Wayne N. Kraft

Detailed measurements of a statistically steady Rayleigh-Taylor mixing layer from small to high Atwood numbers

The self-similar evolution to turbulence of a multi-mode miscible Rayleigh-Taylor (RT) mixing layer has been investigated for Atwood numbers 0.03-0.6, using an air-helium gas channel experiment. Two co-flowing gas streams, one containing air (on top) and the other a helium-air mixture (at the bottom), initially flowed parallel to each other at the same velocity separated by a thin splitter plate. The streams met at the end of the splitter plate, with the downstream formation of a buoyancy unstable interface, and thereafter buoyancy-driven mixing. This buoyancy-driven mixing layer experiment permitted long data collection times, short transients and was statistically steady. Several significant designs and operating characteristics of the gas channel experiment are described that enabled the facility to be successfully run for A t ~ 0.6. We report, and discuss, statistically converged measurements using digital image analysis and hot-wire anemometry. In particular, two hot-wire techniques were developed for measuring the various turbulence and mixing statistics in this air-helium RT experiment. Data collected and discussed include: mean density profiles, growth rate parameters, various turbulence and mixing statistics, and spectra of velocity, density and mass flux over a wide range of Atwood numbers (0.03 ≤ A t ≤ 0.6). In particular, the measured data at the small Atwood number (0.03-0.04) were used to evaluate several turbulence-model constants. Measurements of the root mean square (r.m.s.) velocity and density fluctuations at the mixing layer centreline for the large A t case showed a strong similarity to lower A t behaviours when properly normalized. A novel conditional averaging technique provided new statistics for RT mixing layers by separating the bubble (light fluid) and spike (heavy fluid) dynamics. The conditional sampling highlighted differences in the vertical turbulent mass flux, and vertical velocity fluctuations, for the bubbles and spikes, which were not otherwise observable. Larger values of the vertical turbulent mass flux and vertical velocity fluctuations were found in the downward-falling spikes, consistent with larger growth rates and momentum of spikes compared with the bubbles.

Experimental Investigation of Unstably Stratified Buoyant Wakes

A water channel has been used as a statistically steady experiment to investigate the development of a buoyant plane wake. Parallel streams of hot and cold water are initially separated by a splitter plate and are oriented to create an unstable stratification. At the end of the splitter plate, the two streams are allowed to mix and a buoyancy-driven mixing layer develops. The continuous, unstable stratification inside the developing mixing layer provides the necessary environment to study the buoyant wake. Downstream a cylinder was placed at the center of the mixing layer. As a result the dynamic flows of the plane wake and buoyancy-driven mixing layer interact. Particle image velocimetry and a high-resolution thermocouple system have been used to measure the response of the plane wake to buoyancy driven turbulence. Velocity and density measurements are used as a basis from which we describe the transition, and return to equilibrium, of the buoyancy-driven mixing layer

Numerical Investigation of Single-Mode Richtmyer-Meshkov Instability

The Richtmyer-Meshkov (RM) instability occurs when a shock passes through a perturbed interface separating fluids of different densities. Similarly, RM instabilities may also occur when a perturbed interface between two incompressible fluids of different density is impulsively accelerated. We report work that investigates RM instabilities between incompressible media by way of numerical simulations that are matched to experiments reported by Niederhaus & Jacobs [1]. We also describe a compact, fractional time-step, two-dimensional, finite-volume numerical algorithm that solves the non-Bousinesq Euler equations explicitly on a Cartesian, co-located grid. Numerical advection of volume fractions and momentum is second-order accurate in space and unphysical oscillations are prevented by using Van Leer flux limiters [2,3]. An initial velocity impulse has been used to model the impulsive acceleration history found in the experiments [1]. We report accurate simulation of the experimentally measured early-, intermediate-, and late-time penetrations of one fluid into another.Copyright

Visualizations of Buoyancy Driven Mixing

A collection of visualizations that convey a basic understanding of buoyancy-driven mixing is presented. Buoyancy-driven mixing resulting from the Rayleigh-Taylor instability occurs in a unstably stratified flow when a heavy fluid rests above a light fluid. The difficulty of creating an unstable density stratification and repeatable fluid interface has made studying the Rayleigh-Taylor instability a challenging task. Our experiments utilize a water channel and most recently a gas channel (low speed wind tunnel). The experimental configuration allows unstable perturbations to develop into a mixing layer as they travel downstream. Thus resulting in a repeatable experiment and statistically steady flow. Various visualization techniques have been used to observe the development of the Rayleigh-Taylor instability. Visualizations using Nigrosene dye as a fluid marker are shown in the evolution of single and binary mode perturbations due to the Rayleigh-Taylor instability. In contrast, visualizations of the Rayleigh-Taylor instability developed from multi-mode perturbations are seen for the gas channel using both fog and smoke to visualize the flow. Together these techniques help provide an understanding for the nature and complexity of buoyancy driven mixing.© 2005 ASME

Numerical investigation of internal vortex structure in two dimensional, incompressible Richtmyer-Meshkov flows

Richtmyer-Meshkov (RM) instability occurs when one fluid is impulsively accelerated into a second fluid, such that ρ1 ≠ ρ2 . This research numerically investigates RM instabilities between incompressible media, similar to the experiments reported by Niederhaus & Jacobs [1]. A two-dimensional, finite-volume numerical algorithm has been developed to solve the variable density Navier-Stokes equations explicitly on a Cartesian, co-located grid. In previous calculations, no physical viscosity was implemented; however, small scale fluctuations were damped by the numerical algorithm. In contrast, current simulations incorporate the physical viscosities reported by Niederhaus & Jacobs [1] and are explicitly used. Calculations of volume fraction and momentum advections are second-order accurate in space. Unphysical oscillations due to the higher-order advection scheme are minimized through the use of a Van Leer flux limiting algorithm. An initial velocity impulse [2] has been used to model the impulsive acceleration history found in the experiments of Niederhaus & Jacobs [1]. Both inviscid and viscous simulations result in similar growth rates for the interpenetration of one fluid into another. However, the inviscid simulations (i.e. no explicit viscosity) are unable to capture the full dynamics of the internal vortex structure that exists between the two fluids due to the absence of viscous effects.Copyright

Experimental Investigation of Stratified, Buoyant Wakes

The development of a buoyant plane wake has been investigated experimentally. A water channel has been used as a statistically steady experiment to investigate the plane wakes. Parallel streams of hot and cold water are initially separated by a splitter plate. The streams are oriented such that the cold fluid is above the hot fluid, resulting in an unstable stratification. At the end of the splitter plate, the two streams are allowed to mix and a buoyancy driven mixing layer develops. Downstream of the splitter plate, growth of the turbulent buoyancy-driven mix is disrupted by a cylinder. The cylinder is located at the centerline of the mixing layer and associated wake. As a result the dynamic flows of the plane wake and buoyancy driven mixing layer interact. Particle image velocimetry (PIV), and a high-resolution thermocouple system are used to measure the response of the plane wake to buoyancy driven turbulence. Velocity and density measurements are used as a basis from which we describe the transition, and return to equilibrium, of the buoyancy driven mixing layer. We found for wakes where buoyancy is driving the motion, a remarkably fast recovery of a Rayleigh-Taylor mix in the wake region.Copyright