Results of Detached Eddy Simulations

In simulations of unsteady turbulent flow by Reynolds-averaged approaches (URANS), turbulent time-scales always require special attention. The resolved time-scales of the large-scale motions have to be significantly larger than the high-frequency small-scale motions that are captured by the turbulence model. Problems can occur if parts of the spectrum are modeled as well as resolved. In the present investigations, the entire flow field is checked for the smallest occurring time-scales. Particularly in the near wake behind the Gurney-flap, the turbulent frequencies cover the same range of the spectrum as the resolved time-scales. Consequently, the application of the Reynolds-averaged approach is questionable. It should also be remarked that the turbulent frequencies depend on the time stepping itself [11]. In order to prove the reliability of the simulation, additional DES investigations are performed which should avoid the time-scale problem.

The DES results are obtained on the same numerical meshes and using the same time step like for the URANS results. Fig. gives an impression from where the hybrid method switches between URANS (white) and LES (dark) depending on equation (). The LES mode is clearly limited to the near wake up to about $5h$ downstream of the Gurney-flap, covering the region of strongest unsteady effects and of greatest importance for the flow.

Figure: Regions of URANS (white) and LES (dark) in the hybrid URANS/LES computation.

DES predicts similar mean aerodynamic forces as URANS (table ). The unsteady features of the flow can be compared in a spectrum of predicted lift in fig. . One dominant peak corresponding to roughly the same shedding frequency can be identified in the results of all methods. However, the level of noise in the hybrid URANS/LES simulation is higher than in the Reynolds-averaged method. This typical behavior of DES is caused by the resolution of turbulent fluctuations in the LES region. Such very complex structures appear in the near wake (see fig. , lower figure). Compared to URANS, stronger vortices occur but these are no longer concentrated in a single dominating structure. The prediction of characteristic frequencies compared to experiments can be improved by DES.

Figure: Iso-surfaces of $\lambda_2$ in the wake of a 2d Gurney-flap with $h/c=1\%$ computed by URANS (upper figure) and DES (lower figure).

Figure: Iso-surfaces of $\lambda_2$ in the wake of a 3d Gurney-flap with slits computed by a URANS (upper figure) and DES (lower figure).