High-resolution simulations and modeling of reshocked single-mode Richtmyer-Meshkov instability. I. Comparison to experimental data and to amplitude growth model predictions
The reshocked single-mode Richtmyer-Meshkov instability is simulated in two spatial dimensions using the fifth- and ninth-order weighted essentially non-oscillatory 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 air(acetone)/SF{sub 6} shock tube experiment of Collins and Jacobs [J. Fluid Mech. 464, 113 (2002)]. 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 models) 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 (1997)] nonlinear Pade 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. In Part II [Phys. Fluids (2006)], a comprehensive investigation of mixing induced by the reshocked single-mode Richtmyer-Meshkov instability is performed using the present simulation data to assess and quantify the effects of reshock and other waves on the mixing dynamics, including the post-reshock growth, circulation deposition, mixing profiles and fractions, baroclinic circulation deposition, energy spectra and statistics.
- Research Organization:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 936681
- Report Number(s):
- UCRL-JRNL-221480; TRN: US0805631
- Journal Information:
- Physics of Fluids, vol. 19, N/A, May 1, 2007, pp. 024104-1-024104-19, Vol. 19
- Country of Publication:
- United States
- Language:
- English
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