Abstract
A mixed hyperbolic-parabolic, non conservative, Reynolds Stress Model (RSM), is studied. It is based on an underlying set of Langevin equations, and allows to describe turbulent mixing, including transient demixing effects as well as incomplete mixing. Its mathematical structure is analysed, and specific regimes, related to acoustic-like, Riemann-type, or self-similar solutions, are identified. A second-order accurate numerical scheme is proposed in arbitrary curvilinear geometry. Its accuracy and convergence behaviour are tested by comparison with analytical solutions in the different regimes. The numerical scheme can be generalized to multi-dimensional configurations, with potentially cylindrical symmetry, on unstructured meshes.
Highlights
Turbulent mixing at fluid interfaces plays an important role in a wide variety of domains, ranging from the study of astrophysical objects like supernovae, to engineering applications like Inertial Confinement Fusion (ICF)
Reynolds Stress Model (RSM) are one-point statistical models, which rely on a local-in-space decomposition of instantaneous fields into a mean and a turbulent fluctuating field
Among existing RSMs, the BHR [2] and GSG [19, 20] models are widely used for engineering purposes related to variable-density turbulence and mixing at interfaces
Summary
Turbulent mixing at fluid interfaces plays an important role in a wide variety of domains, ranging from the study of astrophysical objects like supernovae, to engineering applications like Inertial Confinement Fusion (ICF). Self-similarity is an important, generic feature of a wide class of fully developed turbulent regimes, that cannot be disregarded Even though it does not allow the respect of the mass fraction boundedness, this model is only meant to be used as a basis for a RSM. The model (2.7)–(2.13), supplemented with these second-order closures, may be viewed either as an asymptotic limit, in the so-called Boussinesq regime, with constant-in-time mean density ρ (Eq (2.7)), or as a sub-system of larger purpose RSMs dedicated to time-dependent, variable-density, compressible flows (by considering a general Reynolds averaged Navier–Stokes equations, that embeds the present RSM, without Eq (2.7)). Radiation transfer across a TMZ is modified by the heterogeneity level [11]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
