Richtmyer-Meshkov Instability Research Articles

Statistical characteristics of turbulent mixing in spherical and cylindrical converging Richtmyer–Meshkov instabilities

In this paper, the Richtmyer–Meshkov instabilities in spherical and cylindrical converging geometries with a Mach number of approximately 1.5 are investigated by using the high resolution implicit large eddy simulation method, and the influence of the geometric effect on the turbulent mixing is investigated. The heavy fluid is sulphur hexafluoride (SF6), and the light fluid is nitrogen (N2). The shock wave converges from the heavy fluid into the light fluid. The Atwood number is 0.678. The total structured and uniform Cartesian grid node number in the main computational domain is 20483. In addition, to avoid the influence of boundary reflection, a sufficiently long sponge layer with 50 non-uniform coarse grids is added for each non-periodic boundary. Present numerical simulations have high and nonlinear initial perturbation levels, which rapidly lead to turbulent mixing in the mixing layers. Firstly, some physical-variable mean profiles, including mass fraction, Taylor Reynolds number, turbulent kinetic energy, enstrophy and helicity, are provided. Second, the mixing characteristics in the spherical and cylindrical turbulent mixing layers are investigated, such as molecular mixing fraction, efficiency Atwood number, turbulent mass-flux velocity and density self-correlation. Then, Reynolds stress and anisotropy are also investigated. Finally, the radial velocity, velocity divergence and enstrophy in the spherical and cylindrical turbulent mixing layers are studied using the method of conditional statistical analysis. Present numerical results show that the geometric effect has a great influence on the converging Richtmyer–Meshkov instability mixing layers.

Contribution of Mach number to the evolution of the Richtmyer-Meshkov instability induced by a shock-accelerated square light bubble

The Richtmyer-Meshkov (RM) instability has long been an interesting subject due to its fundamental significance in scientific research. In the current study, the contribution of shock Mach number on the evolution of the RM instability induced by a shock-accelerated square light bubble is investigated numerically. The shock Mach number causes significant changes in flow morphology, resulting in complex wave patterns, vorticity generation, vortex formation, and bubble deformation. The Mach number effects are explored in detail through various physical phenomena such as vorticity production, kinetic energy, dissipation rate, and enstrophy.

Alfvén Number for the Richtmyer–Meshkov Instability in Magnetized Plasmas

Abstract The magnetohydrodynamical (MHD) evolution of the Richtmyer–Meshkov instability (RMI) is investigated using two-dimensional MHD simulations. The RMI is suppressed by a strong magnetic field, whereas the RMI amplifies an ambient magnetic field by many orders of magnitude if the seed field is weak. We have found that the suppression and amplification processes can be evaluated continuously along with the amplitude of the Alfvén number R A , which is defined as the ratio of the linear growth velocity of the RMI to the Alfvén speed at the interface. When the Alfvén number is less than unity, the Lorentz force acting on the fluid mitigates the unstable motion of the RMI significantly, and the interface oscillates stably in this limit. If R A ≳ 1, on the other hand, the surface modulation increases due to the growth of the RMI. The maximum strength of the magnetic field is enhanced up to by a factor of R A . This critical feature is universal and independent of the initial Mach number of the incident shock, the Atwood number, corrugation amplitude, and even the direction of the initial magnetic field.

Convergent Richtmyer–Meshkov instability on a light gas layer with perturbed inner and outer surfaces

The instability of an annular helium gas layer surrounded by air with sinusoidal inner and outer interfaces, formed by a novel soap-film technique, impacted by a cylindrically convergent shock is experimentally studied in a semi-annular shock tube. Detailed evolution of the interfaces and wave patterns is captured by a high-speed Schlieren system. The focus is placed on the influences of layer thickness and phase difference between the inner and outer interfaces on the instability development. It is found that the larger the layer thickness, the quicker the early stage development of the outer interface. This is because the layer thickness affects the arrival time of the reflected shock (RS) at the outer interface and further determines the direction of baroclinic vorticity deposited on the outer interface by RS; namely, RS inhibits or promotes the instability growth depending on the layer thickness. It is also found that phase difference between the inner and outer perturbations produces a negligible (an evident) influence on the early stage (late-stage) instability growth at the outer interface, whereas a considerable (weak) influence on the early stage (late-stage) instability growth at the inner interface. This finding suggests that the early stage development of the outer (inner) interface can be modulated by changing the layer thickness (perturbation phase difference). Empirical coefficient in the Charakhch'an model [J. Appl. Mech. 41, 23–31 (2000)] is calculated to be β=0.52 by comparing the prediction with the experimental results. The model with β=0.52 gives a reasonable prediction of the post-reshock growth rate for all the cases considered in this work.

