Subgrid Scale Model for Finite Difference Simulations of Turbulent Flows in Plane Channels and Annuli

High Reynolds number turbulent flows of incompressible fluids in plane channels and annuli are simulated using a finite difference procedure which integrates the NavierStokes equations in time and in three-dimensional space. This paper describes the finite difference procedure and the subgrid scale (SGS) motion model. The model differs from earlier ones in the following points. The finite difference equations are based on integral conservation equations for each grid volume. As a consequence the SGS stresses are defined as surface mean rather than grid volume mean values of the fluctuating velocity products. This allows us to identify and model the effects of anisotropic grids (especially unequally sided grid volumes) and anisotropic finite difference operators. In this model SGS stresses are split into two parts, one accounting for locally isotropic turbulence, the other for inhomogeneous effects. This results in a model which is meaningful even if the size of the grid volumes is very large. The SGS kinetic energy is calculated using a separate transport equation. The boundary conditions are formulated in a manner consistent with the SGS theory. The method may be used for plane channels and annuli as well, and has been used to simulate flows with up to 65,536 grid volumes. The results agree rather well with experimental values, even for a smaller number of grid volumes.