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On balance laws for mixture theories with phase change

On balance laws for mixture theories with phase change. Wolfgang Dreyer Frank Duderstadt Maren Hantke Gerald Warnecke. WIAS Berlin Otto-von-Guericke-University Magdeburg. Micro-Macro Modelling and Simulation of Liquid-Vapour Flows Strasbourg, January 2008. Motivation.

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On balance laws for mixture theories with phase change

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  1. On balance laws for mixture theories with phase change Wolfgang Dreyer Frank Duderstadt Maren Hantke Gerald Warnecke WIAS Berlin Otto-von-Guericke-University Magdeburg Micro-Macro Modelling and Simulation of Liquid-Vapour Flows Strasbourg, January 2008

  2. Motivation • Model phase transitions • 2 separated phases - carrier phase - disperse phase • 2-phase mixture balance laws involving phase change • Averaging techniques • NOW: close the system Maren Hantke On balance laws for mixture theories with phase change Strasbourg, January 2008

  3. Multi-bubble system Single-bubble system 1D - case Maren Hantke On balance laws for mixture theories with phase change Strasbourg, January 2008

  4. A closed system under prescribed outer pressure, 1D-case Vapour p0 Liquid • Assumptions: • Ideal gas, inviscid • Homogeneity in the gas • Incompressible, inviscid liquid Interface Kinetic relation Maren Hantke On balance laws for mixture theories with phase change Strasbourg, January 2008

  5. Numerical results Light blue: fixed temperature Light blue: fixed temperature green: IE Light blue: fixed temperature green: IE red: PDE Maren Hantke On balance laws for mixture theories with phase change Strasbourg, January 2008

  6. p0 A closed system under prescribed outer pressure, radial symmetric case Vapour Liquid Interface • Assumptions: • Radial symmetry • Ideal gas, inviscid • Homogeneity in the gas • Incompressible, inviscid liquid Kinetic relation Maren Hantke On balance laws for mixture theories with phase change Strasbourg, January 2008

  7. Numerical results Red: fixed temperature Red: fixed temperature green: PDE Maren Hantke On balance laws for mixture theories with phase change Strasbourg, January 2008

  8. Numerical results, fixed initial radius Red: p0=1650 Pa green: p0=1600 Pa light blue: p0=1550 Pa Maren Hantke On balance laws for mixture theories with phase change Strasbourg, January 2008

  9. Numerical results, fixed initial mass Red: p0=1650 Pa green: p0=1600 Pa light blue: p0=1550 Pa Maren Hantke On balance laws for mixture theories with phase change Strasbourg, January 2008

  10. Future work • Can we neglect the temperature differences caused by the phase transition? • Close the averaged system of balance laws • Investigate the droplet system Maren Hantke On balance laws for mixture theories with phase change Strasbourg, January 2008

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