Large eddy simulation of converging Richtmyer–Meshkov instability based on subgrid-scale dissipation similar method

This paper focuses on large eddy simulation of the Richtmyer–Meshkov instability (RMI) in spherical and cylindrical converging geometries with a Mach number [Formula: see text] based on subgrid-scale (SGS) dissipation similar method (SDSM). Based on the converging RMI problem, we obtain from a priori test and theoretical analysis that the suggested method can provide accurate structural correlation while ensuring the computational stability. Comparing the numerical simulation results with direct numerical simulation (DNS) and existing model in converging RMI problem, we could find that the suggested method overcomes some defects of the existing model, such as the Smagorinsky model cannot predict transition accurately and the helicity model can only predicts the quasi-two-dimensional flow precisely. It provides a beneficial tool for the research of converging RMI.

Laser astrophysics experiment on the amplification of magnetic fields by shock-induced interfacial instabilities.

Laser experiments are becoming established as tools for astronomical research that complement observations and theoretical modeling. Localized strong magnetic fields have been observed at a shock front of supernova explosions. Experimental confirmation and identification of the physical mechanism for this observation are of great importance in understanding the evolution of the interstellar medium. However, it has been challenging to treat the interaction between hydrodynamic instabilities and an ambient magnetic field in the laboratory. Here, we developed an experimental platform to examine magnetized Richtmyer-Meshkov instability (RMI). The measured growth velocity was consistent with the linear theory, and the magnetic-field amplification was correlated with RMI growth. Our experiment validated the turbulent amplification of magnetic fields associated with the shock-induced interfacial instability in astrophysical conditions. Experimental elucidation of fundamental processes in magnetized plasmas is generally essential in various situations such as fusion plasmas and planetary sciences.

A volume-of-fluid reconstruction based interface sharpening algorithm for a reduced equation model of two-material compressible flow

In this paper we present a numerical method for the simulation of two-material flows governed by the compressible unsteady Euler equations. A system of six equations is used, with a pressure relaxation step which ensures convergence to the equivalent five-equation model. The numerical method employs a volume-of-fluid interface tracking method in order to maintain a sharp interface indefinitely, along with a robust update procedure for interfacial cells which ensures density and internal energy positivity. Numerical results are presented for a range of test cases, including for liquid–gas shock–bubble interaction and cylindrically convergent Richtmyer–Meshkov instability between metal and air. Results are in agreement with theoretical data, and compare well to other approaches designed to sharpen the material interface in the five-equation model.

Effects of the secondary baroclinic vorticity on the energy cascade in the Richtmyer–Meshkov instability

We investigate the effect of the secondary baroclinic vorticity (SBV) on the energy cascade in the mixing induced by the multi-mode Richtmyer–Meshkov instability (RMI). With the aid of vorticity-based simplified models and the vortex-surface field, we find that the effect of the SBV peaks at a critical time when the vortex reconnection widely occurs in the mixing zone. Before the critical time, spikes and bubbles evolve almost independently, and we demonstrate that the variation of the kinetic energy spectrum induced by the SBV has the $-1$ scaling law at intermediate wavenumbers using the model of vortex rings. This SBV effect causes the slope of the total energy spectrum at intermediate wavenumbers to evolve towards $-3/2$ at the critical time. Subsequently, the SBV effect diminishes and the energy spectrum decays to the $-5/3$ law. Inspired by the vortex dynamics, we develop a model for estimating the mixing width and validate the model using numerical simulations of the multi-mode RMI with various modes of initial perturbations. This model captures the nonlinear growth of the mixing width before the self-similar growth stage.

Dynamics of cellular flame deformation after a head-on interaction with a shock wave: reactive Richtmyer–Meshkov instability

