Selected validational testcases and discussion

The above mentioned SALSA modification has been validated against a sequence of fundamental building-block flows, e.g channel flows, plane mixing layers or backward-facing step flows, which are beyond the scope of the note. Apart from the above mentioned skin-friction deviations, no significant differences between the SA model and the present suggestion can be observed in equilibrium boundary layers. The investigation of free-shear flows reveals a reduction of 10 % of the spreading rate when compared to the SA model. In severe non-equilibrium flows, however, the adjustments show improved results which will be illustrated by three exemplary testcases. It should be noted that the predictive accuracy of Edward's variant (SAE) was generally very close to the SA model for all the investigated cases.

The first example focuses upon a generic wing-body configuration at $\alpha=12^o$, $Re=2.7\cdot 10^6$, $Ma=0.2$ which emerged from an industrial design process [4]. The block-structured computational grid consists of roughly 2.2 million nodes in 48 blocks with $Y^+$ in the range of 0.3$< \$Y$^+<$5 for the points closest to the walls. Fig.1 illustrates the geometry and the pressure distribution. Since the wing as highly optimised for transonic cruise conditions the flow separates at the leading edge in large areas on the outer wing due to the high angle of attack chosen here. Both one-equation models cannot capture the structure of the flow at separation, nonetheless, Fig.1 reveals that the results for the SALSA model come close to explicit algebraic stress models (EASM).

The second example refers to the results obtained for the simulation of the 2D flow around an ONERA A-Airfoil at $Re=2\cdot 10^6$, $M=0.15$ and an angle of attack $\alpha =13.3^o$ [5]. The simulation is performed on a C-type, block-structured grid consisting of 281x78 volumes with fixed transition at 12% and 30% chordlength on the upper and lower side, respectively, of the profile. The testcase features a laminar (pre-transitional) separation in conjunction with a pressure induced trailing-edge separation downstream of $X/C\simeq0.825$ of the suction side. Results depicted by Fig.2 reveal that the flow reversal is underestimated with any model. The suggested SALSA model is closest to the experiments, which is caused by a better representation of the near-wall distribution of the shear stress $\overline{u'v'}$. In comparison to the SA approach, the present model returns approximately 10% smaller skin-friction values along the equilibrium part of the suction side of the airfoil. Downstream of $X/C=0.7$, the predicted displacement thickness of the SALSA model exceeds the SA value by 90 %, which are still more than 10 % smaller than experimental data.

Finally, the predicted pressure distributions around a an RAE-2822 airfoil [6] exhibiting weak (case 9) and strong (case 10) shock-boundary-layer interaction are presented in figure 3. All models reasonably capture the experimental results for less-challenging case 9. For case 10, the considerable predictive differences occur. However, neither model is able to render the correct pressure level on the upper surface in the recovery regime aft of the shock.