IJMEMES logo

International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749 . Open Access


Similarity Solutions of Strong Shock Waves for Isothermal Flow in an Ideal Gas

Similarity Solutions of Strong Shock Waves for Isothermal Flow in an Ideal Gas

Astha Chauhan
Department of Applied Science and Engineering, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India.

Rajan Arora
Department of Applied Science and Engineering, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India.

DOI https://dx.doi.org/10.33889/IJMEMS.2019.4.5-087

Received on March 16, 2018
  ;
Accepted on July 15, 2019

Abstract

Self-similar solutions of the system of non-linear partial differential equations are obtained using the Lie group of invariance technique. The system of equations governs the one dimensional and unsteady motion for the isothermal flow of an ideal gas. The medium has been taken the uniform. From the expressions of infinitesimal generators involving arbitrary constants, different cases arise as per the choice of the arbitrary constants. In this paper, the case of a collapse of an implosion of a cylindrical shock wave is shown in detail along with the comparison between the similarity exponent obtained by Guderley's method and by Crammer's rule. Also, the effects of the adiabatic index and the ambient density exponent on the flow variables are illustrated through the figures. The flow variables are computed behind the leading shock and are shown graphically.

Keywords- Lie group, Shock waves, Rankine-Hugoniot conditions, Similarity solutions, Ideal gas.

Citation

Chauhan, A., & Arora, R. (2019). Similarity Solutions of Strong Shock Waves for Isothermal Flow in an Ideal Gas. International Journal of Mathematical, Engineering and Management Sciences, 4(5), 1094-1107. https://dx.doi.org/10.33889/IJMEMS.2019.4.5-087.