Simulation and Reynolds-averaged Navier-Stokes modeling of a three-component Rayleigh-Taylor mixing problem with thermonuclear burn

Two self-similar Reynolds-stress transport models with anisotropic eddy viscosity

Two Reynolds-averaged Navier-Stokes models with full Reynolds-stress transport (RST) and tensor eddy viscosity are presented. These new models represent RST extensions of the k-2L-a-C and k-ϕ-L-a-C models by Morgan [Phys. Rev. E 103, 053108 (2021)10.1103/PhysRevE.103.053108; Phys. Rev. E 105, 045104 (2022)10.1103/PhysRevE.105.045104]. Self-similarity analysis is used to derive constraints on model coefficients required to reproduce expected growth parameters for a variety of canonical flows, including Rayleigh-Taylor (RT) and Kelvin-Helmholtz (KH) mixing layers. Both models are then applied in one-dimensional simulation of RT and KH mixing layers, and the expected self-similar growth rates and anisotropy are obtained. Next, models are applied in two-dimensional simulation of the so-called "tilted rocket rig" inclined RT experiment [J. Fluids Eng. 136, 091212 (2014)10.1115/1.4027587] and in simulation of a shock-accelerated localized patch of turbulence. It is found that RST is required to capture the qualitative growth of the shock-accelerated patch, and an anisotropic eddy viscosity provides substantial improvement over a Boussinesq treatment for the tilted rocket rig problem.

Large-eddy simulation and Reynolds-averaged Navier-Stokes modeling of three Rayleigh-Taylor mixing configurations with gravity reversal

High-fidelity large-eddy simulation (LES) is performed of Rayleigh-Taylor (RT) mixing in three different configurations involving gravity reversal. In each configuration, LES results are compared with one-dimensional Reynolds-averaged Navier-Stokes (RANS) results, and a deficiency in a commonly used transport equation for the mass-flux velocity, a_{j}, is identified. In the first configuration, a classical two-component RT mixing layer is allowed to develop before it is subjected to rapid acceleration reversal. In the second configuration, a three-component RT mixing layer with an intermediate density layer is allowed to develop before being subjected to rapid acceleration reversal. Finally, in the third configuration, a light layer is interposed between two heavy layers; in this configuration, only one interface is RT-unstable at a time as it undergoes rapid acceleration reversal. In all cases, a commonly used buoyancy production closure in the a_{j} transport equation is shown to lead to significant over-prediction of mixing layer growth after gravity reversal. An alternative formulation for this closure is then presented which is shown to more accurately capture the stabilization effect of gravity reversal.