The density ratio dependence of self-similar Rayleigh–Taylor mixing

Abstract

Previous research on self-similar mixing caused by Rayleigh–Taylor (RT) instability is summarized and a recent series of high resolution large eddy simulations is described. Mesh sizes of approximately 2000 ×1000 × 1000 are used to investigate the properties of high Reynolds number self-similar RT mixing at a range of density ratios from 1.5 : 1 to 20 : 1. In some cases, mixing evolves from ‘small random perturbations’. In other cases, random long wavelength perturbations ( k −3 spectrum) are added to give self-similar mixing at an enhanced rate, more typical of that observed in experiments. The properties of the turbulent mixing zone (volume fraction distributions, turbulence kinetic energy, molecular mixing parameter, etc.) are related to the RT growth rate parameter, α . Comparisons are made with experimental data on the internal structure and the asymmetry of the mixing zone (spike distance/bubble distance). The main purpose of this series of simulations is to provide data for calibration of engineering models (e.g. Reynolds-averaged Navier–Stokes models). It is argued that the influence of initial conditions is likely to be significant in most applications and the implications of this for engineering modelling are discussed.

Turbulent mixing and beyond: non-equilibrium processes from atomistic to astrophysical scales II

“…This part II of the Theme Issue consists of the following papers: the paper by Sreenivasan & Abarzhi on acceleration and turbulence in Rayleigh-Taylor (RT) mixing [1]; by Meshkov on experimental studies of unstable interfaces [2]; by Youngs on numerical modelling simulations of self-similar regimes in mixing flows [3]; by Grinstein et al [4] on a pragmatic approach for reproducing complex multiphase flows in simulations; by Glimm et al [5] on the so-called alpha problem; by Nevmerzhitskiy on the implementation and diagnostics of RT/Richtmyer-Meshkov (RM) mixing in experiments [6]; by Livescu on high resolution approaches for numerical modelling of RT instabilities [7]; by Statsenko et al [8] on subgrid scale models applied to RT/RM mixing; by Prestridge et al analysing the RM mixing experiments conducted over the past decade [9]; by Levitas on mixing applications in reactive flows [10]; by Pudritz & Kevlahan on supersonic processes and shock waves in interstellar media [11]; and by Anisimov et al [12] summarizing the status of our understanding of RT mixing. We observe the development of the Rayleigh-Taylor instability (RTI) when fluids of different densities are accelerated against the density gradient [13,14].…”

“…Youngs [3] reviews the history of studies of RTI from considerations of the so-called single mode dynamics to self-similar turbulent mixing and makes an assessment of the applicability of self-similar hypothesis for modelling turbulent mixing layers. To provide data for calibration of engineering models, a sequence of highly resolved three-dimensional numerical simulations has been conducted for fluids with contrast densities and for those with similar densities, in the case of weakly compressible flows, by employing the monotone integrated large eddy simulation (LES) numerical methods.…”

Evolution of mixing width induced by general Rayleigh-Taylor instability

“…As is well known, however, α A 2 is highly dependent on the fluid properties (such as viscosity, miscibility) [7,17] and initial perturbations [20,24,25]. Therefore, for other systems with notably different media and/or perturbations, slightly different values of parameters α 0 2 and/or α 1 2 may be used.…”

A spectral anelastic Navier–Stokes solver for a stratified two-miscible-layer system in infinite horizontal channel

“…The value of α b has been the object of large debates over the last decades. The consensus is now that values of α b are between 0.020 and 0.030 for miscible fluids [25,57], provided that turbulence has been seeded by small wavelength perturbations. As a global validation of the method, we use the data of a large-scale Boussinesq simulation, referenced line BM, Table 3.…”

“…It is well-known that Boussinesq RT-mixing layers follow a self-similar law such as h b ∼ α b At g t 2 , where h b is the bubble (or spike) height and α b is a constant [57]. The value of α b has been the object of large debates over the last decades.…”