Calculations of subsonic and supersonic turbulent reacting mixing layers using probability density function methods

Abstract

A particle method applying the probability density function (PDF) approach to turbulent compressible reacting flows is presented. The method is applied to low and high Mach number reacting plane mixing layers. Good agreement is obtained between the model calculations and the available experimental data. The PDF equation is solved using a Lagrangian Monte Carlo method. To represent the effects of compressibility on the flow, the velocity PDF formulation is extended to include thermodynamic variables such as the pressure and the internal energy. Full closure of the joint PDF transport equation is made possible in this way without coupling to a finite-difference-type solver. The stochastic differential equations (SDE) that model the evolution of Lagrangian particle properties are based on existing models for the effects of compressibility on turbulence. The chemistry studied is the fast hydrogen–fluorine reaction. For the low Mach number runs, low heat release calculations are performed with equivalence ratios different from one. Heat release is then increased to study the effect of chemical reaction on the mixing layer growth rate. The subsonic results are compared with experimental data, and good overall agreement is obtained. The calculations are then performed at a higher Mach number, and the results are compared with the subsonic results. Our purpose in this paper is not to assess the performances of existing models for compressible or reacting flows. It is rather to present a new approach extending the domain of applicability of PDF methods to high-speed combustion.