Code-to-Code Comparisons for the Problem of Shock Acceleration of a - PowerPoint PPT Presentation

Code-to-Code Comparisons for the Problem of Shock Acceleration of a Diffuse Dense Gaseous Cylinder J.A. Greenough 1 , W.J. Rider 2 , C. Zoldi 2 , J.R. Kamm 2 8 th IWPCTM December 9-14, 2001 Pasadena, CA 1 Lawrence Livermore National Laboratory, 2 Los Alamos National Laboratory

Motivation • Focus on computational issues as cause for disagreement between Rage and ongoing LANL shock/cylinder experiments: • Large scale (dipole aspect ratio) differences • Quantitative velocity measurements (PIV) • Remove experimental uncertainities/unknowns: • Use well-defined initial conditions • Analysis and comparisons based on computational data • Use different codes for comparison

Motivation • Use this research to also examine: • What does convergence mean for evolving flows & instabilities? • What are the resolution requirements for “fully-resolved” calculations of this class of flow? • What quality of results can we obtain from low-order codes (second- order) in this regime? • Our guide will be existing & on-going experiments

Experimental Configuration • “Pour” SF 6 in the shocktube as a laminar stream • LANL experiments seed gas with glycol/water droplets (original CalTech experiments used biacetyl) • Laser sheet illumination with multiple frames per experiment

Comparison Between Experiment and Simulation 50 µs 190 µs 330 µs 470 µs 610 µs 750 µs 0.001 0.008 Shock log density (g/cc)

Quantitative Measurements 180 1.8 J 1.6 160 J J 140 1.4 J Height (cm) B B simulation B simulation 120 1.2 J B experiment 100 1 B Count 80 J 0.8 B 60 Width B J 0.6 experiment 40 0.4 0 200 400 600 800 Height 20 Time (µs) 1.8 0 10 20 30 40 50 60 70 Velocity Magnitude (m/s) 1.6 0 J 1.4 Width (cm) J B J 1.2 B Simulation has larger velocities J 1 B J and smaller lengths compared to B 0.8 B B J the experimental data. 0.6 J B 0.4 0 200 400 600 800 Time (µs)

Codes • Rage (LANL; Gittings et al.) • Eulerian (Lagrange + Remap); directionally split • Unstructured AMR (point-wise adaptivity) • Multi-component formulation (mass fraction); one energy equation • Euler equations (inviscid) • Cuervo (LANL; Rider & Kamm) • Eulerian (direct); directionally and temporally unsplit • Rectangular uniform grids • single-component formulation (gamma blending); one energy equation • Navier-Stokes equations (constant properties) • Raptor (LLNL; Greenough et al.) • Eulerian (direct); directionally split • Block-structured AMR (patch-based adaptivity) • VOF formulation (volume fraction); N energy equations • Navier-Stokes equations (Chapman-Enskog, Sutherland’s formula)

Model Problem Air • Inflow/outflow B.C.’s M s = 1.2 • Moving frame with post- interaction velocity near zero • ρ SF6 = ρ 0 exp(-r 2 / δ ), r= √ (x-x 0 ) 2 +(y-y 0 ) 2 , δ =0.0902; D=0.5cm 0.5cm SF 6 5 cm (y) (2.5cm, 2.5cm) • LANL pre-shock conditions 2D=1cm • t final = 0.8 msec • ∆ x = 125 µ m, 62.5 µ m, 31.25 µ m, 15.625 µ m, 7.8125 µ m 5 cm (x)

Integral Lengths/Flow 125 micron zoning, t = 0.8 msec Rage Raptor Cuervo 1.49cm 1.51 cm 1.64 cm 1.38 cm 1.40cm 1.44cm

Integral Lengths/Flow 62.5 micron zoning, t = 0.8 msec Rage Raptor (N-S) Cuervo 1.61 cm 1.46cm 1.51 cm 1.38cm 1.45cm 1.35 cm

Integral Lengths/Flow 31.25 micron zoning, t = 0.8 msec Rage Raptor (N-S) 1.58 cm 1.46cm 1.36 cm 1.37cm

