David L. Youngs

Numerical simulation of turbulent mixing by Rayleigh-Taylor instability

Abstract Two-dimensional hydrodynamic codes are used to simulate the growth of perturbations at an interface between two fluids of different density due to Rayleigh-Taylor instability. Problems where the interface is subjected to a constant acceleration and where it is accelerated and decelerated by shock waves are considered. Emphasis is placed on the case when the initial perturbation consists of many different wavelength modes. Results are compared with the experimental data of Andronov et al. (1976) and Read (1983). The use of a simple empirical model of the mixing process based on the equations of two-phase flow is discussed.

A comparative study of the turbulent Rayleigh–Taylor instability using high-resolution three-dimensional numerical simulations: The Alpha-Group collaboration

The turbulent Rayleigh–Taylor instability is investigated in the limit of strong mode-coupling using a variety of high-resolution, multimode, three dimensional numerical simulations (NS). The perturbations are initialized with only short wavelength modes so that the self-similar evolution (i.e., bubble diameter Db∝amplitudeu200ahb) occurs solely by the nonlinear coupling (merger) of saturated modes. After an initial transient, it is found that hb∼αbAgt2, where A=Atwood number, g=acceleration, and t=time. The NS yield Db∼hb/3 in agreement with experiment but the simulation value αb∼0.025±0.003 is smaller than the experimental value αb∼0.057±0.008. By analyzing the dominant bubbles, it is found that the small value of αb can be attributed to a density dilution due to fine-scale mixing in our NS without interface reconstruction (IR) or an equivalent entrainment in our NS with IR. This may be characteristic of the mode coupling limit studied here and the associated αb may represent a lower bound that is insensiti...

Three‐dimensional numerical simulation of turbulent mixing by Rayleigh–Taylor instability

Three‐dimensional simulation of the mixing of miscible fluids by Rayleigh–Taylor instability is described for density ratios, ρ1/ρ2, in the range 1.5 to 20. Significant dissipation of density fluctuations and kinetic energy occurs via the cascade to high wave numbers. Comparison is made with experimental measurements of the overall growth of the mixing zone and of the magnitude of density fluctuations. The differences between 2‐D and 3‐D simulation are discussed.

Modelling turbulent mixing by Rayleigh-Taylor instability

Abstract Direct two-dimensional numerical simulation and experiments, in which small rocket motors accelerate a tank containing two fluids, have been used to investigate turbulent mixing by Rayleigh-Taylor instability at a wide range of density ratios. The experimental data obtained so far has been used to calibrate an empirical model of the mixing process which is needed to make predictions for complex applications. The model devised, which is a form of turbulence model, is based on the equations of multiphase flow. These equations describe velocity separation arising from the action of a pressure gradient on fluid fragments of different density. The dissipation arising from the drag between the fluid fragments is treated as a source of turbulence kinetic energy which is then used to define turbulent diffusion coefficients. Gradient diffusion processes are thereby included in the model.

Self-similarity and internal structure of turbulence induced by Rayleigh–Taylor instability

This paper describes an experimental investigation of mixing due to Rayleigh{Taylor instability between two miscible fluids. Attention is focused on the gravitationally driven instability between a layer of salt water and a layer of fresh water with particular emphasis on the internal structure within the mixing zone. Three-dimensional numerical simulations of the same flow are used to give extra insight into the behaviour found in the experiments. The two layers are initially separated by a rigid barrier which is removed at the start of the experiment. The removal process injects vorticity into the flow and creates a small but signicant initial disturbance. A novel aspect of the numerical investigation is that the measured velocity eld for the start of the experiments has been used to initialize the simulations, achieving substantially improved agreement with experiment when compared with simulations using idealized initial conditions. It is shown that the spatial structure of these initial conditions is more important than their amplitude for the subsequent growth of the mixing region between the two layers. Simple measures of the growth of the instability are shown to be inappropriate due to the spatial structure of the initial conditions which continues to influence the flow throughout its evolution. As a result the mixing zone does not follow the classical quadratic time dependence predicted from similarity considerations. Direct comparison of external measures of the growth show the necessity to capture the gross features of the initial conditions while detailed measures of the internal structure show a rapid loss of memory of the ner details of the initial conditions. Image processing techniques are employed to provide a detailed study of the internal structure and statistics of the concentration eld. These measurements demonstrate that, at scales small compared with the conning geometry, the flow rapidly adopts self-similar turbulent behaviour with the influence of the barrier-induced perturbation conned to the larger length scales. Concentration power spectra and the fractal dimension of iso-concentration contours are found to be representative of fully developed turbulence and there is close agreement between the experiments and simulations. Other statistics of the mixing zone show a reasonable level of agreement, the discrepancies mainly being due to experimental noise and the nite resolution of the simulations.

