Robert F. Benjamin

Simulation of shock‐generated instabilities

Direct 2‐D numerical simulation of the fluid instability of a shock‐accelerated thin gas layer shows flow patterns in agreement with experimental images. The Eulerian‐based hydrodynamics code features Adaptive Mesh Refinement that allows the code to follow the vorticity generation and the complex flow resulting from the measured initial perturbations. These experiments and simulations are the first to address in quantitative detail the evolution of the Richtmyer–Meshkov instability in a thin fluid layer, and to show how interfluid mixing and vorticity production depend sensitively on initial perturbations in the layer.

Experimental observations of the mixing transition in a shock-accelerated gas curtain

Richtmyer–Meshkov instability of a thin curtain of heavy gas (SF6) embedded in air and accelerated by a planar shock wave (Mach 1.2) leads to the growth of interfacial perturbations in the curtain and to mixing. Our experiments produce a phenomenological description of the mixing transition and incipient turbulence during the first millisecond after the shock interaction. Growth of scales both larger and smaller than that of initial perturbations is visually observed and quantified by applying a wavelet transform to laser-sheet images of the evolving gas curtain. Histogram and wavelet analyses show an abrupt mixing transition for a multimode initial perturbation that is not apparent for single-mode perturbations.

Sensitivity of x‐ray film. II. Kodak No‐Screen film in the 1–100‐keV region

The absolute sensitivity of Kodak No‐Screen x‐ray film was measured for 11 photon energies between 1 and 8 keV using filtered fluorescent radiation. The shapes of the density‐vs‐exposure curves were observed to be a function of the photon energy. This calibration was demonstrated to be consistent with two earlier calibrations of No‐Screen response for photon energies between 5 and 100 keV and with a theoretical model of film sensitivity by Brown, Criss, and Birks.

Evolution of a shock-accelerated thin fluid layer

Multi-exposure flow visualization experiments with laser-sheet illumination provide growth-rate measurement of Richtmyer–Meshkov instability of a thin, perturbed heavy-gas layer embedded in a lower-density gas and accelerated by a planar shock wave. The measurements clearly show the three-stage transition to turbulence of this gas-curtain instability and the single-event coexistence of the three primary flow morphologies discovered previously. The shock-induced circulation for each event is estimated using a simple model based on Richtmyer–Meshkov instability and an infinite linear array of vortex points. These estimates are consistent with simplified flow simulations using a finite-core vortex-blob model.

Nonlinear growth of the shock-accelerated instability of a thin fluid layer

Richtmyer-Meshkov instability causes spatially periodic perturbations initially imposed on a shock-accelerated, thin gas layer to develop into one of three distinct flow patterns. Planar laser-induced fluorescence imaging of the evolving layer, produced by a perturbed SF 6 planar jet in air, shows an apparent flow bifurcation that is observed as mushroom-shaped or sinuous-shaped interfacial patterns. Analysis of this nonlinear instability growth, accomplished by modelling the flow field as a row of line vortices, predicts that the layer thickness grows logarithmically at later times and compares well with our measurements. Because the row of vortices is unstable, the model also provides an explanation for the appearance of the three observed interfacial patterns.

Stretching of material lines in shock-accelerated gaseous flows

A Mach 1.2 planar shock wave impulsively accelerates one of five different configurations of heavy-gas (SF6) cylinders surrounded by lighter gas (air), producing one or more pairs of interacting vortex columns. The interaction of the columns is investigated with planar laser-induced fluorescence in the plane normal to the axes of the cylinders. For the first time, we experimentally measure the early time stretching rate (in the first 220μs after shock interaction before the development of secondary instabilities) of material lines in shock-accelerated gaseous flows resulting from the Richtmyer-Meshkov instability at Reynolds number ∼25000 and Schmidt number ∼1. The early time specific stretching rate exponent associated with the stretching of material lines is measured in these five configurations and compared with the numerical computations of Yang et al. [AIAA J. 31, 854 (1993)] in some similar configurations and time range. The stretching rate is found to depend on the configuration and orientation of ...

A quantitative study of the interaction of two Richtmyer-Meshkov-unstable gas cylinders

We experimentally investigate the evolution and interaction of two Richtmyer–Meshkov-unstable gas cylinders using concentration field visualization and particle image velocimetry. The heavy-gas (SF6) cylinders have an initial spanwise separation of S/D (where D is the cylinder diameter) and are simultaneously impacted by a planar, Mach 1.2 shock. The resulting flow morphologies are highly reproducible and highly sensitive to the initial separation, which is varied from S/D≈1.2 to 2.0. The effects of the cylinder–cylinder interaction are quantified using both visualization and high-resolution velocimetry. Vorticity fields reveal that a principal interaction effect is the weakening of the inner vortices of the system. We observe a nonlinear, threshold-type behavior of inner vortex formation around S/D=1.5. A correlation-based ensemble-averaging procedure extracts the persistent character of the unstable flow structures, and permits decomposition of the concentration fields into mean (deterministic) and fluc...

INFLUENCE OF INITIAL CONDITIONS ON THE FLOW PATTERNS OF A SHOCK-ACCELERATED THIN FLUID LAYER

Previous observations of three flow patterns generated by shock acceleration of a thin perturbed, fluid layer are now correlated with asymmetries in the initial conditions. Using a different diagnostic (planar laser Rayleigh scattering) than the previous experiments, upstream mushrooms, downstream mushrooms, and sinuous patterns are still observed. For each experiment the initial perturbation amplitude on one side of the layer can either be larger, smaller, or the same as the amplitude on the other side, as observed with two images per experiment, and these differences lead to the formation of the different patterns.

X-ray calibration of RAR 2490 film for application to laser plasma experiments

An x-ray sensitometric calibration of Kodak RAR 2490 film has been performed over the 0.28-8.04-keV range of photon energies. The characteristic curves (optical density D vs exposure H) are fit well over the entire range by a two-parameter, analytic function, loglo(1O(D) - 1) = A log(10)H + B. Solarization is found to occur at an exposure of 2 x 10(3) photons/(microm)(2) for 1.49-keV photons. Comparison with other films is made.

Shock loading a rippled interface between liquids of different densities

Experimental results of the nonlinear growth of perturbations on a shocked interface between liquids having a density ratio of 10 are reported. After the shock passes from the higher‐density liquid into the lower‐density liquid, spikes of the higher‐density liquid are observed to grow into the other liquid without producing severe turbulence. The measured growth is compared with analytical estimates. The time‐resolved shadowgraphs provide excellent data for testing hydrodynamics models.