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Brookhaven Science Associates U.S. Department of Energy 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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Brookhaven Science Associates U.S. Department of Energy Talk outline n Theoretical and numerical ideas implemented in the FronTier-MHD code. Numerical example: the 3D Rayleigh-Taylor instability problem. n Numerical simulation of hydro and MHD processes in the Muon Collider Target. n Cavitation modeling and numerical simulation of CERN neutrino factory target experiments. n Further development of cavitation models and the simulation of hydrodynamic processes in the SNS target.
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Brookhaven Science Associates U.S. Department of Energy The system of equations of compressible magnetohydrodynamics: an example of a coupled hyperbolic – parabolic/elliptic subsystems
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Brookhaven Science Associates U.S. Department of Energy Constant in time magnetic field approximation The distribution of currents can be found by solving Poisson’s equation:
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Brookhaven Science Associates U.S. Department of Energy Numerical methods for the hyperbolic subsystem. The FronTier Code n The FronTier code is based on front tracking. Conservative scheme. n Front tracking features include the absence of the numerical diffusion across interfaces. It is ideal for problems with strong discontinuities. n Away from interfaces, FronTier uses high resolution (shock capturing) methods n FronTier uses realistic EOS models: - SESAME - Phase transition (cavitation) support
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Brookhaven Science Associates U.S. Department of Energy 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.
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Brookhaven Science Associates U.S. Department of Energy Methods for the parabolic/elliptic subsystem Triangulated tracked surface and tetrahedralized hexahedra conforming to the surface. For clarity, only a limited number of hexahedra have been displayed. Finite elements based on vector (Whitney) elements. Dynamic finite element grid conforming to the moving interface. Point shifting method with rectangular index structure.
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Brookhaven Science Associates U.S. Department of Energy Whitney elements Let be a barycentric function of the node i with the coordinates x i Whitney elements of degree 0 or “nodal elements”: Whitney elements of degree 1 or “edge elements”: Whitney elements of degree 2 or “facet elements”:
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Brookhaven Science Associates U.S. Department of Energy 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.
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Brookhaven Science Associates U.S. Department of Energy FronTier simulation of a 3D Rayleigh-Taylor mixing layer
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Brookhaven Science Associates U.S. Department of Energy Applications: Muon Collider Target Numerical simulation of the interaction of a free mercury jet with high energy proton pulses in a 20 T magnetic field
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Brookhaven Science Associates U.S. Department of Energy 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
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Brookhaven Science Associates U.S. Department of Energy
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MHD simulations: stabilizing effect of the magnetic field. a)B = 0 b)B = 2T c)B = 4T d)B = 6T e)B = 10T
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Brookhaven Science Associates U.S. Department of Energy Velocity of jet surface instabilities in the magnetic field
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Brookhaven Science Associates U.S. Department of Energy Evolution of a liquid metal jet in 20 T solenoid
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Brookhaven Science Associates U.S. Department of Energy Equation of state: the problem of cavitation n Material properties strongly influence the wave dynamics. The wave dynamics is significantly different in the case of cavitating flows. n The one-phase stiffened polytropic EOS for liquid led to much shorter time scale dynamics and did not reproduce experimental results at low energies. n An important part of our research is EOS modeling for cavitating and bubbly flows.
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Brookhaven Science Associates U.S. Department of Energy 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.
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Brookhaven Science Associates U.S. Department of Energy Analytical model: Isentropic EOS with phase transitions A homogeneous EOS model Gas (vapor) phase is described by the polytropic EOS reduced to an isentrope.
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Brookhaven Science Associates U.S. Department of Energy The mixed phase Mixed phase is described as follows:
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Brookhaven Science Associates U.S. Department of Energy The liquid phase The liquid phase is described by the stiffened polytropic EOS:
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Brookhaven Science Associates U.S. Department of Energy CERN neutrino factory target experiments Schematic of the experimental setup
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Brookhaven Science Associates U.S. Department of Energy Mercury splash (thimble): experimental data CERN neutrino factory target experiments Energy deposition: 5 J/g 30 J/g
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Brookhaven Science Associates U.S. Department of Energy Mercury splash (thimble): numerical simulation Energy deposition = 15 J/g
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Brookhaven Science Associates U.S. Department of Energy 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. n Direct (tracked bubbles) and continuum (new eos model) simulations.
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Brookhaven Science Associates U.S. Department of Energy 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:
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Brookhaven Science Associates U.S. Department of Energy Direct simulation approach: a system of tracked bubbles n Mean particle radius = 2mm n One phase mercury EOS for the liquid, the ideal gas EOS for the bubble gas n 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
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Brookhaven Science Associates U.S. Department of Energy Direct simulation: the pressure evolution 80 bubbles 130 bubbles Max pressure at the bottom, t = 37 Total max pressure at the bottom 1 phase fluid322 80 bubbles3.8~10 130 bubbles2.1~7
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Brookhaven Science Associates U.S. Department of Energy Future research n Futher work on the EOS modeling for cavitating and bubbly flows. n Futher studies of the muon collider target issues. Studies of the cavitation phenomena in a magnetic field. n Studies of hydrodynamic issues of the cavitation induced erosion in the SNS target. n Studies of the MHD processes in liquid lithium jets in magnetic fields related to the APEX experiments.
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