Richtmyer-Meshkov Instability Research Articles

Numerical study of Richtmyer-Meshkov instability in finite thickness fluid layers with reshock

Numerical study of Richtmyer-Meshkov instability in finite thickness fluid layers with reshock

Divergent Richtmyer–Meshkov instability under different shock strengths

Richtmyer–Meshkov (RM) instability at a single-mode interface impacted by a cylindrical divergent shock with low to moderate Mach numbers is investigated experimentally. The motion of an unperturbed interface is first examined to obtain the background flow. The shocked interface moves uniformly at the early stage, but later decelerates. The stronger the incident shock, the larger the interface deceleration, which is reasonably predicted by a one-dimensional model considering the effect of postshock non-uniformity. Such a deceleration greatly inhibits the growths of harmonics of an initially perturbed interface and, consequently, the divergent RM instability presents very weak nonlinearity from early to late stages. Particularly, higher-Mach-number cases present weaker nonlinearity due to larger deceleration there. This abnormal linear growth regime is reported for the first time. Benefiting from this, the incompressible linear model holds validity at all stages of divergent RM instability. It is also found that compressibility inhibits the initial growth rate, but produces a weak influence on the subsequent instability growth.

Resistive diffusion in magnetized ICF implosions: Reduced magnetic stabilization of the Richtmyer–Meshkov instability

Resistive diffusion is typically regarded to be negligible in magnetized ICF experiments, with magnetic flux effectively compressed during the implosion. In this work the Richtmyer–Meshkov instability at the ice-ablator interface is taken as an example for investigating resistive effects. For a high temperature (≈100eV) interface with magnetic field applied perpendicular to shock propagation, perturbation growth is suppressed by magnetic tension. However, for lower temperature interfaces the resistive diffusion prevents substantial magnetic field twisting at small scales. ICF implosion simulations are then used to assess magnetic diffusivity at different interfaces; the ice-ablator interface is found to be too resistive for the magnetic fields to enhance stability. For Rayleigh–Taylor growth at the hot-spot edge, on the other hand, resistivity is estimated to only be a secondary effect, as seen in previous simulation studies.

On the power-law exponent of multimode Richtmyer–Meshkov turbulent mixing width

Turbulent mixing induced by the Richtmyer–Meshkov (RM) instability occurs extensively in natural phenomena and engineering applications. Among the physical quantities characterizing the RM turbulent mixing, the mixing width has prominent importance. The total mixing width h can be divided into the spike mixing zone width hs and the bubble mixing zone width hb. For multimode perturbed RM problems that commonly occur in engineering practice, early instability develops rapidly into the self-similar regime. In this regime, it is widely accepted that hs,bt∼tθs,b, where t is the time and θs,b is the power-law exponent. However, this scaling law is associated with two open questions. (1) How should a reasonable reference interface be selected to segment h into hs and hb? (2) Are the resulting θs and θb equal to each other or not? To answer these two questions, in this study, we propose a general definition of reference interface based on the position corresponding to any fixed value of either the mass fraction, volume fraction, or density. Under this definition, the invariance of fraction and density profiles by self-similar transformation leads to hs,bt∼tθs,b with θs=θb. The general definition covers those provided in linear electronic motor experiment [Dimonte and Schneider, “Density ratio dependence of Rayleigh–Taylor mixing for sustained and impulsive acceleration histories,” Phys. Fluids 12, 304–312 (2000)] and shock tube experiment [Krivets et al., “Turbulent mixing induced by Richtmyer-Meshkov instability,” AIP Conf. Proc. 1793, 150003 (2017)]. Moreover, these two definitions are proved to be, respectively, special cases of newly proposed general definition. Finally, it is deduced that θs≠θb observed in high-density ratio experiments is possibly because the turbulent mixing has not entered a self-similar regime. Compared to the low-density ratio cases, mixing of high-density ratio is much more difficult to enter the self-similar regime.

Unfolding of shocked hydrodynamic instability at SF[formula omitted] elliptical interface: Physical insights from numerical simulations