Molecular mixing in Rayleigh-Taylor instability

Mixing produced by Rayleigh–Taylor instability at the interface between two layers is the subject of a comparative study between laboratory and numerical experiments. The laboratory experiments consist of a layer of brine initially at rest on top of a layer of fresh water. When a horizontal barrier separating the two layers is removed, the ensuing motion and the mixing that is produced is studied by a number of diagnostic techniques. This configuration is modelled numerically using a three-dimensional code, which solves the Euler equations on a 180 3 grid. A comparison of the numerical results and the experimental results is carried out with the aim of making a careful assessment of the ability of the code to reproduce the experiments. In particular, it is found that the motions are quite sensitive to the presence of large scales produced when the barrier is removed, but the amount and form of the mixing is not very sensitive to the initial conditions. The implications of this comparison for improvements in the experimental and numerical techniques are discussed.

Simulation of transition and turbulence decay in the Taylor–Green vortex

Conventional large-eddy simulation (LES) and monotone integrated LES (MILES) are tested in emulating the dynamics of transition to turbulence in the Taylor–Green vortex (TGV). A variety of subgrid scale (SGS) models and high-resolution numerical methods are implemented in the framework of both incompressible and compressible fluid flow equations. Comparisons of the evolution of characteristic TGV integral measures are made with previously reported and new direct numerical simulation (DNS) data. The computations demonstrate that the convective numerical diffusion effects in the MILES methods can consistently capture the physics of flow transition and turbulence decay without resorting to an explicit SGS model, while providing accurate prediction of established theoretical findings for the kinetic energy dissipation, energy spectra, enstrophy and kinetic energy decay. All approaches tested provided fairly robust computational frameworks.

The influence of initial conditions on turbulent mixing due to Richtmyer-Meshkov instability

This paper investigates the influence of different three-dimensional multi-mode initial conditions on the rate of growth of a mixing layer initiated via a Richtmyer-Meshkov instability through a series of well-controlled numerical experiments. Results are presented for large-eddy simulation of narrowband and broadband perturbations at grid resolutions up to 3 x 10 9 points using two completely different numerical methods, and comparisons are made with theory and experiment. It is shown that the mixing-layer growth is strongly dependent on initial conditions, the narrowband case giving a power-law exponent θ ≈ 0.26 at low Atwood and θ ≈ 0.3 at high Atwood numbers. The broadband case uses a perturbation power spectrum of the form P(k) ∝ k -2 with a proposed theoretical growth rate of θ = 2/3 . The numerical results confirm this; however, they highlight the necessity of a very fine grid to capture an appropriately broad range of initial scales. In addition, an analysis of the kinetic energy decay rates, fluctuating kinetic energy spectra, plane-averaged volume fraction profiles and mixing parameters is presented for each case.

On entropy generation and dissipation of kinetic energy in high-resolution shock-capturing schemes

This paper addresses entropy generation and the corresponding dissipation of kinetic energy associated with high-resolution, shock-capturing (Godunov) methods. Analytical formulae are derived for the rate of increase of entropy given arbitrary jumps in primitive variables at a cell interface. It is demonstrated that for general continuously varying flows the inherent numerical entropy increase of Godunov methods is not proportional to the velocity jump cubed as is commonly assumed, but it is proportional to the velocity jump squared. Furthermore, the dissipation of kinetic energy is directly linked to temperature multiplied by change in entropy at low Mach numbers. The kinetic energy dissipation rate is shown to be proportional to the velocity jump squared and the speed of sound. The leading order dissipation rate associated with jumps in pressure, density and shear waves is detailed and further shown that at low Mach number it is the dissipation due to the perpendicular velocity jumps which dominates. This explains directly the poor performance of Godunov methods at low Mach numbers. The analysis is also applied to high-order accurate methods in space and time and all analytical results are validated with simple numerical experiments.

Richtmyer–Meshkov turbulent mixing arising from an inclined material interface with realistic surface perturbations and reshocked flow

This paper presents a numerical study of turbulent mixing due to the interaction of a shock wave with an inclined material interface. The interface between the two gases is modeled by geometrical random multimode perturbations represented by different surface perturbation power spectra with the same standard deviation. Simulations of the Richtmyer–Meshkov instability and associated turbulent mixing have been performed using high-resolution implicit large eddy simulations. Qualitative comparisons with experimental flow visualizations are presented. The key integral properties have been examined for different interface perturbations. It is shown that turbulent mixing is reduced when the initial perturbations are concentrated at short wavelengths. The form of the initial perturbation has strong effects on the development of small-scale flow structures, but this effect is diminished at late times.