Session Z09: Flow Instability: Richtmyer-Meshkov (12:15pm - 1:00pm CST)

Effects of Surface Tension on the Richtmyer-Meshkov-Instability-Induced Perturbation Growth in Fully Compressible and Inviscid Fluids

We present novel numerical simulations investigating the Richtmyer-Meshkov instability (RMI) with surface tension. With a fully nonlinear, compressible numerical formulation which directly models surface tension on a volume-of-fluid interface, we validate and bridge existing theoretical models of surface tension's effects on the RMI in linear, transitional and nonlinear post-shock growth regimes. We propose a dimensional scheme, from which we first develop scaled models for the perturbation growth in the small-amplitude (linear) oscillatory regime, where good collapses of simulation data are found under the scalings. Next, we heuristically identify a criterion for transition into a nonlinear oscillation regime. Finally, we show good agreement with nonlinear theory for asymptotic interface growth in the limit of small surface tension. These results highlight the utility of our model for compressible problems featuring surface tension, and pave the way for a broader investigation into mixed compressible/incompressible problems.   

Time-resolved PIV measurements on 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 ($\mathrm{SF}_\mathrm{6}$). 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 with both the incident and reshocked instability growth regimes visible. Information on the growth of the RMI, including measurements of the growth exponent, $\theta$, anisotropy, and turbulent kinetic energy decay are presented.   

Deterministic Initial Conditions studies of the Richtmyer-Meshkov instability

To advance our study of the Richtmyer-Meshkov instability and the transition to turbulence, we need to be able to generate well defined, known, and three-dimensional initial conditions. At Los Alamos, this is also a requirement for validating predictive capabilities of models and simulations. The Vertical Shock Tube facility at Los Alamos has recently been studying the Richtmyer-Meshkov instability using membranes generated via additive manufacturing. These particle packed membranes break easily and allow us to avoid non-diffuse initial conditions while providing deterministic initial conditions. Our first studies with two-dimensional sinusoidal interfaces are being used to determine the effects these types of membranes have on the growth and flow. We use simultaneous PIV and PLIF diagnostics to capture spatially and temporally resolved density and velocity measurements at two locations in time of a shocked air/SF6 interface (A $=$ 0.6) with a shock speed of M $=$ 1.2. We are studying two ka$_{\mathrm{0}}$ values: 0.24 and 0.72. Preliminary shots show bubble and spike growth that follows the expected growth rate of Sadot \textit{et al}.   

Growth of Richtmyer-Meshkov turbulence when reshocked in the same direction.

This work extends the theta-group study [1] by investigating the effect of multiple shocks originating in the heavier fluid, and their effect on the subsequent evolution of the Richtmyer-Meshkov (RM) turbulent mixing layer. Our objective is to investigate the effect of the second shock arrival time on several turbulent flow features. By varying the time of second shock impact, we control the properties of the interface (composition of perturbation wavelengths and amplitudes) prior to this event. Our primary interest is to quantify mixing properties resulting from the RM instability, which is one of the sources of mixing-led deterioration of fusion yield in ICF. While RM-driven turbulent mixing has been extensively investigated, the majority of studies have focused on mixing from either a single incident shock or a reflected shock in the opposite direction. In a departure from these studies, we study mix properties from second shock of direct relevance to recent efforts to optimize the timing and strength of shocks in ICF [2]. Similarly, in SCRAMJET applications, to satisfy the requirement of minimal residence times for the fuel jets, a shock train is used to repeatedly shock and achieve turbulence in the flow. [1] B. Thornber et al. , Phys. Fluids 29, 105107 (2017). [2] H.F. Robey et al., Phys. Rev. Lett., 108, 215004 (2012).   

