Evolution of a shock-accelerated thin fluid layer

Rightley, Paul; Vorobieff, Peter; Benjamin, R. F.

doi:10.1063/1.869299

Cited by 56 publications

(54 citation statements)

References 18 publications

(43 reference statements)

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“…Previous RM experiments investigating transition to turbulence, despite their novelty (Rightley, Vorobieff & Benjamin 1997;Vorobieff, Rightley & Benjamin 1998, 1999, suffered from unstable initial conditions that led to (non-repeatable) large-scale features that had not fully dissociated into smaller vortices as expected from a turbulence cascade (see figure 2a of Vorobieff et al 1998). The present experimental facility has been upgraded (see Balakumar et al 2008) to stabilize the initial conditions from experiment to experiment, allowing accurate ensemble averaging and Reynolds Density self-correlation in developing Richtmyer-Meshkov turbulence 295 decomposition.…”

Section: Measurement Of the Dscmentioning

confidence: 99%

Evolution of the density self-correlation in developing Richtmyer–Meshkov turbulence

et al. 2013

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Turbulent mixing in a Richtmyer-Meshkov unstable light-heavy-light (air-SF 6 -air) fluid layer subjected to a shock (Mach 1.20) and a reshock (Mach 1.14) is investigated using ensemble statistics obtained from simultaneous velocity-density measurements. The mixing is driven by an unstable array of initially symmetric vortices that induce rapid material mixing and create smaller-scale vortices. After reshock the flow appears to transition to a turbulent (likely three-dimensional) state, at which time our planar measurements are used to probe the developing flow field. The density selfcorrelation b = − ρv (where ρ and v are the fluctuating density and specific volume, respectively) and terms in its evolution equation are directly measured experimentally for the first time. Amongst other things, it is found that production terms in the b equation are balanced by the dissipation terms, suggesting a form of equilibrium in b. Simultaneous velocity measurements are used to probe the state of the incipient turbulence. A length-scale analysis suggests that an inertial range is beginning to form, consistent with the onset of a mixing transition. The developing turbulence is observed to reduce non-Boussinesq effects in the flow, which are found to be small over much of the layer after reshock. Second-order two-point structure functions of the density field exhibit a power-law behaviour with a steeper exponent than the standard 2/3 power found in canonical turbulence. The absence of a significant 2/3 region is observed to be consistent with the state of the flow, and the emergence of the steeper power-law region is discussed.

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Section: Measurement Of the Dscmentioning

confidence: 99%

Evolution of the density self-correlation in developing Richtmyer–Meshkov turbulence

et al. 2013

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“…Knowledge of the initial conditions and the shock properties suffices to produce realistic estimates of the vorticity field that forms shortly after the shock interaction. The subsequent vortex dynamics can be simulated with a relatively simple 'vortex blob' model [9]. Thus, the emergence and evolution of the disordered features that leads to turbulence can be isolated and quantified in greater detail.…”

Section: Introductionmentioning

confidence: 99%

“…Works in the second group, gas-curtain studies, deal with two nearby density interfaces resulting in a curtain of heavy gas (usually sulfur hexafluoride mixed with gaseous or aerosol tracer) embedded in a lighter gas (air). Investigations of the flow in a shock-accelerated gas curtain have been carried out by Jacobs et al [6,7], Budzinski et al [8], Rightley et al [9,10] and Vorobieff et al [11].…”

Section: Introductionmentioning

confidence: 99%

Shock-driven gas curtain: fractal dimension evolution in transition to turbulence

Vorobieff

Rightley

Benjamin

1999

Physica D: Nonlinear Phenomena

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We present estimates of the Hausdorff fractal dimension of a planar section of the interfaces on the sides of a thin curtain of heavy gas (SF 6 ) embedded in air and accelerated with a planar shock wave at Mach 1.2. As the Richtmyer-Meshkov instability develops, eventually leading to a transition to turbulence in the curtain, the fractal dimension of the interfaces increases from an initial value not exceeding 1.10 to a maximum value 1.36 ± 0.07. This value is close to that experimentally measured for fully developed turbulence. The growth of the fractal dimension is closely related to mixing in the flow. It represents an important and previously unmeasured property in the transition to turbulence due to Richtmyer-Meshkov instability.

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“…As in the case of experiments, the quantitative data obtained from these simulations were mainly limited to the consideration of perturbation amplitude growth. Numerical studies of the reshocked single-mode impulsive Richtmyer-Meshkov instability experiment of Jacobs, Jones, and Niederhaus 20,21 were performed by Kotelnikov and Zabusky 22 and Kotelnikov, Ray, and Zabusky 23 using the vortex-in-cell method and the contour advection semi-Lagrangian method ͑n.b., the Jacobs et al 24 and Rightley et al 25 Mach 1.2 experiment with reshock was also simulated using a Godunov method 23 ͒. Kremeyer et al 26 used a fifth-order WENO method to simulate the Richtmyer-Meshkov instability in a shock tube containing gases with different initial transverse density profiles to investigate shock splitting and, in particular, the role of shock bowing and vorticity dynamics.…”

Section: Introductionmentioning

confidence: 99%

High-resolution simulations and modeling of reshocked single-mode Richtmyer-Meshkov instability: Comparison to experimental data and to amplitude growth model predictions

2007

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The reshocked single-mode Richtmyer-Meshkov instability is simulated in two spatial dimensions using the fifth-and ninth-order weighted essentially nonoscillatory shock-capturing method with uniform spatial resolution of 256 points per initial perturbation wavelength. The initial conditions and computational domain are modeled after the single-mode, Mach 1.21 air͑acetone͒/SF 6 shock tube experiment of Collins and Jacobs ͓J. Fluid Mech. 464, 113 ͑2002͔͒. The simulation densities are shown to be in very good agreement with the corrected experimental planar laser-induced fluorescence images at selected times before reshock of the evolving interface. Analytical, semianalytical, and phenomenological linear and nonlinear, impulsive, perturbation, and potential flow models for single-mode Richtmyer-Meshkov unstable perturbation growth are summarized. The simulation amplitudes are shown to be in very good agreement with the experimental data and with the predictions of linear amplitude growth models for small times, and with those of nonlinear amplitude growth models at later times up to the time at which the driver-based expansion in the experiment ͑but not present in the simulations or models͒ expands the layer before reshock. The qualitative and quantitative differences between the fifth-and ninth-order simulation results are discussed. Using a local and global quantitative metric, the prediction of the Zhang and Sohn ͓Phys. Fluids 9, 1106 ͑1997͔͒ nonlinear Padé model is shown to be in best overall agreement with the simulation amplitudes before reshock. The sensitivity of the amplitude growth model predictions to the initial growth rate from linear instability theory, the post-shock Atwood number and amplitude, and the velocity jump due to the passage of the shock through the interface is also investigated numerically.

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Evolution of a shock-accelerated thin fluid layer

Cited by 56 publications

References 18 publications

Evolution of the density self-correlation in developing Richtmyer–Meshkov turbulence

Evolution of the density self-correlation in developing Richtmyer–Meshkov turbulence

Shock-driven gas curtain: fractal dimension evolution in transition to turbulence

High-resolution simulations and modeling of reshocked single-mode Richtmyer-Meshkov instability: Comparison to experimental data and to amplitude growth model predictions

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