Revealing the True Nature of the Experiment

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 column’s 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). • Tracer particles embedded in the flow help us understand intimate relationship between pressure-induced vertical motions and large scale horizontal flows, as indicated by the following sequence. Fluid located near the vortex cores experiences strong vertical acceleration. That acceleration is highly uneven within lateral layers leading to formation of shear layers and promoting vertical mixing. Localized downflows form at late times. 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 flowfield’s 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. Ma=1.2 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. simulation experiment The raw experimental image provides therelative 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 cylinder’s 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.