The solution of coupled flow and chemistry problems. (29th August 2007) - Holm-Christensen, O.; Jones, I.P.; Wilkes, N.S.; Splawski, B.A.; Stopford, P.J.
Computational Fluid Dynamics has had remarkable success in the solution of many industrial problems. One area of current difficulty is in the interaction of flow and chemistry, where there is a strong feedback between the fluid flow and the chemistry, and where the details of the chemical interactions are very important, for example in the production of pollutants. For turbulent flows, the conventional models typically assume a small number of reactions, with the overall time scales for the reactions determined by the turbulent mixing, rather than by the shorter time scales of the chemical reactions. However, it is now becoming important to include detailed chemical interactions into multi-dimensional CFD calculations. These problems can have a range of relevant time scales, leading to stiff and highly non-linear systems of equations, which cause the traditional CFD algorithms to converge very slowly. This paper describes an approach implemented in CFX 4.2 based upon operator splitting, where the flow and chemistry are effectively decoupled, with appropriate solvers used for the different models. In this case, a Newton method is used for the chemical interactions, with the coupled non-linear equations for the chemical species and enthalpy solved using a direct method at each point. These are coupled to calculations for the advection and diffusion of the species using the standard solver in CFX-4.2. The method also uses an automatic acceleration procedure, based upon the different time scales for the flow and the chemistry, to obtain faster convergence. The paper also presents some industrial applications of the coupled flow and chemistry solver. These applications include: comparisons of the method against results from the Chemkin package, for a large number of chemical reactions; laminar combustion in small scale systems, such as a domestic gas burner; complex chemical reactions in radial packed beds. These applications illustrate the experience gained with the method on these challenging problems and highlight the benefits to be gained from the coupled solver.