Subsonic Jet Flows for a Given Surrounding Pressure from Finitely Long Convergent Nozzles


报告题目 Subsonic Jet Flows for a Given Surrounding Pressure from Finitely Long Convergent Nozzles

报告人: 王春朋 (吉林大学教授)

时间地点:2017年4月13日(星期四)15:00 -- 16:00理科楼数学系B203 

摘要: This talk concerns the compressible subsonic jet flows for a given surrounding pressure from a class of two-dimensional finitely long convergent nozzles with straight solid walls. These nozzles have the same vertex and the same inlet, which is an arc centered at the vertex. For a given surrounding pressure and a given incoming mass flux belonging to a suitable open interval, we seek a subsonic jet flow with the given incoming mass flux such that the flow velocity at the inlet is along the normal direction, the flow satisfies the slip condition at the wall, and the pressure of the flow at the free boundary coincides with the given surrounding pressure. In general, one part of the free boundary is the particle path connected with the wall of the nozzle and the other part is a level set of the velocity potential. It is more convenient to solve this subsonic jet flow problem in the potential plane, where it is formulated as a free boundary problem with mixed Dirichlet-Neumann boundary conditions on a streamline. However, the problem may be ill-posed in general because of the boundary condition at the inlet. We identify a suitable space of flows in terms of the minimal speeds and the maximal velocity potential differences for its well-posedness. It is shown that there is an optimal interval such that there is uniquely a subsonic jet flow in the space when the length of the nozzle belongs to this interval, while there is not such a flow for the nozzles whose lengths are beyond this interval. Furthermore, the properties of the flows are investigated.