The Richtmyer–Meshkov (RM) instability widely exists in variety of industrial and scientific applications, such as in inertial confinement fusion, astrophysics explosions, supersonic combustion, bubble dynamics and cavitation. This study investigates the unfolding physical phenomena of RM instability at SF6 elliptical bubbles using numerical simulations. In contrast to cylindrical bubble, both shocked horizontal/vertical-aligned elliptical bubbles with different aspect ratios are considered, emphasizing the aspect ratio effects on flow morphology, complex wave patterns, interface deformation, vorticity generation, and interface features. For this purpose, a two-dimensional system of compressible Navier–Stokes-Fourier equations for multicomponent flows are solved using by a mixed modal discontinuous Galerkin method. Numerical simulations illustrate that the aspect ratio of elliptical bubbles have a significant influence on the vortex dynamics and the associated RM instability flows in contrast to the cylindrical bubble. In horizontal-aligned elliptical bubbles, some additional complex waves pattern, including inward jet and secondary vortex rings are observed. While, in vertical-aligned elliptical bubbles, the interface between two primary vortex rings is always vertical and has a “hippocampus” appearance due to the enhancement of downstream velocity. The baroclinic vorticity due to misalignment of density and pressure gradients at interface affects the bubble deformation and induces the Kelvin–Helmholtz instability, which leads to turbulent mixing. It is observed that the complexity of the vorticity fields is enhanced with increasing aspect ratios. Further, these aspect ratio effects result in integral diagnostic of important spatially integrated fields, and various interface features.

Effects of compressibility on Richtmyer–Meshkov instability of heavy/light interface

Experimental and numerical studies on the evolution of shock-accelerated SF6/air interface with small initial amplitude are conducted. The effect of compressibility on the early development of perturbation is highlighted by varying shock intensity and fluid properties. The startup process is analyzed when rarefaction waves are reflected and the characteristic time of the startup process is provided. The relationship between the phase inversion process and the startup process under different incident shock strengths is clarified. According to the startup time, a new start point for normalization is given, which can better normalize the amplitude growth at the early stage. In addition, the effects of incident shock strength and physical properties of fluids on the linear growth rate are highlighted through numerical simulations. The incompressible linear model loses validity when the incident shock is strong, and the existing rotational model is verified to provide excellent predictions under any shock strengths. The decrease in adiabatic exponent of the heavy fluid or the increase in adiabatic exponent of the light fluid can reduce the linear growth rate. As the absolute value of Atwood number increases, the adiabatic exponent of the heavy fluid has a more significant effect on the linear growth than that of the light fluid.

Robust implementation of Physical Regime Sensitivity and demonstration on Richtmyer–Meshkov Instability experiments

We present a robust analytic implementation of Physical Regime Sensitivity (PRS), which quantifies sensitivity of an experiment or application to regimes of a material model’s independent variables rather than to model parameters. The new PRS implementation is tested on impact-driven Richtmyer–Meshkov Instability (RMI) strength experiments on tantalum. Sequential PRS hydrocode simulations perturbed strength in local regimes of independent variables like strain rate to quantify the resulting effects on experimentally measured maximum spike velocities in the instabilities. The numeric behavior of the sensitivity calculation is investigated regarding mesh convergence and the parameters controlling the strength perturbation. The sensitivities generally converge with mesh size at least as quickly as the underlying RMI simulations. A wide range of perturbation amplitudes produced similar normalized sensitivities, indicating the perturbation is not changing physical behavior in the simulation. Adjusting the range (width) over which the strength is perturbed allows for resolving fine sensitivity features covering narrow regimes of independent variables or more broad regimes for general interpretation. For interpreting RMI, PRS shows that the maximum spike velocity of the instability is most sensitive to a narrow regime of strain rates near 107/s, which occurs inside the spike as strength effects arrest the instability. The PRS analyses revealed that a modification to the experimental metric used to assess strength would better isolate the strength effects in the regimes of most interest. Using the new metric to generate pressure PRS curves revealed that sensitivities to strength at near-zero pressure were 3.5 times greater than at the high-pressure shock state, supporting the practice of using RMI to isolate strain rate effects when combined with high-pressure experiments. It is also shown that a simple, calibrated constant strength model can reproduce PRS sensitivities of a complex, multivariate Preston–Tonks–Wallace strength model quite well, which supports the robustness of PRS and its utility for experimental design and interpretation prior to the availability of a sophisticated material strength model.

Numerical Simulation of the Interaction between a Planar Shock Wave and a Cylindrical Bubble

Three-dimensional (3D) computational fluid dynamics (CFD) simulations have been carried out to investigate the complex interaction of a planar shock wave (Ma = 1.22) with a cylindrical bubble. The unsteady Reynolds-averaged Navier–Stokes (URANS) approach with a level set coupled with volume of fluid (LSVOF) method has been applied in the present study. The predicted velocities of refracted wave, transmitted wave, upstream interface, downstream interface, jet, and vortex filaments are in very good agreement with the experimental data. The predicted non-dimensional bubble and vortex velocities also have great concordance with the experimental data compared with a simple model of shock-induced Rayleigh–Taylor instability (i.e., Richtmyer–Meshkov instability) and other theoretical models. The simulated changes in the bubble shape and size (length and width) against time agree very well with the experimental results. Comprehensive flow analysis has shown the shock–bubble interaction (SBI) process clearly from the onset of bubble compression up to the formation of vortex filaments, especially elucidating the mechanism on the air–jet formation and its development. It is demonstrated for the first time that turbulence is generated at the early phase of the shock cylindrical bubble interaction process, with the maximum turbulence intensity reaching about 20% around the vortex filament regions at the later phase of the interaction process.

