Three-dimensional investigations

The first set of three-dimensional simulations are based on URANS with the LLR $k$-$\omega$ model using a time step of $\Delta t=0.002 c/u_0$. Investigations of the 2d geometry by a three-dimensional approach result in an almost completely two-dimensional flow field. All analysis are based on the $\lambda_2$-criteria which represents the second eigenvalue of a combination of the strain and vorticity tensors. $\lambda_2$ forms a proper tool to indicate the location of the vortex cores [23]. Although snapshots from iso-surfaces of $\lambda_2$ show 3d effects especially in the near wake behind the suction side, the overall flow field is characterized by the shedding of two-dimensional rolls (fig. , upper figure).

Compared to the two-dimensional computations, lower lift but higher fluctuations are predicted by the three-dimensional URANS (results shown in table ) which is caused by additional low-frequency 3d oscillations that contribute to $c_l\,'$ and that are also responsible for higher drag. $c_d$ however, still remains significantly lower than in the experiments.

In the spectra of the unsteady lift coefficient (fig. ), the typical characteristics of URANS computations can clearly be observed: Beside a dominant peak at the shedding frequency, only the higher harmonics are visible and almost no broadband noise is predicted. Compared to the two-dimensional results, the level of noise in the 3d case is significantly larger and a second peak at lower frequency appears which corresponds to the 3d effects.

Figure: Frequency spectra of lift obtained by URANS and DES for a 2d Gurney with $h/c=1\%$.