Compressible Rayleigh-Taylor Instability Research Articles

Investigation of effects of initial interface conditions on the two-dimensional single-mode compressible Rayleigh–Taylor instability: Based on the discrete Boltzmann method

The Rayleigh–Taylor (RT) instability in inertial confinement fusion implosions evolves at the unstable interface of two fluids when the light fluid is pushing the heavy one. The effects of the initial amplitude and transition layer on the compressible RT instability are investigated numerically by using the discrete Boltzmann method. On the one hand, during the RT evolution, higher initial amplitudes initially increase the global density gradient and non-equilibrium area, with a subsequent reversal. The increasing initial amplitude leads to an initial rise followed by a decline in the system’s maximum Mach number. On the other hand, the impact of the transition layer is generally opposite to the one of initial amplitude in the RT process. These findings offer significant insights into controlling and understanding RT instability in fusion implosion scenarios, emphasizing novel aspects relative to existing literature.

Heat transfer and transport property contrast effects on the compressible Rayleigh-Taylor instability

Heat transfer and transport property contrast effects on the compressible Rayleigh-Taylor instability

Effects of Inclined Interface Angle on Compressible Rayleigh-Taylor Instability: A Numerical Study Based on the Discrete Boltzmann Method.

Rayleigh-Taylor (RT) instability is a basic fluid interface instability that widely exists in nature and in the engineering field. To investigate the impact of the initial inclined interface on compressible RT instability, the two-component discrete Boltzmann method is employed. Both the thermodynamic non-equilibrium (TNE) and hydrodynamic non-equilibrium (HNE) effects are studied. It can be found that the global average density gradient in the horizontal direction, the non-organized energy fluxes, the global average non-equilibrium intensity and the proportion of the non-equilibrium region first increase and then reduce with time. However, the global average density gradient in the vertical direction and the non-organized moment fluxes first descend, then rise, and finally descend. Furthermore, the global average density gradient, the typical TNE intensity and the proportion of non-equilibrium region increase with increasing angle of the initial inclined interface. Physically, there are three competitive mechanisms: (1) As the perturbed interface elongates, the contact area between the two fluids expands, which results in an increasing gradient of macroscopic physical quantities and leads to a strengthening of the TNE effects. (2) Under the influence of viscosity, the perturbation pressure waves on both sides of the material interface decrease with time, which makes the gradient of the macroscopic physical quantity decrease, resulting in a weakening of the TNE strength. (3) Due to dissipation and/or mutual penetration of the two fluids, the gradient of macroscopic physical quantities gradually diminishes, resulting in a decrease in the intensity of the TNE.

Compressible Rayleigh–Taylor instability subject to isochoric initial background state

The effect of compressibility on the single-mode Rayleigh–Taylor instability is examined using two (2D) and three-dimensional (3D) direct numerical simulations. To isolate compressibility from background stratification effects, this work employs a constant density profile on each side of the interface. The numerical simulations are performed at various Reynolds numbers using the gas kinetic method for static Mach numbers up to M = 0.4. The most important finding is that compressibility acting in isolation enhances the instability and perturbations grows faster with increasing Mach number, unlike previous results with background isothermal state, which show suppression of the instability at higher static Mach numbers. In addition, compressibility is also shown to increase the bubble-spike asymmetry. While the instability grows faster for the 3D case, the findings are qualitatively similar in 2D and 3D. The dynamical reasons underlying the effect of compressibility are elucidated by examining the evolution of vorticity and turbulent kinetic energy transport equations.

The influences of acceleration on compressible Rayleigh–Taylor instability with non-equilibrium effects

Rayleigh–Taylor (RT) instability is a classical interface instability of great importance in nature and engineering fields. In this paper, the influences of acceleration on the compressible RT instability is investigated by using the discrete Boltzmann method based on non-equilibrium statistical physics. The differences in RT systems with various accelerations have been analyzed through the physical gradients and non-equilibrium measures. It is interesting to find that the global temperature gradient, the maximum Mach number, and the non-equilibrium strength increase initially, reduce afterwards, and have peaks in the dynamic process. Specifically, in the early stage, the global temperature gradient of the fluid system is higher for a case with larger acceleration, and there is an exponential relationship between them. Moreover, the maximum Mach number is located at the heavy fluid that drops fast in the system’s midsection, rises more sharply, and reaches the peak earlier for a larger acceleration. In addition, for a larger acceleration, the non-equilibrium strength rises (reduces) faster in the early (later) stage, and presents an exponential relationship between them in the early stage as well. From the kinetic perspective, these results further enrich our understanding of the physical mechanism of the compressible RT instability with both hydrodynamic and thermodynamic non-equilibrium effects.

