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CivilComp Proceedings
ISSN 17593433 CCP: 86
PROCEEDINGS OF THE ELEVENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: B.H.V. Topping
Paper 217
Phenomenological Transient Finite Element Modelling of a TwoPhase Flow with Dynamic Phase Change Z. Sari, I. Jancskar, L. Szakonyi and A. Ivanyi
Department of Information Technology, University of Pécs, Hungary Z. Sari, I. Jancskar, L. Szakonyi, A. Ivanyi, "Phenomenological Transient Finite Element Modelling of a TwoPhase Flow with Dynamic Phase Change", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Civil, Structural and Environmental Engineering Computing", CivilComp Press, Stirlingshire, UK, Paper 217, 2007. doi:10.4203/ccp.86.217
Keywords: twophase flow, phase transition, hysteresis, finite element modelling.
Summary
In this paper a diffuse interface model of an annulartype twophase
flow with phasechange is presented. The model setup is a
horizontal steam tube with close to the saturation inlet conditions.
At a point some distance downstream of the entrance, vapor begins to
condense and a thin liquid film evolves on the interior wall of the
tube. The rate of condensation is directly linked to the rate at
which heat is transported across the film from the interface to the
surface. Modeling the heat transfer and fluid flow associated with
this liquidvapor phase change process requires additional elements
to the governing equations of the singlephase convective transport
regarding to the nonequilibrium effects and dynamic interactions
between the phases. The twophase flow is assumed as a homogeneous
phase mixture consists of a single fluid with continuous variation
of thermodynamic state variables forming a diffuse
interface [1]. To describe the phase transition it is
necessary to select a so called order parameter (phi), which
differs in the two phases. The energy balance equation involves the
time derivative of the order parameter as a consequence of the
dependence of the internal energy on phi. The evolution
equation of phi is a hysteresis operator based on a
LandauGinzburg freeenergy density approximation [2].
A nonequilibrium assumption, i.e. the finite speed of phase transformation, enables some degree of supersaturation in the cluster without phase change. The upper limit of the acceptable supersaturation has to be determined. This limit has to be between the vapor spinodal and equilibrium curve. The theoretical limit, the spinodal of vapor supersaturation is proportional to p/p_{c} [3], where p_{c} is the critical pressure. In this work a T/T_{c} (T_{c} is the critical temperature) dependent supersaturation limit is introduced. The applied hysteresis model of the vaporliquid phase transition can improve other macroscale heat transfer models as well that are associated with boiling and condensation phenomena and are treated until now as virtually isothermal heat transfer processes. The presented model has been implemented into a finite element simulation and proved to be very effective and numerically stable. References
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