A Generalized Approach to One-Dimensional Gas Dynamics

Abstract

We present a Generalized Compressible Flow Function (Γ) which is shown to have direct application in the treatment of many simplified one-dimensional flow processes. Those particular processes treated in this paper are: (a) the familiar adiabatic flows, with or without friction, with area variations always allowed; (b) the little-discussed diabatic flows, with or without friction, with area variations allowed under certain conditions; and (c) the discontinuous normal shock process. Moreover, the Γ function is shown to have significance in a generalized flow process having an arbitrary combination of heat transfer, friction, and area variation. Development of the Γ function is given in some detail. A large scale plot of pressure ratio (p/pt) versus Γ is given along with Generalized Compressible Flow Tables for the convenience of the user. Schematic isentropic, Fanno, Rayleigh, and isothermal flow maps are presented in terms of the conventional enthalpy-entropy diagram, and again in terms of the pressure ratio —Γ diagram. Numerical examples are included to illustrate the solution of typical problems through the use of the Generalized Compressible Flow Tables.