Interaction of a Mach 1.2 Shock with a Single Cylinder

Vikram Dwarkadas, Greg Weirs and Tomek Plewa

This page shows simulations from the interaction of a shock with a cylinder of gas. The cylinder is composed of Sulphur Hexafluoride (SF6). The rest of the shocktube is filled with air. A shock of Mach number 1.2 is introduced into the shock tube and allowed to impact the cylinder. The experiment was carried out at Los Alamos National Lab. Experimental setup is shown here (PDF File) (although this is for two cylinders rather than one). The initial conditions (volume concentration through a cross-section of the cylinder) are shown here (GIF image) . Simulations were carried out with the FLASH code, Version 2.3, at the ASCI FLASH Center. The PPM method, without steeping, was used. Refinement was done on the first rather than second derivatives (which is the default for FLASH). The calculations included 2 fluids, air and SF6.

Questions to be answered

Any study of this kind raises a few questions, and we list here a few issues that come to mind and need to be addressed:
  • Do the simulations converge with increasing level of resolution? Is this convergence reflected in both external appearance as well as diagnostics such as velocity, concentration etc?
  • What is the influence of various numerical techniques such as the hydrodynamic method, effect of discontinuity steepening etc?
  • The maximum concentration of SF6 is not known. How do different concentrations affect the solution?
  • How well are the initial and boundary conditions characterized, for example how clearly is the shock delineated?
  • In 2 dimensions we neglect vertical motions of the SF6 gas? Are those important, and if so how do we get a handle on them?

    Available Diagnostics and Observables

  • Overall morphology, gas density distribution, SF6 concentration, velocity field - Are all these quantities available, and if so is it meaningful to use them for comparison? How should such a comparison be made?
  • How well is the experiment repeatable, i.e. can instabilities such as the Kelvin-Helmholtz instability that are seen in some of the results be reproduced easily? What are the typical mesurement errors?
  • What additional data is required to analyse the experiment? For example, we need to know physical properties of SF6 such as viscosity.
  • What is the Reynolds number for the experimental setup, as well as the simulations?

    The results below show density snapshots of the evolution of the cylinder cross-section. Clicking on the images or the "density" and other links will bring up animated 'gif' movies.

    6level 7level 8 level 9 level 10 level
    Max Conc =0.6 Density Density Density Pressure Density Density
    Density
    (showing blocks)     		Density
    (showing blocks)     		Density
    (showing blocks)     		Pressure
    (showing blocks)     		Density
    (showing blocks)     		Density
    (showing blocks)
    Max Conc =0.8 Density Density Density   Density Density
    Density
    (showing blocks)     		Density
    (showing blocks)     		Density
    (showing blocks)     		  Density
    (showing blocks)     		Pressure
    Max Conc =0.8
    Blocksize= 16X16     		  Density    
      Density
    (showing blocks)     		   
    Max Conc =0.8
    Blocksize= 32X32     		  Density    
      Density
    (showing blocks)     		   
    Max Conc =0.6
    Steepening Used     		  Density    
      Density
    (showing blocks)     		   
    3D run (4 levels) Density      

    vikram@flash.uchicago.edu