Session EW: Instability: Richtmyer-Meshkov/Rayleigh-Taylor III

An experimental study of the turbulent development of Richtmyer-Meshkov instability prior to, and following, reshock

Richtmyer-Meshkov instability is investigated utilizing shock tube experiments. The instability is generated by the impulsive acceleration of the interface between two gases of different densities by an incident plane shock wave. The interface is created by forcing air seeded with smoke through a plenum at the top of the driven section, and SF$_{6}$ through a plenum at the bottom of the test section. Random, multi-mode, initial perturbations are imposed on the interface by the excitation of Faraday internal waves using two synchronized loudspeakers that oscillate the gases vertically. The study focuses on the late-time growth of the turbulent mixing zone after shock interaction and the growth of the mixing zone following reshock. The objective of these experiments is to determine the dependence of the post reshock growth rate on the reflected shock strength and whether the growth rate is independent of the mixing zone characteristics immediately before the reflected shock wave impacts the layer. A systematic study is made for the different Mach numbers and different reflected shock arrival times. It is found that the growth rate of the mixing zone is constant immediately after reshock. However, a noticeable reduction in the growth rate occurs after a very short period of time.   

Nonideal Effects in Single Mode Richtmyer-Meshkov Instability Shock Tube Experiments

Shock tube experiments on the late time Richtmyer-Meshkov instability (RMI) are presented. The growth of the instability from a diffuse sinusoidal initial perturbation impacted by a Mach 1.2 shock wave (SW) is studied. The RMI develops from an air-SF6 interface in a 2.0 m long test section. The RMI is visualized using planar Mie scattering using an Nd:YLF laser for illumination and recorded using high speed CMOS cameras. This visualization system allows the recording of the time history of the RMI. Measured growth rates are found to be greater than those predicted by models and numerical simulations. In addition, measurements of SW accelerated flat interfaces show them to accelerate after SW interaction. A numerical investigation was then undertaken to investigate the effects of boundary layers and openings in the shock tube test section. These simulations show that openings tend to reduce the impulsive drive affecting the interface but still produce constant interface velocity. However, the presence of boundary layers tends to produce an acceleration similar to that observed in the experiments. It is proposed that this boundary layer induced interface acceleration leads to enhanced growth due to the Rayleigh-Taylor instability.   

Turbulence in reshocked Richtmyer-Meshkov unstable fluid layers

Advances in the implementation of high resolution PIV (150um vector-to-vector resolution) and PLIF (50um resolution) diagnostics have allowed the experimental measurement and characterization of turbulent mixing in Richtmyer-Meshkov unstable fluid layers after reshock (Balakumar et. al., Phys. Fluids, 2008). Using instantaneous PLIF data obtained at closely spaced intervals of time, we illustrate the rapid disintegration of the primary wavelengths of the initial interface and the beginning of a turbulence cascade generating smaller flow structures after reshock. The enhanced mixing is reflected in the variation of the density probability distribution function between the pre-reshock and post-reshock states. The density self-correlation is observed to exhibit a double-peaked structure and mild non-Boussinesq effects are observed in a layer with varicose initial interfacial perturbations. Density and velocity pdfs are used to examine the streamwise asymmetry of the mixing layer with large fluctuations occurring preferentially upstream of the centerline. Other turbulence statistics including the 2nd and 4th order structure functions, RMS statistics (both velocity and density) and turbulence intensity are also presented.   

Simulation of Material Mixing in Shocked and Reshocked Gas-Curtain Experiments

The unique combination of shock and turbulence emulation capabilities supports direct use of implicit large eddy simulation (ILES) as an effective simulation anzatz in shock-driven mixing research. This possibility is demonstrated in the context of a prototypical case study for which available laboratory data can be used to test and validate the ILES modeling. The particular ILES strategy tested here is based on a nominally-inviscid simulation model using LANL's RAGE code and adaptive mesh refinement. An SF6 gas curtain is formed by forcing SF6 through a linear arrangement of round nozzles into the shocktube test section. Once a steady state is achieved, the gas curtain is shocked (M=1.2), and its later evolution subject to Ritchmyer-Meshkov flow instabilities, transition, and non-equilibrium turbulence phenomena are investigated based on high resolution simulations for shocked and reshocked cases. The gas curtain used at initialization for the RAGE simulations was separately simulated using a 3D Navier-Stokes-Boussinesq code. Various approaches to introducing weak 3D perturbations to emulate the noise inherent in the experimental setup were tested with special focus on addressing initial condition effects on late-time mixing.   

Modeling the Richtmyer-Meshkov Instability through Baroclinic Vorticity Production

The Richtmyer-Meshkov instability (RMI) is modeled using the baroclinic term in the vorticity transport equation and the results are compared to numerical simulations. The baroclinic vorticity production equation, ${d\omega } \mathord{\left/ {\vphantom {{d\omega } {dt}}} \right. \kern-\nulldelimiterspace} {dt}={\left( {\nabla \rho \times \nabla p} \right)} \mathord{\left/ {\vphantom {{\left( {\nabla \rho \times \nabla p} \right)} {\rho ^2}}} \right. \kern-\nulldelimiterspace} {\rho ^2}$, is simplified using an impulsive hydrostatic pressure gradient. Using this approximation, one can calculate the vorticity field from an initial density field and the post-shock 1D velocity. An analytic equation for circulation and perturbation growth rate is found for a single mode interface which proves accurate up to moderate Atwood numbers and Mach numbers. This model also accurately predicts the behavior of a more complicated interface with an arbitrary density field. The growth rate from the compressible RMI simulation and an incompressible simulation initiated with the same initial density field and the model's velocity field compare very favorably at low Mach numbers.   

