Session CW: Instability: Richtmyer-Meshkov/Rayleigh-Taylor II

Mach number effects in shock-driven instabilities with simultaneous velocity and density measurements

Experiments are performed to study the effects of incident shock Mach number on the development of a varicose-perturbed, heavy-gas curtain (air-SF$_{6}$-air). Incident shock strength is varied from Mach 1.2 to Mach 1.8, and the dynamic evolution of the gas curtain is observed using Planar Laser-Induced Fluorescence (PLIF) and Particle Image Velocimetry (PIV). Previous work at the Los Alamos Gas Shock Tube (Orlicz et al. Phys. Fluids 2009, and subsequent experiments), has demonstrated that the evolution of the total mixing width of the curtain scales with velocity. However, the evolution of the instantaneous mixing rate, which measures smaller scale flow features, does not scale with velocity. This suggests that while integral mixing width is a good first order measure of the flow, it is alone insufficient to fully measure the effects of Mach number on the mixing. The implementation of simultaneous PIV/PLIF allows us to gather more complete measurements consisting of the time evolution of paired vorticity and density fields in the flow, and therefore, a more complete picture of the dependency on Mach number.   

Effect of shear on mixing in R-T mixing layers at low Atwood numbers

Effect of shear on R-T mixing is studied at two different Atwood numbers using the gas channel facility at Texas A\&M University. The channel basically consists of two streams separated by a splitter plate. Pure air flows on top of the plate where as the lower density air Helium mixture flows on bottom and R-T mixing starts right after the splitter plate. Two different techniques, high resolution digital image analysis and simultaneous 3 wire cold wire Anemometry are used to measure R-T mixing growth rates. Results obtained from both the techniques are compared. Temperature is used as a marker to identify the streams and density is calculated from the temperature measured using a cold wire. Experiments are performed at Atwood numbers 0.04 and 0.1. At these Atwood numbers, effect of shear is studied by varying the velocity of one of the streams (mainly top stream). Simultaneous 3 wire cold wire Anemometry is performed at the vertical center line at three different axial locations. Different parameters obtained from these measurements including, $\theta$ (molecular mixing parameter), $\overline{{\rho^{'}}^2}$ and vertical turbulent mass flux $\overline{{\rho^{'} v^{'}}}$ and their effect on mixing growth rate are discussed.   

Miscible and immiscible liquid experiments and simulations on the Rayleigh-Taylor instability

Experiments and numerical simulations are presented in which an incompressible system of two liquids is accelerated to produce the Rayleigh-Taylor instability. In these experiments, the initially stable, stratified liquid combination is accelerated downward in one of two experimental apparatuses: a weight and pulley system in which a fluid filled container is accelerated on a rail system, or a new LIM apparatus which uses linear induction motors to accelerate the tank (which is attached to an aluminum plate) to produce much greater acceleration levels. Both miscible and immiscible liquid combinations are used. In both apparatuses the resulting fluid flows are visualized with backlit imaging using LED backlights in conjunction with monochrome high-speed video cameras, both of which travel with the moving fluid filled containers. Initial perturbations are either unforced and allowed to progress from background noise or forced by vertically oscillating the liquid combination to produce parametric internal waves. The results experiments are compared to numerical simulations performed using the CFD code Miranda.   

Experiments and theory on binary mixture evaporation in Hele-Shaw cells

Evaporation of binary mixtures is studied using a Hele-Shaw cell. Refractive index variations during the evaporation are followed using a Mach-Zehnder interferometer. A Rayleigh-Taylor instability, due to the evaporation-induced density stratification, is observed during the process, both for simple and more complex mixtures. A theoretical model is developed for 1D concentration profiles before instability, in order to facilitate the interpretation of the experimental results. In the case of the aqueous solutions of ethanol, it takes into account evaporation of both the solute and the solvent. However, in the case of polymer solutions, only the solvent evaporates, and the properties of the solution (viscosity, diffusion coefficient, saturated vapor pressure, etc.) strongly depend on the time-dependent polymer concentration. The concentration profiles obtained from the theoretical model are compared to the experiments, for both systems.   

Experimental investigation of Rayleigh Taylor instability in elastic-plastic materials

The interface of an elastic-plastic plate accelerated by a fluid of lower density is Rayleigh Taylor (RT) unstable, the growth being mitigated by the mechanical strength of the plate. The instability is observed when metal plates are accelerated by high explosives, in explosive welding, and in volcanic island formation due to the strength of the inner crust. In contrast to the classical case involving Newtonian fluids, RT instability in accelerated solids is not well understood. The difficulties for constructing a theory for the linear growth phase in solids is essentially due to the character of elastic-plastic constitutive properties which has a nonlinear dependence on the magnitude of the rate of deformation. Experimental investigation of the phenomena is difficult due to the exceedingly small time scales (in high energy density experiments) and large measurement uncertainties of material properties. We performed experiments on our Two-Wheel facility to study the linear stage of the incompressible RT instability in elastic-plastic materials (yogurt) whose properties were well characterized. Rotation of the wheels imparted a constant centrifugal acceleration on the material interface that was cut with a small sinusoidal ripple. The controlled initial conditions and precise acceleration amplitudes are levied to investigate transition from elastic to plastic deformation and allow accurate and detailed measurements of flow properties.   

