Robust Numerical Wall Functions Implemented in OpenFOAM

Licentiate thesis, 2016

This thesis presents two new numerical wall models for computing Reynolds-Averaged- Navier-Stokes (RANS) equations with low-Reynolds-number turbulence models. The objective is to considerably reduce the total central processing unit (CPU) cost of the numerical simulations of wall bounded flows while maintaining the accuracy of any low-Reynolds-number turbulence model. When calculating turbulent flow problems, a tremendous speed-up may be achieved by decoupling the solution of the boundary layer from the bulk region by use of a wall function. However, most wall functions are quite limited and based on assumptions which are not valid in complex, non-equilibrium flows. A decade ago, the numerical wall function was born at the University of Manchester [9], [7], solving boundary-layer-type transport equations across the boundary layer on a separate sub-grid. This approach removed most assumptions, but introduced a strong coupling to the turbulence model, and hence, made it cumbersome to implement and maintain. The present wall functions solve full momentum and energy equations on a sub-grid, using face fluxes of advection and dissipation to transfer the solution to and from the sub-grid. The innovative use of face fluxes, decouples the wall function from the turbulence models’ production and dissipation terms, and hence, makes it general to all low-Reynolds- number turbulence models. It has been tested on channel flow, axisymmetric impinging jet, and backward facing step using Launder-Sharma turbulence model [16]. Compared to low-Reynolds-number calculations, the results show perfect agreement to one-sixth of the computational cost. Further on, an attempt to update the general recommendation on grid design for low-Reynolds-number turbulence models is also made.