Towards simulation of detonation-induced shell dynamics with the Virtual Test Facility Ralf Deiterding, Fehmi Cirak, Dan Meiron



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Towards simulation of detonation-induced shell dynamics with the Virtual Test Facility

  • Ralf Deiterding, Fehmi Cirak, Dan Meiron

  • Caltech

  • Comref 2005, Heidelberg

  • Jan. 27, 2005


Outline of presentation

  • Detonation simulation

    • Governing equations
    • A reliable Roe-type upwind scheme
    • Validation via cellular structure simulation in 2D and 3D
    • Work mostly supported by German priority research program “Analysis und Numerik von Erhaltungsgleichungen”
    • R. Deiterding, Parallel adaptive simulation of multi-dimensional detonation structure, PhD thesis, BTU Cottbus, 2003. ! http://www.cacr.caltech.edu/~ralf
  • Structured Adaptive Mesh Refinement (SAMR)

  • Moving embedded complex boundaries

    • Ghost fluid method
    • Validation
  • Fluid-structure coupling

    • Efficient level-set construction
    • Incorporation of coupling scheme into SAMR
    • Outline of implementation
  • Detonation-induced dynamic shell response

    • Preliminary elastic investigation




Structured AMR - AMROC

  • Framework for dynamically adaptive structured finite volume schemes

    • http://amroc.sourceforge.net
  • Provides Berger-Collela AMR

    • Hierarchical multi-level approach
    • Time step refinement
    • Conservative correction at coarse-fine interface available
  • Provides ghost fluid method

    • Multiple level set functions possible
    • Fully integrated into AMR algorithm
    • Solid-fluid coupling implemented as specialization of general method
  • Hierarchical data structures

    • Refined blocks overlay coarser ones
    • Parallelization capsulated
    • Rigorous domain decomposition
  • Numerical scheme only for single block necessary

    • Cache re-use and vectorization possible


Ghost fluid method

  • Implicit boundary representation via distance function , normal n=r/ |r|

  • Treat an interface as a moving rigid wall



Verification test for GFM

  • Lift-up of solid body in 2D when being hit by Mach 3 shock wave

  • Falcovitz et al., A two-dimensional conservation laws scheme for compressible flows with moving boundaries, JCP, 138 (1997) 83.

  • H. Forrer, M. Berger, Flow simulations on Cartesian grids involving complex moving geometries flows, Int. Ser. Num. Math. 129, Birkhaeuser, Basel 1 (1998) 315.

  • Arienti et al., A level set approach to Eulerian-Lagrangian coupling, JCP, 185 (2003) 213.



Validation case for GFM



Implicit representations of complex surfaces



CPT in linear time

  • Problem reduction by evaluation only within specified max. distance

  • The characteristic / scan conversion algorithm.

    • For each face/edge/vertex.
      • Scan convert the polyhedron.
      • Find distance, closest point to that primitive for the scan converted points.
  • Computational complexity.

    • O(m) to build the b-rep and the polyhedra.
    • O(n) to scan convert the polyhedra and compute the distance, etc.


Coupled simulation – time splitting approach



Time step control in coupled simulation

  • Eulerian AMR + non-adaptive Lagrangian FEM scheme

    • Exploit AMR time step refinement for effective coupling
    • Lagrangian simulation is called only at level lc
    • AMR refines solid boundary at least at level lc
    • One additional level reserved to resolve ambiguities in GFM (e.g. thin structures)
    • Inserting sub-steps accommodates for time step reduction from the solid solver within an AMR cycle
    • Updated boundary info from solid solver must be received before regridding operation (grey dots left)


AMROC with GFM in VTF



Detonation driven fracture

  • Experiments by T. Chao, J.E. Shepherd

  • Motivation

    • Interaction of detonation, ductile deformation, fracture
  • Expected validation data

    • Stress history of cylinder
    • Crack propagation history
    • Species concentration and detonation fine structure
  • Modeling needs

  • Test specimen: Al 6061

    • Young’s modulus 69GPa, density 2780 kg/m3
    • Poisson ratio 0.33
    • Tube length 0.610m, outer diameter 41.28mm
    • Wall thickness 0.80mm
  • Detonation: Stoichiometric Ethylene and Oxygen

    • Internal pressure 80 kPa
    • CJ pressure 2.6MPa
    • CJ velocity 2365m/s


Initial investigation in elastic regime



Detonation modeling

  • Modeling of ethylene-oxygen detonation with one-step reaction model

    • Arrhenius kinetics: kf(T) = k exp (-EA/RT)
    • Equation of state for Euler equations: p = (-1)( e -  (1-Z) q0)
    • Adjust parameters to match CJ and vN state of C2 H4+3 O2 CJ detonation at
    • p0=0.8 MPa and T0=295 K as close as possible
    • Chosen parameters: q0=5,518,350 J/kg, EA=25,000 J/mol, k=20,000,000 1/s


Detonation modeling - Validation



Shell reponse under prescribed pressure

  • Use of 1-D detonation pressure leads to excellent agreement in phase length experiment and shell simulation

  • Taylor wave drives oscillation, not von Neumann pressure, already very good agreement, if average pressure is prescribed via appropriate shock

  • Further work to assess steadiness of detonation in experiment

  • Next step is to redo strain gauge measurements



Tests towards fully coupled simulations



Treatment of shells/thin structures

  • Thin boundary structures or lower-dimensional shells require artificial “thickening” to apply ghost fluid method

    • Unsigned distance level set function 
    • Treat cells with 0<
    • Leaving unmodified ensures correctness of r
    • Refinement criterion based on  ensures reliable mesh adaptation
    • Use face normal in shell element to evaluate in  p= pu– pl
  • about ~107 cells required to capture correct wall thickness in fracturing tube experiment with this technique (2-3 ghost cells within wall, uniform spatial discretization)



Coupled simulations for thin shells



Performance of coupled thin shell code

  • Coupled simulation with standard Euler equations (Roe+MUSCL, dimensional splitting)

  • AMR base mesh 40x40x80, 2 additional levels with refinement factor 2, ~3,000,000 cells.

  • Modeled tube thickness 0.0017 mm, (2x thicker than in experiment).

  • Solid Mesh: ~ 5,000 elements.

  • Calculation run on 26 fluid CPUs, 6 solid CPUs P4: ~4.5h real time



Conclusions and outlook

  • Detonation simulation

    • Fully resolved detonation structure simulations for basic phenomena in 3D possible for smaller detailed reaction systems
    • Combination of mixed explicit-implicit time-discretization with parallel SAMR and reliable higher order scheme
  • Cartesian scheme for complex embedded boundaries

    • Accurate results can be obtained by supplementing GFM with SAMR
    • With well developed auxiliary algorithms an implicit geometry representation can be highly efficient
    • Future goal: Extend implementation from diffused boundary method GFM to accurate boundary scheme based on
  • Detonation-induced fracturing tube

    • Fully coupled AMR simulations with fracture using GFM with thin shell technique
    • Detonation model to propagate three-dimensional Ethylen-Oxygen detonation with CJ velocity
    • Redo experiments with mixture that allows direct simulation, e.g. Hydrogen-Oxygen


AMROC Scalability

  • Domain based partitioning creates unnecessary waiting times in AMR algorithm, because single levels are not thoroughly balanced

  • Scalable AMR requires (R.Rotta, R.Deiterding):

    • Parallel inter-level operations to allow slight differences in level decomposition
    • Fast parallel partitioning technique that considers block structure and aims to preserve data locality, but balances single level work almost perfectly



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