High-order methods for plastic deformation in multi-material Richtmyer-Meshkov instabilities

Shock-wave / material-interface interactions are key phenomena in a variety of high-velocity material impact, detonation, and inertial confinement fusion applications. We present recent developments of a high-order method for Eulerian simulation of material undergoing large elasto-plastic deformation that is focused toward simulating these interactions. Particular emphasis is laid on new advancements of the methods for solving the kinematic equations describing plastic deformation and the associated strain hardening of the material. The accuracy and stability of a variety of treatments for these kinematic equations are explored in the context of a test suite of developing Richtmyer-Meshkov instabilities between two materials with finite strength. Superior stability is demonstrated for methods based on the plastic deformation Finger tensor as opposed to methods based on the inverse deformation gradient tensors. The underlying numerical methods utilize a tenth-order compact-difference scheme; in this context, a new application of the Localized Artificial Diffusivity (LAD) method that facilitates capturing of strain discontinuities in the kinematic equations is also discussed.   

Numerical Simulation of the 3D Shock-Driven Kelvin-Helmholtz Instability

We describe the development and structure of a three-dimensional shock-driven Kelvin-Helmholtz instability generated by the interaction of a planar shockwave with an inclined cylinder of dense gas. In simulations an inclined cylinder of gas is initially at rest, surrounded by solid boundaries. Then the gas cylinder undergoes shock acceleration, producing a Richtmyer-Meshkov instability in the radial direction of the cylinder and a Kelvin-Helmholtz instability in the axial direction. The gas is either pure sulfur hexafluoride or a mixture of sulfur hexafluoride, acetone and air. The gas column is surrounded by air resulting in a range of considered Atwood numbers of 0.61-0.67. In simulations the Mach number is in the range of 1.2-2.0 and the cylinder angle is in the range 0-30 degrees with respect to the plane of the shock. The wall effects on the Kelvin-Helmhotz instability development were studied. The initial gas density profiles in the simulations matched those acquired in experiment. Simulations were conducted using the University of New Mexico FIESTA code, which is a C++ code designed for next-generation exascale GPU architectures. FIESTA uses a fifth-order WENO scheme and a second-order Runge-Kutta scheme for spatial and temporal discretization respectively.   

Mixing Layer Growth of Richtmyer-Meshkov Instability at High Mach Number

There has been considerable investigation of the growth of the mixing layer that forms due to the Richtmyer-Meshkov instability when a shock passes a density interface with initial perturbations. However, there have been fewer studies in systems at high Mach numbers. In these systems, compressibility effects in the post shock regime may be significant as the turbulent fluctuations also become a significant fraction of the speed of sound. We have been investigating such systems using a gun-driven 40-mm aluminum slug to send an $\mathrm{M}=8.9$ shock into a shock tube filled with xenon and argon (postshock density ratio $r=3.5$, Atwood number $\mathrm{At}=0.55$). The gases are separated by a 3-D printed plastic membrane with sinusoidal initial conditions of $kh_0=0.24$ and $0.72$. We use proton radiography to acquire a sequence of 21 line-of-sight integrated fields of quantitative density per shot, and compute growth rates and mix widths to investigate the effect of initial conditions. The possibility of using such data to make quantitative estimates of density statistics (such as the parameter $b$ in the BHR RANS closure model) is also investigated.   

Pressure wave reflection off a shock-accelerated particle curtain

We present an experimental and numerical study of a planar shock interaction with a falling particle curtain, where massive particles account for about 5\% of the curtain’s volume before the shock arrives, and the remaining volume is filled with air at atmospheric pressure. Experiments are conducted at the University of New Mexico shock tube at Mach numbers between 1.2 and 2.0. A multiphase Atwood number characterizing the initial conditions under consideration approaches unity, suggesting that the particle inertia likely dominates the post-shock curtain movement. Despite the modest volume fraction of the particles, even a relatively thin (2~mm) curtain produces a reflected pressure wave in experiments. This pressure wave can be reproduced numerically with a computationally inexpensive one-dimensional model based on a particle source in cell (PSIC) method. We also compare experimental and numerical results characterizing the post-shock propagation of the curtain, and discuss what dimensionless parameters besides the multiphase Atwood number are necessary to characterize the flow.