Simultaneous velocity and density measurements of fully-developed Rayleigh-Taylor turbulent mixing
Mikhaeil, Mark Maged
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The dynamics of molecular mixing and the energy transfer process in the Rayleigh- Taylor instability (RTI) are studied through the collection and analysis of simultaneous density-velocity field measurements. Statistically stationary experiments are performed in the “convective-type” gas tunnel facility, with density contrast achieved through the injection of helium into the bottom stream. To observe the structure of the self-similar regime, three experiments at Atwood number 0.1 are captured at three outer-scale Reynolds numbers, 520, 2260, and 4050. To study the mixing and dynamics of the flow, both particle image velocimetry (PIV) and laser induced fluorescence (LIF) are employed simultaneously. This allows, for the first time in an RTI flow, the simultaneous field measurement of velocity and density. Together, these can be used to measure statistics of velocity, density and velocity-density cross- correlated terms. The experimental understanding of the interaction between the large-scale motion of the RTI bubble and spike structures and the resulting mixing and energy transfer will serve as a useful validation tool for predictive turbulence models. This will help develop our understanding of a variety of physical phenomena, most importantly the ignition of Type Ia supernovae, and the implosion of the inertial confinement fusion (ICF) fuel target. Statistics of the volume fraction, density, and velocity show self-similar collapse of RTI profiles at large Reynolds number Re > 2000. The probability density function of the volume fraction shows an increase in mixed material at the center of the mixing region as Reynolds number increases, but the presence of unmixed entrained fluid in the core persists. Flat velocity profiles indicate homogeneous turbulence characteristics in the core of the mixing region. Significant anisotropy develops in the flow, with horizontal velocity fluctuations being only 60 % of the vertical velocity fluctuations. Meanwhile, the turbulent mass flux, the leading term in the production of turbulent kinetic energy in the flow, is shown to be asymmetric with increased peak towards the spike. Measurements of the molecular mixing show that mixing is maximized at the core of the flow and increases with increased Reynolds number. However, the rate of mixing peaks at Reynolds number around 2260, suggesting a regime transition in the flow around this Reynolds number. The analysis of the density-specific-volume correlation shows that the potential for mixing is mostly limited in the flow by the relative concentrations of the top and bottom fluid. The transport equation of b shows that it is mostly produced in the core of the mixing region, but that the spatial evolution of its profile is the result of transport by bulk motion of the bubble and spike. Energy transfer from gravitational potential energy to turbulent kinetic energy and viscous dissipation is observed to occur in the experiment with a ratio of dissipated energy to potential energy released of 38%. The analysis of the turbulent kinetic energy transport equation budget reveals that production is the dominant mechanism towards the growth of turbulent kinetic energy of the flow, and is asymmetrically skewed towards the spike. The viscous dissipation is also skewed towards the spike, suggesting that it serves as a balancing mechanism for the growth rate of turbulent kinetic energy. The budget of turbulent kinetic energy reveals the nature of the energy transfer process in the flow, from the production of turbulent kinetic energy at the core of the flow to its transport to the edges by large-scale fluctuations of the bubble and spike structures.