diff --git a/modules/navier_stokes/doc/content/source/fvbcs/INSFVTurbulentViscosityWallFunction.md b/modules/navier_stokes/doc/content/source/fvbcs/INSFVTurbulentViscosityWallFunction.md index 5d70645d228f..0df2d34f9ece 100644 --- a/modules/navier_stokes/doc/content/source/fvbcs/INSFVTurbulentViscosityWallFunction.md +++ b/modules/navier_stokes/doc/content/source/fvbcs/INSFVTurbulentViscosityWallFunction.md @@ -20,9 +20,18 @@ without the need of fully resolving the gradients at the near wall region. \tau_w = /frac{ \mu_w u_p}{y_p} \end{equation} -To obtain the relationship between the wall shear stress and the dimensionless wall distance, -four different formulations are supportedas defined by the -[!param](/FVBCs/INSFVTurbulentViscosityWallFunction/wall_treatment) parameter. +where: + +- $\mu_w = \mu + \mu_t$ is the total viscosity evaluated at the wall face +- $\mu_t$ is the turbulent viscosity, evaluated at the wall for the purpose of this boundary condition +- $\mu$ is the kinematic viscosity, evaluated at the wall for the purpose of this boundary condition +- $\tau_w$ is the wall-shear stress +- $u_p$ is the wall-parallel velocity at the centroid +- $y_p$ is the wall normal distance to the centroid + +To impose a correct boundary condition for $\mu_t$, as seen in the Equation above, we need to compute $\tau_w$ using analytical +relationships between the wall shear stress and the dimensionless wall distance $y^+$. For this purpose, four different +formulations are supported as defined by the [!param](/FVBCs/INSFVTurbulentViscosityWallFunction/wall_treatment) parameter. To set the grid spacing for the first cell near the wall in your mesh, we recommend using the Auxiliary Kernel [RANSYPlusAux.md] @@ -46,6 +55,7 @@ for the turbulent viscosity. where: - $\rho$ is the density +- $\mu$ is the kinematic viscosity - $u_{\tau} = \sqrt{\frac{\tau_w}{\rho}}$ is the friction velocity and $\tau_w$ is the wall friction - $y_p$ is the distance from the boundary to the center of the near-wall cell - $u_p$ is the parallel velocity to the boundary computed at the center of the near-wall cell