Numerical investigation of the thermal-caloric imperfections on entropy enhancement across normal shock waves
Merouane Salhi and Mohamed Roudane
Changes in flow properties across a normal shock wave are calculated for a real gas, thus giving us a better affinity to the real behavior of the waves. The purpose of this work is to develop shock-wave theory under the gaseous imperfections. Expressions are developed for analyzing the supersonic flow of such a thermally and calorically imperfect gas. The effects of molecular size and intermolecular attraction forces are used to correct a state equation, focusing on determination of the impact of upstream stagnation parameters on a normal shock wave. Flow through a shock wave in air is investigated to find a general form for normal shock waves. At Mach numbers greater than 2.0, the temperature rise is considerably below, and hence the density rise is well above, that predicted assuming ideal gas behavior. It is shown that caloric imperfections in air have an appreciable effect on the parameters developed in the processes considered. Computation of errors between the present model based on real gas theory and a perfect gas model shows that the influence of the thermal and caloric imperfections associated with a real gas is important.
Keywords: Supersonic flow; normal shock wave; high temperatures; high pressures; stagnation parameters; real gas model; thermal and caloric imperfections; entropy