Abstract

Mixing driven by transient buoyancy flows.II. Flow dynamics

The chaotic advection of the interface between two miscible liquids inside a closed cavity, generated by a damped oscillatory buoyancy-driven (BD) regular flow field, is investigated experimentally for BD mixing. The Lagrangian history of interface motion, determined using the planar laser-induced fluorescence and the photographic full-field view method, is contrasted against the Eulerian flow field measured from particle image velocimetry. Chaotic advection stretches and folds the interface at an early stage to produce an asymmetric pairwise Rayleigh–Taylor (RT) morphology (RTM) structure from long wavelength RT instability and short-time Richtmyer–Meshkov instability and its fractal interface structure at a high impulsive-Reynolds number. The mechanism of folding, from global bifurcation of the flow field, caused by a hyperbolic point, served as an organizing center for multiple vortex interactions. The intermediate-stage kinematics of the RTM structure exhibits RT mixing and shows unfolding of the lamellar structure from the net effect of stretching, folding, and molecular diffusion prior to its breakdown; and it has a probabilistic outcome of exhibiting topological transitions through a breakup of the RTM structure in phase space from necking singularity and pinch-off, indicating sensitivity to the initial conditions. The effectiveness of mixing determined from mixing efficiency is contrasted against mechanical and lamellar models of mixing. The determination of topological entropy, from an approximate Gaussian distribution of the interface length stretch, yields time scale for information decay comparable to time scale for which a low-order horseshoe map emerges from flow, indicating local chaos of the interface. The late-stage breakdown of the RTM structure from internal and wall collision drives the interaction between advection and diffusion, which indicates that critical mixing time scales as the logarithmic of Peclet number, comparable to time-periodic sine flow and blinking vortex flow chaotic mapping models.

Experimental generation of spherical converging shock waves

Spherical converging shock waves with incoming Mach number 1.18 are generated in a conical test chamber fitted to a conventional square-section shock tube. A wave cutter is employed to ensure a proper shock transition from the square to a cylindrical straight pipe installed upstream of the convergent section. The incident planar wave is transformed into a spherical shock by the use of an ellipsoidal membrane acting as a gas lens separating two gases with different densities. The transmitted shock wave propagates within the conical section, and accelerates towards the apex. The trajectory and the shape of the shock wave are both characterized by planar Mie scattering. The spherical shock follows the similarity solution proposed by Guderley (1942), whose trajectory agrees very well with the numerical simulation of the Chester-Chisnell-Whitham (CCW) theory for the geometry considered. The procedure demonstrated here provides a potential method for future investigations of shock focusing and Richtmyer–Meshkov instability in spherical geometry.

Impact of bulk viscosity on flow morphology of shock-accelerated cylindrical light bubble in diatomic and polyatomic gases

Shock-accelerated bubbles have long been an intriguing topic for understanding the fundamental physics of turbulence generation and mixing caused by the Richtmyer–Meshkov instability. In this study, the impact of bulk viscosity on the flow morphology of a shock-accelerated cylindrical light bubble in diatomic and polyatomic gases is investigated numerically. An explicit mixed-type modal discontinuous Galerkin scheme with uniform meshes is employed to solve a two-dimensional system of unsteady physical conservation laws derived rigorously from the Boltzmann–Curtiss kinetic equations. We also derive a new complete viscous compressible vorticity transport equation including the bulk viscosity. The numerical results show that, during the interaction between a planar shock wave and a cylindrical light bubble, the bulk viscosity associated with the viscous excess normal stress in diatomic and polyatomic gases plays an important role. The diatomic and polyatomic gases cause significant changes in flow morphology, resulting in complex wave patterns, vorticity generation, vortex formation, and bubble deformation. In contrast to monatomic gases, diatomic and polyatomic gases produce larger rolled-up vortex chains, various inward jet formations, and large mixing zones with strong, large-scale expansion. The effects of diatomic and polyatomic gases are explored in detail through phenomena such as the vorticity generation, degree of nonequilibrium, enstrophy, and dissipation rate. Furthermore, the evolution of the shock trajectories and interface features is investigated. Finally, the effects of bulk viscosity on the flow physics of shock-accelerated cylindrical light bubble are comprehensively analyzed.

Accelerating In-Transit Co-Processing for Scientific Simulations Using Region-Based Data-Driven Analysis

Increasing processing capabilities and input/output constraints of supercomputers have increased the use of co-processing approaches, i.e., visualizing and analyzing data sets of simulations on the fly. We present a method that evaluates the importance of different regions of simulation data and a data-driven approach that uses the proposed method to accelerate in-transit co-processing of large-scale simulations. We use the importance metrics to simultaneously employ multiple compression methods on different data regions to accelerate the in-transit co-processing. Our approach strives to adaptively compress data on the fly and uses load balancing to counteract memory imbalances. We demonstrate the method’s efficiency through a fluid mechanics application, a Richtmyer–Meshkov instability simulation, showing how to accelerate the in-transit co-processing of simulations. The results show that the proposed method expeditiously can identify regions of interest, even when using multiple metrics. Our approach achieved a speedup of 1.29× in a lossless scenario. The data decompression time was sped up by 2× compared to using a single compression method uniformly.

