Scale-Resolving Hybrid (SRH) Turbulence

The Scale-Resolving Hybrid (SRH) turbulence model is a continuous hybrid RANS-LES model that combines the accurate prediction capabilities of LES with the low numerical cost of RANS. On fine meshes and when the time step is small, the SRH approach allows a RANS model to continuously switch to LES mode and resolve unsteady information of large-scale turbulent structures. In Simcenter STAR-CCM+, this hybrid method can be applied to K-Epsilon and K-Omega models.

The equations that are solved for the SRH approach are obtained by a spatial-temporal filtering. Each solution variable $ϕ$ is decomposed into a filtered value $\bar{\tilde{ϕ}}$ and a subfiltered value $ϕ'$ :

Figure 1. EQUATION_DISPLAY

ϕ = \bar{\tilde{ϕ}} + ϕ'

(256)

where $ϕ$ represents velocity components, pressure, energy, or species concentration.

The SRH filter ensures that for large filter time-width, the transport equations are equivalent to the RANS equations, and for short filter-width, the equations are equivalent to LES. Between these time scales, the time step and the mesh size determine the resolution of the turbulent structures. For more background information, see [337].

Inserting the decomposed solution variables into the Navier-Stokes equations results in filtered transport equations for mass, momentum, and energy that look identical to the transport equations that are solved for RANS and LES simulations. However, the stress tensor $T_{S F S}$ now represents the subfiltered scale stresses.

These stresses are modeled using the Boussinesq approximation:

Figure 2. EQUATION_DISPLAY

T_{S F S} = 2 μ_{t} S - \frac{2}{3} ρ k_{S F S} I

(257)

where:

$S$ is the strain rate tensor given by Eqn. (1130) and computed from the resolved velocity field $\bar{\tilde{v}}$ .
$ρ$ is the density.
$k_{S F S}$ is the subfilter scale turbulent kinetic energy.
$I$ is the identity tensor.

The turbulent eddy viscosity $μ_{t}$ is defined by the respective RANS model and is a function of turbulent time scale and turbulent kinetic energy. For the SRH approach, the subfilter scale turbulent kinetic energy $k_{S F S}$ is given by the solution of a transport equation that looks identical to the respective RANS equation. However, $ε$ is replaced with $ψ_{H} ε$ where the parameter $ψ_{H}$ incorporates a shielding function that prevents the LES mode from being applied in the near-wall regions.