Simulations of a Shock-Accelerated Gas Cylinder and Comparison with Experimental Images and Velocity Fields Cindy A. Zoldi (Los Alamos National Laboratory and SUNY at Stony Brook) 8th IWPCTM California Institute of Technology Pasadena, California December 9-14, 2001 Cindy Zoldi - IWPCTM 2001 3/15/02
Collaborators Experimenters: Kathy Prestridge (LANL, DX-3) Bob Benjamin (LANL, DX-3) Paul Rightley (LANL, DX-3) Peter Vorobieff (UNM) Chris Tomkins (LANL, P-22/DX-3) Mark Marr-Lyon (LANL, DX-3) Computational Scientists: RAGE: Mike Gittings (LANL/SAIC, X-2) Mike Steinkamp (LANL, X-3) Cuervo: Bill Rider (LANL, CCS-2) Jim Kamm (LANL, CCS-2) CHAD: Barbara Devolder (LANL, X-5) Manjit Sahota (LANL, T-3) Thesis Advisors: James Glimm (Stony Brook) David Sharp (LANL, T-3) Cindy Zoldi - IWPCTM 2001 2 3/15/02
Outline • Purpose of research • Experimental apparatus • Simulation setup • Qualitative and quantitative comparisons • Future work Cindy Zoldi - IWPCTM 2001 3 3/15/02
Our View of Scientific Modeling Nature Experiments Diagnostics Validation, Model intuition Computer Theory simulation (equations) Verification How well do computer simulations approximate nature? Cindy Zoldi - IWPCTM 2001 4 3/15/02
Richtmyer-Meshkov Instability What is the Richtmyer-Meshkov instability? It occurs when a shock wave collides with an interface between two different materials causing perturbations on the interface to grow. Example: Shock moving from air into SF 6 gas (Note: ρ air < ρ SF6 ) Material Material Material Interface Interface Interface Shocked SF 6 Air Air Reflected Transmitted Incident Shock Shock Shock Cindy Zoldi - IWPCTM 2001 5 3/15/02
DX-3 Gas Shock Tube • Gas cylinder composed of SF 6 and surrounded by ambient air • SF 6 seeded with glycol droplets to aid in visualizing the flow and to enable the PIV capability Consult the following paper for more information on the experimental setup: P. M. Rightley, P. Vorobieff, and R. F. Benjamin. Evolution of a shock-accelerated thin fluid layer. Phys. Fluids , 9(6):1770-1782, 1997. Cindy Zoldi - IWPCTM 2001 6 3/15/02
Test Section of the Shock Tube • 2 lasers: SF chamber • Customized, frequency 6 PIV doubled Nd:YAG Fog Fog generator generator • 10 Hz ‘New Wave’ at 532 nm IC • 3 cameras: Gas cylinder • Intensified CCDs, 1134x468 Laser • Initial Conditions (IC), sheet Dynamic (DYN), and PIV air air suction • 8 pulses: • 7 pulses for ICs and dynamic DYN shock images with ∆ t=140µs • 8th pulse for PIV Cindy Zoldi - IWPCTM 2001 7 3/15/02
RAGE: Radiation Adaptive Grid Eulerian Code Multi-dimensional Eulerian hydrodynamic code • Initial grid -- level 1 Directionally-split second order Godunov scheme • 3 4 Continuous adaptive mesh refinement (CAMR) • � Each cell can be coarsened or refined by a factor of two in each timestep 1 � Only one level of refinement change possible 2 between adjacent cells � Refinement decisions can be modified for each material or defined for regions of computation Subdivided cells 2 and 6 Running in parallel on ASCI machines (Blue Mountain) • 3 4 Substantial validation has been performed on shocked • interface problems � Shocked curtain, single mode RMI, NOVA 7 8 experiments 1 11 12 5 9 10 RAGE was originally developed by Michael L. Gittings Cindy Zoldi - IWPCTM 2001 8 3/15/02
Cylinder Simulation Setup 64 cm 7.68 cm ... ... Shock ρ =0.95e-3 g/cc Air P=0.8 Bar Shock ρ = 4.84e-3 g/cc SF 6 P = 0.8 bar • Mach 1.2 shock in air hitting a cylinder of SF 6 • Ideal gases: γ SF6 = 1.09 γ air =1.4 • RAGE grid: level 1 = 0.64 cm (approx 80 zones across the diameter level 7 = 0.01 cm of the initial cylinder) Cindy Zoldi - IWPCTM 2001 9 3/15/02
Comparison Between Experimental and Computational Images ICs 50 µs 190 µs 330 µs 470 µs 610 µs 750 µs Shock Cindy Zoldi - IWPCTM 2001 10 3/15/02
Quantitative Measurements 1.8 1.8 J simulation 1.6 1.6 J J experiment J 1.4 J B 1.4 B J B Height (cm) B Width (cm) J 1.2 Width J B 1.2 B J 1 B 1 B Height J J 0.8 B 0.8 B B J B B J 0.6 0.6 J B 0.4 0.4 0 200 400 600 800 0 200 400 600 800 Time (µs) Time (µs) The height and width of the evolving cylinder are 15% larger in the experiment than in the simulation Cindy Zoldi - IWPCTM 2001 11 3/15/02
Velocity Fields Experiment 10 m/s 10 m/s Simulation 50 m/s 50 m/s Cindy Zoldi - IWPCTM 2001 12 3/15/02
