Growth Of Richtmyer-Meshkov Instability Research Articles

Modal Discontinuous Galerkin Simulations of Richtmyer–Meshkov Instability at Backward-Triangular Bubbles: Insights and Analysis

This paper investigates the dynamics of Richtmyer–Meshkov instability (RMI) in shocked backward-triangular bubbles through numerical simulations. Two distinct gases, He and SF6, are used within the backward-triangular bubble, surrounded by N2 gas. Simulations are conducted at two distinct strengths of incident shock wave, including Ms=1.25 and 1.50. A third-order modal discontinuous Galerkin (DG) scheme is applied to simulate a physical conservation laws of two-component gas flows in compressible inviscid framework. Hierarchical Legendre modal polynomials are employed for spatial discretization in the DG platform. This scheme reduces the conservation laws into a semi-discrete set of ODEs in time, which is then solved using an explicit 3rd-order SSP Runge–Kutta scheme. The results reveal significant effects of bubble density and Mach numbers on the growth of RMI in the shocked backward-triangular bubble, a phenomenon not previously reported. These effects greatly influence flow patterns, leading to intricate wave formations, shock focusing, jet generation, and interface distortion. Additionally, a detailed analysis elucidates the mechanisms driving vorticity formation during the interaction process. The study also thoroughly examines these effects on the flow fields based on various integral quantities and interface characteristics.

Freeze out of multi-mode Richtmyer–Meshkov instability using particles

Richtmyer–Meshkov instability (RMI) occurs when a shock wave traverses an interface separated by two fluids with different densities. Achieving “freeze out” (i.e., “killing” of RMI), a critical objective in RMI research for engineering applications, remains an open problem in the context of multi-mode RMI. Here, we introduce particles into the flow field to achieve freeze out, which is attributed to the momentum non-equilibrium effect inherent in the gas–particle phases. This effect facilitates the transfer of momentum and energy from the fluid to the particles, thereby mitigating the amplification of initial perturbations within the mixing zone. We developed a one-dimensional model to predict the velocities of the mixing zone boundaries in multiphase RMI. The growth of RMI was suppressed by controlling the velocities of the mixing zone boundaries through particle effects. A non-dimensional freeze out criterion was derived, incorporating the gas–particle coupling along with the particle volume fraction effect. The condition for freezing a multi-mode RMI was specially designed to estimate the required particle volume fraction to achieve the freeze out. A series of simulations were conducted using a well-verified compressible multiphase particle-in-cell method to validate the realization of freeze out. Further analysis reveals that the designed condition exhibits applicability across a spectrum of multi-mode perturbations, including both broadband and narrowband perturbations, as well as various initial Mach numbers.

Richtmyer–Meshkov instability at high Mach number: Non-Newtonian effects

The Richtmyer–Meshkov instability (RMI) occurs when a shock wave passes through an interface between fluids of different densities, a phenomenon prevalent in a variety of scenarios including supersonic combustion, supernovae, and inertial confinement fusion. In the most advanced current numerical modeling of RMI, a multitude of secondary physical phenomena are typically neglected that may crucially change in silico predictions. In this study, we investigate the effects of shear-thinning behavior of a fluid on the RMI at negative Atwood numbers via numerical simulations. A parametric study is carried out over a wide range of Atwood and Mach numbers that probes the flow dynamics following the impact on the interface of the initial shock wave and subsequent, reflected shocks. We demonstrate agreement between our numerical results and analytical predictions, which are valid during the early stages of the flow, and examine the effect of the system parameters on the vorticity distribution near the interface. We also carry out an analysis of the rate of vorticity production and dissipation budget which pinpoints the physical mechanisms leading to instability due to the initial and reflected shocks. Our findings indicate that the shear-thinning effects have a significant impact on instability growth and the development of secondary instabilities, which manifest themselves through the formation of Kelvin–Helmholtz waves. Specifically, we demonstrate that these effects influence vorticity generation and damping, which, in turn, affect the RMI growth. These insights have important implications for a range of applications, including inertial confinement fusion and bubble collapse within non-Newtonian materials.