Three-dimensional shock–flame interactions: effect of wall friction

Multi-dimensional numerical simulations were performed to study the interactions between shock wave and premixed flame. The three-dimensional (3D) fully-compressible, reactive Navier–Stokes equations were solved using a high-order numerical method on a dynamically adapting mesh. The effect of wall friction on the shock–flame interaction was examined by varying wall boundary condition on sidewall. The simulations agree with previous experiment in terms of flame perturbation and flame evolution. The results show two effects of wall friction on flame–shock interaction: (1) flame stretching and (2) damping of local flame perturbation very close to the no-slip wall. The stretch effect leads to non-uniform development of the perturbated flame and consequently a significantly higher growth rate in both global flame perturbation and averaged pressure in the no-slip case compared to the free-slip case. By contrast, the damping effect locally moderates the flame perturbation in close proximity to the no-slip wall because less vorticity is deposited on this part of flame during shock–flame interaction. Quantitative analysis of vortex dynamics suggests that vorticity generation that is produced by baroclinic torque and enhanced by the dilation term during shock–flame interaction causes a growth of flame perturbation via Richtmyer–Meshkov instability. Nevertheless, the vorticity generation is greatly weakened in close proximity to the no-slip wall by the viscous torque and viscous dissipation terms due to friction.

Revisiting the Polarization of the Emission of the Internal Shock in the Jet of Blazars

Recent Imaging X-ray Polarimetry Explorer (IXPE) observations of blazars tend to support the shock model for the X-ray emission, but report a low degree of polarization (Π ∼ 10%) in X-rays compared with the previous theoretical expectations in the shock model. In order to reconcile the theoretical expectations with observations, we revisit the polarization of the shock emission by considering different types of directions in the distribution of the shock-generated magnetic fields (sgMFs). Here, w sg ′ ∝ ( sin θ ′ ) ζ sg ?> with θ ′ = 0 ?> along the shock normal direction is used to describe the direction in the distribution of sgMFs in the shock comoving frame. It is found that the polarization in the X-ray and radio emission for a general jet in blazars can be described as &Pgr; ∼ 44.5 [ 1 − exp ( − ζ sg / 2.6 ) ] % ?> and &Pgr; ∼ 20 [ 1 − exp ( − ζ sg / 2.4 ) ] % ?> , respectively. Correspondingly, one can have ζ sg ∼ 1−1.5 according to IXPE observations. Besides the sgMFs, the magnetic fields generated by the Richtmyer–Meshkov instability (RMI) (rmMFs) are supposed to be present in the jets. The direction of the rmMFs is mainly distributed along the shock normal in the simulations and thus w rm ′ ∝ ( cos θ ′ ) ζ rm ?> is adopted to describe the direction of the distribution in rmMFs. We find that rmMFs are likely to significantly affect the polarization properties at low-frequency emission, especially when the sgMFs decay rapidly. Based on contemporaneous radio and X-ray observations, we find that the emission of electrons in rmMFs makes a significant contribution to the low-frequency emission and the ordered background magnetic fields can be neglected.

MULTIVALUED WAVES AND THE RICHTMYER–MESHKOV INSTABILITY AS THE CAUSES OF THE FORMATION OF GALAXIES

A few months ago, the Max Planck Institute (Dresden, Germany) organized an International Seminar for outstanding researchers of such a remarkable phenomenon as “extreme waves”. The seminar was led by such famous professors as Nail Akhdiev (Australian National University, Canberra, Australia) [1], Helmut Brand (University of Bayreuth, Germany) [2] and Amin Chabchub (Kyoto University, Japan) [3]. Thе phenomenon of "Extreme waves" is remarkable since widely spread in Nature, and at the same time it is used widely in technology. In particular it is used in modern optical communications (nonlinear optics). The results of the Workshop are widely discussed by experts. They preview promising new directions springing from group efforts. This article is a review of my seminar presentation. At the same time, it includes some results of my book, which is being prepared for publication. The main outlines of this book are outlined by Marat Aksanovich Ilgamov in his article [5]. The book is devoted to multivalued waves existing in various scalar fields. An attempt is made to describe, on this basis, the entire variety of fundamental physical phenomena of the world around us, starting with quantum phenomena and ending with the emergence and initial development of the Universe. It is known that Einstein tried to build a unified (interdisciplinary) field theory that would unite all interactions in nature into a single system. My report to Dresden made an attempt to use this idea, which was developed in the mentioned book and this article. The first three parts of this article examine the stability of Richtmyer–Meshkov and Faraday waves. The last part discusses the theory of the origin of the Universe proposed in [4, 12]. The birth of galaxies in the first moments of the process of spherical expansion of our Universe is associated with the Richtmyer–Meshkov instability.