Time-resolved particle image velocimetry measurements of the turbulent Richtmyer–Meshkov instability

Abstract

Ion kinetic effects on the evolution of Richtmyer–Meshkov instability and interfacial mix

Plasma effects, such as the multi-component kinetic diffusion and self-generated electromagnetic fields, are recognized as a pivotal key to understanding the physics of interface evolution in inertial confinement fusion and supernova remnants. In this work, a two-dimensional hybrid fluid-PIC code is used to investigate the ion kinetic effects of the single-mode Richtmyer–Meshkov instability (RMI) at the interface between hydrogen plasma and carbon plasma. After an electrostatic shockwave passing through the perturbed interface, the RMI, which reshapes the interface, grows via the vorticity depositing as well as the self-generated magnetic field. After scaling the growth of the interfacial mix region with time, the density transition layer has been found to exceed the disturbance wavelength and lead to a suppression of the instability evolution finally.

Modeling the Richtmyer–Meshkov Instability Development Using the Discontinuous Galerkin Method and Locally Adaptive Meshes

Modeling the Richtmyer–Meshkov Instability Development Using the Discontinuous Galerkin Method and Locally Adaptive Meshes

Impact of a thermally stratified energy source on the bow shock wave and aerodynamic characteristics of a body

This paper presents numerical modelling of a thermally stratified energy source’s effect on the supersonic flow past a body “double-wedge - plate”. A multiple generation of the Richtmyer-Meshkov instabilities was obtained. These instabilities cause almost complete destruction of the bow shock front inside the source area and form a new multi-vortex mechanism of affecting the streamlined body. The defining parameters of the effect of stratified and homogeneous energy sources with equal values of total energy are analysed. The possibility of a significant decrease in the temperature at the vertex of the double-wedge and in the average front surface temperature due to the redistribution of source energy between layers has been established.

The Effect of Liquid Tamping Media on the Growth of Richtmyer–Meshkov Instability in Copper

The Richtmyer–Meshkov instability (RMI) arises at an impulsively accelerated interface between two materials of different density. Historically, this instability was studied in fluids. Recently, RMI studies have been extended to investigate material properties of solids. Material strength at high strain-rates in solids have been extracted from the amplitude and growth of the RMI spike in an untamped environment, specifically, the metal-vacuum interface. This technique has also been shown to elucidate material properties in a distended tamping media, metal-porous solid interface. Here, a bridge to understanding the nonlinear mechanical behavior of copper into a liquid tamping media is investigated experimentally and computationally. We show the RMI growth rate and resulting profile are dependent on initial shock strength, as well as the nondimensional perturbation, with an initial Atwood number of $$-0.78$$ . Data collected from a tamped liquid environment range in metal breakout pressures up to ten GPa. This information is used to calibrate and validate numeric model parameters. The oscillatory shock front in the liquid tamping media is used to approximate the viscosity from a transient 1-D analytic approximation. The viscosity is found to be in agreement with other experimental work, however is not determined to be the only dissipative force in the experiment. Hydrocode simulations of our experiments show reasonable alignment with current and previously published work.

A dislocation-based dynamic strength model for tantalum across a large range of strain rates

We present a dislocation-based strength model for tantalum that captures the plastic deformation at high strain rates above 103s−1. The model has its origins in molecular dynamic simulations and it is implemented in a 3D continuum framework. We calibrate and validate the model using Split Hopkinson Pressure Bar, plate impact, and Richtmyer–Meshkov instability experiments. With the validated model, we can computationally generate stress–strain curves at strain rates of 103−107s−1 for samples with various initial dislocation densities. Based on the results, we show that the dynamic yield strength of annealed tantalum at high strain rates is followed by softening since mobile dislocation densities rapidly increase due to the high shear stress. This strain-softening is evident only at the high strain rate regime and it is much less pronounced in cold-worked Ta.

Behavior of a shock-accelerated heavy cylindrical bubble under nonequilibrium conditions of diatomic and polyatomic gases

The physical problem of a shock-accelerated bubble has long been a fascinating subject in the study of the Richtmyer-Meshkov (RM) instability. In the current study, the behavior of a shock-accelerated heavy cylindrical bubble under the nonequilibrium conditions of diatomic and polyatomic gases is investigated numerically in describing the RM instability. In contrast to a monatomic gas, the generation of larger rolled-up vortex chains, different kinds of outward jet formation, and large mixing zone with strong and large expansion are observed in diatomic and polyatomic gases.