An a priori DNS study of the shadow-position mixing model

The modeling of mixing by molecular diffusion is a central aspect for transported probability density function (tPDF) methods. In this paper, the newly-proposed shadow position mixing model (SPMM) is examined, using a DNS database for a temporally evolving di-methyl ether slot jet flame. Two methods that invoke different levels of approximation are proposed to extract the shadow displacement (equivalent to shadow position) from the DNS database. An approach for a priori analysis of the mixing-model performance is developed. The shadow displacement is highly correlated with both mixture fraction and velocity, and the peak correlation coefficient of the shadow displacement and mixture fraction is higher than that of the shadow displacement and velocity. This suggests that the composition-space localness is reasonably well enforced by the model, with appropriate choices of model constants. The conditional diffusion of mixture fraction and major species from DNS and from SPMM are then compared, using mixing rates that are derived by matching the mixture fraction scalar dissipation rates. Good qualitative agreement is found, for the prediction of the locations of zero and maximum/minimum conditional diffusion locations for mixture fraction and individual species. Similar comparisons are performed for DNS and the IECM (interaction by exchange with the conditional mean) model. The agreement between SPMM and DNS is better than that between IECM and DNS, in terms of conditional diffusion iso-contour similarities and global normalized residual levels. It is found that a suitable value for the model constant c that controls the mixing frequency can be derived using the local normalized scalar variance, and that the model constant a controls the localness of the model. A higher-Reynolds-number test case is anticipated to be more appropriate to evaluate the mixing models, and stand-alone transported PDF simulations are required to more fully enforce localness and to assess model performance.