Session LP: Richtmyer-Meshkov/Rayleigh Taylor Instabilitities II

Mixing Characteristics in Buoyancy-Driven, Variable Density Turbulence

The mixing between two incompressible fluids with different densities in an unstable stratified configuration, as occurs in the Rayleigh-Taylor instability, is examined using Direct Numerical Simulations. The statistically homogeneous case is considered as a unit problem for variable density turbulence. It involves both the transition to turbulence and the decay of turbulence as the friction forces overcome buoyancy generation. No Boussinesq approximation is made so that high Atwood numbers are allowed. The two fluids are initially non-premixed with a double-delta PDF and the flow is dominated at early times by transport mixing rather than diffusion. At early times buoyancy production is important at all scales leading to anisotropy at all scales. Later, only the large scales remain anisotropic. Numerical results are used to examine the morphology of the scalar structures and the influence of various parameters on the mixing progress.   

Energetics within the mixing layer of miscible Rayleigh-Taylor turbulence.

We present recent measurements taken within the turbulent mixing layer generated by two miscible fluids that are initially Rayleigh-Taylor unstable. The measurements are done using simultaneous particle tracking, to obtain velocity measurements, and laser induced fluorescence, to get a local estimate of the density field. Both types of data are captured in a time resolved manner and with high spatial resolution. These measurements allow us to determine the mechanisms involved in transferring energy in the system (both to and from the measurement volume as well as from scale to scale). The results presented will demonstrate that most of the evolution in the kinetic energy is caused by the advection of kinetic energy whereas little energy evolution is mediated by buoyancy from density differences (potential energy terms). This observation is in agreement with recent theoretical work (M. Chertkov, PRL, 2003).   

Rayleigh-Taylor instability for immiscible fluids of arbitrary viscosities: Magnetic levitation investigation and theoretical model

A magnetic field gradient was used to draw down a low density paramagnetic fluid below a more dense fluid in a Hele-Shaw cell. \ On turning off the field a Rayleigh-Taylor instability was observed \textit{in situ}, and the growth of the most unstable wavevector was measured vs. time. \ A theory for the instability that permits different viscosities for two immiscible fluids was developed, and good agreement was found with the experimental results. The technique of magnetic levitation promises to broaden significantly the accessible parameter space of gravitational interfacial instability experiments.   

Rayleigh-Taylor-like instability in supercritical fluids

This paper concerns the numerical study of the stability of a two-layer system filled with a single pure supercritical fluid subjected to an initial temperature difference. The very large compressibility and the very low heat diffusivity of near-critical fluids lead to a Rayleigh-Taylor like gravitational instability of the heat diffusion layer. This instability is similar to the one of two miscible fluids where molecular species diffusion coefficient is replaced by the heat diffusion coefficient. Our numerical results are consistent with the dispersion relation derived by Duff \textit{et al.} [1962] for a system of two miscible fluids (argon-bromine mixture falling into helium or air). We show also that when the thickness of the lower layer becomes smaller than the heat diffusion length based on the maximum growth rate, the system is stable. A linear stability diagram has been established as a function of three parameters: the thickness of the lower layer, the density difference between the two layers and the distance to the critical point. As one approaches the critical point, the high initial stratification (due to the high compressibility) of this Rayleigh-Taylor-like configuration has the effect of stabilizing the system.   

Molecular measurements in large Schmidt number Rayleigh-Taylor mixing

Current progress on experimental molecular mixing measurements in a small Atwood number, liquid phase, turbulent Rayleigh-Taylor mixing layer using an open-loop water channel facility is reported. In the experiments, the pH of the heavy (salt) and light (fresh) water streams is controlled by adding a set volume of either acid or alkali to each stream. As the two streams molecularly mix, the chemical reaction between the acid and alkali is marked by a Phenolphthalein chemical indicator, which is imaged under backlit conditions. Calibration of the imaging process provides a quantitative relationship between the amount of light absorption and the fraction of molecularly mixed fluid. The current mixing measurements are compared with previous measurements of molecular mixing in Rayleigh-Taylor experiments and simulations of various Atwood and Schmidt numbers. This research was sponsored by the U.S. DOE National Nuclear Security Administration under the Stewardship Science Academic Alliances program through DOE Research Grant \#DE-FG03-02NA00060.   