Numerical simulations of elastic-plastic Richtmyer-Meshkov instability of multiple interfaces.

The elastic-plastic Richtmyer-Meshkov instability of multiple interfaces is investigated by numerical simulation using a multimaterial solid mechanics algorithm based on an Eulerian framework. This Richtmyer-Meshkov instability problem is realized by a copper layer that is flanked by vacuum and a copper block of different material strength. The research efforts are directed to reveal the influence of the layer thickness and material strength on the deformation of the perturbed solid-vacuum interface impacted by an initial shock. By varying the initial thickness (x_{I}) of the copper layer and the yield stress (σ_{Y2}) of the copper block, two deformation modes, which have been identified as the broken mode and the stable mode, are closely scrutinized. For a fixed x_{I} and a decreasing σ_{Y2}, the reflected rarefaction waves (RRWs), developing after the initial shock impacts the perturbed interface 1 (I1) between vacuum and the copper layer, become stronger after traveling across the interface 2 (I2). Subsequently, the velocity of I2 becomes larger, causing the width of I1 to grow larger. This width growth of I1 leads to a final separation of the spike from I1 and, consequently, the deformation mode changes from the stable mode to the broken mode. For a fixed σ_{Y2} and a decreasing x_{I}, the RRWs impact I2 at an earlier moment with a greater strength and thus the deformation mode changes from the stable mode to the broken mode. Meanwhile, the comparison of the spike width of cases whose deformation mode is the broken mode shows that there exists a maximum value of rescaled spike width, at which the deformation mode changes from the stable mode to the broken mode.

Implementation and assessment of a low-dissipative OpenFOAM solver for compressible multi-species flows

An ever-increasing number of engineering problems regard the numerical simulation of fluid flows with high-density ratio, shock wave onset, and different chemical species. In such conditions, obtaining reliable results depends on the ability of the numerical algorithm to offer a stable and robust time and space discretization of the governing equations while simultaneously limiting the numerical diffusivity.This work presents the extension and the assessment of a low-dissipative Navier–Stokes solver for compressible, multi-specie flows. We first studied the Richtmyer–Meshkov instability to test the code on fluid flows involving shock waves and species interactions for ideal gas. Then, we simulated a benchmark case regarding a cryogenic coaxial injector often used in rocket engines to explore the solver’s capability in representing high-Reynolds-number supercritical flows of multi-species real gases with large density gradients. Finally, we studied the flow in complex geometries like a high-pressure gasoline injector for propulsion application. The results demonstrate the capability of the present approach in the cases investigated.

Analysis of the interaction of a shock with two square bubbles containing different gases

The shock–bubble interaction problem remains of interest to researchers to study shock accelerated in-homogeneous flows and the Richtmyer–Meshkov instability. In the present work, simulations have been performed using the high-order Direct Flux Reconstruction scheme to study such interactions when a Mach 1.22 shock is incident on two configurations: one in which a helium bubble is in front of SF6, and, the other in which SF6 is in front of helium; in both cases, the ambient gas is nitrogen. High-order schemes are often preferred for such cases since these interactions usually involve small-scale flow features that are better resolved using high-order methods. When helium is in front of SF6, the helium bubble traverses along the initial horizontal surface of the SF6 and nitrogen, and with time, moves ahead of SF6. There are no regions of pure helium for this case at later stages. When SF6 is placed in front of helium, a separation of helium takes place in two parts, one of which mixes with SF6 while the other remains mostly pure even at later stages. A jet of nitrogen can also be seen moving at very high speeds, penetrating the region of pure helium.

