A unified wall function for compressible turbulence modelling

Turbulence modelling near the wall often requires a high mesh density clustered around the wall and the first cells adjacent to the wall to be placed in the viscous sublayer. As a result, the numerical stability is constrained by the smallest cell size and hence requires high computational overhead. In the present study, a unified wall function is developed which is valid for viscous sublayer, buffer sublayer and inertial sublayer, as well as including effects of compressibility, heat transfer and pressure gradient. The resulting wall function applies to compressible turbulence modelling for both isothermal and adiabatic wall boundary conditions with the non-zero pressure gradient. Two simple wall function algorithms are implemented for practical computation of isothermal and adiabatic wall boundary conditions. The numerical results show that the wall function evaluates the wall shear stress and turbulent quantities of wall adjacent cells at wide range of non-dimensional wall distance and alleviate the number and size of cells required.