Transition to turbulence in shock-accelerated flows without reshock

A numerical investigation of turbulence transition in shock-accelerated flow is described. Large-eddy simulations are performed for a heavy--light, SF$_6$--air ($A\simeq -0.67$) perturbed, density interface impacted by a shock wave of Mach number 1.5, 3.0 or 5.0. For these shock strengths, the initial perturbation amplitude is chosen such that the post-shock amplitude is about 25\% of the initial perturbation dominant wavelength. The flow is computed in the frame of the unperturbed, post-shock interface and the LES uses periodic boundary conditions in the directions transverse to the main flow. This allows two isotropic directions within the mixing regime enabling calculation of instantaneous radial spectra. The spectra are obtained at the center-plane of the mixing zone at various times during the layer growth. Results indicate that the power spectra of the velocity components approach a $k^{-5/3}$ scaling, signaling a transition to turbulence accompanying a reorganization of the deposited kinetic energy. A spectral measure of the flow anisotropy shows a tendency to isotropy of the flow, although the axial-velocity power spectrum contains, at almost every scale, more than a third of the total kinetic energy. A budget of the plane-averaged, root-mean square vorticity accounts for the different sources of vorticity fluctuation and their evolution following the shock interaction.   

The Effect of Eccentricity on the Stability of Spiral Flows

The instability mechanisms acting on the flow of fluid between two concentric cylinders where an axial pressure gradient is also present have been extensively studied and understood over the past three decades [1,2]. The eccentricity of one cylinder axis with respect to the other disrupts the axial symmetry that allows for the simplified analytical description of the base flow and introduces a radial component of the base flow. In the present study, a small eccentricity is introduced and the variation of the flow over the tangential direction is described by the first Fourier mode in $/theta$. With the origin at the center of the inner cylinder, the modifications to the governing equations are discussed, as well as the deviation in the boundary conditions given by the changing distance of the wall from the center. An analytical formulation of the base flow is derived and the bases for a linear stability calculation are laid.\\[4pt] [1] Hasoon, M.A. and Martin, B.W., The stability of viscous axial flow in an annulus with a rotating inner cylinder, Proc. R. Soc. London, A, 325, 1977\\[0pt] [2] DiPrima, R.C. and Pridor, A., The stability of viscous flow between rotating concentric cylinders with an axial flow, Proc. R. Soc. London, A, 266, 1979   

The effects of initial conditions on single and two-mode Rayleigh-Taylor instability

The dependence on initial conditions of single and two-mode Rayleigh-Taylor instability (RTI) is investigated using Direct Numerical Simulations (DNS). A new stage, chaotic development, was found at very late time of single-mode RTI, after the re-acceleration stage. We found that details of the shape of the initial perturbation, such as the diffusion thickness and perturbation amplitude, have a strong effect on the growth rate during the early and late time development, but minimal during the potential flow regime, such that the Goncharov ``terminal velocity'' result remains robust. The early time evolution is sensitive to diffusive effects and the dependence on initial conditions can be minimized by increasing the Reynolds and/or Schmidt numbers. At very late time, single-mode RTI transitions into a chaotic development stage, with strong sensitivity to initial conditions. We have also studied the effect of initial conditions on two-mode RTI, and found that the growth is strongly affected by the combination of mode numbers and amplitudes as well as the phase shift between modes. At late times, the motions become quite complicated, however some new phenomena, such as ``leaning,'' ``ejection,'' and ``mode resonance,'' can be identified as significantly influencing the growth rate.   

On Initial Conditions for Turbulent Rayleigh-Taylor Mixing

Rayleigh-Taylor (RT) instability occurs when the pressure gradient opposes the density gradient at a perturbed interface between two media. For fluids, the instability causes mixing which, in time, turns turbulent. This fundamental instability is observed in natural phenomena such as salt dome formation, or supernovae explosions, and in engineering applications such as heat exchangers and sprays in internal combustor, or in the implosion phase of Inertial Confinement Fusion (ICF). Non negligible effects of initial conditions (ICs) on the development and turbulent mixing of the Rayleigh-Taylor instability, create an opportunity for prediction and ``design'' of RT turbulence for engineering purposes. Most turbulence models used for studying engineering applications are defined for fully developed turbulence, and therefore do not account for initial conditions effects. Our research seeks a rational methodology to provide initial conditions in variable density turbulence models. We report our methodology for following the evolution of the mixing layer based on the composition of the initial perturbation spectrum, and extracting profiles of relevant variables for the turbulence model. Metrics defining the time at which the turbulence model should relay our model, and when ICs-induced anomaly(s) will occur in late time turbulent mixing will also be discussed. Handling of late time anomaly in the turbulence model will be suggested.   

Effect of initial conditions on a high Schmidt-number Rayleigh-Taylor mixing layer

An experimental investigation of the effect of initial conditions in spatiotemporal evolution of a high Schmidt number, low Atwood number (0.00075), reactive, turbulent Rayleigh-Taylor (RT) mixing layer will be presented. A horizontal solid barrier separating the participating fluids, contained in a static tank, is withdrawn to produce the RT unstable configuration and is similar in configuration to experiments of Dalziel (JFM-1999). The physical shape of the barrier coupled with the wake left on its withdrawal; define the spatial structure of initial perturbations. Passive control of initial conditions is attained by varying the shape of the barrier for a defined withdrawal rate. The design of the barrier is guided by integrated large-eddy simulations of the Euler equations in three dimensions with numerical dissipation, to the desired effect. Backlit imaging is used to study the temporal evolution of the RT mixing layer. Diffusion limited neutralization reaction in the presence of an indicator is used as a marker to quantify the extent of molecular mixing of the two fluids. The evolution of bubble growth coefficient, molecular mixing parameters and probability density functions are analyzed to draw comparison with existing numerical and experimental data.