# An Overview of Hybrid RANS-LES Models Developed for Industrial CFD
## 2 Large Eddy Simulation of Wall-Bound Flows
In this approach, the stream- and spanwise resolution are identical to those in a WFLES grid, however the wall-normal direction can be resolved through the viscous sublayer. This is achieved by blending a RANS model near the wall with a LES model away from the wall. The switch takes place in the logarithmic layer. WMLES can either be achieved by using a transport-equation-based model (IDDES, SBES) or an algebraic (Prandtl mixing length) model in the inner layer ([PERSON] et al. [23]. Figure 2 shows the results of WFLES and WMLES approaches for channel flows with different \(Re_{\tau}=\frac{u_{\tau}H/2}{v}\) numbers, using a grid of around 5 \(\times\) 10\({}^{5}\) cells for all Re numbers (\(u_{\tau}\) = friction velocity, \(H\) = channel height, and \(v\) = kinematic viscosity). Both methods provide a good representation of the expected linear-logarithmic correlations. It is interesting to note that the current WFLES implementation avoids the well-known log-layer mismatch when applying a wall function in the center of the first cell. This is achieved through careful computation of velocity gradients in this cell. The application of the WFLES approach in external automotive applications has received increased attention, at least for models involving reduced Re numbers (e.g., [PERSON] et al. [32]). A classical starting point for validation of methods for such applications is the Ahmed car body approach, a strongly simplified geometry involving the main features of a hatchback car. WFLES simulations were carried out for a 25\({}^{\circ}\) slant angle case. Three octree meshes with different grid sizes (mesh 1 = 7 \(\times\) 10\({}^{6}\); mesh 2 = 35 \(\times\) 10\({}^{6}\); mesh 3 = 100 \(\times\) 10\({}^{6}\)) were used. Resolved turbulent flow structures can be seen in Figure 3, with a clear increase in detail under mesh refinement conditions. Figure 4 shows the resulting velocity profiles in the critical region above the slant. This region is characterized in the experiments by a closed separation bubble from the slant onset halfway down the slant. The WFLES solutions provide a reasonable agreement with the experimental data in the study by [PERSON] and [PERSON] [33], albeit not with the same detail. All WFLES solutions tend to predict an acceleration at the slant onset that is not seen in the experiment. This seems to be caused by a lack of wall-normal resolution in the WF grids near the geometric singularity at the slant onset. As a result of this acceleration, the flow exhibits a reduced separation tendency downstream of the slant. With mesh refinement, the flow also accelerates too strongly towards the end of the slant. WMLES were performed on the same geometry, using y + \(\sim\)1 meshes of a different size (mesh 1 = 10 \(\times\) 10\({}^{6}\); mesh 2 = 20 \(\times\) 10\({}^{6}\); mesh 3 = 40 \(\times\) 10\({}^{6}\)) in the slant region. As can be seen in Figure 5, in these meshes, the acceleration around the slant is avoided, pointing to an advantage of this approach over WFLES, due to the finer wall-normal resolution. The agreement with the experiment is generally improved relative to the WFLES results, but again shows a tendency towards reduced separation size downstream of the slant onset, especially for the finer meshes. Note that this case is notoriously difficult to compute  
Figure 2: Velocity profiles for LES of channel flows for different Re numbers in logarithmic scale compared to experimental correlation (Reichardt’s law). **Left**: WFLES. **Right**: WMLES. with LES (at least at the experimental Re number), as seen in a comparative study by [PERSON] et al. (2017), whereby different groups produced solutions ranging from fully stalled to non-separated. Similarly to the findings of [PERSON] et al., it is concluded that much finer meshes would be required to achieve mesh-independent solutions for this case when covering the boundary layer in any form of LES. Simulations using a hybrid RANS-LES method for this case will be discussed in the next section.