New phenomena in variable-density Rayleigh–Taylor turbulence

Abstract

This paper presents several issues related to mixing and turbulence structure in buoyancy-driven turbulence at low to moderate Atwood numbers, A, found from direct numerical simulations in two configurations: classical Rayleigh-Taylor instability and an idealized triply periodic Rayleigh-Taylor flow. Simulations at A up to 0.5 are used to examine the turbulence characteristics and contrast them with those obtained close to the Boussinesq approximation. The data sets used represent the largest simulations to date in each configuration. One of the more remarkable issues explored, first reported in (Livescu and Ristorcelli 2008 J. Fluid Mech. 605 145-80), is the marked difference in mixing between different density fluids as opposed to the mixing that occurs between fluids of commensurate densities, corresponding to the Boussinesq approximation. Thus, in the triply periodic configuration and the non-Boussinesq case, an initially symmetric density probability density function becomes skewed, showing that the mixing is asymmetric, with pure heavy fluid mixing more slowly than pure light fluid. A mechanism producing the mixing asymmetry is proposed and the consequences for the classical Rayleigh-Taylor configuration are discussed. In addition, it is shown that anomalous small-scale anisotropy found in the homogeneous configuration (Livescu and Ristorcelli 2008 J. Fluid Mech. 605 145-80) and Rayleigh-Taylor turbulence at A = 0.5 (Livescu et al 2008 J. Turbul. 10 1-32) also occurs near the Boussinesq limit. Results pertaining to the moment closure modelling of Rayleigh-Taylor turbulence are also presented. Although the Rayleigh-Taylor mixing layer width reaches self-similar growth relatively fast, the lower-order terms in the self-similar expressions for turbulence moments have long-lasting effects and derived quantities, such as the turbulent Reynolds number, are slow to follow the self-similar predictions. Since eddy diffusivity in the popular gradient transport hypothesis is proportional to the turbulent Reynolds number, the dissipation rate and turbulent transport have different length scales long after the onset of the self-similar growth for the layer growth. To highlight the importance of turbulent transport, variable density energy budgets for the kinetic energy, mass flux and density-specific volume covariance equations, necessary for a moment closure of the flow, are provided.

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

“…The simulations provide much of the data needed to calibrate an engineering model and produce coefficient sets for a range of values of α. High Reynolds number DNS is now becoming feasible for the relatively simple problem considered here, see for example Livescu et al [22], and could provide very valuable confirmation of the results presented here. However, the use of three-dimensional simulation on more complex problems (e.g.…”

A new framework for simulating forced homogeneous buoyant turbulent flows

“…Note the close agreement between this theoretical PDF curve and the PDF data calculated from the density field data. Consistent with previous studies of variable density turbulent mixing [3][4][5], the density PDFs in all test cases are skewed toward lower density values. To be more quantitative, the skewness (S) and flatness (F) are calculated for cases Se2, Be2, Pa06e2, and Ie2 according to,…”

“…First, it was observed that buoyant flows have an asymmetric mixing rate. This manifests through a skewed density probability density function (PDF) and indicates that the more dense fluid in the RT unstable configuration mixes at a slower rate than the less dense fluid [3][4][5]. Second, as a consequence of this, the penetration depth of larger density fluids exceeds that of lower density fluids [3].…”

Numerical simulations of two-fluid turbulent mixing at large density ratios and applications to the Rayleigh–Taylor instability

“…whereas the caloric equation of state is 20) where the specific heat at constant pressure for the mixture is calculated as the mass fractionweighted sum of the individual specific heats. Gases obeying equation (2.20) are usually called 'perfect'; in this case, the specific heats vary with temperature owing to energy contributions beyond those contained in translational motions.…”

“…HRT allows the study of turbulence and mixing without the complications owing to inhomogeneities or mixing layer edges, but retaining the basic nonlinearities and energy production mechanism as the classical RTI case. DNS results for the incompressible RTI problem are reported in references [15,25,87] with the MIRANDA code on up to 3072 3 meshes and references [20,88,89] with the CFDNS code on up to 4096 2 × 4032 meshes. All MIRANDA runs have been performed at A = 0.5, whereas CFDNS has been used for A = 0.04-0.9.…”