Session X36: Flow Instability: Richtmyer-Meshkov

Inhomogeneous vortex-shock interactions

Vortex rings have been observed to form following shock interaction in some configurations of the Richtmyer-Meshkov instability. These rings tend to propagate outside of the interfacial mixing region once formed, significantly enhancing mixing and transport into the otherwise-uniform bulk fluid. A series of experiments have been conducted to isolate and investigate the evolution of such rings upon M = 2.0 shock interaction, consisting of simultaneous PIV/high-speed PLIF imaging of inhomogeneous vortex rings at several Atwood numbers (0.06, 0.20, 0.51, and 0.66). Circulation production is shown to depend strongly on Atwood number, with contributions from vorticity deposition due to shock curvature across the vortex core.   

Convergence of High-Order and Low-Order Accuracy Simulations for Richtmyer-Meshkov Instability

Simulations of variable density mixing induced by the interaction between a Mach 1.45 shock and subsequent re-shock with the interface between two ideal gases at high Atwood number (sulphur hexafluoride and air) contain a wide range of spatial scales. Sixth-order spatially accurate shock-capturing simulations of this flow for a series of grid resolutions demonstrated excellent agreement of global quantities such as mixing layer width and slower but eventual convergence of quantities sensitive to the smallest scales of motion such as total dissipation [Wong et al., Phys. Rev. Fl., 2022]. Simulations of a similar configuration with the same spatial resolutions are performed with the lower-order multiphysics hydrocode xRage with two different hydrodynamics schemes to assess the convergence. The convergence within the first shock and reshocked regimes are addressed and the ability of lower order code to predict the salient features and detailed statistics of the flow is assessed.   

Effect of wall vortices on RMI shock tube experiments

The Richtmyer-Meshkov Instability (RMI) is frequently studied in shock tubes, where the walls and relatively narrow cross sections introduce boundary layers that influence the development of the RMI. Traditional RMI analysis assumes statistically two-dimensional flow and sufficient distance from wall effects; however, previous work has shown that vortices form in the boundary layer upon re-shock due to baroclinic vorticity deposition.  Experiments investigating this phenomenon were conducted in the Wisconsin Shock Tube Laboratory at UW-Madison using planar laser-induced florescence and particle image velocimetry for the cases of a Mach 1.56 & 1.25 shock wave and an interface with Atwood numbers of 0.7 and 0.5. The results look at the temporal development of these vortices as well as the overall effects shock strength and Atwood number have on these wall vortices.   

Shocked Variable-Density Turbulence Studies on the VST

Inertial confinement fusion (ICF) is the process of collapsing millimeter size capsules to generate fusion energy in the compressed fuel. These capsules are comprised of multiple layers of varying densities, and high energy deposited on their outer shells causes the collapse processes. The energy deposition process also creates multiple shocks that traverse these multi-layer capsules, inducing the Richtmyer-Meshkov instability (RMI) as each shock crosses a density boundary. We know from single fluid experiments that multiple shocks of the RMI lead to turbulence, and one can anticipate that shock-turbulence interactions (STI) occur in ICF capsules. STI have been well studied in constant-density fluids, but not in a variable-density setting. The Extreme Fluids team at LANL has developed a series of experiments using the Vertical Shock Tube (VST) to study shock-turbulence interactions. A turbulent layer is setup between air-SF₆ (A ~0.6) and is characterized pre-shock and post-shock. Simultaneous density and velocity measurements are used to look at how the turbulence is affected. By adjusting experimental parameters, we are able to study the effects of STI at different turbulent intensities and Mach numbers. Results from recent experiments will be presented.   

Simulations and models to describe initial condition effects on the multi-mode Richtmyer-Meshkov instability

 

The Richtmyer-Meshkov instability (RMI) is shock driven and affects many phenomena from inertial confinement fusion to supernova explosions. The behavior of single-modes in the RMI has been studied expensively but less is known with broadband perturbations that occur in applications. Here, we describe extensive numerical simulations and modeling of the RMI with broadband perturbations with a wavenumber (k) power spectrum of the form P ∝ k^m. The bubble amplitude h_B is found to grow in two stages. First, there is secular growth in time at a rate consistent with linear theory. Second, when h_B becomes comparable to the average wavelength 2π/〈k〉 of the spectrum, it grows as a power law in time h_B ~ t^θ. This behavior is described and modeled over a wide range of m, spectral width, initial amplitudes and time.   

Rethinking missing mass theory

We perform a series of investigations, both theoretical and numerical, intended to establish a foundational, quantitative understanding of the material outflows generated when a strong shock is driven through an imperfect ("defected") metal surface. Our investigation is limited to tin surfaces with symmetric defects subject to sufficiently strong shock pressures (∼28 GPa) such that the tin completely changes to fluid phase and Richtmyer-Meshkov instability produces outflows of mass from surface defects. Outflow masses are non-dimensionalized by dividing by the "missing mass," which is the product of the pre-shock solid metal density and the pre-shock defect volume. We examine the effects of defect shape, defect aspect ratio, distance between defects, and bump-type defects on outflow mass variability with 2D simulations. Rectangular, triangular, elliptical, and sinusoidal defect shapes are investigated. Bump-type defects are normalized by added mass. Our results suggest that, while missing and added masses are useful quantities for non-dimensionalizing outflow mass, new theories of outflow mass variability should attempt to assimilate patterns of baroclinic variability (the degree of misalignment of density and pressure gradients during shock transit).   

