LA-UR-02-5575 Mu M u ul lt l ti t im i ma m at a te t e er ri r ia i al a l l E Ef E ff f fe f ec e ct c ts t s s i in i n n M M u l t i m a t e r i a l E f f e c t s i n Co C om o mp m pu p ua u at a ti t io i on o na n al a l l S Si S im i mu m ul u la l at a ti t io i on o ns n s s o of o f f C C o m p u a t i o n a l S i m u l a t i o n s o f Ri R ic i ch c ht h tm t my m ye y er e r- r -M - Me M es e sh s hk h ko k ov o v v R R i c h t m y e r - M e s h k o v Ex E xp x pe p er e ri r im i me m en e nt n ts t s s E E x p e r i m e n t s Bill Rider Jim Kamm, Raul Coral-Pinto (MIT), Chris Tomkins and Mark Marr-Lyon Los Alamos National Laboratory 23 September 2002 Workshop on Numerical methods for multimaterial compressible fluid flows Paris, France
LA-UR-02-5575 Outline � Motivation: Multimaterial Fluid instabilities � Validation: perspective & motivation � Richtmyer-Meshkov experiments SGI Bluemountain � Numerical simulation + = 0 Ut ( ) F U x techniques D + + + = - - Ê ˆ t n 1 n n 1 2 / n 1 2 / U U F F Á ˜ D + - Ë ¯ i i x i 1 2 / i 1 2 / � Results & Analysis Compaq Q � Concluding remarks Bill Rider rider@lanl.gov www.ccs.lanl.gov 2
LA-UR-02-5575 Idealized Fluid Interface Instabilities � Kelvin-Helmholtz – Jump in tangential velocity at the fluid interface Exponential = s KH = È ˘ Velocity 1 U k Í ˙ growth rate Jump Í ˙ 2 || Î ˚ � Rayleigh-Taylor – Uniformly accelerated interface between disparate fluids Heavy Exponential Uniform = s RT = 1 Agk growth rate Accel’n Light 0 � Richtmyer-Meshkov – Impulsively accelerated interface between two fluids = s RM = D Linear Impulsive Ak a — ¥— r 1 + p growth rate Accel’n acts as 0 vorticity = r - r r + r = Atwood Number Ê ˆ Ê ˆ source A Á ˜ Á ˜ Ë ¯ Ë ¯ 1 0 1 0 Bill Rider rider@lanl.gov www.ccs.lanl.gov 3
LA-UR-02-5575 Motivation: Experimental Validation of Computations � Use experimental data to assess the validity of numerical methods and models � Richtmyer-Meshkov-driven material mixing � Good agreement on an “integral” scale � Experiments typically image large scales � Some detailed spatial-temporal data are available � Such validation is an essential activity! � Validation bottom line: is the model appropriate for the given physical circumstances? Bill Rider rider@lanl.gov www.ccs.lanl.gov 4
LA-UR-02-5575 Viewgraph A Starting Point: 1997 Norm � Study by Holmes et al.* on RM instability growth: � Comparison of NOVA laser experiments with three different codes � The integral scale compares well— but how do the details Nova/LLNL RAGE FronTier PROMETHEUS compare? *Holmes et al., Richtmyer-Meshkov instability growth: experiment, simulation and theory, J. Fluid Mech. , 389 , pp. 55–79, 1999 Bill Rider rider@lanl.gov www.ccs.lanl.gov 5
LA-UR-02-5575 What About The Small Scales? 960 ∆ x 120 ∆ x � Later time behavior suggested differences among the methods… R-T …and structural Calculation by B. Fryxell variations that depend on the mesh resolution RAGE FronTier PROMETHEUS Bill Rider rider@lanl.gov www.ccs.lanl.gov 6
LA-UR-02-5575 Validation Perspective � Validation is the process of determining that the equations in a simulation code accurately model the physics of interest Viewgraph � Visualization is helpful for understanding Norm flows, but quantification is required to obtain credible, defensible simulations � We want to get the right answers for the right reasons � Validation can only be done in reference to experimental data � Code-to-code comparison (“benchmarking”) does not constitute validation Bill Rider rider@lanl.gov www.ccs.lanl.gov 7
LA-UR-02-5575 Validation Motivation � Both (1) compressible flow features (e.g., shocks) and (2) the presence of large-scale, dynamically evolving structures (e.g., flow instabilities) are readily computed with today’s codes � Many calculations may “look good”, but they can be inaccurate — a challenging situation in an era of increasing reliance on simulation SGI Bluemountain � We must get the � Bigger computers right answers for must provide the right reasons better answers Bill Rider Compaq Q rider@lanl.gov www.ccs.lanl.gov 8
