Anisotropic Porosity Formulation of the Coarse-Grid-CFD (CGCFD)

Computational fluid dynamics (CFD) simulations for large complex geometries such as a complete reactor core of a nuclear power plant requires exceedingly huge computational resources. State of the art computational power and CFD software is restricted to simulations of representative sections of these geometries. The conventional approach to simulate such complex geometries is 1D subchannel analysis employing experimental correlations in the transport models. With the development of the Coarse-Grid-CFD (CGCFD) ( [1], [4], [7]), an alternative to the traditional 1D subchannel analysis becomes available which does not need empirical correlations nor specific model constants. The CGCFD approach is based on strongly under-resolved CFD and the inviscid Euler equations. Although the use of the Euler equations and coarse grids does not resolve the subgrid physics like viscous dissipation or turbulence, the subgrid physical information is taken into account by volumetric source terms derived from fully resolved representative CFD simulations. Non-resolved geometrical information due to the use of very coarse meshes is taken into account by volume porousi-ties and directional surface permeabilities in the finite volume scheme. The volume porosity is defined as the ratio of the control volume that is occupied by the fluid compared to the complete control volume. The surface permeability is defined as the ratio of the individual control surface that is unobstructed to fluid flow compared to the corresponding complete control surface. Due to the use of the volumetric source terms that are derived from fully resolved CFD simulations, distributed resistance used in standart porous media approaches may be omitted and instead be resolved through the volumetric source terms. This is advantageous because the friction factor normally is not very well known in thermal-hydraulic problems and must be derived from comprehensive experiments. Such an anisotropic porosity formulation was originally used in the COMMIX [6] code which was designed to compute complex flow applications in a time when computational resources were limited. The benefits and limitations of our technique are explored by simulating a section of a water rod bundle containing a spacer. General recommendations for the proper application of our technique are presented in this work.