Modeling of turbulent mixing in opposed jet configuration: One-dimensional Monte Carlo probability density function simulation

A one-dimensional numerical model of turbulent mixing in an opposed jet configuration is presented with Monte Carlo simulation of joint scalar probability density function (PDF). The formulation is based on axisymmetric flowfield along its centerline. Due to the one-dimensionality, one can afford a large number of stochastic particles in the PDF Monte Carlo simulation such that statistical uncertainty is reduced to a negligible level. With this accurate numerical representation, we investigate the importance of specification of mixing time (or frequency) in two commonly used mixing models, namely, the modified Curl's mixing model and the interaction by exchange with the mean (IEM) model (or the linear mean square estimation model). The effect of mixing time on the predicted results is investigated by varying the ratio between the turbulence turnover time and the turbulent mixing time. For the experimental data of Sardi et al. (1998), excellent agreement between predictions and the measurements is achieved by using a constant time ratio. A similarly good agreement is also seen in the PDF distributions. An analysis of the computed results reveals a strong correlation between the PDF shape and the peak level of the variance of the mixture fraction. However, it has not been possible for the numerical model to match simultaneously both the variances and the PDF shapes for the experimental results of Mastorakos et al. (1994). Further experiments on the detailed mixing properties in the opposed jet configuration are warranted to establish a comprehensive set of data for validation of numerical models.