Analysis of single-mode Richtmyer–Meshkov instability using high-order incompressible vorticity—streamfunction and shock-capturing simulations

Two- and three-dimensional simulation results obtained using a new high-order incompressible, variable-density vorticity–streamfunction (VS) method and data from previous ninth-order weighted essentially nonoscillatory (WENO) shock-capturing simulations [M. Latini and O. Schilling, “A comparison of two- and three-dimensional single-mode reshocked Richtmyer-Meshkov instability growth,” Physica D 401, 132201 (2020)] are used to investigate the nonlinear dynamics of single-mode Richtmyer–Meshkov instability using a model of a Mach 1.3 air(acetone)/SF6 shock tube experiment [J. W. Jacobs and V. V. Krivets, “Experiments on the late-time development of single-mode Richtmyer–Meshkov instability,” Phys. Fluids 17, 034105 (2005)]. A comparison of the density fields from both simulations with the experimental images demonstrates very good agreement in the large-scale structure with both methods but differences in the small-scale structure. The WENO method captures the small-scale disordered structure observed in the experiment, while the VS method partially captures such structure and yields a strong rotating core. The perturbation amplitude growth from the simulations generally agrees well with the experiment. The simulation bubble and spike amplitudes agree well at early times. At later times, the WENO bubble amplitude is smaller than the VS amplitude and vice versa for the spike amplitude. The predictions of nonlinear single-mode instability growth models are shown to agree with the simulation amplitudes at early-to-intermediate times but underpredict the amplitudes at later times in the nonlinear regime. Visualizations of the mass fraction and enstrophy isosurfaces, velocity and vorticity fields, and baroclinic vorticity production and vortex stretching terms from the three-dimensional simulations indicate that, with the exception of the small-scale structure within the rollups, the VS and WENO results are in good agreement.

Modification of Richtmyer–Meshkov instabilities via layered explosive charge design

In this numerical study, we investigate the effects of layered high explosive (HE) charge design on Richtmyer–Meshkov instability (RMI) in metal plates with sinusoidal surface features. The detonation wave from the HE induces a shock in the metal target that subsequently interacts with the surface features; this results in vortex formation and ultimately RMI. We seek to modify RMI by altering the detonation wave characteristics. The modification is investigated in a twofold manner: first, by varying the initial design of the unconfined surface of the target and second, by varying the charge design and composition. Within a limited scope of this design space, a wide variety of behaviors related to RMI growth are observed. Mechanistic actions, including exaggerated front curvature, behind these modifications are proposed. Charge designs, which modify RMI the most for a select target design, are then presented.

Numerical investigation of shock Mach number effects on Richtmyer–Meshkov instability in a heavy square bubble

This study conducts a two-dimensional numerical investigation of incident shock Mach number effects on the Richtmyer–Meshkov (RM) instability after a shock wave impulsively drives a heavy square bubble. The square bubble is composed of SF6 gas, which is surrounded by nitrogen gas. Five different shock Mach numbers are considered: Ms=1.12, 1.22, 1.4, 1.7, and 2.1. Two-dimensional compressible Euler equations for two-component gas flows are simulated with a high-order modal discontinuous Galerkin solver. For validation, the numerical results are compared with the existing experimental results and are found to be in good agreement. The present results reveal that the incident shock Mach number is critical in the growth of RM instability in a heavy square bubble. The shock Mach number affects flow morphology significantly, resulting in complicated wave patterns, shock focusing, jet creation, bubble deformation, and vorticity generation. The convergent shape of the bubble causes shock focusing, which creates a local high-pressure zone and, as a result, an outward jet generation. It is found that the bubble deforms differently with increasing shock Mach number, and the different shock Mach numbers alter the distance between the shock focusing position and the downstream bubble interface. The effects of shock Mach numbers are investigated in depth through physical phenomena such as vorticity production, kinetic energy, and enstrophy. Finally, the shock Mach number impacts on the time-variations of the shock trajectories and interface structure are thoroughly investigated.

Non-Richtmyer–Meshkov instability ejecta production based on shallow bubble collapse

The study of shock-driven ejecta production has focused on Richtmyer–Meshkov instability (RMI) growth from geometric features of the material surface. Extensive study of this mechanism under both single- and multiple-shock conditions has found that the ejected mass tends to be closely associated with the shocked surface phase, and its temperature is not dramatically greater than the hydrodynamic shock temperature of the bulk. In this work, we propose and demonstrate a new ejecta production mechanism that can occur under multiple-shock conditions based on the collapse of bubbles near the free surface of the material. This mechanism produces ejected mass that is much greater in quantity than observed in the RMI case. The particles are much hotter than predicted by the shock Hugoniot state, and the ejected mass does not appear to be strongly dependent upon initial surface finish. The ejecta source extends into the material with no clear remaining free surface. We name this mechanism Shallow Bubble Collapse (SBC) and discuss the conditions under which it activates. We demonstrate resolved modeling methods that enable the calculation, design, and study of SBC as a mechanism and perform a series of experiments to compare with the models. Under some multiple-shock conditions, SBC ejection produces ten times more ejected mass than RMI growth.

