Three-dimensional Richtmyer-Meshkov Instability Research Articles

Quantitative theory for spikes and bubbles in the Richtmyer−Meshkov instability at arbitrary density ratios in three dimensions

It is known that conducting numerical simulations and experiments for the shock-induced Richtmyer–Meshkov instability in three dimensions is much more difficult and time-consuming than that in two dimensions. Therefore, theories can play a more important role in the study of three-dimensional Richtmyer–Meshkov instability. We present analytical formulas for predicting the behavior of growth rate and amplitude of fingers at the unstable Richtmyer–Meshkov interface. Our theory is for both spikes and bubbles, for the arbitrary density ratio between the two fluids, and for the entire development process from early to late times.

Manipulation of three-dimensional Richtmyer-Meshkov instability by initial interfacial principal curvatures

The characteristics of three-dimensional (3D) Richtmyer-Meshkov instability (RMI) in the early stages are studied numerically. By designing 3D interfaces that initially possess various identical and opposite principal curvature combinations, the growth rate of perturbations can be effectively manipulated. The weighted essentially nonoscillatory scheme and the level set method combined with the real ghost fluid method are used to simulate the flow. The results indicate that the interface development and the shock propagation in 3D cases are much more complicated than those in 2D case, and the evolution of 3D interfaces is heavily dependent on the initial interfacial principal curvatures. The 3D structure of wave patterns induces high pressure zones in the flow field, and the pressure oscillations change the local instabilities of interfaces. In the linear stages, the perturbation growth rate follows regularity as the interfacial principal curvatures vary, which is further predicted by the stability theory of 2D and 3D interfaces. It is also found that hysteresis effects exist at the onset of the linear stages in the 3D case for the same initial perturbations as the 2D case, resulting in different evolutions of 3D RMI in the nonlinear stages.

Laser generated Richtmyer–Meshkov instability and nonlinear wave paradigm in turbulent mixing: I. Central region of Gaussian spot

AbstractA three-dimensional Richtmyer–Meshkov instability (RMI) was generated on metal target by the laser pulse of Gaussian-like power profile in the semiconfined configuration (SCC). The SCC enables the extended lifetime of a hot vapor/plasma plume above the target surface as well as the fast multiple reshocks. The oscillatory pressure field of the reshocks causes strong bubble shape oscillations giving rise to the complex wave-vortex phenomena. The irregularity of the pressure field causes distortion of the shock wave front observed as deformed waves. In a random flow field the waves solidified around the bubbles form the broken “egg-karton” structure – or the large-scale chaotic web. In the coherent flow field the shape oscillations and collapse of the large bubbles generate nonlinear waves as the line- and the horseshoe-solitons. The line solitons are organized into a polygonal web, while the horseshoe solitons make either the rosette-like web or appear as the individual parabolic-like solitons. The configurations of the line solitons are juxtapositioned with solitons simulated by the Kadomtsev–Petviashvili (KP) equation. For the horseshoe solitons it was mentioned that it can be obtained by the simulation based on the cylindrical KP equation. The line and the horseshoe solitons represent the wave-vortex phenomena in which the fluid accelerated by the shock and exposed to a subsequent series of fast reshocks follows more complex scenario than in the open configuration. The RMI environment in the SCC generates complex fluid dynamics and the new paradigm of wave vortex phenomena in turbulent mixing.

Observations of three-dimensional Richtmyer-Meshkov instability on a membraneless gas bubble

We investigate the three-dimensional evolution of shock impact on a membraneless gas bubble. When a shock wave impacts a gas interface, gas layer is generally perturbed via the Richtmyer-Meshkov instability. We show the vortex structure evolves from the merging process of the extending spikes on the compressed D-shaped surface via the Richtmyer-Meshkov instability. The spikes are found to have a linear growth before 11 μs (of 1.4 mm). A ripple-typed fluctuating ring structure is observed and discussed with the scaling relation. We also notice that a thin layer exists in the intersection of the counterpropagating shock shells. The superposition of the rarefaction waves from both sides of the intersection is suspected to be responsible for the density change.

Numerical study of the turbulent mixing of a convergent shock tube

In this paper, we are concerned with physical aspects of three-dimensional Richtmyer–Meshkov instability (RMI) and resulting turbulent mixing phenomena in a convergent geometry. A system of two fluids, a heavy gas (sulfur hexafluoride, SF6) enclosed by a light gas (helium, He), is initially separated by two randomly perturbed interfaces. An artificial feature is imposed at the outer surface of these interfaces to enunciate the presence of a macroscopic perturbation.Numerical results obtained from TURMOIL3D simulations and physical insights into the RMI phenomena in such a configuration are presented and discussed. The density, mass fraction, vorticity, baroclinic vorticity production and simulated density Schlieren fields are provided to qualitatively describe the turbulent mixing process. It is concluded that the discrete feature, in conjunction with random perturbations, significantly influences the RMI and turbulent mixing characteristics.

Shock tube experiments and numerical simulation of the single-mode, three-dimensional Richtmyer–Meshkov instability

A vertical shock tube is used to perform experiments in which an interface is formed using opposed flows of air and SF6. A three-dimensional single-mode perturbation is created by the periodic vertical motion of the gases within the shock tube. Richtmyer–Meshkov instability is produced by an impulsive acceleration by a weak shock wave (Ms=1.2). Planar laser induced fluorescence produces still images, and planar Mie scattering produces movies of the experiment. A three-dimensional numerical simulation of this experiment utilizing the Eulerian adaptive mesh refinement code, RAPTOR, was also conducted. Good agreement is obtained between experiments and the simulations. However, existing late time models, which have a 1/t dependence, disagree with measurements of the late time instability development. In contrast, both the experiments and simulation suggest a t−0.54 late time dependence for the overall growth rate. Comparisons with individual bubble and spike velocities show the bubbles appear to decay approximately at 1/t and the spikes to decay at a much slower rate of t−0.38.

Direct Numerical Simulation of Three-Dimensional Richtmyer–Meshkov Instability

Direct numerical simulation (DNS) is used to study flow characteristics after interaction of a planar shock with a spherical media interface in each side of which the density is different. This interfacial instability is known as the Richtmyer–Meshkov (R-M) instability The compressible Navier–Stoke equations are discretized with group velocity control (GVC) modified fourth order accurate compact difference scheme. Three-dimensional numerical simulations are performed for R-M instability installed passing a shock through a spherical interface. Based on numerical results the characteristics of 3D R-M instability are analysed. The evaluation for distortion of the interface, the deformation of the incident shock wave and effects of refraction, reflection and diffraction are presented. The effects of the interfacial instability on produced vorticity and mixing is discussed.

An arbitrary Lagrangian–Eulerian method with adaptive mesh refinement for the solution of the Euler equations

A new algorithm that combines staggered grid arbitrary Lagrangian–Eulerian (ALE) techniques with structured local adaptive mesh refinement (AMR) has been developed for the solution of the Euler equations. The novel components of the method are driven by the need to reconcile traditional AMR techniques with the staggered variables and moving, deforming meshes associated with Lagrange based ALE schemes. Interlevel coupling is achieved with refinement and coarsening operators, as well as mesh motion boundary conditions. Elliptic mesh relaxation schemes are extended for use within the context of an adaptive mesh hierarchy. Numerical examples are used to highlight the utility of the method over single level ALE solution methods, facilitating substantial efficiency improvements and enabling the efficient solution of a highly resolved three-dimensional Richtmyer–Meshkov instability problem.