Investigation of strong isothermal stratification effects on multi-mode compressible Rayleigh–Taylor instability

Rayleigh–Taylor instability, RTI, occurs at the interface separating two fluids subjected to acceleration when the density gradient and the acceleration are in opposite directions. Previous scientific research primarily considered RTI under the incompressible assumption, which may not be valid in many high-energy-density engineering applications and astrophysical phenomena. In this study, the compressibility effects of the background isothermal stratification strength on multi-mode two-dimensional RTI are explored using fully compressible multi-species direct numerical simulations. Cases under three different isothermal Mach numbers – Ma=0.15, 0.3, and 0.45 – are investigated to explore weakly, moderately, and strongly stratified compressible RTI, respectively, at an Atwood number of 0.04. Unlike incompressible RTI, an increase in the flow compressibility through the strength of the background stratification can suppress the RTI growth and can lead to a termination of the RTI mixing layer growth with a highly molecularly mixed state. Our findings suggest that even at the chosen relatively low Atwood number, the variable-density effects can be significantly enhanced due to an increase in the background stratification for the compressible RTI as different spatial profiles become noticeably asymmetric across the mixing layer for the strongly stratified case. In addition, this study compares the chaotic behavior of the cases by studying the transport of the turbulent kinetic energy as well as the vortex dynamics. The Reynolds number dependence of the results is also examined with three different Reynolds numbers, and the findings for the large-scale mixing and flow quantities of interest are shown to be universal in the range of the Reynolds numbers studied.

A discrete Boltzmann model with symmetric velocity discretization for compressible flow

A discrete Boltzmann model (DBM) with symmetric velocity discretization is constructed for compressible systems with an adjustable specific heat ratio in the external force field. The proposed two-dimensional (2D) nine-velocity scheme has better spatial symmetry and numerical accuracy than the discretized velocity model in literature [Acta Aerodyn. Sin. 40 98108 (2022)] and owns higher computational efficiency than the one in literature [Phys. Rev. E 99 012142 (2019)]. In addition, the matrix inversion method is adopted to calculate the discrete equilibrium distribution function and force term, both of which satisfy nine independent kinetic moment relations. Moreover, the DBM could be used to study a few thermodynamic nonequilibrium effects beyond the Euler equations that are recovered from the kinetic model in the hydrodynamic limit via the Chapman–Enskog expansion. Finally, the present method is verified through typical numerical simulations, including the free-falling process, Sod’s shock tube, sound wave, compressible Rayleigh–Taylor instability, and translational motion of a 2D fluid system.

Bubble re-acceleration behaviours in compressible Rayleigh–Taylor instability with isothermal stratification

The highly nonlinear evolution of the single-mode stratified compressible Rayleigh–Taylor instability (RTI) is investigated via direct numerical simulation over a range of Atwood numbers ( $A_T=0.1$ – $0.9$ ) and Mach numbers ( $Ma=0.1$ – $0.7$ ) for characterising the isothermal background stratification. After the potential stage, it is found that the bubble is accelerated to a velocity which is well above the saturation value predicted in the potential flow model. Unlike the bubble re-acceleration behaviour in quasi-incompressible RTI with uniform background density, the characteristics in the stratified compressible RTI are driven by not only vorticity accumulation inside the bubble but also flow compressibility resulting from the stratification. Specifically, in the case of strong stratification and high $A_T$ , the flow compressibility dominates the bubble re-acceleration characters. To model the effect of flow compressibility, we propose a novel model to reliably describe the bubble re-acceleration behaviours in the stratified compressible RTI, via introducing the dilatation into the classical model that takes into account only vorticity accumulation.

Nonlinear saturation of bubble evolution in a two-dimensional single-mode stratified compressible Rayleigh-Taylor instability

For the compressible Rayleigh-Taylor instability (RTI), density stratification is found to cause different bubble behaviors for different Atwood number (At) values. We propose a modified buoyancy-drag model that interprets the physical mechanism causing these behaviors, and analyze the acceleration behavior of a bubble at high At in detail. This work provides a more comprehensive understanding of the compressibility effects on nonlinear evolution of RTI.

