Turbulence transport equations for variable-density turbulence and their relationship to two-field models

Abstract

This study gives an updated account of our current ability to describe multimaterial compressible turbulent flows by means of a one-point transport model. Evolution equations are developed for a number of second-order correlations of turbulent data, and approximations of the gradient type are applied to additional correlations to close the system of equations. The principal fields of interest are the one-point Reynolds tensor for variable-density flow, the turbulent energy dissipation rate, and correlations for density-velocity and density-density fluctuations. This singlefleld description of turbulent flows is compared in some detail to two-field flow equations for nonturbulent, highly dispersed flow with separate variables for each fleld. This comparison suggests means for improved modeling of some correlations not subjected to evolution equations.

Statistically steady measurements of Rayleigh-Taylor mixing in a gas channel

“…Over the past two decades, advances in modeling of variable density turbulence has led to introduction of various turbulence models which includes: spectral transport models (Besnard et al 1990;1992;Steinkamp et al 1995), two-fluid models (Andrews 1986;Youngs 1989) and Reynolds Stress/Bousinesq models (Snider & Andrews 1996).…”

“…These measurements will be used for validation of predictive turbulent transport models (Andrews 1986;Besnard et al 1990;1992;Snider & Andrews 1996;Steinkamp et al 1995;Youngs 1989) as mentioned earlier.…”

Comprehensive Approaches to Multiphase Flows in Geophysics - Application to nonisothermal, nonhomogenous, unsteady, large-scale, turbulent dusty clouds I. Hydrodynamic and Thermodynamic RANS and LES Models

“…Although RANS approaches have received considerable attention these past decades, these models have led to disappointing results with computer costs being higher and higher as the RANS models become more and more sophisticated [e.g., Sagaut et al, 1997;Lakehal 2002]. RANS approaches have been quite extensively developed for multiphase flows [e.g., Besnard et al, 1987Besnard et al, , 1992Simonin 1996;Kashiwa and Vanderheyden 2000;Peirano et al, 2001]. However, to the best of our knowledge, these multiphase models have never been applied to large-scale geophysical multiphase flows.…”

Introduction to Harlow's scientific memoir

“…The basic Navier-Stokes equations for the derivations are the same as we used for obtaining the constant-density Kepsilon model. By means of suitable manipulations, Rick Rauenzahn and Didier Besnard (visiting from France) joined with me in adding two more equations to describe the transport of the two new quantities [112,129]. Using the initials of the developers, the new technique came to be known as the BHR method.…”