Large eddy simulation of high atwood number rayleigh-taylor mixing

Ilyas Yilmaz,A Mohamad,A Vallati,G Battista,A.C Benim,S.-H Suh,J Taler,R Bennacer,R De Lieto Vollaro

doi:10.1051/e3sconf/201912808001

Abstract

Large eddy simulation of Rayleigh-Taylor instability at high Atwood numbers is performed using recently developed, kinetic energy-conserving, non-dissipative, fully-implicit, finite volume algorithm. The algorithm does not rely on the Boussinesq assumption. It also allows density and viscosity to vary. No interface capturing mechanism is requried. Because of its advanced features, unlike the pure incompressible ones, it does not suffer from the loss of physical accuracy at high Atwood numbers. Many diagnostics including local mole fractions, bubble and spike growth rates, mixing efficiencies, Taylor micro-scales, Reynolds stresses and their anisotropies are computed to analyze the high Atwood number effects. The density ratio dependence for the ratio of spike to bubble heights is also studied. Results show that higher Atwood numbers are characterized by increasing ratio of spike to bubble growth rates, higher speeds of bubble and especially spike fronts, faster development in instability, similarity in late time mixing values, and mixing asymmetry.

Highlights

Rayleigh-Taylor Instability (RTI) occurs when a heavy fluid of density ⇢h on top is supported against the gravity, g, by a light fluid of density ⇢l on bottom [1,2,3]
RTI is characterized by the Atwood number, A, which is given as Penetration of the light fluid into the heavy one as bubbles and penetration of the heavy fluid into the light one as spikes can be modeled in terms of the penetration lengths as hb = ↵bAgt2 and hs = −↵sAgt2. ↵b and ↵s are the growth rates for bubble and spike, respectively
As the primary flow diagnostic, the local mole fraction (LMF) field based on heavy fluid is computed as χ(x, y, z, t)

Summary

Introduction

Rayleigh-Taylor Instability (RTI) occurs when a heavy fluid of density ⇢h on top is supported against the gravity, g, by a light fluid of density ⇢l on bottom [1,2,3]. When it is subject to perturbations, the fluids which are initially in hydrostatic equilibrium start to interpenetrate each other due to the baroclinic vorticity generated by the opposite density and pressure gradients. It can be observed in flows such as type Ia supernovae, Inertial Confinement Fusion (ICF), cavitation bubbles, oceanic and atmospheric currents and many other natural and engineering flows. Penetration of the light fluid into the heavy one as bubbles and penetration of the heavy fluid into the light one as spikes can be modeled in terms of the penetration lengths as hb = ↵bAgt and hs = −↵sAgt.

Objectives

Methods

Results

Conclusion