Design optimization for Richtmyer–Meshkov instability suppression at shock-compressed material interfaces

The Richtmyer–Meshkov instability (RMI) is a phenomenon that occurs at the interface of two substances of different densities due to an impulsive acceleration, such as a shock wave passing through this interface. Under these conditions, the instability can be seen as interface perturbations begin to grow into narrow jets or spikes of one substance that propagate into the other. In some cases, this interface may involve an elastic–plastic material, which can play a significant role in the development and behavior of the RMI. The ability to effectively control RMI jetting and spike growth is one major limiting factor in technological challenges, such as inertial confinement fusion, that involve using high-pressure shock waves to implode a fuel target. The propagation of RMI growth can lead to increased asymmetry in this implosion process and significantly reduce the obtained energy yield. We use hydrodynamics simulations of impactor shock-compression experiments and methods based in design optimization to suppress RMI spike growth by altering the geometry and other properties of a shock-compressed elastic–plastic material target that shares an interface with atmospheric air. These hydrodynamics simulations use an arbitrary Lagrangian–Eulerian method with a high-order finite element approach. Our results demonstrate that RMI suppression can be achieved by intentionally creating a separate upstream interface instability to counteract the growth of long narrow RMI spikes at an interface with initial perturbations.

Exploring implosion designs for increased compression on the National Ignition Facility using high density carbon ablators

It has long been recognized that high compression, and hence good confinement, is essential to achieving high yields in inertial confinement fusion implosions. In pursuit of multi-megajoule yields on the National Ignition Facility (NIF), a new campaign has begun aimed at testing the hypothesis that controlling hydrodynamic stability is key to achieving effective higher compression with the high density carbon ablators currently fielded on NIF. This campaign is built around a new implosion design, called SQ-n, that is derived from the uniquely stable Bigfoot design tested on NIF in 2016–2019. While very stable and with performance that was quite close to one-dimensional expectations, Bigfoot was a relatively high adiabat, and consequently lower compression design. The goal of SQ-n is then to evolve Bigfoot toward a higher compression design but without compromising its unique stability characteristics. Specifically, SQ-n adopts a ramped foot pulse shape to minimize early time Richtmyer–Meshkov instability growth and uses an ablator dopant distribution extending all of the way to the fuel–ablator interface that simulations suggest further reduces perturbation growth. This paper describes the design philosophy pursued with SQ-n, the results of instability modeling of the candidate design, and the experimental campaign planned to test these ideas in the near future.

Chemical reaction of Ni/Al interface associated with perturbation growth under shock compression

The exothermic reaction of Ni/Al laminates always starts from the interface, and the role of interfacial instability in the shock-induced chemical reaction has not been clarified. This work reports the Richtmyer–Meshkov (RM) instability growth, atomic diffusion, and chemical reaction of Ni/Al interface under shock compression based on atomistic simulations. For shocking from Al to Ni, the interface experiences finite collapse and exhibits weak localized reaction. The diffusion of solid Ni to molten Al will be inhibited due to the formation of NiAl phase, and continuous inter-diffusion occurs with the melting of Ni. For shocking from Ni to Al, a small amount of NiAl structure is formed due to the atomic residue during defect collapse. RM instability growth is observed at higher shock intensity, which significantly promotes the atomic mixing and results in a power-law increase in the number of diffusing atoms. Meanwhile, the chemical reaction propagates rapidly from the vortex to the head of the spike accompanied by the decomposition of many clusters, with the nonlinear development of RM instability. The number and the size of Ni clusters no more satisfy the simple power-law relationship for which we propose an improved power-law distribution. Interestingly, the growth of nanoscale perturbation approximately satisfies the logarithmic law with time, but the linear growth stage is inhibited due to significant inter-diffusion, especially for the small wavelength. Thus, the mixing width and the reaction degree are positively correlated with the initial wavelength in our simulation scale, which is contrary to the RM growth law of the free surface.

Influence of initial particle configuration upon sphericity of shock loaded density interface in SPH modelling of Richtmyer-Meshkov instability

The Richtmyer-Meshkov Instability (RMI) occurs when a perturbed interface between two fluids of different densities undergoes impulsive acceleration by, for example, a shock wave. Its study is important for gaining better understanding of processes governing inertial confinement fusion where a spherical solid deuterium-tritium (DT) capsule filled with the DT gas is compressed by a powerful laser [1]. The imploding shock moving to the center of the spherical shell causes the RMI to form on its inner surface due to a large density difference between solid and gaseous DT phases, which leads to a rapid growth of initially present randomperturbations. Usually, the density interface consists of random perturbations (e.g., surface roughness, machining inaccuracies, etc.) which initially grow linearly before nonlinear effects emerge. To improve reliability of shock-driven flow simulations, it is necessary to understand the factors which inuence the RMI growth. Our work aims to find the best initial particle configuration that does not introduce artificial perturbations of the spherical density interface. The shocked interface must preserve spherical symmetry if no perturbations are applied. In order to reduce the number of simulated particles in calculation, it is necessary to adapt spatial resolution, i.e., to increase the concentration of particles in target regions.

