| Summary: | 博士 === 國立交通大學 === 機械工程系所 === 102 === This paper is aimed at developing a numerical method for two-phase flows with phase change on unstructured grids. In this article, two schemes are presented based on VOF (volume-of-fluid) method. The first scheme is to capture the interface by solving the advection equation of the volume fraction directly, termed as FBICS. In order to maintain the sharpness and boundedness of the interface, the convective flux through each cell face is determined by means of flux blending. The weakness of this method is that the interface region will occupy several grid spaces. In the other scheme (termed as CISIT), the interface is reconstructed first using interpolation practice, following by a predicted-correction procedure to handle the movement of the interface. Except for the interface cells, the VOF distribution is uniform, either in 1 or 0, and the interface occupies only one cell in its width. Unlike the PLIC method, the CISIT can be easily extended to unstructured grids with arbitrary geometry and 3-D problems without causing any further complication because its formulation is very simple. In PLIC, the reconstruction of the interface is not straightforward and the procedure to advance the interface is complicated because a large number of interface configurations (16 configurations for 2-D flows and 64 for 3-D flows) must be considered for determining of the flux across cell faces. Tests on a number of cases reveal that results via these two schemes in this study, which can be used on the unstructured grids, give good agreement with exact solutions or experimental data of free surface flows.
In order to simulate the two-phase flow with phase change, the CISIT method is extended to include heat and mass transfer due to phase change. The mass transfer across the phase boundary is determined by taking into account the mass and energy jump conditions at the interface and added as a source term in the continuity equation. Then, the interface is treated as an internal boundary condition in the temperature flied. Finally, the energy equation is solved in an implicit way. Besides, this method is also extended to simulate the heat transfer of two-fluid flows without phase change based on the assumption of the continuity conditions of the temperature and heat flux instead of jump conditions at the interface. Application to film boiling flow on a horizontal plate at a state near the critical pressure shows that the boiling mode will be different at different superheat temperatures. According to different superheat tempera- tures, the boiling flows can be divided into five modes: single-bubble mode ( ), single/multiple bubble mode ( ), single-jet mode ( ), double-bubble mode ( ), and double-jet mode ( ). In the single-bubble mode, good agreement with semi-empirical correlations was obtained in terms of averaged Nusselt number. Furthermore, simulation of film boiling flow on a cylinder demonstrates that this method is applicable to boiling flow with complex geometry.
Finally, the CISIT method with phase change is modified to calculate three-dimensional two-phase flows. Unlike two-dimensional flow, the interface is reconstructed with several non-coplanar triangular interfaces within the grid. First, this method was tested through computations of a number of two-fluid flows without phase change to validate the capability of tracking the interface in three- dimensional flows. In addition, this method was also applied to simulated film boiling flow on a horizontal plate. It can be shown that the space and time averaged Nusselt numbers obtained from the current simulations have good agreement with the semi-empirical correlations of Klimenko, especially for .Finally, the heat transfer model without phase change was used to simulate the molten tin droplet in oil and the octane inlet in water.
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