Impulsive model for the Richtmyer-Meshkov instability

Vandenboomgaerde, M.; Mügler, Claude; Gauthier, Serge

doi:10.1103/physreve.58.1874

Cited by 84 publications

(81 citation statements)

References 10 publications

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“…III A when they are corrected for the case of a diffuse interface by ͑35͒. 47 model ͓Eq. ͑12͔͒ in Fig.…”

Section: Comparison To the Predictions Of Impulsive Modelsmentioning

confidence: 99%

“…Fraley, 45 and Vandenboomgaerde et al; 47 ͑ii͒ the weakly nonlinear perturbation models of Zhang and Sohn, 48 Vandenboomgaerde et al, 49 and Matsuoka et al; 50 and ͑iii͒ the nonlinear empirical model of Sadot et al 51 The bubble and spike velocities were also compared to the predictions of the potential models of Goncharov 53 and Sohn. 54,55 In addition, the bubble amplitude was compared to the prediction of the Mikaelian 58 model.…”

Section: -17mentioning

confidence: 99%

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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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“…III A when they are corrected for the case of a diffuse interface by ͑35͒. 47 model ͓Eq. ͑12͔͒ in Fig.…”

Section: Comparison To the Predictions Of Impulsive Modelsmentioning

confidence: 99%

Section: -17mentioning

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 issues of compression and phase reversals (when a shock or reshock proceeds from a high to a low density fluid) are treated by prescriptions concerning the use of h before or h after , referring to the mixing width before or after the shock/reshock. Prescriptions for the linear regime are given in [3,30,31]. Clearly, h 0 in (4) is h after , as it describes growth immediately after shocks or reshocks have passed and any phase inversion has taken place.…”

Section: The Modelmentioning

confidence: 99%

Testing an analytic model for Richtmyer–Meshkov turbulent mixing widths

Mikaelian

2014

Shock Waves

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We discuss a model for the evolution of the turbulent mixing width h(t) after a shock or a reshock passes through the interface between two fluids of densities ρ A and ρ B inducing a velocity jump V . In this model, the initial growth rate is independent of the surface finish or initial mixing width h 0 , but its duration t * is directly proportional to it:, α and θ are dimensionless, A-dependent parameters measured in past Rayleigh-Taylor experiments, and β is a new dimensionless parameter we introduce via t * = (h 0 / V )β. The mixing width h and its derivativeḣ remain continuous at t = t * since h * = h 0 + 2α A V t * andḣ * = 2α A V . We evaluate β ∼ 6 at A ≈ 0.7 from air/SF 6 experiments and propose that the transition at t = t * signals isotropication of turbulence. We apply this model to the recent experiments of Jacobs et al. (Shock Waves 23:407-413, 2013) on shock and reshock, and discuss briefly the third wave causing an unstable acceleration of the interface. We also consider the experiments of Weber et al. (Phys Fluids 24:074105, 2012) and argue that their smaller growth rates reflect density gradient stabilization.

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“…(33)). A more recent prescription, 33 according to which the incompressible η 0 A is replaced by 1 2 (η 0 A) be f ore + Using the more general Eq. (31) …”

Section: A Linear Regime: Analyticmentioning

confidence: 99%

Boussinesq approximation for Rayleigh-Taylor and Richtmyer-Meshkov instabilities

Mikaelian

2014

Physics of Fluids

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We apply numerical and analytic techniques to study the Boussinesq approximation in Rayleigh-Taylor and Richtmyer-Meshkov instabilities. In this approximation, one sets the Atwood number A equal to zero except where it multiplies the acceleration g or velocity-jump v. While this approximation is generally applied to low-A systems, we show that it can be applied to high-A systems also in certain regimes and to the "bubble" part of the instability, i.e., the penetration depth of the lighter fluid into the heavier fluid. It cannot be applied to the spike. We extend the Boussinesq approximation for incompressible fluids and show that it always overestimates the penetration depth but the error is never more than about 41%. The effect of compressibility is studied by analytic techniques in the linear regime which indicate that compressibility has the opposite effect and the Boussinesq approximation underestimates bubbles by about 14%. We also present direct numerical simulations of two compressible systems which have approximately the same A v: a low-A air/CO 2 system shocked at M s = 1.57, and a high-A air/SF 6 system shocked at M s = 1.24. While the bubbles are approximately equal, the lower-A system has a shorter (less penetrating) spike; however, because its mushrooms are more tightly wound, the low-A system has the larger interface area. C 2014 Author(s)

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Impulsive model for the Richtmyer-Meshkov instability

Cited by 84 publications

References 10 publications

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

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

Testing an analytic model for Richtmyer–Meshkov turbulent mixing widths

Boussinesq approximation for Rayleigh-Taylor and Richtmyer-Meshkov instabilities

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