Specific heat ratio effects of compressible Rayleigh—Taylor instability studied by discrete Boltzmann method

Rayleigh-Taylor (RT) instability widely exists in nature and engineering fields. How to better understand the physical mechanism of RT instability is of great theoretical significance and practical value. At present, abundant results of RT instability have been obtained by traditional macroscopic methods. However, research on the thermodynamic non-equilibrium (TNE) effects in the process of system evolution is relatively scarce. In this paper, the discrete Boltzmann method based on non-equilibrium statistical physics is utilized to study the effects of the specific heat ratio on compressible RT instability. The evolution process of the compressible RT system with different specific heat ratios can be analyzed by the temperature gradient and the proportion of the non-equilibrium region. Firstly, as a result of the competition between the macroscopic magnitude gradient and the non-equilibrium region, the average TNE intensity first increases and then reduces, and it increases with the specific heat ratio decreasing; the specific heat ratio has the same effect on the global strength of the viscous stress tensor. Secondly, the moment when the total temperature gradient in y direction deviates from the fixed value can be regarded as a physical criterion for judging the formation of the vortex structure. Thirdly, under the competition between the temperature gradients and the contact area of the two fluids, the average intensity of the non-equilibrium quantity related to the heat flux shows diversity, and the influence of the specific heat ratio is also quite remarkable.

Viscous effects on the Rayleigh-Taylor instability with background temperature gradient

The growth rate of the compressible Rayleigh-Taylor instability is studied in the presence of a background temperature gradient, Θ, using a normal mode analysis. The effect of Θ variation is examined for three interface types corresponding to the combinations of the viscous properties of the fluids (inviscid-inviscid, viscous-viscous, and viscous-inviscid) at different Atwood numbers, At, and when at least one of the fluids' viscosity is non-zero, as a function of the Grashof number. For the general case, the resulting ordinary differential equations are solved numerically; however, dispersion relations for the growth rate are presented for several limiting cases. An analytical solution is found for the inviscid-inviscid interface and the corresponding dispersion equation for the growth rate is obtained in the limit of large Θ. For the viscous-inviscid case, a dispersion relation is derived in the incompressible limit and Θ = 0. Compared to Θ = 0 case, the role of Θ < 0 (hotter light fluid) is destabilizing and becomes stabilizing when Θ > 0 (colder light fluid). The most pronounced effect of Θ ≠ 0 is found at low At and/or at large perturbation wavelengths relative to the domain size for all interface types. On the other hand, at small perturbation wavelengths relative to the domain size, the growth rate for the Θ < 0 case exceeds the infinite domain incompressible constant density result. The results are applied to two practical examples, using sets of parameters relevant to Inertial Confinement Fusion coasting stage and solar corona plumes. The role of viscosity on the growth rate reduction is discussed together with highlighting the range of wavenumbers most affected by viscosity. The viscous effects further increase in the presence of background temperature gradient, when the viscosity is temperature dependent.

Comprehensive numerical methodology for direct numerical simulations of compressible Rayleigh–Taylor instability

An investigation of compressible Rayleigh-Taylor instability (RTI) using Direct Numerical Simulations (DNS) requires efficient numerical methods, advanced boundary conditions, and consistent initialization in order to capture the wide range of scales and vortex dynamics present in the system, while reducing the computational impact associated with acoustic wave generation and the subsequent interaction with the flow. An advanced computational framework is presented that handles the challenges introduced by considering the compressive nature of RTI systems, which include sharp interfacial density gradients on strongly stratified background states, acoustic wave generation and removal at computational boundaries, and stratification dependent vorticity production. The foundation of the numerical methodology described here is the wavelet-based grid adaptivity of the Parallel Adaptive Wavelet Collocation Method (PAWCM) that maintains symmetry in single-mode RTI systems to extreme late-times. PAWCM is combined with a consistent initialization, which reduces the generation of acoustic disturbances, and effective boundary treatments, which prevent acoustic reflections. A dynamic time integration scheme that can handle highly nonlinear and potentially stiff systems, such as compressible RTI, completes the computational framework. The numerical methodology is used to simulate two-dimensional single-mode RTI to extreme late-times for a wide range of flow compressibility and variable density effects. The results show that flow compressibility acts to reduce the growth of RTI for low Atwood numbers, as predicted from linear stability analysis.