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.

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.

Study on Richtmyer-Meshkov instability at heavy/lightsingle-mode interface

The Richtmyer-Meshkov (RM) instability at a heavy/light single-mode interface is studied both experimentally and numerically in this work, focusing on the interface structure evolution and the perturbation amplitude growth. The difference between the RM instability of the heavy/light interface and the light/heavy case (J. Fluid Mech., 2018, 853: R2) is discussed. Experimentally, an advanced soap film technique is adopted to generate an SF6/air gaseous interface with a controllable shape such that the instability development can be accurately examined. Detailed evolutions of the interface morphology and the wave pattern are captured by a high-speed video camera combined with schlieren photography. It is observed that the interfacial morphology presents an evident stratification after the phase inversion of the interface (the bubble (spike) reverses to be a spike (bubble)), which is mainly ascribed to the droplet cloud produced by the rupture of the soap film impacted by an incident shock wave. Numerically, a high-order accurate solver for compressible multi-phase flow, which has been thoroughly validated in previous shock-interface interaction studies, is employed to simulate the present heavy/light RM instability. The numerical results show good agreements with the experimental ones, which enables us to perform a detailed flow analysis. Different from the light/heavy case, after the shock impact, the heavy/light interface immediately enters the phase reversal process. After the phase reversal, the interface experiences successively the linear and nonlinear growths, which is similar to the light/heavy case. The reliable experimental and numerical results here allow us to examine the validity of the previous linear and nonlinear models for the heavy/light RM instability growth. It is found that the linear model of Meyer & Blewett (Phys. Fluids, 1972, 15: 753–759) gives a good prediction of the perturbation growth at linear stage up to a dimensionless time of 0.7, and the empirical model of Dimonte & Ramaprabhu (Phys. Fluids, 2010, 22: 014104) reasonably predicts the perturbation growth at the nonlinear stage, which is different from the light/heavy case where the model of Zhang & Guo (J Fluid Mech., 2016, 786: 47–61) gives the best prediction as suggested by an elaborate experimental study. Our study may facilitate the thorough understanding of the heavy/light RM instability and also can serve as a benchmark for new models.

Modeling and simulation of a single-mode multiphase Richtmyer–Meshkov instability with a large Stokes number

This study focuses on the effects of a large Stokes number (St) on the perturbation growth in linear and nonlinear stages of a Richtmyer–Meshkov instability (RMI) in a gas-particle system, which to the best of our knowledge has not been previously reported. A linear growth model is developed by linear stability analysis and numerically verified by the compressible multiphase particle-in-cell (CMP-PIC) method. Additionally, the RMI growth characteristics in the nonlinear stage are also investigated by CMP-PIC. For the linear growth model, two major differences characterize the effects of a large St. The first one is that an RMI with a large St, which performs significantly different from the RMI with a small St, is induced and driven only by the density difference of the gas-phase and totally independent of particle density. Second, due to the significant momentum coupling effects between gas and particle phases, which govern the gas-particle flow, the growth rate experiences exponential decay, even in the linear RMI stage. The decay behavior performs markedly different from any previous RMI models, especially those of the original single-phase RMI and the gas-particle RMI with a small St. Notably, in the nonlinear stage of the RMI with a large particle volume fraction, the decay effects are much more pronounced and lead to a fall in the growth rate to almost zero, which is not found in any other type of RMI. These findings offer the possibility to develop a new method to control the development of hydrodynamic instability.

