International Conference
"Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Applications", devoted to the 90th anniversary of professor Nikolai N. Yanenko

Закиров А.Х.  

The study of compressible gas flow with a free jet in the cylinder

Problem of jet flow of liquid and gas have practical applications in various branches of engineering, particularly in the power plants of vehicles. Physical processes of gas exchange in the cylinder with the lowest hydraulic resistance can be reduced to the problem of the theory of jets of compressed gas.
The plane problem of a jet potential flow of compressible gas in distribution mechanism with a subsonic velocity without external forces. During the potential and steady, and polytropic process. It is assumed that the source of the particle flow rate of gas, filling the cavity, form a free surface with an unknown boundary, along which the pressure is constant.
To solve the problem of quasiconformal map the flow region in the physical plane onto the upper half. Introduce the analytic function Zhukovsky. Writing the boundary conditions for the Zhukovskii function, and using the Schwarz integral formula for the upper half-plane, we obtain expressions for the desired function. Further, we find the conjugate complex velocity, the mapping function and the parameters included in the formula.