ASCI Site Review

1
ASC/Alliances Center for Astrophysical
Thermonuclear Flashes
Validation of the FLASH Code Shock-Cylinder
Experiment at Los Alamos National Laboratory
Contributors Experiments (Los Alamos) Chris
Tomkins, Mark Marr-Lyon, Kathy Prestridge, Bob
Benjamin Visualization (Argonne) Brad Gallagher,
Randy Hudson Mike Papka Simulations
(Flash) Vikram Dwarkadas
Greg Weirs, Tomek Plewa, Todd Dupont, George
Jordan

• Revealing the True Nature of the Experiment
• Comparison between 2- and 3-dimensional models
  reveals certain differences in morphology
  indicating additional redistribution of material
  due to vertical motions and coupling between
  horizontal and vertical flows. In light of this
  newly discovered element, 2-D studies appear of
  very limited use. Comparison of realistic 3-D
  model to experiment, shows good overall agreement
  of morphology of large and medium scale
  structures.
• We compared model velocity field to the PIV
  experimental data. We found reasonable agreement
  in structure of the velocity field while model
  velocities were over 50 larger than in
  experiment. This discrepancy does not necessarily
  imply serious problem since our early 3-D
  calculation did not benefit from the detailed
  analysis of the initial conditions.
• Development of genuinely three-dimensional
  structures is clearly revealed by volume
  rendering of the heavy gas distribution. Note the
  initially perfectly radially symmetric
  distribution of heavy gas is deformed due to
  deposition of vorticity along the columns
  surface. Sheets of heavy gas isolated by air
  progressively wrap around vortex cores, with
  small scale structure eventually developing at
  the air-SF6 interfaces. Tilting of the column
  closely resembles the experimental result of
  Jacobs (1993).

• Study Targets
• We study the shock-cylinder interaction to
  validate the FLASH code for vortex-dominated
  flows and discover three-dimensional effects in a
  nominally two-dimensional experiment.
• Our objective is to understand behavior of the
  complete system, including the initial
  conditions.
• We find the flowfields development to be highly
  sensitive to the distribution of heavy gas, SF6,
  prior to the arrival of the shock, i.e. the
  initial conditions are extremely important.
• We provide motivation and guidance for further
  development of the experiment, diagnostics of the
  initial conditions and the resulting
  three-dimensional flowfield as indicated by our
  predictive hydrodynamic model.

2D
3D
3D exp.

• Los Alamos Experiment
• Shock tube with square cross section, initially
  filled with air. Ma1.2 planar shock.
• Dense gas column sulfur hexafluoride (SF6)
  enters from a nozzle in the top wall and falls
  through the test section. Because air and SF6
  interdiffuse, the SF6 distribution is a function
  of height.
• Data taken in a single horizontal plane, 2 cm
  below the top wall. CCD cameras used for imaging
  initial conditions and evolution PIV data for
  analysis of velocity field.

experiment
simulation
The raw experimental image provides the relative
distribution of SF6 in the image plane. This is
the only experimental data we have on the initial
conditions! Note the gas column does not appear
perfectly radially symmetric, as assumed below.

• Matching Initial Conditions
• Simulate the SF6 falling through the test
  section, prior to shock interaction, i.e.
  generate initial conditions for FLASH simulations
• Main goal is to determine maximum initial mole
  fraction, XSF6, in image plane which cannot be
  measured directly.
• We model the initial evolution of the gas column
  by solving a species advection equation, the
  momentum equation, and an elliptic equation for
  the pressure, with constant gravity, viscosity,
  and species diffusion, in axisymmetric geometry.
• Choose inlet velocity and the initial SF6 mass
  fraction, then run until steady state is
  achieved.
• Construct goodness-of-fit map of the initial
  conditions extracting SF6 radial profile in image
  plane and compare to experimental data.

initial conditions
early times

final time
Sample fit results for different nozzle
conditions and resolution of the IC model. Radial
fit to the experimental image is shown with black
solid line. Poor fit is obtained if nozzle
conditions estimated from experimental data are
used (left panel).

• Conclusions
• The FLASH code proved efficient and accurate in
  modeling the shock-cylinder interaction problem.
  We find good overall agreement between the
  experiment and numerical model in both morphology
  and dynamics (Weirs, Dupont, Plewa 2006, Phys.
  Fluids, in preparation).
• The shock-cylinder interaction problem is
  genuinely 3-dimensional. The magnitude of
  vertical motions is similar to that of horizontal
  motions in the cylinders frame of reference.
• Modeling of the initial conditions clearly
  indicates strong vertical stratification. We
  identified a one-parameter family of initial
  conditions which is consistent with the
  experimental data.
• Mixing occurs due to shock-induced horizontal
  shear as well as due to stratification-induced
  vertical shear. We use tracer particles to study
  the interaction between the two processes.
• Development of additional diagnostics (initial
  conditions, vertical plane) is highly desirable
  and will enable critical evaluation of our
  predictive results.

Radial distribution of SF6 in the experimental
image plane corresponding to the best match to
the experimental data with (Y,v)in,SF6(0.82,21).
This work is supported by the Department of
Energy under Contract No. B523820 to the Center
for Astrophysical Thermonuclear Flashes at the
University of Chicago.