Three-Element Aerofoil

Figure 9: Three-element aerofoil: pressure coefficient and streamlines at maximum lift, SALSA computation

A three-element aerofoil in landing configuration, Fig. 9, is computed at $Ma=0.2$, $Re=4.1\cdot10^{6}$ and various angles-of-attack including cases beyond maximum lift. The goal of these simulations is to determine the various turbulence models' capability to predict maximum lift and - at least qualitatively - the lift characteristics beyond stall. A grid with 75,177 points and 9 blocks supplied by DLR is used. A $y^{+}\approx1$ is aspired, however, this could not be guaranteed over all parts of the configuration, so that locally a $y^{+}\approx4$ has to be tolerated. The FLOWer code is employed for the computations, the models investigated include LLR $k$-$\omega$ (albeit with a slightly modified $\omega$-equation), LEA $k$-$\omega$, SALSA and Spalart-Allmaras. As the transition locations are not known, the computations are performed in a fully turbulent fashion. Furthermore, a steady time-marching technique is used since unsteady computations turned out to be prohibitively expensive. This does not constitute a proper validation approach, however, it reflects current industrial methodology.

Fig. 10 displays the computed and measured lift coefficients versus the angle-of-attack, where noticeable differences are visible between the different models evaluated. Wilcox $k$-$\omega$ is not included in this comparison, as the results are very similar to the LEA $k$-$\omega$ ones. The lift coefficients are averaged over a certain amount of multigrid cycles after convergence was reached save some oscillations, which, however, hint to flow unsteadiness.

Figure 10: Three-element aerofoil: lift coefficient vs. angle-of-attack for various turbulence models

In the region well below maximum lift, all models except SALSA slightly overpredict the lift coefficient, whereas SALSA shows a severe underprediction. In this regime, the flow is separated over the rear part of the flap, which is basically resolved by all models. However, the separation length determined by SALSA is obviously too large, which in turn reduces the suction peak not only on the flap but also the slat and the main wing. Approaching maximum lift, the flow over the flap reattaches. Up to maximum lift, the flow remains attached over the whole geometry, see Fig. 9, leading to very similar results for all models investigated, except for LLR $k$-$\omega$, which yields a lift coefficient too low due to an off-surface recirculation zone above the flap affecting the circulation over the whole configuration. If the angle-of-attack is increased beyond this point, LLR $k$-$\omega$ and SALSA show a severe breakdown in lift, which is not found by LEA $k$-$\omega$ and Spalart-Allmaras. The reason for this, however, is different for both models. For SALSA, in the stalled regime, despite the flow over the flap being fully attached, separation occurs on the upper slat surface significantly reducing the suction peak on the slat as well as the overall pressure level on the main aerofoil. According to [20], the latter is caused by a larger slat wake deficit in the slat-separated case leading to a loss of near-surface momentum on the main profile. As can be seen in Figs. 11 and 12, where the pressure coefficient distributions are given for three different angles-of-attack as determined using the one-equation models, this flow feature is captured by SALSA, whereas Spalart-Allmaras misses it completely, mistakenly leading to very similar predictions for the maximum lift and the stall case. Furthermore, an off-surface flow reversal region situated in the wake of the flap is observed in the SALSA computations, which is not present in the Spalart-Allmaras results. LLR $k$-$\omega$, on the other hand, shows a large recirculation region affecting not only the flap but also the main aerofoil. Thus, the flow topology in the stalled case is different for LLR $k$-$\omega$ and SALSA, with the prediction of the latter probably being more realistic.

As it is unclear to date which physical mechanisms constitute the lift-limiting mechanism [20], and also taking the aforementioned limitations into account, final conclusions concerning the models' capabilities cannot be drawn here. However, the ability of LLR $k$-$\omega$ and SALSA to generally predict stall at about the correct angle-of-attack is a promising feature for future investigations on such configurations. LEA $k$-$\omega$ in turn, which has shown promising results in transonic flows, behaves like the standard approaches here, which, in all likelihood, can be attributed to the fact that LEA is cast in terms of the original Wilcox background model.

Figure 11: Three-element aerofoil: pressure coefficient distribution for the Spalart-Allmaras model

Figure 12: Three-element aerofoil: pressure coefficient distribution for the SALSA model