On balance laws for mixture theories with phase changeWolfgang Dreyer Frank Duderstadt Maren Hantke Gerald WarneckeWIAS BerlinOtto-von-Guericke-University MagdeburgMicro-Macro Modelling and Simulation of Liquid-Vapour FlowsStrasbourg, January 2008

Maren Hantke On balance laws for mixture theories with phase changeStrasbourg, January 2008 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 changeStrasbourg, January 2008 Multi-bubble systemSingle-bubble system1D - case

Maren Hantke On balance laws for mixture theories with phase changeStrasbourg, January 2008 A closed system under prescribed outer pressure, 1D-case p0Assumptions: Ideal gas, inviscid Homogeneity in the gas Incompressible, inviscid liquidVapourLiquidInterfaceKinetic relation

Maren Hantke On balance laws for mixture theories with phase changeStrasbourg, January 2008 Numerical resultsLight blue: fixed temperatureLight blue: fixed temperaturegreen: IE Light blue: fixed temperaturegreen: IEred: PDE

Maren Hantke On balance laws for mixture theories with phase changeStrasbourg, January 2008 A closed system under prescribed outer pressure, radial symmetric case Assumptions: Radial symmetry Ideal gas, inviscid Homogeneity in the gas Incompressible, inviscid liquidInterfaceVapourKinetic relationLiquid

Maren Hantke On balance laws for mixture theories with phase changeStrasbourg, January 2008 Numerical results Red: fixed temperatureRed: fixed temperaturegreen: PDE

Maren Hantke On balance laws for mixture theories with phase changeStrasbourg, January 2008 Numerical results, fixed initial radius Red: p0=1650 Pagreen: p0=1600 Palight blue: p0=1550 Pa

Maren Hantke On balance laws for mixture theories with phase changeStrasbourg, January 2008 Numerical results, fixed initial mass Red: p0=1650 Pagreen: p0=1600 Palight blue: p0=1550 Pa

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