulations at h/c= 0.317 are discussed in this section. Ideally a grid dependency study and comparison of the turbulence models would be performed at each ride height because of the changes in physics and flow features, but for time considerations both have only been conducted at this representative height. The grid sensitivity analysis has been modeled with the default settings, incorporating the SA turbulence model. The subsequent examination of the turbulence models gives an idea of the relative strengths and weaknesses of each of the models with respect to the current problem. Finally, based on this examination, one turbulence model has been selected for all the other isolated wing simulations.

Grid sensitivity Three different grid sizes have been constructed to examine the grid dependency of the solution. The baseline grid (see figures 2.16 to 2.18 for an indication of the grid), which has also been used in the rest of the simulations, consists of 3.8 million cells. The finer grid has 5.9 and the coarser 2.7 million cells. This corresponds to a refinement in cell dimension per direction of 15.5% from the baseline to the finer grid and 12.6% from the coarse to the baseline grid. Refinement (and coarsening) has been implemented systematically throughout the grid - including the boundary layer density - but due to the complex block topology and connectivity it was impossible to apply a completely uniform refinement.

The results for the three different grid size cases are presented in table 3.3. The differences in force coefficients due to the changes in grid density are small, less than 0.4% for all of them, considering the considerable changes in the number of grid cells.

Reference results

Furthermore the values consistenly converge in the direction of the experimental values at a diminishing rate. The pitching moment is the only exception to this observation, since the coarse grid value is closer to the experimental data than the baseline grid. This irregularity is most likely caused by a disadvantageous alteration of the pressure distribution, caused by a different discretization of the contour, considering the small value differences. The pressure contours and wake profiles are almost coinciding for the three grid sizes and therefore it has been decided not to present these here. However it is interesting to notice that the global maximum suction value is found in the lower edge vortex core for the baseline and fine grid cases, whereas it is located on the main element suction surface for the coarse grid case instead.

Based on the results shown in table 3.3 it can be concluded that the simulations for this specific grid design approach the asymptotic limit of the force coefficients. It is however expected that bigger steps in correlation improvement can still be made by well considered local refinement instead of global refinement. By including more cells in the vortex regions and at the trailing edges of the elements it should be possible to capture the unsteady phenomena and blunt trailing edge vortex shedding better and this could even have an effect on the steady averaged results. The current grids, including the finest, show no signs of unsteady behaviour for the SA turbulence model and the force coefficients converge completely. The GCI values for the wing simulations have been calculated as well; based on the fine grid these are GCICL= 0.4%, GCICD = 0.6% and GCICM53mm = 0.3%.

The relative large correlation difference in the pitching moment (-18.8% compared to -6.3% for the downforce and +2.1% for the drag) shows a clear disadvantage of having to mount the load cell outside the wing model. It is anticipated that a large part of this correlation difference is caused by uncertainty of the pitching moment calibration, because it is difficult to apply a pure load. Furthermore deformation of the (support) structure will have an influence as well via the required translation of the moment. The experimental downforce and drag values are much less sensitive to these. The experimental pitching moment should therefore be considered as a general indication, which still shows consistent behaviour with model and flow changes, but not as an absolute correct value. Overall, the correlation of the force coefficients is satisfactory and has improved compared to Mahon’s results. It is expected that the main cause for the difference in CL and CD is related

to deformation of the experimental wing and general limitations of the computational method. The influence of the support structure, which has been omitted from the CFD, plays a part as well, just like the resulting difference in blockage.

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Turbulence models After having tested the grid sensitivity for a given turbulence

model (SA), the next step in the correlation of the CFD results is to examine the influence of the turbulence model choice for a given grid (using the baseline grid of the previous section). The grid was completely identical for all of the following turbulence model simulations. Some of the results could possibly be improved by adapting the grid to the specific turbulence model application, but for time considerations this has not been implemented within the current research. The results of the turbulence model comparison have been summarized in table 3.4. Purely looking at the force coefficients, it can be concluded that the SA model correlates best with the experimental data; followed by the standard k-ωand the standard k-²models. The best drag prediction of all by the realizable k-²model is most likely only a result of the lower lift induced drag, since this case predicts a lower downforce value than the previous mentioned models.

