The normal shock waves of real gases and the generalized isentropic exponents

Abstract

When a supersonic gas flow is choked or otherwise disturbed, a shock wave appears. When this shock wave is perpendicular to the direction of the one-dimensional flow, a normal shock wave transforms the flow to a subsonic one. The thermodynamic variables involved are five, i.e. the pressure, the specific volume, the temperature, the enthalpy and the velocity of the flow. To determine their values after the normal Shock, five relations are used namely the equation of state, the enthalpy equation, the laws of conservation of impulse and energy, and the continuity of mass. For the simple case of a perfect gas, these relations are explicit and allow a straightforward solution of the system of the five equations. In the case of a real gas flow the system is solved numerically. The present work considers two other possibilities, i.e. the use of perfect gas like equations describing the phenomenon or the use of the Redlich-Kwong equation of state. Perfect gas like equations may be used now, to describe the phenomenon, after it has been shown that there exist three isentropic exponents, instead of the one used until now, and after it has been observed that the mathematical form of the perfect gas equations fit the real gas isentropic expansion when suitable numerical values of the corresponding constants and exponents are used. The other possibility, the use of the Redlich-Kwong equation of state, allows the calculation of the state variables after the normal shock when only the two constants of this equation and the specific heat of the corresponding perfect gas state (pressure approaching zero) are available. Both methods presented here require the numerical solution of a onevariable equation. In the first method the variable is the Mach number while in the second the specific volume.