Effects of initial conditions and Mach number on turbulent mixing transition of shock-driven variable-density flow
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This thesis presents results on the effects of initial conditions (single- and multi-mode) and incident shock wave Mach numbers (M) on several mixing characteristics in Richtmyer-Meshkov instability (RMI) evolution. These goals are achieved by performing two different experimental campaigns using a shock strength with an incident Mach number of 1.9 and 1.55. Each campaign follows the interface evolution after interaction with incident shock and reflected shock from the wall (reshock). In addition, two different initial perturbations are imposed to study RMI evolution at each Mach number. The first perturbation is a predominantly single-mode long-wavelength interface which is formed by inclining the entire tube to 80° relative to the horizontal, and thus can be considered as half the wavelength of a triangular wave. The second initial condition is a multi-mode interface, containing additional shorter wavelength perturbations due to the imposition of shear and buoyancy on the inclined perturbation of the first case. In both single- and multi-mode cases at each Mach number, the interface consists of a nitrogen-acetone mixture as the light gas over carbon dioxide as the heavy gas (Atwood number, A~0.22). The evolving density and velocity fields are measured simultaneously using planar laser-induced fluorescence (PLIF) and particle image velocimetry (PIV) techniques to provide the first detailed turbulence statistics measurements (i.e., Density, velocity, and density-velocity cross-statistics) using ensemble averaging for shock-accelerated variable density flows at M > 1.5 before and after reshock. The evolution of mixing is investigated via the density fields by computing mixed-mass and mixing layer thickness, along with mixing width, mixedness, and the density self-correlation (DSC). It is shown that the amount of mixing is dependent on both the initial conditions and the incident shock Mach number before reshock. Evolution of the density self-correlation is discussed and the relative importance of different DSC terms is shown through fields and spanwise-averaged profiles. The localized distribution of vorticity and the development of roll-up features in the flow is studied through the evolution of interface wrinkling and length of the interface edge, and indicates that the vorticity concentration shows a strong dependence on the Mach number. The contribution of different terms in the Favre-averaged Reynolds stress is shown, and while the mean density-velocity fluctuation correlation term is dominant, a high dependency on the initial condition and reshock is observed for the turbulent mass-flux term. Regarding the effects of initial conditions, density and velocity data show that a distinct memory of the initial conditions is maintained in the flow before interaction with reshock. After reshock, the influence of the long-wavelength inclined perturbation present in both initial conditions is still apparent, but the distinction between the two cases becomes less evident as smaller scales are present even in the single-mode case. Mixing transition is analyzed through two criteria: Reynolds number (Dimotakis, 2000) and time-dependent length scales (Robey et al., 2003). The Reynolds number threshold is surpassed in all cases after reshock. In addition, the Reynolds number is around the threshold range for the multi-mode, high Mach number case (M~1.9) before reshock. However, the time-dependent length-scale threshold is surpassed by all cases only at the latest time after reshock, while all cases at early times after reshock and the high Mach number case at the latest time before reshock fall around the threshold. The scaling analysis of turbulent kinetic energy spectra after reshock at the latest time, at which mixing transition analysis suggests that an inertial range has formed, indicates power scaling of -1.8±0.05 for the low Mach number case and -2.1±0.1 for the higher Mach number case. This is related to the high anisotropy observed in this flow resulting from strong, large-scale, streamwise fluctuations produced by large-scale shear. This work will help develop the capability to accurately predict and model extreme mixing, potentially leading to advances in a number of fields: energy, environment (atmospheric and oceanographic), aerospace engineering, and most pertinently, inertial confinement fusion (ICF).