# An Overview of Hybrid RANS-LES Models Developed for Industrial CFD
## 3 Global Hybrid RANS-LES Models
Since the SBES model switches sharply from RANS to an existing algebraic LES model, the \"grey zone\" of the intermediate RANS-LES eddy viscosities is avoided and resolved turbulence can form quickly. This can be seen for the mixing layer (Morris and Foss [39]) shown in Figure 9, where the SBES model develops fine-grained turbulence, while the DDES approach maintains 2D structures  
Figure 8: Contours of eddy viscosity ratios for the CS0 diffuser for SBES (**left**) and DDES (**right**) models. Figure 6: Computational domain for the CS0 axisymmetric diffuser. Figure 7: Contours of blending functions overset by vorticity iso-lines for CS0 diffuser for SBES (**left**) and DDES (**right**) models. in the same grid of 2 \(\times\) 10\({}^{6}\) cells. More modern DES versions such as DDES-SLA [17] also help to reduce the delay of resolved structures. The CPU cost for SBES can be minimized by recognizing that the RANS part of the flow typically follows a slower time scale than the LES part. It is, therefore, possible to update the two-equation RANS model part with a larger time step than the cheaper LES model. Updating the RANS part at only every 3 rd to 5 th time step leads to a decrease of around 20% in the overall computational time. The cost per time step for the SBES is then only marginally higher than for a pure LES model on the same mesh. To demonstrate the capabilities of SBES, the Ahmed car body at 25\({}^{\circ}\) was computed with the SBES model using a combination of the SST-RANS and the WALE-LES models. The flow conditions are taken from the experiment by [PERSON] and [PERSON] [33], with a Reynolds number based on a car height of Re\({}_{\text{H}}\) = 7.68 \(\times\) 10\({}^{5}\). The simulation was carried out on a moderate 14 \(\times\) 10\({}^{6}\)-cell hex grid. Figure 10 shows the resolved turbulent structures around the car body. As expected, only the separated region behind the slant onset is covered by the LES model, whereas the attached boundary layers are computed in RANS mode. Figure 11 shows a comparison of RANS and SBES velocity profiles around the back of the car. The SBES formulation captures the experimental data with high accuracy and corrects the known deficiency of over-separation of RANS models (here SST) for this case. Figure 10: Resolved turbulent structures for the SBES simulation (Q-criterion iso-surface; color = velocity). Figure 9: Iso-surfaces of the Q-criterion colored in line with the velocity magnitude. Left part: DDES model; right part: SBES model. Mesh 1 has 2 million cells. (\(Q=1/2\left(\Omega^{2}-S^{2}\right)\) with \(W\)-Vorticity and S-Strain Rate). Another interesting characteristic of the SBES model is that it can operate in WMLES mode, once triggered into scale-resolving mode. This can be seen in Figure 12 for a channel flow. All grids are in the range of 500,000 cells, with y + -1. The simulations were started from a LES solution to trigger the SBES model into SRS mode. Interestingly, SBES produces similar resolved structures as IDDES, which was specifically designed for this purpose. It needs to be stressed that IDDES does not provide the strong shielding capabilities of SBES in RANS mode, and therefore is only of limited use in industrial flows. Figure 13 shows the corresponding time-averaged velocity profiles in logarithmic scale. Both IDDES and SBES show a slight mismatch near the RANS-LES interface for the high-Re case, however capture the overall flow with good accuracy (\(Re_{\tau}=u_{\tau}h/\
u\) with \(u_{\tau}\)- friction velocity, h = half height of the channel, \(\
u\) = kinematic viscosity). The option to run SBES inside the boundary layer in both RANS and WMLES models offers many interesting opportunities. It allows complex geometries to be run and triggers the WMLES mode only once the mesh is of sufficient resolution to support it. The triggering process can be initiated by a synthetic turbulence generator.