A comparison of two- and three-dimensional single-mode reshocked Richtmyer–Meshkov instability growth

The growth dynamics of two- and three-dimensional single-mode reshocked Richtmyer–Meshkov instability are compared systematically using data from high-resolution implicit large-eddy simulations of a model of the Mach 1.3 air(acetone) and sulfur hexafluoride (Jacobs and Krivets, 2005) shock tube experiment. The vorticity deposition by the incident shock and the dynamics of interface evolution are examined quantitatively and qualitatively. The perturbation amplitudes from the two- and three-dimensional simulations are compared to the experimental data and to the predictions of several nonlinear instability growth models. It is shown that the perturbation amplitudes from the two- and three-dimensional simulations with matching initial Richtmyer velocity are in excellent agreement with the experimental data. In addition, the dynamics of reshock (not considered in the experiment) are described in detail, and the post-reshock mixing layer amplitude growth rate is compared to the predictions of several reshock models. It is shown that using two-dimensional simulations to understand three-dimensional dynamics is valid only at early-to-intermediate times before reshock; at intermediate-to-late times after reshock the three-dimensional growth is generally larger than the corresponding two-dimensional growth. The reshock dynamics are also different between two and three dimensions. The quantitative results, together with visualizations of the flow field, were also used to contrast the difference between two- and three-dimensional vorticity and enstrophy dynamics.

Linear simulations of the cylindrical Richtmyer-Meshkov instability in magnetohydrodynamics

Numerical simulations and analysis indicate that the Richtmyer-Meshkov instability (RMI) is suppressed in ideal magnetohydrodynamics (MHD) in Cartesian slab geometry. Motivated by the presence of hydrodynamic instabilities in inertial confinement fusion and suppression by means of a magnetic field, we investigate the RMI via linear MHD simulations in cylindrical geometry. The physical setup is that of a Chisnell-type converging shock interacting with a density interface with either axial or azimuthal (2D) perturbations. The linear stability is examined in the context of an initial value problem (with a time-varying base state) wherein the linearized ideal MHD equations are solved with an upwind numerical method. Linear simulations in the absence of a magnetic field indicate that RMI growth rate during the early time period is similar to that observed in Cartesian geometry. However, this RMI phase is short-lived and followed by a Rayleigh-Taylor instability phase with an accompanied exponential increase in the perturbation amplitude. We examine several strengths of the magnetic field (characterized by β=2pBr2) and observe a significant suppression of the instability for β ≤ 4. The suppression of the instability is attributed to the transport of vorticity away from the interface by Alfvén fronts.

The Growth of Richtmyer-Meshkov Instability under Multiple Impingements

The growth of multi-mode Richtmyer-Meshkov instability under multiple impingements and the effect of initial shock strength on the growth of RMI are numerically investigated. We obtain the time evolution of turbulent mixing zone width for initial shock with different strength. The results show that the turbulent mixing zone width grows in a different manner at different stage but strictly in a similar way for the initial shock with different strength. Also, the initial shock strength has a significant effect on the growth rate of turbulent mixing zone width, especially before reshock, but can not change the growth laws in the whole process.

Direct simulation Monte Carlo investigation of the Richtmyer-Meshkov instability

The Richtmyer-Meshkov instability (RMI) is investigated using the Direct Simulation Monte Carlo (DSMC) method of molecular gas dynamics. Due to the inherent statistical noise and the significant computational requirements, DSMC is hardly ever applied to hydrodynamic flows. Here, DSMC RMI simulations are performed to quantify the shock-driven growth of a single-mode perturbation on the interface between two atmospheric-pressure monatomic gases prior to re-shocking as a function of the Atwood and Mach numbers. The DSMC results qualitatively reproduce all features of the RMI and are in reasonable quantitative agreement with existing theoretical and empirical models. Consistent with previous work in this field, the DSMC simulations indicate that RMI growth follows a universal behavior.

An in-flight radiography platform to measure hydrodynamic instability growth in inertial confinement fusion capsules at the National Ignition Facility

A new in-flight radiography platform has been established at the National Ignition Facility (NIF) to measure Rayleigh–Taylor and Richtmyer–Meshkov instability growth in inertial confinement fusion capsules. The platform has been tested up to a convergence ratio of 4. An experimental campaign is underway to measure the growth of pre-imposed sinusoidal modulations of the capsule surface, as a function of wavelength, for a pair of ignition-relevant laser drives: a “low-foot” drive representative of what was fielded during the National Ignition Campaign (NIC) [Edwards et al., Phys. Plasmas 20, 070501 (2013)] and the new high-foot [Dittrich et al., Phys. Rev. Lett. 112, 055002 (2014); Park et al., Phys. Rev. Lett. 112, 055001 (2014)] pulse shape, for which the predicted instability growth is much lower. We present measurements of Legendre modes 30, 60, and 90 for the NIC-type, low-foot, drive, and modes 60 and 90 for the high-foot drive. The measured growth is consistent with model predictions, including much less growth for the high-foot drive, demonstrating the instability mitigation aspect of this new pulse shape. We present the design of the platform in detail and discuss the implications of the data it generates for the on-going ignition effort at NIF.