Hybrid LES/RANS models

Hybrid RANS/LES methods involve modifications to existing Reynolds-averaged closures to provide a scale-resolving functionality in regions of the computational domain with sufficient grid resolution to support the resolution of turbulent structures. In practice, this usually implies an attempt at resolving some fraction of the turbulence in free shear flows and possibly the outer portion of turbulent boundary layers. Given this vision, a large percentage of the hybrid RANS/LES models can be represented as some sort of blend between the equations governing the Reynolds-averaged and spatially-filtered Navier-Stokes equations (or a sub-set of these equations). For instance, some hybrid formulations involve a blending of the modeled turbulent viscosity, e.g., Choi et al. (2009) and Gieseking et al. (2011):

\begin{equation}F \,[{\rm eddy\, viscosity}] + (1 – F) \,[{\rm SGS\, viscosity}]\,,\end{equation}

while others suggest a blend of the turbulent length scale, e.g., Shur et al. (2008)

\begin{equation}F \,[{\rm modeled\, RANS\, turbulent\, length\, scale}] + (1-F)\, [{\rm SGS\, length\, scale}]\,,\end{equation}

where \(F\) is a blending function that is unity in regions of the flow intended for RANS, and zero in regions intended to be scale-resolved. While not all hybrid RANS/LES models are designed to provide a wall-modeled LES functionality, several formulations have been developed with this simulation strategy in mind. However, it should be emphasized that for any hybrid RANS/LES formulation to function as an effective wall-modeled LES, the underlying grid must provide a level of grid resolution that can capture a high fraction of the turbulence energy in the outer portion of the boundary layer. This requirement forces the use of more isotropic grid elements within the boundary layer as compared with hybrid RANS/LES formulations that treat the entire boundary layer as a RANS region. While there is no substitute for grid resolution studies to gauge the appropriateness of grids developed for this purpose, there are some useful guidelines to consider when constructing grids for hybrid RANS/LES simulations with wall-modeled LES functionality.