To the problem of modeling gas flows behind the front of a strong shock wave using an effective adiabatic index

Abstract

In problems with strong shock waves (the problem of a strong explosion, the motion of bodies with high supersonic speeds, the problem of supersonic piston expansion), a significant increase in temperature occurs in the perturbed region of the flow. Therefore, when determining the parameters of the gas flow behind the front of a strong shock wave, it is necessary to take into account the real properties of the gas. This greatly complicates the construction of approximate analytical solutions. However, studies show that the influence of the real properties of the gas on the gas-dynamic parameters of the flow can be taken into account by changing the adiabatic index, that is, by introducing an effective adiabatic exponent. If the gas behind the shock wave is in a state of thermodynamic equilibrium, then the effective adiabatic index changes little in the entire flow zone. This makes it possible to simulate the flow behind the shock wave front by some perfect gas, the adiabatic index of which is determined depending on the Mach number and the thermodynamic state of the gas by the shock front. To obtain more accurate solutions to problems with strong shock waves, the model must allow a break in the adiabatic index at the shock wave. In the present work, an explicit expression is obtained for the gas parameters behind the front of an intense shock wave under the assumption that the adiabatic index undergoes discontinuity during the transition of gas particles through the surface of the shock wave. The plane and axisymmetric case are considered.