1. Shock focusing and Converging Geometries - in the context of the VTF validation D.J.Hill S.I. meeting - June 2, 2005

2. Outline History and motivation Center validation experiment: (P.Dimotakis A.Lam) Converging wedge, 3 Phases Review of experiment to date Preliminary 2D calculations Proposed 2D calculations Aid in further design of experiment Viscous boundary effects Physical effects Computational issues/questions Other Experiments of interest Conical convergent channel (Sturtevant and others) Example calculations

3. Background / Motivation One of four primary validation experiments Shock focusing and fluid instability in converging geometry Detonation driven fracture Dynamic deformation and phase transformation Dynamic fracture, fragmentation, contact Experimental Lead – P. Dimotakis “First shock” achieved 7/04 VTF-computations Initial simulations done by Ravi Samtaney – PPL o With clawpack in AMROC o Additionally with Ravi’s own unigrid code As of mid-May –> D.Hill

4. Experimental facility: GALCIT 17  shock-tube

5. Hinge-plate assembly design and implementation (P.Dimotakis) Two plates with sharp leading edges joined by an adjustable hinge Rounded hinge (1/4″ radius) desingularizes apex and shock rebound Accessible from test-section rear and sides Plates can be angled over a range of 6º – 15º wrt horizontal. Angles measured to within 0.1 Assembly can be removed with plate angles fixed Required for membrane replacement in Phase-1 experiments

6. Validation experiment sequence Phase-0 (no membrane): Study of shock reflection, wave interaction, and compressible turbulence Phase-1: Shock refraction to produce converging shock Hinge plates fitted with suitably shaped membrane Test section and driven test gas mixtures must have different W and  to achieve finite-amplitude wave cancellation. Phase-2: Second circular membrane for study of interface instabilities (RMI) in converging flow Counts # of membranes Phase 1 Phase 0

7. Phase-0  Experimental data P.Dimotakis and A.Lam  w1 = 14.06   0.21   w2 = 9.94   0.21  M s = 1.502  0.007 U s = 527  2 m/s M s = 1.514  0.007 U s = 531  2 m/s M s = 1.503  0.007 U s = 527  2 m/s 0-036 0-034 0-035 Very thin (laminar) boundary layers  2  17.6  0.2 vs. theoretical 17.3 High-Re flow behind Mach-stem shock Also discernible: Portion of incident shock propagating outside hinge-plate assembly Small disturbance from small opening on bottom plate used to inject helium to tune schlieren system Mach reflection pattern as expected Schlieren images show: Incident planar shock: U s  0.53 mm/s Triple point Mach stem Reflected wave Slipstream (shear layer) Incident shock Triple point Mach stem Reflected wave Slipstream 17.6 

8. Phase 0 - Euler code validation R.Samtaney and R.Dieterding 0-035  w1 = 14.06   0.21   w2 = 9.94   0.21  Simulation by R. Samtaney using clawpack solver in AMROC.

9. Phase 1 and simulation needs Interface (contact surface) ‘C’ originally computed using simplified “optics” approach. Confirmed using nonlinear shock-polar analysis. – Dimotakis and Samtaney Required interface is well- approximated by an elliptical segment Initial simulations have been done by R.Samtaney To aid in further experiment design, sensitivity to Mach number, interface shape, and constituent gases need to be examined -> Need for more simulations: 2D and 3D

10. Dimotakis Simulation: “Order one” code requirements Phase 1 Strong shocks Complex Geometry Acoustic BCs multi-species Phase 0 Strong shocks Complex Geometry Acoustic BCs Phase 2 Strong shocks Complex Geometry Acoustic BCs multi-species LES

11. Preliminary WENO-TCD calculations 2D simulations Phase 0 o Air (molecular weight 28.8, gamma 1.4) o Mach 1.5 shock o Constructed an analytic level set Computational savings over brep Easily exported to 3D case /amroc/weno/applications/euler/2d/Wedge/ Mach stem and RMI example o Same conditions as above, but with a solid wedge and a second gas present /amroc/weno/applications/euler/2d/Triangle/

12. Phase 0: examples amroc/weno/applications/eule/2d/Wedge/

13. Non-symmetric external wedge An Example of Shocks - complex boundaries and Richtmyer- Meshkov Instablity Mach 1.5 shock in Air interacts with a non- symmetric wedge Followed by an SF6 interface Temperature plots with density shadows amroc/weno/applications/euler/2d/Triangle/

14. Boundary layer effects in converging hinge-plate assembly BL will grow as converging shock travels into wedge 3D effect: BLs grow along wedge hinge plates and along vertical walls BL slows converging shock and alters its shape Negative displacement thickness Rounded hinge removes apex singularity

15. Additional Experiments: Conical Geometry Setchel,Strom,Sturtevant -1972 o 10 degree half angle. o Argon at 1.5 Torr o Mach 6 shock Milton, Takayama -1998, Milton et al -1986 o 10,20,30 degree half angle o Mach 2.4, gamma 1.4 Kumar, Hornug, Sturtevant – 2003 o Air-SF6, Mach 1.55 o Perturbed interface – RMI. Similar to “Phase 0” - one gas only Two gases with perturbed interface

16. Experimental Data: Shock speed Shock speed during convergent phase is measured on the centerline of the cone Shock speed after reshock is also available for Sturtevant ‘72 From Milton and Takayama –Shock Waves 1998

17. Shock diagram in conical geometry From Kumar,Hornung,Sturtevant –Physics of Fluids 2003 Jumps in shock speed correspond to shock-stem collisions on the axis of symmetry

18. 2D simulations: wedge vs. cone Mach 6 shock Argon (gamma = 5/3, molecular weight 39.9) 10 degree half angle Aperture diameter 15.3 cm amroc/weno/applications/euler/2d/Conical-Sturtevant72/ (UseSoure 1 in solver.in for geometric source term)

19. Axi-Symmetric Flow equations v u z r Geometric source term Exploit axi-symmetry to simulate the Converging conical geometry. The divergence operator in cylindrical co-ordinates produces a geometric source Advantage: reduction of dimension Disadvantage: loss of conservation

20. Prior to reflection: Density and Pressure t=0.0001 sec --note curved mach-stem In conical case t=0.000165 sec -- conical case far advanced and higher pressures

21. After reflection: t=0.00042 sec

22. Work Ideas - Future Further Validate code by comparing with experiments of Sturtevant ’72 2D and 3D runs Wide-ranging sensitivity study of Phase 1 Examine Mach number, constituent gases, lens shape etc Requires 2D and 3D simulations Predictive Phase 2 runs. Etc..