For a full understanding of the relative performances of the turbulence models it does however not suffice to look at these integral parameters only. A further examination of the on- and off-surface correlation is necessary to reveal whether the correlation is the result of a correct prediction of the flow features or that it is a coincidental combination of several errors. Figure 3.22 shows the chordwise pressure distributions at the centre and at the wing tip for the baseline ride height ofh/c= 0.317. This figure also includes the experimental data of Mahon, as well as his CFD result with the SA model. At centre span, figure 3.22 (a), the turbulence models perform very similarly from a qualitative perspective. They also all show improvement compared to Mahon’s results in predicting the suction values, which is mainly a result of the improved CAD geometry and grid technique. The tip results, figure 3.22 (b), give a more diverse impression, due to differences in the prediction of the tip vortices. The SA and standard k-²and k-ωmodels correlate best with the experimental data, but the RNG k-², the k-ωSST and the RSM models predict considerably less suction on the second part of the main element and the first part of the flap. In contrast, the suction on the last part of the flap is widely overpredicted by the k-ω SST model - leading to the highest pitching moment coefficient of all - and to a lesser extent by the RNG k-² model.

The behaviour of the k-ω SST model has been traced back to a large separated zone at the juncture of the suction side of the flap with the endplate (see figure 3.23 (a) and (b) for a presentation of this separation at the juncture for a different case). All turbulence models, except for the RNG k-², predict a small elongated separated zone in this region, but the k-ω SST model result shows a much wider zone, which also covers a part of the

Reference results

endplate underneath the flap. The overprediction of the suction at the tip of the flap from x/c= 0.6 onwards features a plateau with relatively constant pressure, which is typical for separated flow. The discrepancies in the pressure distribution at the tip for the RNG k-² and RSM models are the result of vortex breakdown in the simulation results. Both models predict a considerable region of reversed flow at the vortex core underneath the flap. This is reflected in the lower suction on the second part of the main element and the first part of the flap, which is similar to the physics seen in the experiments at lower ride heights in force region (b). The realizable k-² model is the only other model that shows flow reversal in the vortex core, but at a much smaller scale, which can also be concluded from the limited influence on the pressure distribution. Only the SA model predicts a lower CP in the vortex core than in the suction peak on the main element, see the CP

global values in table 3.4. This is typical for a strong vortex and the additional vortex strength might explain why the SA model gives the best force coefficient correlation, since the lower edge vortex effect is best predicted (see figure 3.22).

Correlation of the wake profiles, shown in figure 3.24, reveals that all models have improved on the results of Mahon by better prediction of the velocity deficit in the main element wake and by showing a more continuous curve in the wall jet area. The wake velocity deficits and the confluence point between the two wakes are best resolved by the standard k-ω model, which is in line with the expectations resulting from the turbulence models discussion in section 2.4.7. The SA model performs adequately but is definitely not among the best models when it comes to the wake prediction. The standard k-²model shows a distinctive velocity deficit at the top of the wall jet region, but it is impossible to judge whether this is more or less realistic than the outcomes for the other models as a result of the previously discussed limitations of the experimental data.

A final aspect that needs to be discussed for the various turbulence models is the convergence behaviour. The SA model is extremely robust and converges completely without any signs of potential problems. The RNG and realizable k-²models as well as the RSM model were however much more critical and required more effort to converge. For example these cases had to be started from a SA solution and with first order turbulence discretization during the beginning of the simulation. The turbulent viscosity ratio was automatically limited by the solver in a few cells (in the order of a 100) for each of these cases, but without any destabilizing effects. Flow reversal in the vortex core on the pressure outlet was experienced in the RSM solution, indicating that this unphysical boundary condition was not ideal for this turbulence model. Therefore it is anticipated

Reference results

that some of the applied models may perform better after some turbulence model specific grid and solver setting modifications. A few models did also pick up a degree of flow unsteadiness once converged, see theC_Lvariations in table 3.4 for an indication.

Based on these results it has been decided to continue the isolated wing simulations using the SA turbulence model. The standard k-²and k-ω models would be good alterna- tives, but the robustness and relative low computational cost of the SA makes it preferable. The flow reversal in the vortex core underneath the flap for the RNG, realizable k-²and for the RSM model is in disagreement with the experimental results for this height and the large separated zone on the flap tip predicted by the k-ω SST model has not been found in experiments either, making the results of these models questionable for the current grid and solver settings.