Statistical velocity-density measurements in Rayleigh-Taylor mixing

A gas channel facility using helium and air is used to perform statistical measurements of both velocity and density in a Rayleigh-Taylor mixing layer. In the experiment, two gas streams of different densities (heavy over light) flowing parallel to each other are initially separated by a thin splitter plate. At the end of the splitter plate the two fluids are allowed to mix and the Rayleigh-Taylor instability develops. The gas channel facility uses two streams of different gases (air above a air/helium mixture). By changing the helium content in the second stream the density stratification is modified. Instantaneous velocity and density measurements inside the mixing layer are obtained using a combined hot-wire / cold-wire anemometry technique where temperature is used as a fluid marker. Both anemometers are used to yield simultaneous velocity and density measurements which allows for determination of Reynolds stresses and their spectra.   

PLIF flow visualization of magnetically stabilized Rayleigh-Taylor instability.

Experiments are presented that utilize the properties of paramagnetic fluids to study Rayleigh-Taylor instability. The fluids, a miscible combination of a paramagnetic salt solution and another nonmagnetic liquid, are contained in a tank placed between the poles of a large electromagnet. The suspension of the heavy paramagnetic fluid over the lighter non-magnetic fluid is attained by the gradient field principle. Rayleigh-Taylor instability is initiated by switching off the current to the electromagnet, which results in the heavy fluid falling due to gravity. The resulting instability is visualized using planar laser-induced fluorescence (PLIF). Results will be presented for experiments initiated with either a nominally flat interface or a curved interface generated by the applied magnetic field. The experiments initiated with a flat initial interface develop a random surface pattern with dominant length scale well approximated by the fastest growing wavelength given by viscous linear stability theory. Experiments initiated with a curved interface develop similar to the single-mode instability.   

Direct Numerical Simulation of Rayleigh-Taylor Instability

Results from a 3072 x 3072 x 3072 point Direct Numerical Simulation of Rayleigh-Taylor instability indicate that the alpha parameter cannot be accurately measured by fitting a curve to the width of the mixing region, but can only be obtained by recourse to the similarity equation for the growth rate. The data further establish that the ratio of kinetic energy to released potential energy is not constant, except perhaps at extremely large Reynolds numbers. The simulated flow attains a Reynolds number of 32,000, surpassing the mixing transition. The latter stages of the calculation reveal a weak Reynolds number dependence, which may have profound consequences for modeling very high Reynolds number flows.   

Rayleigh--Taylor problem for a liquid-liquid phase interface

A linear stability analysis of the two-dimensional Rayleigh---Taylor problem for an incompressible fluid undergoing a liquid-liquid phase transformation is presented. Both inviscid and viscous fluids are considered and interfacial tension is taken into account. Instability is possible only when the phase with the higher density is above that with the lower density. Study of the inviscid case shows that the exchange of mass between the phases decreases significantly both the range of unstable wave numbers and the maximum growth rate for unstable perturbations as compared to those arising classically. For a linearly viscous fluid, the shear and dilational viscosities of the interface are taken into account as are the migrational viscosities associated with the motion of the interface relative to the underlying fluid. When no mass exchange occurs between the phases in the base state and the interfacial viscosities are neglected, the growth rates exceed by at least an order of magnitude those for the classical Rayleigh---Taylor problem. The various interfacial viscosities slow the growth rates of disturbances but do not influence the range of unstable wave numbers. For both the inviscid and viscous cases, interfacial tension plays the same stabilizing role. We extend the result to three-dimensional disturbance and find that any instability that may be present for a three-dimensional disturbance is also present for a two-dimensional disturbance involving a smaller wave length.   

Large Atwood number, miscible-liquid experiments on the Rayleigh-Taylor and Richtmyer-Meshkov instabilities.

Experiments are presented in which an incompressible system of two miscible liquids with a large density difference ($A\approx 0.5)$ is accelerated to produce the Richtmyer-Meshkov (RM) or Rayleigh-Taylor (RT) instabilities. The initially stably stratified liquid combination is contained within a rectangular tank that is accelerated on a vertical rail system. In the RM Experiments the tank is released from the top of the rail system, after which it impacts a spring that introduces the impulsive acceleration and the RM instability develops while the tank is in freefall. In the RT experiments, the same rail system is used; however, instead of impacting a spring the tank is accelerated downward using a weight and pulley system. The resulting fluid flows are observed using backlit photography. The initial perturbations are either forced (by oscillating the tank in the horizontal direction to produce a standing wave) or random (due to molecular motion or background noise). Measurements taken from the data compare well with theory and models for both the RM and RT instabilities.