Adaptive wavelet collocation method simulations of Rayleigh–Taylor instability

Numerical simulations of single-mode, compressible Rayleigh–Taylor instability are performed using the adaptive wavelet collocation method (AWCM), which utilizes wavelets for dynamic grid adaptation. Due to the physics-based adaptivity and direct error control of the method, AWCM is ideal for resolving the wide range of scales present in the development of the instability. The problem is initialized consistent with the solutions from linear stability theory. Non-reflecting boundary conditions are applied to prevent the contamination of the instability growth by pressure waves created at the interface. AWCM is used to perform direct numerical simulations that match the early-time linear growth, the terminal bubble velocity and a reacceleration region.

Compressible Rayleigh–Taylor Instability with Preheat inInertial Confinement Fusion

The compressible Rayleigh–Taylor instability of accelerated ablationfront is analysed in consideration of the preheat effects, and thecorresponding eigen-problem is solved numerically using thefourth-order accurate two-point compact difference scheme. Both thegrowth rate and perturbation profiles are obtained, and the obtainedgrowth rate is close to the results of direct numerical simulation. Ourresults show that the growth rate is more reduced and the cutoffwave length becomes longer as preheat increases.

2D pseudo-spectral parallel Navier–Stokes simulations of compressible Rayleigh–Taylor instability

A 2D Fourier–Chebyshev pseudo-spectral numerical method for the full Navier–Stokes equations with a dynamical domain decomposition technique has been parallelized on a SPMD machine, a CRAY-T3E. The parallelism is based on the distribution of data among processors and on simultaneous computations on each subdomain. The SHMEM paradigm is used for communication between processors. Comparisons between the vectorial and the parallel versions of spectral derivatives with Fourier and Chebyshev expansions are presented. Performances versus the number of processors and collocation points are also studied. The numerical code is then used to simulate single and multimode Rayleigh–Taylor flows. The influence of the physical diffusion between species is emphasized on a single mode configuration. A simulation with 22 initial perturbation modes is also carried out and analyzed.

Parallel computations of 3-D Rayleigh-Taylor instability

Results are described of computations of 3-D compressible Rayleigh-Taylor instability. The instability is an important mixing mechanism in a variety of flows such as supernovae and inertial confinement fusion. The code uses Flux Corrected Transport to solve the Euler equations of hydrodynamics. Results of the simulations have been characterized by considering differing resolutions and in terms of growth-rates, Mach number evolution, pattern formation, and (weakly) turbulent structures.

96/04197 Trajectories of burning coal particles in highly swirling reactive flows

Results are described of computations of 3-D compressible Rayleigh-Taylor instability. The instability is an important mixing mechanism in a variety of flows such as supernovae and inertial confinement fusion. The code uses Flux Corrected Transport to solve the Euler equations of hydrodynamics. Results of the simulations have been characterized by considering differing resolutions and in terms of growth-rates, Mach number evolution, pattern formation, and (weakly) turbulent structures.

96/04181 Scaling in bouyancy driven turbulent premixed flames

Results are described of computations of 3-D compressible Rayleigh-Taylor instability. The instability is an important mixing mechanism in a variety of flows such as supernovae and inertial confinement fusion. The code uses Flux Corrected Transport to solve the Euler equations of hydrodynamics. Results of the simulations have been characterized by considering differing resolutions and in terms of growth-rates, Mach number evolution, pattern formation, and (weakly) turbulent structures.

96/04190 Study of carbon deposition in coke ovens

Results are described of computations of 3-D compressible Rayleigh-Taylor instability. The instability is an important mixing mechanism in a variety of flows such as supernovae and inertial confinement fusion. The code uses Flux Corrected Transport to solve the Euler equations of hydrodynamics. Results of the simulations have been characterized by considering differing resolutions and in terms of growth-rates, Mach number evolution, pattern formation, and (weakly) turbulent structures.

Supersonic interface instabilities of accelerated surfaces and jets

The compressible Rayleigh–Taylor instability of a supersonic accelerated contact discontinuity between two gases is studied by numerically solving the two-dimensional Euler equations. The computed solutions exhibit a complicated set of nonlinear waves comprised of spike and bubble bow shocks, terminal shocks within the spike and bubble, Kelvin–Helmholtz rollup of the spike tip, and contact surface waves. The spike appears to attain a finite growth of aspect ratio approximately equal to 2. The propagation of a supersonic slab jet is also studied numerically, in order to compare and contrast the jet wave structure with that of the supersonic accelerated surface.