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On balance laws for mixture theories with phase change

This paper presents the development of balance laws for two-phase mixture theories involving phase change, focusing on liquid-vapor flows. It explores the modeling of phase transitions between separated phases, including carrier and disperse phases, and applies averaging techniques to close the system under specific conditions. Numerical results are provided for both single-bubble and multi-bubble systems, factoring in varying pressure conditions. The findings pave the way for future investigations into temperature effects and droplet dynamics in phase transition systems.

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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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