A Monte Carlo Method for the PDF Equations of Turbulent Reactive Flow

Abstract —A Monte Carlo method is presented which simulates the transport equations of joint probability density functions (pdf's) in turbulent flows. (Finite-difference solutions of the equations are impracticable, mainly because of the large dimensionality of the pdf's). Attention is focused on an equation for the joint pdf of chemical and thermodynamic properties in turbulent reactive flows. It is shown that the Monte Carlo method provides a true simulation of this equation, and that the amount of computation required increases only linearly with the number of properties considered. Consequently, the method can be used to solve the pdf equation for turbulent flows involving many chemical species and complex reaction kinetics. Test calculations are reported that demonstrate the method and determine the influence of the numerical parameters. The method is then used to calculate pdf's of temperature in a turbulent mixing layer, and the calculations are found to be in good agreement with the measurements of Batt (1977). The method has previously been used to calculate the joint pdf of three reactive species in a premixed flame (Pope, 1981a).