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 fl ow variable distributions in the fl ow fi eld behind the shock waves are discussed. The azimuthal fl uid 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 fl uid and V is the shock wave velocity. Approximate analytical solutions of the considered problem are obtained by expressing the fl ow variables as power series in (C/V)2 . The closed form solutions are constructed for the fi rst 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. 
   
Author:  G. Nath
Keywords:  rotating medium, shock wave, power series method, perfect gas, similarity solution
Page:  152