A Hybrid Finite Volume/PDF Monte Carlo Method to Capture Sharp Gradients in Unstructured Grids

The hybrid finite volume/PDF Monte Carlo method has both the advantages of the finite volume method’s efficiency in solving flow fields and the PDF method’s exactness in dealing with chemical reactions. It is, therefore, increasingly used in turbulent reactive flow calculations. In order to resolve the sharp gradients of flow velocities and/or scalars, fine grids or unstructured solution -adaptive grids have to be used in the finite volume code. As a result, the calculation domain is covered by a grid system with very large variations in cell size. Such grids present a challenge for a combined PDF/Monte Carlo code. To date, PDF calculations have generally been carried out with large cells, which assure that each cell has a statistically meaningful number of particles. Smaller cells would lead to smaller numbers of particles and correspondingly larger statistical errors. In this paper, a particle tracing scheme with adaptive time step and particle splitting and combination is developed, which allows the PDF/Monte Carlo code to use any grid that is constructed in the finite volume code. This relaxation of restrictions on the grid makes it possible to couple PDF/Monte Carlo methods to all popular commercial CFD codes and, consequently, extend existing CFD codes’ capability to simulate turbulent reactive flow in a more accurate way. To illustrate the solution procedure, a PDF/ Monte Carlo code is combined with FLUENT to solve a turbulent diffusion combustion problem in an axisymmetric channel.