Direct numerical simulation and Lagrangian modeling of joint scalar statistics in ternary mixing

Abstract

Direct numerical simulation (DNS) results are presented for the joint statistics of two inhomogeneous scalar fields, one due to a mixing layer source and the other due to a contiguous top-hat source. These two sources form the basis for all scalar mixing across three streams. The results are used to assess the performance of a Lagrangian stochastic modeling system incorporating the interaction with the conditional mean mixing model at two different times: A near-field time when there is little spatial overlap between the two scalar fields, and a far-field time when there is strong overlap. In the near field we find that for both the model and the DNS, the joint probability density function is essentially confined to two lines in concentration phase space; the diagonal ψ1+ψ2=1 and the axis ψ1=0, where ψ1 and ψ2 are the phase space concentrations for the mixing layer and top-hat scalars, respectively. The model and DNS results along these sections are in excellent quantitative agreement for a range of statistics. In the far field the DNS results show significant levels of probability density throughout the concentration domain ψ1+ψ2⩽1, but the model results have a much more limited range in the top-hat scalar, with less unmixed fluid reflecting excessive mixing. This inevitably results in quantitative differences in other statistics, but the conditional mean diffusion for the model shows semiquantitative agreement with the DNS. The most striking difference between model and DNS results in the far field is shown in the conditional mean velocity for which the model shows oscillations in sign not present in the DNS.