High-fidelity Numerical Simulations of Compressible Turbulence and Mixing Generated by Hydrodynamic Instabilities.

Abstract

High-speed flows are prone to hydrodynamic interfacial instabilities that evolve to turbulence, thereby intensely mixing different fluids and dissipating energy. The lack of knowledge of these phenomena has impeded progress in a variety of disciplines in science and engineering. In this work, my goal is to develop accurate and efficient numerical schemes and employ them to study compressible turbulence and mixing generated by interactions between shocked (Richtmyer-Meshkov) and accelerated (Rayleigh-Taylor) interfaces.

To accomplish my goal, a hybrid high-order central/discontinuity-capturing finite difference scheme is first presented. The underlying principle is that, to accurately and efficiently represent both broadband motions and discontinuities, non-dissipative methods are used where the solution is smooth, while the more expensive and dissipative capturing schemes are applied near discontinuous regions. The interface capturing approach is extended to central differences, such that smooth distributions of varying specific heats ratio can be simulated without generating spurious pressure oscillations. I verified this approach using the Richtmyer-Meshkov instability simulations.

Using a novel set-up, I perform direct numerical simulations of freely decaying turbulent multi-material mixing starting from an unperturbed material interface between two fluids in a pre-existing isotropic turbulent velocity field in the presence and absence of gravity. In the absence of gravity, the energy dissipation rate is matched in each fluid, such that anisotropy in the initial set-up solely comes from the density gradient. At large scales, the mixing region grows self-similarly after an initial transient period. In this regime, the growth of the mixing regions scales as time to the power of 2/7 for Batchelor turbulence, as predicted by energy budget arguments for large Reynolds numbers. Results suggest that a large density ratio between the two fluids is required to produce anisotropy at the Taylor microscale, while the flow remains isotropic at the dissipation scales.

Having identified the role of density gradient alone, I revisit the problem in the presence of gravity in a Rayleigh-Taylor unstable configuration. Now, the baroclinic vorticity due to the gravitational field provides energy that drives the initially decaying turbulent field. The resulting turbulence is found to be anisotropic across all scales.