Two-Layer Models

A two-layer model solves for $k$ but prescribes $\epsilon$ algebraically with distance from the wall in the viscosity dominated near-wall flow regions. In Simcenter STAR-CCM+, this approach is available with both the Standard and the Realizable K-Epsilon models.

For the two-layer models the dissipation rate near the wall is simply prescribed as:

where:

• $l_{\epsilon }$ is a length scale function that is calculated depending on the Model Variant.

As per the suggestion of Jongen [307], the following wall-proximity indicator is used to combine the two-layer formulation with the full two-equation model:

where:

• ${\text{Re}}_d$ is the wall-distance Reynolds number given by Eqn. (1134).
• ${\text{Re}}_y^{*}$ defines the limit of applicability of the two-layer formulation and is a Model Coefficient.
• $A$ determines the width of the wall-proximity indicator and is defined such that the value of $\lambda$ is within 1% of its far-field value for a given variation of $\Delta {\text{Re}}_y$:

  $$A=\frac{\left|\Delta {\text{Re}}_y\right|}{\mathrm{atanh}0.98}$$

  (1195)

  where $\Delta {\text{Re}}_y$ is a Model Coefficient.

The turbulent viscosity from the K-Epsilon model ${{\mu }_t|}_{k-ϵ}$ is then blended with the two-layer value as follows:

where:

• ${\left(\frac{{\mu }_t}{\mu }\right)}_{2layer}$ is calculated depending on the Model Variant.