Effect of the Stagnation Temperature on the Conical Shock Wave Produced in a Real Gas

This study aims to develop a novel numerical algorithm based on a mathematical model to ascertain the characteristics of supersonic flow passing through a conical shock wave by considering the real gas effects in contrast to the perfect gas assumption. Air is considered to be the working fluid. The model incorporates variations in the specific heat at constant pressure due to changes in the temperature and the density. The stagnation temperature is a crucial factor in the analysis. The mathematical framework involves solving a system of first-order nonlinear differential equations with three interrelated variables using initial conditions. The numerical solution is achieved by means of adaptation of the higher order Runge–Kutta method. The parameters associated with the conical shock wave can be determined by employing a new model featuring an oblique shock waves under the real gas conditions. A comparative analysis with the perfect gas model is conducted at low stagnation temperatures, upstream Mach numbers, and cone deviation angles, including an estimation of the divergence between the real and perfect gas models. The study is focused on using air as the working fluid.