Analytical solution for the propagation of shock waves in a rotating medium: power series solution

In this study an approximate analytical solution is obtained for the propagation of a cylindrical shock wave in a rotating perfect gas. The flow variable distributions in the flow field behind the shock waves are discussed. The azimuthal fluid velocity is assumed to vary according to the power law with the distance from the line of symmetry in an undisturbed medium, and the initial density is taken to be constant. The shock wave is assumed to be strong for small ratio (C/V)² , where C is the sound speed in an undisturbed fluid and V is the shock wave velocity. Approximate analytical solutions of the considered problem are obtained by expressing the flow variables as power series in (C/V)² . The closed form solutions are constructed for the first order. A comparison is made between the solutions obtained for rotating and nonrotating media. It is shown that the shock strength decreases due to rotation, whereas it increases with the adiabatic gas exponent.
  Автор:  Nath G.
Ключевые слова:  rotating medium, shock wave, power series method, perfect gas, similarity solution
Организация:  Department of Mathematics, Motilal Nehru National Institute of Technology
Стр:  155