On recontamination and directional-bias problems in Monte Carlo simulation of PDF turbulence models
Turbulent combustion can not be simulated adequately by conventional moment closure turbulence models. The difficulty lies in the fact that the reaction rate is in general an exponential function of the temperature, and the higher order correlations in the conventional moment closure models of the chemical source term can not be neglected, making the applications of such models impractical. The probability density function (pdf) method offers an attractive alternative: in a pdf model, the chemical source terms are closed and do not require additional models. A grid dependent Monte Carlo scheme was studied, since it is a logical alternative, wherein the number of computer operations increases only linearly with the increase of number of independent variables, as compared to the exponential increase in a conventional finite difference scheme. A new algorithm was devised that satisfies a restriction in the case of pure diffusion or uniform flow problems. Although for nonuniform flows absolute conservation seems impossible, the present scheme has reduced the error considerably.