Standard k-epsilon, RNG k-epsilon, Realizable k-epsilon turbulence models

Understand how the flow solver calculates the near-wall turbulent viscosity for various k-epsilon turbulence models and for models with immersed boundary meshes.

The flow solver calculates the near wall turbulent viscosity as

• l_t = f_lκy is the turbulence length scale.
• f_l is the damping factor. For more information, see Mixing length turbulence model.

In the log-law region, the near-wall relation is given by:

• U_f is the fluid velocity at distance y from the wall.
• κ is the Von Karman constant.
• is a dimensionless wall distance for a wall bounded flow:
• is the shear velocity.

Using the previous equations, the wall shear stress, τ_w, is given by:

The near wall transport equation for Standard k-epsilon model is replaced by:

where f_ε is a near wall damping function [17] given by:

The near wall production of turbulent kinetic energy is evaluated from:

The k-epsilon models always uses the standard wall function to approximate the mean velocity field in the near-wall region of the boundary layer.

Immersed boundary method

When you use the standard k-epsilon turbulence model with immersed boundary meshes, the following equations are used based on the Dirichlet boundary condition in the IBM discretization method, to compute the k and ε values, respectively:

where:

• is the node sector average of the wall distance value, assessed at the halo node, where the flow solver applies the imposed boundary condition.
• f_ε is the near wall damping function.

The near wall damping function is:

where A_ε = 3.8 is the damping function constant.

The near wall production of turbulent kinetic energy is computed as:

The near wall turbulent viscosity is computed as:

where f_μ is the damping function and computed as:

where A_μ = 63 is the damping function constant.