Session P10: Flow Instability: Richtmyer-Meshkov

Numerical simulations of Richtmyer-Meshkov Instabilities in Newtonian and Non-Newtonian fluids

The development of Richtmyer-Meshkov instabilities in Newtonian and Non-Newtonian fluids is studied using numerical simulations. This study reveals the influence of non-Newtonian effects on the development of Richtmyer-Meshkov instability characteristics such as amplitude, span, stream, and neck. The simulations show how these structures impact the mixing process and the energy distribution.  This work is conducted using deuterium and melted polymer which are  treated as Newtonian and non-Newtonian fluids, respectively. The results are compared with simulation cases where both fluids are treated as Newtonian fluids. In this case, it is assumed that the non-Newtonian effects are negligible due to high pressure gradients.  This research aims to show a correlation between non-Newtonian effects and energy distribution at conditions relevant to planar shock-induced inertially-confined nuclear fusion experiments.   

Richtmyer-Meshkov instability studies of a repeatable initial condition

Seen during supernova explosions and in inertial confinement fusion applications, the Richtmyer-Meshkov instability (RMI) is created by a shock wave accelerating fluids of different densities into each other. The vertical shock tube facility at Los Alamos National Laboratory is well-equipped to obtain experimental validation in support of physics-based models of the RMI phenomena. However, the effects of initial interface characteristics on the late time growth of the mixing region remain unclarified from previous experimental and numerical results. To establish a controllable sinusoidal interface between low-density air and high-density SF₆, we crossflow gases over an oscillating splitter plate while using simultaneous particle image velocimetry and planar laser-induced fluorescence for combined measurements of velocity and density fields. We present preliminary quantitative observations of the time evolution of RMI initiated with various periodic perturbations, and continue to improve control of initial conditions at the interface. Using the velocity and density fields from these measurements, we further estimate the turbulence parameters required to initialize a Besnard-Harlow-Rauenzhan turbulence model, greatly improving our ability to model the experiments.   

The investigation of RMI at an air/solid interface using Pagosa

Richtmyer-Meshkov instability (RMI) occurs when there has a baroclinic generation of vorticity resulting from the misalignment of density and pressure gradients on a density-stratified interface. Accelerated by the incident shock, the interface becomes unstable, fingers grow to form bubbles of light fluid, while spikes are formed in heavy fluid. RMI is a key problem in many fields, such as deflagration-to-detonation transition (DDT) as well as inertial confinement fusion (ICF) and supernovae explosions. Therefore, its research is of scientific and engineering significance. This work will investigate the Richtmyer-Meshkov instability at a solid/air interface using a hydrocode Pagosa. We first verify the ability of Pagosa to handle the Rayleigh-Taylor instability (RTI) and the RMI at an air/SF₆ interface. Subsequently, we explore the RMI at a solid/air interface. The ultimate goal is to assess the effect of the initial perturbation (including the wavenumber, the amplitude etc) , the initial solid-gas ratio, the solid-material yield stress on the interface behavior.

Key words: Pagosa; RMI; Solid; Air; shock wave   

Experiments on the influence of shock-to-reshock time on the development of the Richtmyer-Meshkov instability in a dual-driver vertical shock tube.

Experiments on the Richtmyer-Meshkov Instability (RMI) using Particle Image Velocimetry (PIV) in a dual driver vertical shock tube are presented. Two shock waves generated at opposite ends of a vertical shock tube travel in opposing directions, impacting a perturbed interface formed between Air and Sulfur Hexaflouride (SF6). Perturbations are formed using a pair of voice coil driven pistons that generate Faraday waves on the interface. The order in which the two shocks arrive at the interface as well as the temporal separation in their arrival are controllable. Shock strengths are chosen to result in halted interface motion after passage of the second shock wave, permitting a long observational window in which the instability can develop. Four vertically stacked cameras are used to view the instability growth. This permits a wide range of shock-to-reshock timings to be studied in both the incident and reshocked instability growth regimes. Light shock first and heavy shock first configurations are examined. Information on the growth of the RMI, including measurements of the growth exponent, θ, anisotropy, and turbulent kinetic energy decay are presented. The influence of the shock-to-reshock time on these parameters is discussed.   

Formation and scaling of vortex dipoles generated from shock-accelerated interfaces

Vortex dipoles are known to emerge in a variety of flows relevant to astrophysics, high energy density physics, and inertial confinement fusion, where they can significantly affect the flow through the transport of vorticity. We systematically study the generation and scaling of such dipoles utilizing a numerical platform involving a shock passing through a grooved interface separating two dissimilar fluids. As the shock passes through the interface, it deposits baroclinic vorticity that induces a complex phase inversion process ultimately resulting in the ejection of a dipole. By modulating the aspect ratio of the groove, the amount of vorticity in the flow available to the dipole is controlled. Based on the aspect ratio of the groove, we find that two distinct flow regimes emerge. For small aspect ratios, a single dipole is generated that contains the majority of the vorticity deposited by the shock. Beyond a critical groove aspect ratio, however, the circulation of the ejected dipole saturates, and the additional vorticity in the flow accumulates in a jet that trails the leading dipole. This behavior suggests the existence of fundamental formation number governing the scaling of dipoles generated from shock-accelerated interfaces, including those in Richtmyer-Meshkov flows.   

High-Speed Simultaneous Velocity and Concentration measurements of the Richtmyer-Meshkov Instability Upon Re-Shock

The Richtmyer-Meshkov instability of a twice-shocked gas interface is investigated in the vertical shock tube of the Wisconsin Shock Tube Laboratory at the University of Wisconsin– Madison. The initial condition is a shear layer, containing broadband perturbations, formed at the interface between a helium-acetone mixture and argon.