LA-UR-02-5575 Shock Tube Experiments at LANL (DX-3) � Low-speed ( M ≤ 2) shock tube facility where SF 6 + glycol fog form diffuse “target” struck by shocked air Gas Curtain 1.28 m 3.20 m 0.23 m 0.69 m Shock Nozzle Side View Driver Driven Test End Section Section Section Section Diaphragm Laser Sheet Camera Snapshots at Analysis indicates ∆ t ≈ 100 µs of that the glycol fog the SF 6 curtain accurately follows impacted by the SF 6 M =1.2 shock Rightley et al. “Evolution of a Modal Downstream shock-accelerated thin fluid layer”, coupling Phys. Fluids . 9 , 1770–1792, 1997. “mushrooms” Bill Rider rider@lanl.gov www.ccs.lanl.gov 9
LA-UR-02-5575 Shock Tube Experiments: Gas Cylinders � Recent experiments have used SF chamber gas cylinders as the target Particle Image 6 Velocimetry PIV � Experiments conducted by Fog Fog data have generator Generator been collected Benjamin, Prestridge, IC Rightley, Vorobieff (UNM), and Zoldi. Gas cylinder D = 3mm cylinder Single Laser sheet Air Air Zoldi. “A numerical and experimental study of a shock-accelerated heavy gas cylinder”, Ph.D. Thesis, SUNY Stony Brook, 2002. Suction Shock cylinder Double DYN D S D = 3mm, S/D = 1.5 Tomkins et al.. “Flow morphologies of two shock-accelerated gas cylinders”, J. Visualization , to appear, 2002. Bill Rider rider@lanl.gov www.ccs.lanl.gov 10
LA-UR-02-5575 Shock Tube Experiments: Gas Cylinders � Experiments are quite repeatable Bill Rider rider@lanl.gov www.ccs.lanl.gov 11
LA-UR-02-5575 PIV Data and Analysis Analysis: two-frame cross-correlation Bill Rider rider@lanl.gov www.ccs.lanl.gov 12
LA-UR-02-5575 Results: A Wide Variety of Modern Methods � MUSCL split*, MUSCL unsplit, ENO**, WENO**, DG***, PPM****, TVD,… � All numerical results are more-or-less self- consistent and not consistent with the experimental data at late time Image Smooth Import Compute Initial Grid Level Density+Velocity Vol. Fraction Vol. Fraction *Gittings & Zoldi (LANL), ** Aslam (LANL), *** Lowrie (LANL), **** Flash Code (UChicago) Bill Rider rider@lanl.gov www.ccs.lanl.gov 13
LA-UR-02-5575 Physical Situation of Interest � Shocks and rarefactions leading to mixing Shocks Shock (M=1.2) accelerated Shock (M=1.2) accelerated are double SF 6 double SF 6 cylinders cylinders “easy,” r Simulation of experiments at LANL Simulation of experiments at LANL shock Mixing is “hard” strong expansion — ◊ r u Acoustic waves weak shocks 2.5µs 200µs 400µs 600µs 35µs � Typically modeled by the compressible Euler Æ • equations (or Navier-Stokes in Re ) limit Bill Rider rider@lanl.gov www.ccs.lanl.gov 14
LA-UR-02-5575 Turbulent Mixing? Certainly not � Flowfield characterization -Is it turbulent? fully developed = G n ª or isotropic � Curtain Re 10 000 , = Ï 0 01 . mm = l n ª - h Re T 150 600 u Ì T m ( ) ª Ó 1 m l T = ∂ ∂ - u / u x 1 mm 2 5 . mm = G n ª � Single cylinder (5 mm) Re 70 000 , = l n ª - Re T 800 2500 u T ( ) ª l T = ∂ ∂ - u / u x 2 mm 5 mm = G n ª � Double cylinder(3mm,S/D=1.5) Re 30 000 , = l n ª - Re T u 600 1500 T ( ) ª l T = ∂ ∂ - u / u x 2 mm 4 mm Bill Rider rider@lanl.gov www.ccs.lanl.gov 15
LA-UR-02-5575 Quantitative Analysis Methods � Fractal dimension measures the complexity of an interface and is computed as: log[1/( N ( r )] 0 -2 Df = ( ) N(r) = min # boxes È ˘ lim log 1 N r -4 Í ˙ = -6 slope D Í ˙ Î ˚ -8 r = box size log f r Æ -10 r 0 0 1 2 3 4 5 log( r ) � Structure function of order p is defined as: ~ l a p The exponent a characterizes ∫ x + - x Ê ˆ S ( ) ( x ) ( ) x l l Á ˜ p Ë ¯ the (local) scaling behavior p th correlation at length scale l � Wavelet coefficients provide a local, scale dependent Volume Fraction Wavelet Coeff’t “lens” into the data: 2 · ( ) Ò - y x a b Wavelet Ê ˆ a n , , , f x = Á ˜ Ë ¯ coefficient Scale Wavelet Data Bill Rider rider@lanl.gov www.ccs.lanl.gov 16
LA-UR-02-5575 A Recent Comparison to Current Experiments Curtain Cylinder Double Cylinder Experiment FWHM IC=0.5 cm S/D=1.5 S/D=1.2 S/D=2.0 Calculation CWT Spectrum CWT Spectrum 2.5 0.03 2.8 0.03 Local D f Local D f 2.3 2.6 Comparison 0.02 0.02 2.1 2.4 0.01 0.01 1.9 2.2 1.7 0 2.0 0 0.0 0.5 1.0 0 0.5 1 0.0 0.5 1.0 0 0.5 1 Scale (cm) Scale (cm) Scale (cm) Scale (cm) Bill Rider rider@lanl.gov www.ccs.lanl.gov 17
LA-UR-02-5575 Improved Characterization of Initial Conditions Use Rayleigh scattering to see if the fog and SF 6 diffuse from each other. They do! Bill Rider rider@lanl.gov www.ccs.lanl.gov 18
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