A model for turbulent mixing based on shadow-position conditioning

Abstract

In the modeling and simulation of mixing and reaction in turbulent flows using probability density function (PDF) methods, a key component is the mixing model, which represents the mixing effected by molecular diffusion. A new model, called the shadow-position mixing model (SPMM), is introduced and its performance is illustrated for two test cases. The model involves a new variable—the shadow position—and mixing is modeled as a relaxation of the composition to its mean conditional on the shadow position. The model is constructed to be consistent with turbulent dispersion theory, and to be local in the composition space, both to adequate approximations. The connections between the SPMM and previous mixing models are discussed. The first test case of a scalar mixing layer shows that the SPMM yields scalar statistics in broad agreement with experimental data. The second test case of a reactive scalar mixing layer with idealized non-premixed combustion shows that the SPMM correctly yields stable combustion, whereas simpler models incorrectly lead to extinction. The model satisfies all required realizability and transformation properties and correctly yields Gaussian distributions in appropriate circumstances. The SPMM is generally applicable to turbulent reactive flows using different PDF approaches in the contexts of both Reynolds-averaged Navier-Stokes modeling and large-eddy simulation.