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Richtmyer-Meshkov Instability in Converging Geometries


Lombardini, Manuel (2008) Richtmyer-Meshkov Instability in Converging Geometries. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/5SNE-4003.


We investigate the Richtmyer-Meshkov instability (RMI) in converging geometries analytically and computationally. The linear, or small amplitude, regime is first covered as it is the onset to subsequent non-linear stages of the perturbation growth. While the plane interaction of a shock with a slightly perturbed density interface is classically viewed as a single interface evolving as baroclinic vorticity have been initially deposited on it, we propose a simple but more complete model characterizing the early interaction between the interface and the receding waves produced by the shock-interface interaction, in the case of a reflected shock. A universal time scale representing the time needed by the RMI to reach its asymptotic growth rate is found analytically and confirmed by ideal gas computations for various incident shock Mach numbers MI and Atwood ratios A, and could be useful especially for experimentalists in non-dimensionalizing their data.

Considering again linear perturbations, we then obtain a general analytical model for the asymptotic growth rate reached by the instability during the concentric interaction of an imploding/exploding cylindrical shock with a cylindrical interface containing three-dimensional orthogonal perturbations, in the azimuthal and axial directions. Stable perturbations, typical of the converging geometry, are discovered. Comparisons are made with simulations where the effects of compressibility, wave reverberations, and flow convergence are isolated. Azimuthal and axial perturbation evolution are compared with results obtained for the plane RMI at comparable initial wavelengths.

A second interaction occurs when the transmitted shock, produced by the incident converging shock impacting the interface, converges to the axis and reflects to reshock the initially accelerated interface. This leads to highly non-linear perturbation growth. To isolate the complex wave interaction process, the interface is considered initially unperturbed so that the flow is radially symmetric. An accurate visualization procedure is performed to characterize the underlying physics behind the reshock event. We study extensively the cylindrical and spherical geometry, for various MI and for the air → SF6 (A=0.67) and SF6 → (A=-0.67) interactions, and draw important differences with the equivalent plane configuration.

A hybrid, low-numerical dissipation/shock-capturing method, embedded into an adaptive mesh refinement framework is optimized in order to achieve large-eddy simulations of the self-similar cylindrical converging shock-driven RMI and the turbulent mixing generated by the reshock. Computations are produced for MI=1.3 and 2.0, and for air -> SF6 SF6 -> air interfaces. We develop statistics tools to study extensively the growth of the turbulent mixing zone using cylindrical averages as well as various measures such as probability density functions of the mixing and turbulent power spectra, with the objectives of understanding the turbulent mixing in this particular geometry.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:compressible flows; computational fluid dynamics; hydrodynamic stability; large-scale computing; Richtmyer-Meshkov instability; turbulence and turbulent mixing
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Aeronautics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Pullin, Dale Ian
Thesis Committee:
  • Pullin, Dale Ian (chair)
  • Meiron, Daniel I.
  • Shepherd, Joseph E.
  • Colonius, Tim
Defense Date:2 May 2008
Non-Caltech Author Email:manuel.lombardini (AT)
Funding AgencyGrant Number
Academic Strategic Alliances Program (ASAP) of the Advanced Simulation and Computing (ASC)B341492
Record Number:CaltechETD:etd-05302008-140331
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2319
Deposited By: Imported from ETD-db
Deposited On:02 Jun 2008
Last Modified:25 Oct 2023 22:52

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