# Evaluation AC1-09

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# Vortex breakdown above a delta wing with sharp leading edge

Application Challenge AC1-09   © copyright ERCOFTAC 2023

# Comparison of Test Data and CFD

An overview is given of the computational results obtained by the different partners.

In terms of the mean pressure coefficient, the different computations are reasonably clustered in the vicinity of the experimental data (Figure 8). The largest difference with the experiment is found at the first station (${\displaystyle {\left.x/c_{r}=0.2\right.}}$), where all computations show a clear suction peak due to the main vortex (and some also a smaller peak due to secondary separation), whereas the experiment shows a plateau. In the computations, the main vortex starts to develop immediately from the apex. In the experiment, however, it seems that the vortex starts further downstream along the leading edge, more resembling the vortex development of a round leading edge. Possibly, this may be related to the relative bluntness of the leading-edge angle. There may also be a Reynolds number effect, because at a higher Reynolds number (${\displaystyle {Re_{\text{mac}}=2\cdot 10^{6}}}$), the experiment does show a clear suction peak (Furman and Breitsamter, 2009). At the other four stations, the computed pressure distributions compare reasonably well with the experiment in terms of the location of the main suction peak and the level of the pressure plateau outboard of the main peak, indicating no or only weak secondary separation. The level of the suction peak is underpredicted at the station ${\displaystyle {\left.x/c_{r}=0.6\right.}}$ where the experiment shows vortex breakdown, but the computations do not (see below). At the other stations, the suction peak in most computations is close to or just below the experiment.

The level of the main suction peak, which indicates the strength of the main vortex, depends on the level of resolved turbulence. If the turbulence is underresolved, then the vortex will be too strong; if the level of turbulence is too high, then the vortex will be too weak. Hence, the initial development of the vortex and turbulence in the vortex is vital. With a standard DES method, the shear layer emanating from the leading edge is stable over a significant part of the wing (Figure 3a), so that there is insufficient resolved turbulence, leading to a strong, compact, main vortex. Including the high-pass-filtered (HPF) SGS model, the level of the subgrid stresses is significantly reduced and the shear layer becomes unstable close to the apex. Much higher levels of resolved turbulence are then obtained, weakening the main vortex and more in-line with the experiment. Consequently, the resolved turbulent kinetic energy compares fairly well with the experiment, at all three cross planes (see Figure 9). Only the peak level is overpredicted (consistent with the underprediction of the suction peak). In particular, the experiment shows a clear local minimum at the core of the vortex from station ${\displaystyle {\left.x/c_{r}=0.6\right.}}$ and further downstream, whereas the computation still shows a clear peak at ${\displaystyle {\left.x/c_{r}=0.6\right.}}$ and a plateau or a slight local minimum further downstream. Other results with DDES and IDDES methods compare less favourably with the experiment and also show significant variation between the different computations. In particular for the upstream sections, the DDES results show low levels of resolved turbulence (some more than others, most likely depending on the numerical method and in particular the level of numerical dissipation), as explained above.

In terms of the RMS of the pressure coefficient, a large variation between the results is found (Figure 10). A number of results strongly overpredict the level, while some others initially show a very low level (correlating to a low level of resolved turbulence). Only the HPF DX-LES computation essentially has the right level at all stations, consistent with the resolved turbulent kinetic energy, but still the details of the distribution differ from the experiment. There are also a few unexpected results: the DLR SA-DDES computation shows significant RMS levels near the symmetry plane ${\displaystyle {\left.\eta =0\right.}}$ and on the lower side of the wing. The CFSE SST-IDDES shows the same behaviour for the first two stations and also has very high RMS levels below the vortex at ${\displaystyle {\left.x/c_{r}=0.2\right.}}$, which then drop to very low levels at ${\displaystyle {\left.x/c_{r}=0.4\right.}}$. This makes the reliability of these two computations questionable.

The occurrence of vortex breakdown can be seen in the time-averaged velocity field (Figure 11).

In the experiment, a very low axial velocity is present in the vortex core at ${\displaystyle {\left.x/c_{r}=0.6\right.}}$, indicating that the initial vortex breakdown has taken place well before this location. All computations clearly show vortex breakdown at ${\displaystyle {\left.x/c_{r}=0.8\right.}}$, but not at ${\displaystyle {\left.x/c_{r}=0.6\right.}}$, with exception of the DLR SA-DDES result. This result shows an initial sign of vortex breakdown at ${\displaystyle {\left.x/c_{r}=0.6\right.}}$, but not as strongly as the experiment, indicating the initial vortex breakdown is also downstream of the experiment. Thus, it appears that none of the computations obtain the same vortex breakdown location as the experiment, even though there is a significant variation in for example resolved turbulence between the computations.

The occurrence of secondary separation can also, in principle, be seen in the time-averaged velocity field (Figure 11). For all computations, the time-averaged velocity vectors are parallel to the surface below the main vortex. Following the velocity vectors towards the leading edge, they point away from the surface, which indicates secondary separation. For the experiment, the flow pattern is less clear. Note in particular that the velocity field of the experiment is not tangential to the wing surface below the primary vortex, indicating some error in the measurements or postprocessing. Therefore, no conclusion can be drawn about secondary separation in the experiment from the time-averaged velocity field. The distribution of the turbulent kinetic energy (Figure 9), however, does suggest a shear layer separating from the surface between the main vortex and the leading edge, indicating secondary separation in the experiment as well.

Based on the available results, no definitive conclusion can be drawn about which basic DES-type method (SA-DES, SST-DES, or X-LES) is most suitable for this test case. All partners have used different models in combination with different solvers. Thus, the influence of the numerical methods on the results may still be significant. Also, statistical convergence has not been verified for all results. One can conclude, however, that the X-LES method with the HPF SGS model shows the best comparison with the experiment in terms of resolved turbulence and pressure fluctuations. This can be attributed not to the X-LES method itself, but to the HPF SGS model, which strongly improves the initial development of resolved turbulence in the shear layer. This modification of the SGS model could also be used in other DES-type methods. Using the stochastic variant of X-LES does not significantly alter the results once the HPF SGS model has been included. The location of vortex breakdown is closest to the experiment for the DLR SA-DDES computation; this computation, however, appears to be less reliable when looking at the resolved turbulent kinetic energy and in particular the RMS levels of pressure. Finally, the delayed modification of DES (or X-LES) does not appear to have a strong effect on the results for this case and on this grid.

Contributed by: J.C. Kok, H. van der Ven (National Aerospace Laboratory NLR Amsterdam, The Netherlands), E. Tangermann (Airbus Defence and Space München, Germany), S. Sanchi (Computational Fluids and Structures Engineering Lausanne, Switzerland), A. Probst and K.A. Weinman (German Aerospace Center DLR Göttingen, Germany), L. Temmerman (NUMECA International Brussels, Belgium) — '

© copyright ERCOFTAC 2023