Shock focusing and Converging Geometries - in the context of the VTF validation

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Shock focusing and Converging Geometries - in
the context of the VTF validation

• D.J.Hill

Galcit Nov 1, 2005
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Simulation Technology (ie the VTF code) R.
Deiterding

• Computational engine
• Parallel 3-D Eulerian AMR framework AMROC with a
  suite of CFD solvers
• Todays results Van Leer with MUSCL
  reconstruction WENO
• Fluid-solid coupling capability
• Level set based
• Implementation as Ghost Fluid Method

• Interpolation operations e.g. with solid
  surface mesh
• Mirrored fluid density and velocity values UFM
  into ghost cells
• Solid velocity values US on facets
• Fluid pressure values in surface points (nodes or
  face centroids)

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Non-symmetric external wedge

• An Example of Shocks -complex boundaries and
  Richtmyer-Meshkov Instability
• 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/
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Existing Experiments Conical Geometry

• Setchel,Strom,Sturtevant -1972
• 10 degree half angle.
• Argon at 1.5 Torr
• Mach 6 shock
• Milton, Takayama -1998, Milton et al -1986
• 10,20,30 degree half angle
• Mach 2.4, gamma 1.4
• Kumar, Hornug, Sturtevant 2003
• Air-SF6, Mach 1.55
• Perturbed interface RMI.

Similar to Phase 0 - one gas only
Two gases with perturbed interface
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Guderleys Implosion Problem (1942)

• Cylindrical or Spherical Shocks
• Assumptions of Strong Shock (independent of the
  flow ahead of the shock)
• Similarity variable

Cylindrical Spherical
Cp/Cv n (1-n)/n n (1-n)/n
5/3 0.815625 0.226054 0.688377 0.452692
7/5 0.835217 0.197294 0.717173 0.394364
6/5 0.861163 0.161220 0.757142 0.320756
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Simulation configuration for Conical shocktube
SSS 72

• Mach 6 shock
• Argon (gamma 5/3, molecular weight 39.9)
• 10.17 degree half angle
• Aperture diameter 15.3 cm
• Probe width 3.22 mm
• Simulations used analytic levelset with the GFM
  capability of the VTF

Vtf/amroc/clawpack/applications/euler/2d/Conical_S
hocktube/ And Vtf/amroc/clawpack/applicati
ons/euler/3d/Conical_Shocktube/
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Experimental Data Shock speed along centerline

• Shock speed during convergent phase is measured
  on the centerline of the cone
• Normalized by initial shock speed (Mach 6)
• Speeds over Mach 18 at last
• measurement
• Shock speed after reshock is also available for
  Sturtevant 72

From Setchell, Strom and Stutevant JFM 1972
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Shock diagram in conical geometry
SSS JFM 1972
Jumps in shock speed correspond to Machstem
collisions on the axis of symmetry
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Axi-Symmetric Flow equations- Can use 2D solver!
Exploit axi-symmetry to simulate the Converging
conical geometry. The divergence operator in
cylindrical co-ordinates produces a geometric
source
r
v
u
z
Advantage reduction of dimension Disadvantage
loss of conservation
Geometric source term
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Visualization of VTF Conical shocktube simulation

• Leading shock (blue) and reflected shocks.
  Plotted as Isosurface of Artificial 3D Schlieren
  (magnitude of density gradient) colored by
  density. 90 degree wedge removed for display.
  Time 0.0016 sec.

Mach 6 shock in Conical shock tube Plane cut
colored by density. Both shock And reshock
shown.
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Validation Comparison with experiment

• Shock detection algorithm based on pressure
  curvature
• Shock speed calculated from Rankine-Hugoniot jump
  conditions
• No real gas corrections, but affects may be
  important for highest Mach numbers

For M18 (Vs/Vo 3)
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Comparison of Wedge and ConePrior to reflection
Density and Pressure
t0.0001 sec --note curved mach-stem In conical
case
t0.000165 sec -- conical case far advanced and
higher pressures
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After reflection t0.00042 sec
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ASC converging shock experiments (P. Dimotakis)

• Phase 0 A single gas is used, the shock
  interacts with the boundary of the wedge
  producing shock mach stems, reflected shocks and
  triple points. The focusing of the shock is
  achieved by the successive reflection of the
  shock
• Phase 1 Two gases are used. The driver gas in
  the shocktube, and a lens gas in the wedge. The
  shape of the boundary (contact) between the two
  gases has been specially designed to curve the
  shock producing a circular shock centered on the
  apex of the wedge. P. Dimotakis R. Samtaney
• Phase 2 A third gas is used. It is placed within
  the wedge after the lens. Purturbations on the
  contact between this gas and the lens gas will
  give rise to a Richtmyer-Meshkov instability, and
  the acceleration towards the apex will also have
  aspects of the Rayleigh-Taylor instability

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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 inPhase-1
  experiments

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Phase 0 ? Euler code validation R. Samtaney
qw1 14.06? ? 0.21? qw2 9.94? ?
0.21?
0-035
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Comparison of target experiments Phase 0 and
Phase 1
Smooth circular shock in produced by Phase 1 no
triple points
Phase 0 vs Phase 1
Guderly exponent n0.874 Compared with expected
n0.835
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Phase 2 Configuration

• As in the Phase 1 simulations, there is a
  shocktube gas (gas1) and a lens gas (gas2)
  related by a density ratio Rho2 / Rho1 1.4.
• In addition to these two gases, there is a target
  gas inside the wedge (gas3). We take 1.09 gas2 by
  Rho3/Rho2 5.
• This would be consistent with using Air for the
  lensing gas and SF6 for the target gas.
• The extended clawpack solvers were used for this
  simulation, the input files and code are found in
  the repository. A base resolution of 250x100 was
  used with 4 additional levels of refinement
  (factors 2,2,2,2).

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Phase 2 Simulation Animations of Density
With initial perturbations
With out Initial perturbations
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Issues of Interest

• Boundary Layers How important are they?
• More important during reshock?
• What is the sensitivity of the Lens design,
  (Phase 1) to
• Mach Number
• Lens shape
• Need to explore in full 3D simulation using low
  dissipation method with LES for the mixing zone