Varying Peak SF 6 Concentration 100 1.8 F 1.6 100% peak F F 80 1.4 F B 80% peak Height (cm) B J J B H J H 1.2 60% peak F B H J 60 H Count 1 experiment B J H F 0.8 40 B J H Width H J F B 0.6 20 0.4 0 200 400 600 800 Height Time (µs) 0 0 10 20 30 40 50 60 70 1.8 Velocity Magnitudes (m/s) 1.6 F 1.4 Width (cm) F B F 1.2 Smaller peak SF 6 concentrations B J J H F 1 H B J result in smaller velocities and F H B J 0.8 B H J smaller lengths F H B J H 0.6 F B J H 0.4 0 200 400 600 800 Time (µs) Cindy Zoldi - IWPCTM 2001 13 3/15/02
Varying Density Gradient at the Air/ SF 6 Interface Experiment • Differences are visible in the density images with the initially diffuse interface producing the Experimental Initial Conditions best visual agreement with the experiment • No significant differences Sharp Interface exist in the heights/widths and velocities Diffuse Interface How well characterized are the experimental initial conditions? Cindy Zoldi - IWPCTM 2001 14 3/15/02
Mesh Refinement Experiment A coarser simulation shows “better” visual agreement with the experiment Diffuse Interface - fine ∆ x = 0.01 Jet velocity: coarse simulation: 62 m/s fine simulation: 69 m/s Coarser resolution: Diffuse Interface - coarse ∆ x = 0.02 • less rollup in vortex • less evidence of secondary instability • smaller jet velocity Cindy Zoldi - IWPCTM 2001 15 3/15/02
New Velocity Measurements PIV image The new velocity field has vectors every 187 µm Last dynamic image compared to every 537 µm obtained previously. Cindy Zoldi - IWPCTM 2001 16 3/15/02
Location of Velocity Magnitudes Experiment Simulation X X Largest velocities occur in the back-flow area and the smallest velocities occur in the vortex core Cindy Zoldi - IWPCTM 2001 17 3/15/02
Comparison of Experimental and Computational Velocity Magnitudes Experiment Simulation X X The experiment and the computation have similar velocities in the vortex core Cindy Zoldi - IWPCTM 2001 18 3/15/02
Histogram of Velocity Magnitudes 600 Both the experiment and the computation have a peak velocity simulation 500 experiment of 15 m/s. 400 The magnitudes of the back-flow Count velocities form the tail of 300 the histogram. 200 Large disagreement still exists 100 between the experimental and computational back-flow 0 0 10 20 30 40 50 60 70 velocities. Velocity Magnitude (m/s) Cindy Zoldi - IWPCTM 2001 19 3/15/02
Jet Velocity of a Vortex Pair Γ Model the evolving cylinder as a vortex pair composed of two idealized incompressible rectilinear vortices with equal and opposite circulations a U jet For steady state flow (i.e., vortices stationary), the jet velocity U jet between the two vortices is equal to*: U jet = 3 Γ / 2 π a Γ Experiment: U jet = 37 m/s (predicted) Simulation: U jet = 59 m/s (predicted) U jet = 36 m/s (observed) U jet = 69 m/s (observed) Are the predicted velocities qualitatively consistent with the circulation and vortex spacings measured in the experiment and the simulation? ∗ L. Prandtl and O.G. Tietjens. Fundamentals of Hydro- and Aeromechanics, McGraw-Hill Book, 1934. Cindy Zoldi - IWPCTM 2001 20 3/15/02
Vortex Spacing 1 The experiment has larger vortex spacings compared to the simulation J 0.75 Vortex Spacing (cm) J B The experimental and computational J J B B B vortex spacings are in the range of B B B B B Jacobs’ measurements* 0.5 B B Note: The vortex spacing is 0.25 simulation B determined using flow visualization experiment J RS theory 0 0 200 400 600 800 Time ( µ s) ∗ J. W. Jacobs. The dynamics of shock accelerated light and heavy gas cylinders. Phys. Fluids A , 5(9):2239, 1993. Cindy Zoldi - IWPCTM 2001 21 3/15/02
Circulation Values 10000 Predictions of circulation: RS: Rudinger & Somers (1960) 8000 PB: Picone and Boris (1988) J Circulation (cm 2 /s) SZ: Samtaney & Zabusky (1994) H 6000 The computational circulation value right after shock passage agrees well 4000 simulation J with the theoretical predictions of PB PB J and SZ. 2000 SZ H RS J We need early-time PIV to determine 0 the corresponding experimental 0 200 400 600 800 Time ( µ s) circulation value. Using the PIV results at 750 µs we find that: Γ experiment < Γ simulation Cindy Zoldi - IWPCTM 2001 22 3/15/02
Recommend
More recommend
