APPLICATION OF PDF METHODS TO COMPRESSIBLE TURBULENT FLOWS

A particle method applying the probability density function (PDF) appr oach to turbulent compressible flows is presented. The method is appli ed to several turbulent flows, including the compressible mixing layer , and good agreement is obtained with experimental data. The PDF equat ion is solved using a Lagrangian/Monte Carlo method. To accurately acc ount for the effects of compressibility on the flow, the velocity PDF formulation is extended to include thermodynamic variables such as the pressure and the internal energy. The mean pressure, the determinatio n of which has been the object of active research over the last few ye ars, is obtained directly from the particle properties. It is therefor e not necessary to link the PDF solver with a finite-volume type solve r. The stochastic differential equations (SDE) which model the evoluti on of particle properties are based on existing second-order closures for compressible turbulence, limited in application to low turbulent M ach number flows. Tests are conducted in decaying isotropic turbulence to compare the performances of the PDF method with the Reynolds-stres s closures from which it is derived, and in homogeneous shear flows, a t which stage comparison with direct numerical simulation (DNS) data i s conducted. The model is then applied to the plane compressible mixin g layer, reproducing the well-known decrease in the spreading rate wit h increasing compressibility. It must be emphasized that the goal of t his paper is not as much to assess the performance of models of compre ssibility effects, as it is to present an innovative and consistent PD F formulation designed for turbulent inhomogeneous compressible flows, with the aim of extending it further to deal with supersonic reacting flows. (C) 1997 American Institute of Physics.