Accurate and computationally efficient mixing models for the simulation of turbulent mixing with PDF methods

Different simulation methods are applicable to study turbulent mixing. When applying probability density function (PDF) methods, turbulent transport, and chemical reactions appear in closed form, which is not the case in second moment closure methods (RANS). Moreover, PDF methods provide the entire joint velocity-scalar PDF instead of a limited set of moments. In PDF methods, however, a mixing model is required to account for molecular diffusion. In joint velocity-scalar PDF methods, mixing models should also account for the joint velocity-scalar statistics, which is often under appreciated in applications. The interaction by exchange with the conditional mean (IECM) model accounts for these joint statistics, but requires velocity-conditional scalar means that are expensive to compute in spatially three dimensional settings. In this work, two alternative mixing models are presented that provide more accurate PDF predictions at reduced computational cost compared to the IECM model, since no conditional moments have to be computed. All models are tested for different mixing benchmark cases and their computational efficiencies are inspected thoroughly. The benchmark cases involve statistically homogeneous and inhomogeneous settings dealing with three streams that are characterized by two passive scalars. The inhomogeneous case clearly illustrates the importance of accounting for joint velocity-scalar statistics in the mixing model. Failure to do so leads to significant errors in the resulting scalar means, variances and other statistics.