On the Non-Dimensionalisation of the Navier-Stokes Equations. On its Implementation in FLOWer. Related User-Guide.

Abstract

The DLR code FLOWer handles the non-dimensionalised form of the Reynolds-averaged Navier-Stokes equations. The report intends to give a clear view of the background, of all explicit or implicit conventions used and of the actual implementation. In doing so, it has been kept in mind the underlying original question: How can I transform FLOWer results into dimensional quantities? The first part is devoted to the non-dimensionalisation of the Navier-Stokes equations on a theoretical level excluding any reference to a CFD code. This process is extended in the second part to the Reynolds-averaged equations and to transport equation turbulence models. The third section examines implementation details in the frame of FLOWer 116.3. Finally simple recipes are provided to go back and forth from user-supplied dimensional geometry and flow conditions to non-dimensional FLOWer input parameters and output results.