Application of a second-moment closure model to mixing processes involving multicomponent miscible fluids

Abstract

A second-moment closure model is proposed for describing turbulence quantities in flows where large density fluctuations can arise due to mixing between different density fluids, in addition to compressibility or temperature effects. The turbulence closures used in this study are an extension of those proposed by Besnard et al., which include closures for the turbulence mass flux and density-specific-volume covariance. Current engineering models developed to capture these extended effects due to density variations are scarce and/or greatly simplified. In the present model, the density effects are included and the results are compared to direct numerical simulations (DNS) and experimental data for flow instabilities with low to moderate density differences. The quantities compared include Reynolds stresses, turbulent mass flux, mixture density, density-specific-volume covariance, turbulent length scale, turbulence and material mix time scales, turbulence dissipation, and mix widths and/or growth rates. These comparisons are made within the framework of three very different classes of flows: shear-driven, Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Overall, reasonable agreement is seen between experiments, DNS, and averaging models.

Keywords:

• turbulence
• mixing
• variable density
• Reynolds stress
• closure model
• Rayleigh–Taylor
• Richtmyer–Meshkov
• direct numerical simulation
• shocks
• Favre average
• compressible flows
• density fluctuations

Acknowledgements

This work was supported by the U.S. Department of Energy, subcontract #DE-AC52-06NA25396.