The interface is accelerated with a shock of nominal strength M=1.76 with an initial Atwood number A=0.5.

Concurrent, high-speed planar laser-induced fluorescence (PLIF) and particle image velocimetry (PIV) are performed using a pulse-burst laser operating at 20,000 Hz. The 266 nm and 532 nm laser outputs are co-propagated into the shock tube, forming a dual wavelength light sheet. Acetone is added to the helium to act as a fluorophore; 200 nm titanium dioxide particles are added to both the helium and the argon to perform PIV. Images are collected with two high-speed CMOS cameras.

Presented preliminary results will include integral measures, such as thickness and mixedness; spectral quantities, including scalar and kinetic energy spectra; combined moments and structure functions.   

Wavelength selection in shock-induced Kelvin-Helmholtz instability

We conducted experimental shock-tube studies of a tilted, shock-accelerated heavy gas cylinder where we observed perturbation growth on the upstream and downstream density interfaces initially bounding the heavy gas in the nominal plane of symmetry of the flow. The dominant perturbation wavelength away from the shock-tube wall was highly repeatable for the same initial conditions, and varied with the column tilt angle and Mach number. We proposed a simple geometrically-based explanation for the wavelength selection mechanism, using two-dimensional considerations. Recently conducted numerical simulations of tilted and shock-accelerated gas curtains (two-dimensional) and cylinders (three-dimensional) suggest that the same physics are indeed responsible for interfacial perturbation growth in both the two- and three-dimensional formulation: baroclinic vorticity deposition on the leading and trailing edge of the curtain (cylinder) produces shear layers, leading to shock-driven Kelvin-Helmholtz instability (SDKHI). The dominant perturbation wavelength can be similarly explained by the geometric parameters of the shock-compressed curtain or cylinder. Additional examination of experimental and numerical data also reveals a second SDKHI wavelength near one of the walls of the shock tube due to reflected shock interacting with the solid boundary.   

Interaction of a heavy-particle curtain with shock and reshock

A gravity-driven particle curtain is accelerated by a planar shock, which is then reflected from a wall perpendicular to the shock direction. We visualize the curtain evolution at several initial curtain thicknesses (2, 4, 6 mm) in the streamwise direction and for Mach numbers ranging from 1.1 to 2.0. Additionally we record pressure traces from multiple transduces both upstream and downstream of the initial location of the curtain. Non-uniformities in the initial particle concentration in the curtain result in differences in the local average density, in turn triggering shock-driven multiphase instability (SDMI), most clearly observable on the trailing (upstream) edge of the curtain. We also observe the effects of the gradual particle seeding density decrease along the vertical curtain extent due to falling particle acceleration. Despite the modest (about 5%) particle fraction in the curtain, particle inertia effects appear quite prominent.   

Modeling of Shock Tube Experiments of a Perturbed Diffuse Interface Subjected to the Richtmyer-Meshkov Instability

When a shock wave impinges upon a perturbed interface separating two fluids of different densities, any perturbations along the interface grow due to the Richtmyer-Meshkov instability, possibly leading to a turbulent mixing region. In this study, we discuss the modeling of experiments performed at the Vertical Shock Tube facility at Los Alamos of a single-mode perturbation along an air/SF6 interface impulsively accelerated by a shock (shock Mach number Ms=1.2). In particular, using the radiation-hydrodynamics code xRAGE, we consider a diffuse interface between the air and SF6, and investigate the effects of the diffusion layer on the flow evolution. From experimental measurements, we accurately estimate the initial size of the diffusion layer and use it to initialize our simulations, allowing us to compare the perturbation growth with the experiments. Using the velocity and density fields from these measurements, we further estimate the turbulence parameters required to initialize a Besnard-Harlow-Rauenzhan (BHR) turbulence model, greatly improving our ability to model the experiments.   

High-speed simultaneous velocity & density measurement of compressible multifluid shock-vortex interaction

In the intermediate stages of Richtmyer-Meshkov/Rayleigh-Taylor instability development, prior to the development of turbulence, vortical flow structures are commonly observed at the outer extents of the mixing region. The evolution of these structures upon reshock may play an important role in the tails of the mixedness distribution, but they are difficult to repeatably study because of the inherently unstable mixing process.

To capture these vortex-shock interaction events in isolation, an ensemble of simultaneous PLIF/PIV measurements were acquired at 20 kHz following the firing of a small, open-ended, argon-filled shock tube (D = 2.2 cm) upwards into ambient nitrogen. The measurements capture the initial propagation of the argon vortex ring as well as its perturbation upon M=1.75 shock and subsequent reshock.   

Comparison of 2D and 3D simulations of a shock accelerated inclined gas column

In our study, we conduct 3D large eddy simulations of a shock passing through a cylindrical column of gas in air.  In simulations, a gas column, initially at rest, is inclined at an angle of 30 degrees with respect to an approaching shock propagating at Mach 2.0.  After the column is accelerated by the shock, instabilities develop on the surface of the gas column:  a Richtmyer-Meshkov instability in the radial direction of the cylinder and a Kelvin-Helmholtz instability in the axial direction.  Statistical properties and turbulent kinetic energy spectra in both the radial and axial directions are collected at different times.  Results are compared with experimental data and our previous two-dimensional simulations.  The overall flow morphology in 3D simulations compares well with experimental data and our previous 2D simulations.  However, the flow features in 3D simulations develop earlier than in 2D simulations.  This earlier development better agrees with experimental data.  The effects of artificial viscosity modelling on simulation results are also investigated. Simulations were conducted using the University of New Mexico FIESTA code, which is a gas dynamics code designed for exascale GPU architectures.