Wall Boundary Conditions

AcuSolve supports three different approaches for computing the flow near no-slip walls. These options enable you to choose whether you want to compute the near wall flow profile explicitly or approximate the near wall flow using a wall function.

The first option for computing turbulent boundary layers is to fully resolve them. When computing the near wall gradients explicitly, AcuSolve integrates the governing equations directly to the wall. As a result, this option is more accurate, provided that sufficient mesh density is used.

y^{+}

$y^{+}$ (defined below) of the first mesh point must be less than 10 (preferably 5); otherwise, gross errors in traction, heat flux, and mass transfer may result. This option is typically used for applications where the near wall flow profile plays an important role in the physics of the simulation, that is, cases having adverse pressure gradients, flow separation, and so on. This option is activated by specifying the turbulence_wall_type = low_reynolds_number (or low_re) parameter in the SIMPLE_BOUNDARY_CONDITION command.(1)

y^{+} = \frac{ρ y u^{*}}{μ}

$y^{+} = \frac{ρ y u^{*}}{μ}$

where $μ$ $μ$ is the viscosity, $u^{*} = \sqrt{\frac{τ_{w}}{ρ}}$ $u^{*} = \sqrt{\frac{τ_{w}}{ρ}}$ is the turbulent friction velocity, $τ_{w}$ $τ_{w}$ is the wall shear stress, $ρ$ $ρ$ is the density.

The second type of wall treatment for turbulent boundary layers allows you to approximate the near wall flow field, without using fine near wall mesh, by employing wall functions. This approach can greatly reduce the size of a mesh by eliminating the need for fine mesh spacing normal to no-slip walls. When this approach is applied, AcuSolve assumes a shape for the near wall flow field. This assumed profile is based on the “Law of the Wall” for turbulent boundary layers. The “Law of the Wall” is a relation that is based on theoretical and experimental arguments and relates the stream wise velocity profile with the normal distance from the wall. This relation was formulated for fully developed boundary layers with favorable pressure gradients. This option is activated by specifying the turbulence_wall_type = wall_function (or func) parameter in the SIMPLE_BOUNDARY_CONDITION command. $y^{+}$ $y^{+}$ of the first mesh point may be as large as 300.