| Summary: | 碩士 === 國立高雄海洋科技大學 === 輪機工程研究所 === 95 === From the physical point of view, there exists natural separation phenomenon of liquid and gas phases in their coexisting region described by the van der Waals equation of state. Therefore, we can take advantage of this characteristic to simulate two-phase flow problems without thickening the phase boundary, and to keep the simulation stability and accuracy. However, this phenomenon also reveals pressure will decrease with increasing density in the two-phase coexisting regions, which will lead to a non-hyperbolic system of Euler equations. Conventional upwind schemes can not employed to solve such a non-hyperbolic equation system since they are derived based on a hyperbolic system.
To circumvent the above-mentioned problem, we used a numerical method which can be applied to solve an arbitrary system irrespective of its hyperbolicity to calculate two-phase flow problems based on the van der Waals equation of state. Detailed solution procedures are provided in this article and several one-dimensional and two-dimensional two-phase flow problems are successfully solved with this proposed method. Numerical experiments are also conducted to investigate influences of some scheme parameters. Its worth to emphasize that the numerical method proposed in this article also successfully simulates the phenomenon of liquid evaporation and gaseous coagulation, as well as the jet clashing and water-drop impacting problems. From the numerical results, one can conclude that the present numerical method can be a useful tool to simulate two-phase flow. It is also helpful the present method can be served as a basis to develop more complicated schemes for the understanding about physical phenomenon of phase transition flow problems in the future.
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