Feasible Parameters of Ohmic Areas of YBaCuO Thin Films Switched via Moving Unstable Border between Superconducting and Normal States

A system of two equations based on one of the classical electricity laws was used to determine the sizes and temperatures of ohmic areas formed under action of overcritical nanosecond electrical pulses. Calculations were performed at five points for three experimentally obtained voltage–current (V-I) dependences for samples with the same geometry but different critical current density values. The system included two additional conditions to satisfy the known descriptive model of transition from superconducting (SC) to a normal (N) state—S-N switching—and to obtain physically acceptable solutions over the entire current range of V-I dependence. The solution for each point takes the form of a function, since the initial temperature increase of the primary channel across the film is entered as a parameter. Two modes of concentrated energy release in the channel were disclosed. Their random appearance leads to an unexpected degradation of the sample. As such, the obtained results correspond to the situations occurring during the experiments. The validity of applying additional conditions to the system is discussed. In the discussion, it is also explained at which moments the moving S-N border acquires the velocity of the order of ~106 m/s, comparable to the Fermi velocity. Consideration to describe the moving unstable S-N border as being constantly in a state of Richtmyer–Meshkov instability is presented.

Reducing Richtmyer–Meshkov instability jet velocity via inverse design

In this work, we detail a novel application of inverse design and advanced manufacturing to rapidly develop and experimentally validate modifications to a shaped charge jet analog. The shaped charge jet analog comprises a copper liner, a high explosive (HE), and a silicone buffer. We apply a genetic algorithm to determine an optimal buffer design that can be placed between the liner and the HE that results in the largest possible change in jet velocity. The use of a genetic algorithm allows for discoveries of unintuitive, complex, yet optimal buffer designs. Experiments using the optimal design verified the effectiveness of the buffer and validated the machine learning approach to hydrodynamic design optimization.

Simulations and models for the Richtmyer–Meshkov instability with broadband perturbations

The Richtmyer–Meshkov instability (RMI) is shock driven and affects many phenomena from inertial fusion to supernova explosions. The behavior of single-modes in the RMI has been studied extensively but less is known with the broadband perturbations that occur in applications. Here, we describe extensive numerical simulations and modeling of the RMI with broadband perturbations with an initial power spectrum of the form P ∝ km, where k is the wavenumber. The hydrodynamic condition is the same as in the θ-Group Collaboration [Thornber et al., “Late-time growth rate, mixing, and anisotropy in the multimode narrowband Richtmyer–Meshkov instability: The θ-group collaboration,” Phys. Fluids 29, 105107 (2017)] with a Mach ∼1.86 shock and gamma-law = 5/3 fluids with Atwood number A = −0.5. The bubble amplitude hB is found to grow in two stages. Initially, hB undergoes a phase-inversion and grows linearly in time (t) at a rate consistent with a linear theory. Asymptotically, hB grows as a power law ∼tθ when k|hB| > O(1), where k is the average wavenumber for the initial spectrum. The RMI behavior in simulations and modeling agree over a wide range of exponent m, spectral width, initial amplitude, and time. The agreement is quantified objectively using statistical analysis.

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.

Parametric effects on Richtmyer–Meshkov instability of a V-shaped gaseous interface within linear stage

The Richtmyer–Meshkov instability of a V-shaped air/SF6 gaseous interface is numerically studied via a high-order finite difference scheme and a localized artificial diffusivity method. The oblique angle of the interface ranges from 20° to 75°, and the incident shock Mach number varies from 1.05 to 1.75. The wave patterns and the vortex structures are visualized during the interface evolution. A cavity is observed at the spike fingertip when the oblique angle decreases, which proves to be formed due to Mach reflection of the transmitted shock through velocity decomposition. By analyzing the linear growth rates of the interface, a modified empirical model for the reduction factor is suggested with model coefficients acquired by linear fitting for different Mach numbers. With shock polar analysis (SPA) method and visualization of the wave configuration, a criterion is proposed to explain the non-monotonic dependence of the linear growth rate on the oblique angle. In addition, Mach number effects on the linear growth rate are discussed by the SPA method, especially the anomalous behavior of the Mach 1.05 case.

Numerical investigations of spike velocity of microjetting from shock-loaded aluminum and tin

Microjetting is induced by the interaction between incident shock wave and material free surface. Moreover, spike velocity is one of the most important parameters to quantify the microjetting processes. The spike velocity over a wide range of shock and surface conditions for aluminum and tin is achieved via systematical Eulerian peridynamic simulations. The four popular spike velocity models are assessed according to the simulation data. The results indicate that the model proposed by Dimonte et al. based on Richtmyer–Meshkov instability (RMI) mechanism is in best agreement with the simulated spike velocities. The further analysis highlights that the dependence of adiabatic index on material states should be taken into account because it can impact the RMI flows. Then an improved spike velocity model is proposed and the comparative investigations indicate that it exhibits an overall better prediction compared to the original velocity model.