An explicit Runge-Kutta method for turbulent reacting flows calculations

Abstract

The paper deals with a numerical method for the solution of the conservation equations governing steady, reacting, turbulent viscous flows in two dimensional geometries, in both cartesian and axisymmetric coordinates. These equations are written in Favre-averaged form and closed with a first order model. A two-equation K-ɛ model, where low Reynolds number and compressibility effects are included, and a modified eddy-breack up model are used to simulate fluid mechanics turbulence, chemistry and turbulence-combustion interaction. The solution is obtained by using a pseudo-unsteady method with improved perturbation propagation properties. The equations are discretized in space by using a finite volume formulation. An explicit, multi-stage, dissipative Runge-Kutta algorithm is then used to advance the flow equations in the pseudo-time. The method is applied to the computation of both diffusion and premixed turbulent reacting flows. The computed temperature distributions compare favorably with experimental data.