Two-dimensional nonstationary causal stochastic model for turbulence/radiation interactions in flames

Abstract

A new stochastic method is presented to treat turbulence/radiation interactions. In order to simulatethe random field of instantaneous mixture fraction distributions along the radiation path, a two-dimensional (2D) nonstationary causal stochastic model is proposed. The model can account for not only the first-order correlations both in time space and geometric space but also the first-order cross correlation. Also presented is a general proof that in the simulation of the mixture fraction, the contributions from the first-order correlations in time and geometric spaces are important and so is the contribution from the first-order time-geometric space cross correlation. Furthermore, the second- and higher-order correlation terms are proved to be negligibly small. They provide the foundation for the general development of the present two-dimensional and future three-dimensional stochastic models for turbulence-radiation interactions. Finally, application of the proposed two-dimensional causal model to simulate the radiation process in turbulent carbon monoxide/hydrogen/air flames is illustrated. The predicted mean and fluctuating radiation properties are found to be in good agreement with experimental data.