Second-order modelling of a variable-density mixing layer

Publisher Website
Google Scholar
Abstract
A conventional (non-density-weighted) averaging method is used to study variable-density turbulent flows, in particular, a helium-nitrogen mixing layer. A careful order-of-magnitude analysis is carried out, first in relative density fluctuations, and then in the ratio of cross-stream to streamwise lengthscales. In this way it is shown that, to lowest order, in jets and shear layers, the turbulence is unafffected by the density fluctuations, and conventional models can be used. The non-uniform density distribution influences only the mean-continuity and mean-momentum equations. Calculations (using a new form for the scalar-dissipation equation based on relaxation to an equilibrium timescale ratio) show good agreement with experiment. Calculation with a less truncated system indicates that neglected terms have little effect. We use a modified Patankar-Spalding method that overcomes numerical stability difficulties.