RAE 2822 Aerofoil

Figure 1: RAE 2822 Case 10: Pressure distribution and streamlines

The RAE 2822, Fig.1, is a supercritical aerofoil [17], which has become a standard testcase for turbulence modelling validation. Two cases of transonic flows are considered, i.e. a subcritical one where little or no separation occurs downstream of the shock position (``Case 9'', $Ma=0.73$, $Re=6.5 \cdot 10^{6}$, $\alpha=2.8^{\circ}$) and a supercritical one, where the shock-boundary-layer interaction induces massive separation (``Case 10'', $Ma=0.75$, $Re=6.2 \cdot 10^{6}$, $\alpha=2.8^{\circ}$).

Unfortunately, the experiments suffer from wind tunnel influences, which cannot be quantified a posteriori. Several corrections have been suggested, however, as, none can be considered superior, the flow conditions used in [18] have been selected for comparability reasons. The computations presented here are performed with the TAU solver on a structured mesh (albeit computed in an unstructured manner) with $312\cdot65$ nodes generated by DLR. Transition is fixed at 3% chord length. Turbulence models included here are RQEVM + Wilcox $k$-$\omega$ and EARSM + Kok $k$-$\omega$, Wilcox $k$-$\omega$ serves as baseline reference.

In Figs. 2 and 3, the pressure distribution is given for both cases. Turning the attention to the shock location, it is evident that Wilcox $k$-$\omega$, while being able to quite accurately predict Case 9, computes the shock about 8% chord length too far downstream for Case 10. In contrast, both EASM results yield a much better shock location for Case 10, almost identical to the experiments. Looking at Case 9, it can be seen that, compared to Wilcox, the results of the EASM are only slightly worse, thus, the over-all gain in predictive accuracy is encouraging.

Figure 2: RAE 2822: Pressure distribution for Case 9

Figure 3: RAE 2822: Pressure distribution for Case 10