# An Overview of Hybrid RANS-LES Models Developed for Industrial CFD
## 2 Large Eddy Simulation of Wall-Bound Flows  
To understand the motivation for the use of hybrid models, one must discuss the limitations of LES. LES has been the most widely explored SRS model over recent decades. It is based on the concept of resolving only large scales of turbulence and modeling the small scales. The classical motivation for LES is that the large scales are problem-dependent and difficult to model, whereas the smaller scales are more universal and isotropic and can be modeled more easily. LES is based on filtering the Navier-Stokes equations over a finite spatial region (typically the grid volume) and is aimed at only resolving the portions of turbulence larger than the filter width. Turbulence structures smaller than the filter are then modeled--typically using a simple eddy viscosity model. It is generally agreed that LES eddy viscosity models only model dissipation, not the physics of the feedback from small and large scales (\"backscatter\"). As a result, within the LES framework, all features and effects of the flow that are of interest and relevant to engineers must be resolved in space and time. This makes LES a very CPU-expensive technology. Most demanding is the application of LES to wall-bound flows. In the logarithmic near-wall layer, the turbulent length scale, \(\mathrm{L}_{t}\), of the large eddies can be expressed as:  
\[\mathrm{L}_{t}=\kappa y \tag{1}\]  
where \(y\) is the wall distance and \(\kappa\) is a constant. In other words, even the (locally) largest scales become very small near the wall and require a high resolution in all three space dimensions and in time. The linear dependence of \(\mathrm{L}_{t}\) on \(y\) indicates that the turbulence length scales approach zero near the wall, meaning an infinitely fine grid would be required to resolve them. However, this is not the case, as the molecular viscosity prevents scales smaller than the Kolmogorov limit. This is manifested by the viscous or laminar sublayer, a region very close to the wall, where small-scale turbulence is damped and does not need to be resolved. However, the viscous sublayer thickness is a function of the Reynolds number, Re, of the flow. At higher Re numbers, the viscous sublayer becomes thinner, thereby allowing the \"survival\" of smaller eddies that need to be resolved. This is depicted in Figure 1, showing a sketch of turbulence structures in the vicinity of the wall (e.g., channel flow with the flow direction oriented toward the observer). The left part of the picture represents a situation with a low Re number with the right part shows situation with a higher Re number. The grey box indicates the viscous sublayer for the two Re numbers. The structures inside the viscous sublayer (circles inside the grey box) are depicted but not active due to viscous damping. Only the structures outside of the viscous sublayer (i.e., above the grey box) exist and need to be resolved. Due to the reduced thickness of the viscous sublayer in the high Re case, substantially more resolution is required to resolve all active scales. The Wall-Resolved LES (WRLES) approach is, therefore, prohibitively expensive for moderate to high Reynolds numbers. This is the main reason why WRLES is not suitable for most engineering flows. The Reynolds number scaling can be reduced by the application of Wall Functions (WFLES) with ever increasing y+ values for higher Re numbers. There has been a renewed interest in recent years in advanced wall functions (e.g., [PERSON] et al. [28], [PERSON] et al. [29], [PERSON] et al. [30], and Lozano-Duran [31]). In principle, the application of WFLES allows the resolution of a boundary layer volume using a constant number of cells, independent of the Reynolds number. Figure 1: Sketch of turbulence structures for wall-bound channel flow with a viscous sublayer: (**a**) low Re number; (**b**) high Re number (light grey area = viscous sublayer). The final alternative to WRLES and WFLES is the Wall-Modeled LES (WMLES) approach.