Integral Lengths/Flow 15.125 micron zoning 7.8125 micron zoning 3.90625 micron zoning Raptor (N-S) Rage Raptor (N-S) 1.58 cm 1.46cm 1.46cm Ran out of machine 1.36 cm 1.35cm 1.35cm

Integral Lengths - Summary Length Convergence Rates Convergence Rates Cuervo ∼ ∆ x 1.28 Cuervo ∼ ∆ x 0.74 Width Raptor ∼ ∆ x 1.58 Raptor ∼ ∆ x 0.28

Mixing Fraction θ = Σ f SF6 (1-f SF6 ) ∆ x ∆ y (Σ f SF6 ∆ x ∆ y) (Σ (1-f SF6 ) ∆ x ∆ y) o Convergence Rates Cuervo ∼ ∆ x 0.28 Raptor ∼ ∆ x 1.02

Vortex Spacing • Experimental data range shown for comparison • cf. J.W. Jacobs, Phys. Fluids 1993; M=1.095, D=0.43 Convergence Rates Raptor ∼ ∆ x 0.87

Circulation Budget • Deposition by shock (positive) • Counter-sign production (baroclinic) • Late-time equilibration

Flow Dynamics • Early time • Vortex blob deposition (shock-passage time ~ 30 µ sec) • Intermediate time • Blob dipole transformation • Counter-sign production • Later time • Dipole configuration established • Balanced net vorticity (i.e. Γ ~ constant)

Flow Dynamics - Density t = .08msec t = .12msec t = .22msec t = .35msec t = .47msec t = .58msec t = .70msec t = . 82msec

Flow Dynamics - Vorticity t = .08msec t = .12msec t = .22msec t = .35msec t = .47msec t = .58msec t = .70msec t = . 82msec

Flow Dynamics – Baroclinic Generation t = .08msec t = .12msec t = .22msec t = .35msec t = .47msec t = .58msec t = .70msec t = . 82msec

Raptor Summary 31.25 µ m, 15.625 µ m, 7.8125 µ m Increasing Resolution Inviscid Increasing Resolution Viscous

NEW Raptor Summary No prelax, viscosity fix 31.25 µ m, 15.625 µ m, 7.8125 µ m Increasing Resolution Inviscid Increasing Resolution Viscous

Lengthscale estimates • Using order of magnitude considerations (Tennekes and Lumley) • U ≈ 2,000 cm/sec, ν ≈ 0.1 cm 2 /sec, L = 0.1 cm Re = 2,000 • η /L ∼ Re -0.75 η ∼ 3 µ m (Kolmgorov scale) • λ /L ∼ Re -0.5 λ ∼ 90 µ m (Taylor scale) L = 0.1cm • At 7.8125 µ m resolution, we have about 12 points/ λ resolvable ρ

Conclusions • Have we demonstrated convergence? • Maybe. Some diagnostics show convergence while others do not. • Include addition diagnostics (statistical, wavelet analysis). M=1.2 Diffuse Interface R-M • Have demonstrated what resolutions and physics are required for resolved Air+Acetone calculations. • Directly compute mm wavelength vortices. This is a robust feature present in analogous flow (Jacobs’ Diffuse mm scale vortices Interface R-M). • Rage calculations appear to be the out- lier; much more structure and different SF 6 integral measurements. Vorticity? Courtesy of Prof. J.W. Jacobs

NEEDS • High(er) resolution experimental imaging • PLIF visualization. LANL facility appears to generate a “more stable” evolving flow better pictures. Isolate mm-scale vortices • More direct measurements • Mixing measurements (Rayleigh scattering). Complementary to Helium jet work by J. Budzinski. • More computing resources (never have enough) would allow definitive simulations. • e.g. highest resolution run took ~ 70 hrs wall clock on 128 CPU’s of an SP-3; AMR required 4.7 Mzones compared to 43 Mzones single grid.

LANL Experimental Activity • No outer flow seeding Varying the seeding densities & light intensity Images courtesy C. Tomkins, LANL, DX-3