# An Overview of Hybrid RANS-LES Models Developed for Industrial CFD
## 3 Global Hybrid RANS-LES Models  
Many hybrid RANS-LES methods have been developed in the last two decades, following the original proposal by [PERSON] [8]. From an industrial standpoint, mostly models of the DES family, and in the case of ANSYS the SAS (e.g., [PERSON] and [PERSON] [11], [PERSON] et al. [12]) and SBES models ([PERSON] [19]), have had wider impacts. Since the introduction of the SBES model, it has essentially replaced the older hybrid models in ANSYS and is now widely used in many applications (see [PERSON] et al. [35], [PERSON] and [PERSON] [36], [PERSON] and [PERSON] [37]). The SBES model is considered by the current authors as \"optimal\", as it satisfies the following properties:  
* It is a building block method, allowing existing RANS and LES methods to be combined;
* Allows asymptotic shielding of the RANS boundary layer under mesh refinement;
* Provides an optimal \"transition\" from RANS to LES;
* Can operate in WMLES mode;
* Is low cost. The SBES model is based on the blending of existing RANS and LES models using:  
\[\tau_{\rm ij}^{\rm SBES}=f_{\rm SBES}\cdot\tau_{\rm ij}^{\rm RANS}+(1-f_{\rm SBES })\cdot\tau_{\rm ij}^{\rm LES} \tag{2}\]  
where \(\tau_{\rm ij}^{\rm RANS}\) is the RANS part and \(\tau_{\rm ij}^{\rm LES}\) the LES part of the modeled stress tensor. If both model portions are based on eddy viscosity concepts, the formulation simplifies to a blend of the eddy viscosities:  
\[\
u_{\rm t}^{\rm SBES}=f_{\rm SBES}\cdot\
u_{\rm t}^{\rm RANS}+(1-f_{\rm SBES })\cdot\
u_{\rm t}^{\rm LES} \tag{3}\]  
The key element is the blending function \(f_{\rm SBES}\), which is \(f_{\rm SBES}=1\) inside boundary layers and \(f_{\rm SBES}=0\) for separated and free shear flows. It is essential that the function remains at \(f_{\rm SBES}=1\) inside boundary layers to shield the boundary layer from any impact from the LES model. Premature switching to the LES model inside the boundary layer would result in failure. This can be demonstrated for a diffuser flow, as shown in Figure 6. In this test case, the boundary layer flows in the axial direction of the inner cylinder. A pressure gradient is imposed by an outwards expanding slip wall. The pressure gradient results in significant thickening of the boundary layer. The purpose of this test is not to demonstrate the accuracy of the RANS models, but to show the behavior of different shielding functions and their impacts on the eddy viscosity distribution inside the boundary layer. Figure 5: Velocity profiles in the center plane for three meshes of WMLES compared to experimental data on different WMLES meshes. Figure 7 shows the comparison of SBES and DDES shielding functions for the diffuser flow. The SBES shielding covers the entire boundary layer, including the rapid growth area due to the separation bubble, while DDES preserves only the thin boundary layer near the inlet. This means that in the adverse pressure gradient region, the shielding properties of DDES are substantially impaired for this case. This has consequences for the eddy viscosity fields shown in Figure 8. The ratio of the eddy viscosity to molecular viscosity for the SBES approach corresponds to the ratio for the SST model, while the DDES model produces much reduced levels in the adverse pressure gradient region. This can lead to grid-induced separation (GIS), a highly undesirable situation, whereby grid refinement leads to artificial separations ([PERSON] and [PERSON] [38]). The RANS-LES transition is an artificial process that occurs in the region where the hybrid model switches from RANS mode to LES mode. In this process, the upstream RANS turbulence content is lost, as the RANS model is essentially turned off, while no resolved LES content is yet available. To preserve the consistency of the simulation, it is essential that the resolved turbulence is created as quickly as possible in order to achieve a balanced flow field. This \"transition\" process depends on many details, such as the grid resolution, the numerical dissipation, and the details of the hybrid model.