Gas-kinetic methods for low speed cavity flow in slip regime

Abstract

In this thesis, low speed cavity flow is investigated in the slip regime ranged from Knudsen number Kn=0.001 to Kn=0.1. Under such a high Knudsen number, the no-slip boundary condition becomes not applicable since the existence of rarefaction effect which causes the flow sliding along the stationary or driven flow. In this cavity flow case, the lid of the cavity is driven by velocity that makes the motion of flow inside the cavity. Velocity slip becomes significant along the lid of the cavity as the Knudsen number increases. Three numerical schemes utilized in this study are conducted by directional splitting gas kinetic BGK scheme, multidirectional gas kinetic BGK scheme and unified gas kinetic BGK scheme. Both directional splitting gas kinetic BGK scheme and multidirectional gas kinetic BGK scheme are conducted with the conjunction of gas kinetic slip boundary condition to analysis the slip velocity of the cavity flow. The numerical results are validated with DSMC results and both directional splitting and multidirectional gas kinetic scheme can give very convincing results up to Kn=0.05 and relatively satisfied results at Kn=0.1. Among these two schemes in some test cases, the secondary vortices are captured from the Multidirectional BGK scheme while Directional Splitting BGK scheme does not capture the secondary vortices at the corners of the cavity. Meanwhile, the slip velocity using unified gas kinetic BGK scheme match with the DSMC solutions very accurate and consistent. The main advantages of using these scheme to conduct the analysis of the flow field as compare to DSMC are that DSMC method is computational expensive and associated with excessive statistical fluctuations in low speed flows. In order to further understand the flow behavior, the velocity profile along the vertical symmetric line and horizontal symmetric line are simulated at different Knudsen numbers within the slip regime. The results show that the velocity profiles become flatten as the Knudsen number increases.

Date of Award	2013
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology