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ARIES Project Meeting on Liquid Wall Chamber Dynamics May 5-6, 2003, Livermore, CA

ARIES Project Meeting on Liquid Wall Chamber Dynamics May 5-6, 2003, Livermore, CA. Numerical Simulation of Hydrodynamic Processes in High Power Liquid Mercury Targets Roman Samulyak Center for Data Intensive Computing Brookhaven National Laboratory U.S. Department of Energy rosamu@bnl.gov.

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ARIES Project Meeting on Liquid Wall Chamber Dynamics May 5-6, 2003, Livermore, CA

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  1. ARIES Project Meeting on Liquid Wall Chamber DynamicsMay 5-6, 2003, Livermore, CA Numerical Simulation of Hydrodynamic Processes in High Power Liquid Mercury Targets Roman Samulyak Center for Data Intensive Computing Brookhaven National Laboratory U.S. Department of Energy rosamu@bnl.gov

  2. Talk outline Theoretical and numerical ideas implemented in the FronTier-MHD code. Numerical example: the 3D Rayleigh-Taylor instability problem. Numerical simulation of hydro and MHD processes in the Muon Collider Target. Cavitation modeling and numerical simulation of CERN neutrino factory target experiments. Further development of cavitation models and the simulation of hydrodynamic processes in the SNS target.

  3. The system of equations of compressible magnetohydrodynamics: an example of a coupled hyperbolic – parabolic/elliptic subsystems

  4. Constant in time magnetic field approximation The distribution of currents can be found by solving Poisson’s equation:

  5. Numerical methods for the hyperbolic subsystem. The FronTier Code The FronTier code is based on front tracking. Conservative scheme. Front tracking features include the absence of the numerical diffusion across interfaces. It is ideal for problems with strong discontinuities. Away from interfaces, FronTier uses high resolution (shock capturing) methods FronTier uses realistic EOS models: - SESAME - Phase transition (cavitation) support

  6. Resolving interface tangling by using the grid based method 3D: We reconstruct the interface using micro-topology within each rectangular grid cell. There are 256 possible configurations for the crossings of the cell edge by the interface. Through elementary operations of rotation, reflection and separation these can be reduced to the 16 cases shown on the left.

  7. Methods for the parabolic/elliptic subsystem • Finite elements based on vector (Whitney) elements. • Dynamic finite element grid conforming to the moving interface. Point shifting method with rectangular index structure. Triangulated tracked surface and tetrahedralized hexahedra conforming to the surface. For clarity, only a limited number of hexahedra have been displayed.

  8. Whitney elements Let be a barycentric function of the node i with the coordinates xi Whitney elements of degree 0 or “nodal elements”: Whitney elements of degree 1 or “edge elements”: Whitney elements of degree 2 or “facet elements”:

  9. Elliptic/Parabolic Solvers • 3D version of the Chavent -Jaffre mixed-hybrid finite element formulation. • Instead of solving the Poission equation, • we solve for better accuracy. • The parallel solver is based on the domain decomposition. Linear systems in subdomains are solved using direct methods and the global wire basket problem is solved iteratively.

  10. FronTier simulation of a 3D Rayleigh-Taylor mixing layer

  11. Applications: Muon Collider TargetNumerical simulation of the interaction of a free mercury jet with high energy proton pulses in a 20 T magnetic field

  12. Simulation of the Muon Collider target. The evolution of the mercury jet due to the proton energy deposition is shown.No magnetic field. t = 0 t = 80

  13. MHD simulations: stabilizing effect of the magnetic field. • B = 0 • B = 2T • B = 4T • B = 6T • B = 10T

  14. Velocity of jet surface instabilities in the magnetic field

  15. Evolution of a liquid metal jet in 20 T solenoid

  16. Equation of state: the problem of cavitation Material properties strongly influence the wave dynamics. The wave dynamics is significantly different in the case of cavitating flows. The one-phase stiffened polytropic EOS for liquid led to much shorter time scale dynamics and did not reproduce experimental results at low energies. An important part of our research is EOS modeling for cavitating and bubbly flows.

  17. Thermodynamic properties of mercury (ANEOS data) Thermodynamic properties of mercury were obtained using the ANEOS data. Isotherms of the specific internal energy, pressure and entropy as functions of density are shown in a large density – temperature – pressure domain which includes liquid, vapor and mixed phases.

  18. Analytical model: Isentropic EOS with phase transitions • A homogeneous EOS model • Gas (vapor) phase is described by the polytropic EOS reduced to an isentrope.

  19. The mixed phase • Mixed phase is described as follows:

  20. The liquid phase • The liquid phase is described by the stiffened polytropic EOS:

  21. CERN neutrino factory target experimentsSchematic of the experimental setup

  22. Mercury splash (thimble): experimental data CERN neutrino factory target experiments Energy deposition: 5 J/g 30 J/g

  23. Mercury splash (thimble): numerical simulation Energy deposition = 15 J/g

  24. Hydrodynamic processes in the SNS target The mercury target for SNS will consist of a sealed stainless steel chamber filled with mercury interacting with 20 kJ proton pulses at frequency 60 Hz. The desired target lifetime implies that the target should withstand ~1.e+8 proton pulses. The pitting of walls was observed experimentally after 200-1000 pulses. Future targets will require much higher beam intensities. An effective approach capable of reducing the strength of rarefaction and shock waves is to use bubbly layers near flanges and bubbles in the bulk mercury. Direct (tracked bubbles) and continuum (new eos model) simulations.

  25. Further development of continuum homogeneous equation of state models for bubbly flows The (modified) Rayleigh-Plesset equation gives a dynamic closure for the fluid dynamics equation:

  26. Direct simulation approach: a system of tracked bubbles Mean particle radius = 2mm One phase mercury EOS for the liquid, the ideal gas EOS for the bubble gas Uniform in x and gaussian in y initial energy deposition with the center at the container top resulting in the maximum pressure 500 bar. Initial density Initial pressure

  27. Direct simulation: the pressure evolution 80 bubbles 130 bubbles

  28. Future research Futher work on the EOS modeling for cavitating and bubbly flows. Futher studies of the muon collider target issues. Studies of the cavitation phenomena in a magnetic field. Studies of hydrodynamic issues of the cavitation induced erosion in the SNS target. Studies of the MHD processes in liquid lithium jets in magnetic fields related to the APEX experiments.

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