Sensitivity of Shock Accelerated Multi-Component Compressible Flows

Numerical simulation of Richtmyer-Meshkov instability (RMI) is conducted using an improved localized artificial diffusivity (LAD) method which is used to treat discontinuities in the form of material-interfaces and shocks in the flow-field. The RMI occurs on a cylindrical interface between air and SF$_{6}$ accelerated by a Mach 1.2 shock initially in air. Navier-Stokes simulation is conducted to accurately predict the mixing between the two fluids. The initial conditions for the 2-D simulations are matched to previous experimental work by Tomkins et al (JFM 2008). Sensitivity of the mixing rate to mesh resolution is explored to arrive at grid converged results. The study on initial condition sensitivity indicates that the initial pressure and density gradient are critical parameters which determine the primary vortex generation responsible for the flow development. The effect of presence of the third species (acetone used as a tracer particle in the experiments to obtain contour fields using PLIF) is shown to be non-negligible and an estimate of the amount of the tracer species that was present in the initial experimental set-up is given.   

Effects of Initial Conditions on the Planar Richtmyer-Meshkov Instability

In the large eddy simulation (LES) approach, large-scale energy-containing structures are resolved, smaller structures are filtered out, and unresolved subgrid effects are modeled. Extensive recent work has demonstrated that predictive under-resolved simulations of the velocity fields in turbulent flows are possible without resorting to explicit subgrid models, when using a class of physics-capturing high-resolution finite-volume numerical algorithms. This strategy is denoted implicit LES (ILES) [1]. Tests in fundamental applications ranging from canonical to complex flows indicate that ILES is competitive with conventional LES in the LES realm proper - flows driven by large scale features. The performance of ILES in the substantially more difficult problem of under-resolved material mixing driven by under-resolved velocity fields and initial conditions is the focus of the present work. Progress in addressing relevant resolution issues in RAGE simulations of planar shocked and reshocked driven turbulence is reported. [1] F.F. Grinstein, L.G. Margolin, and W.J. Rider 2007, Eds., Implicit Large Eddy Simulation: Computing Turbulent Flow Dynamics, Cambridge.   

Experimental Study of a Shock-Accelerated Gas Flow Non-Uniformly Seeded With Droplets

We present an experimental study of a gas flow which is partially seeded with a modest volume fraction of submicron-sized droplets and subjected to shock acceleration. Under these conditions an instability similar to Richtmyer-Meshkov develops. In our experiments, a planar shock front traveling horizontally through air meets a vertical column of gas (either air or SF6) that is seeded with particles. After shock interaction, the column is compressed and deformed, and a pair of counter-rotating vortices forms. The evolution of the flow is tracked with a multiple-CCD digital camera, allowing to capture up to four laser sheet-illuminated images per single experiment. We discuss the flow features in shocked and reshocked flows at a range of Mach numbers from 1.2 to 2.   

Modeling a Shock-Accelerated Fluid - Multiphase Fluid Interface

The hydrocode SHAMRC has been used in the past to study the formation and growth of the Richtmyer Meshkov Instability (RMI). While RMI involves impulsively accelerating two continuous fluids of differing densities, a similar class of instabilities has been recently described for multiphase flow. In this scenario, a shock wave passes through a region seeded with particles which have a non-trivial mass and density much greater than that of the surrounding and embedding fluid, resulting in a higher effective density in the seeded region. As the volume of the particles is small, there is no pressure gradient between the two regions. The simulations described here attempt to model the first order formation and growth phenomenon of this new class of instability by approximating the second phase as a continuous fluid with an averaged density. The strength of the shock and the packing density of the tracer particles are varied to provide a wide range of instability growth rates. Finally, these growth rates are scaled and compared to experimental data.   

Effect of multi-mode initial conditions in shock-driven flows

Carefully imposed initial conditions have been shown to control late time turbulence and mixing in buoyancy-driven flows [\textit{Dimonte et al., 2004; Banerjee {\&} Andrews, 2009}]. This is important in understanding and prediction of Inertial Confinement Fusion. We report the experimental results on the initial condition parameters, namely amplitude ($\delta )$ and wavelength ($\lambda )$ of perturbations, that impact the material mixing and transition to turbulence in shock-driven, Richtmyer-Meshkov instability. A detailed study on the impact of $\delta $ and $\lambda $ on turbulence in a heavy gas varicose curtain (air-SF$_{6}$-air) is undertaken. Experiments were conducted with stable, membrane-free initial conditions at shock Mach number, \textit{Ma} = 1.2 and Atwood number, \textit{At }= 0.67. The effect of multi-mode initial conditions on mixing and transition was quantitatively measured using simultaneous Particle Image Velocimetry (PIV) and Planar-Laser Induced Fluorescence (PLIF). The turbulence statistics were measured for different combinations of $\delta $, $\lambda $. The results obtained are being compared with data from ongoing 3-D numerical simulations.