Richtmyer-Meshkov Instability Coupled with a Chemical Reaction

The Richtmyer-Meshkov Instability (RMI) and the resulting mixing at an interface between two fluids when accelerated impulsively is of great importance in astrophysics, proposed high-speed combustion systems, and pursuits towards inertial confinement fusion. Experimental studies on RMI often use inert gases, whereas in the applications of interest involving the RMI, the instability occurs in tandem with either chemical or nuclear reactions. Preliminary work has been done on designing an experimental study of the RMI that includes the effect of heat release, in this case coming from chemical reactions. The proposed experiments will be conducted at the Wisconsin Shock Tube Laboratory at UW-Madison and involve the combustion of acetone. Computational results based on the Cantera and CONVERGE codes will be presented showing the feasibility of shock-initiated combustion and its overall impact on the RMI.   

Modelling the effects of convergence on the Richtmyer-Meshkov instability in planar geometry

In spherical or cylindrical geometry, the Richtmyer-Meshkov instability (RMI) and Rayleigh-Taylor instability behave differently to planar geometry due to the Bell-Plesset effect. The Bell-Plesset encompasses the effects on the growth rate of the mixing layer that arise from the geometric convergence of the mixing layer which is a result of the changing radius and wavelength, as well as the change in density of the fluids because of the compression of the mixing layer. To understand the effect of convergence, a potential flow model was derived for the linear regime of RMI in planar geometry with transverse strain. This model was compared to two-dimensional direct-numerical simulations of single-mode RMI. The model and simulation showed agreement within the linear regime and demonstrated that a compressive strain-rate increases the growth rate, whilst an expansive transverse strain-rate decreases the growth rate. The investigation into the effects of transverse strain-rates were extended to a three-dimensional multi-mode narrowband case. The effects of the linear-regime model are not observed to occur for developing multi-mode mixing layer. Instead, the compressive transverse strain caused a decrease in mixing layer growth and vice versa. The ability for buoyancy-drag and RANS models to model this effect of convergence is discussed, as well as potential corrections to the models.   

Effect of a diffuse interface on the Richtmyer-Meshkov instability

The Richtmyer-Meshkov (RM) instability occurs when a shock wave interacts with a perturbed material interface separating two fluids of different densities, and is important in inertial confinement fusion (ICF) because of the material mixing it may lead to. ICF capsules are often subjected to material preheating causing the separating interface to expand and become a finite diffusion layer before shock arrival. In this work, we numerically investigate the role of the size of the initial diffusion layer on perturbation growth and fluid mixing in a simplified planar geometry. We simulate the interaction between a shock (shock Mach number Ms = 1.21) and a single-mode perturbation (wavelength λ ≈ 6 cm, amplitude a0 ≈ 0.2 cm) imposed on an air/SF6 diffuse interface. The size of the initial diffusion layer δ is varied by controlling the ratio 0.1 ≤ δ/λ ≤ 0.5. We quantify its effect on the flow dynamics by investigating the interface morphology, vorticity distribution, mixing layer width, and interface length. To understand its effect on late-time fluid mixing, we subject the interface to reshock and use a mix model to obtain turbulence quantities such as the turbulent kinetic energy and Reynolds stresses.

This work was supported by the U.S. Department of Energy through the Los Alamos National Laboratory. Los Alamos National Laboratory is operated by Triad National Security, LLC, for the National Nuclear Security Administration of U.S. Department of Energy (Contract No. 89233218CNA000001).   

Experiments on the Richtmyer-Meshkov instability of two nearby interfaces

The Ricthmyer-Meshkov instability of two nearby interfaces separating three gases of differing densities is studied experimentally in a vertical shock tube. The two interfaces are formed in the shock tube test section using opposed gas flows where the heaviest of the three gases (SF6) enters at the bottom of the test section and flows upward and the lightest gas (either air or helium) enters at the top of the driven section and flows downward. The intermediate gas (either air or CO2) enters the test section through porous metal plates forming an intermediate layer with 50 mm thickness. All three gases exit the shock tube through small holes at the interface locations, leaving two flat, stable interfaces separating the three gases. A nearly 2-dimensional, sinusoidal initial perturbation is given the lower interface by oscillating the shock tube in the lateral direction to produce a standing wave. A shock wave is generated by puncturing a polypropylene diaphragm that then travels downward in the shock tube where it impacts the fluid layer to produce the instability. The gas layer is visualized using time-resolved, planar Mie scattering.  Measurements of the growth in perturbation amplitude are obtained and compared with equivalent single-interface configurations.   

High-Resolution Simulations of Transitional Triple-Point Shock Interactions

This work concerns the evolution of the Ritchmyer-Meshkov instability (RMI) in a rather unconventional setting: a 3D periodic extension of the triple point canonical problem. The time frame of the study includes reshock of the interface, making this a case which hasn't been studied before. The nature of the transition to turbulence is particularly investigated, which is dependent on the initial conditions, shock induced transition, and other instability mechanisms such as secondary baroclinic instability. These aspects were examined using an ensemble of configurations of the problem at various resolutions for different initial conditions, along with an appropriate mesh convergence study. In particular, the initial conditions were dictated in the form of interfacial perturbations made up of a superposition of Fourier modes. It was found that perturbations dominated by low wavenumber content showed a ballistic scaling at early times and led to greater turbulent kinetic energy production at late times. However, the turbulent kinetic energy spectra still showed prominent traces of the initial conditions. Perturbations containing a broadband content on the other hand exhibit a diffusive scaling at early times, and the spectral content at late times resembles that of isotropic turbulence.