Fluid mechanics-One-dimensionnal compressible flow

The flow of compressible fluids, whether gases or vapors, is an issue in many areas of industry and transportation. Examples include steam and gas turbines, turbojet and rocket engines, reciprocating engines and the movement of various bodies through the air at high speeds. This is also the case for certain speed measurement or flow regulation instruments, for example.

In all their generality, these flows are three-dimensional, often adiabatic, sometimes isothermal, always strictly irreversible due to the viscosity, however low, of the gases or vapors involved. Despite this generality, simpler analyses, based on the assumptions of one-dimensional flow and perfect gas reversibility, are important because they lead to results close to reality and provide an immediate understanding of the problems posed. The aim of this article is to achieve this understanding.

To this end, the basic equations of fluid mechanics and thermodynamics - the equations of state, mass, energy and momentum - are applied to this type of flow. The fundamental notions of speed of sound and generating state or stopping point are introduced.

An important part of the text is devoted to analyzing the particularities of isentropic flow in a perfect gas, in terms of the evolution of parameters such as velocity, pressure, temperature and cross-sectional area of the flow. Particular emphasis is placed on the importance of the notion of critical sound velocity and its quality as an invariant of a given flow. This basic analysis is then applied to the case of convergent or convergent-divergent nozzle flows and its various specificities of subsonic, supersonic flow with or without the presence of shock waves or expansion waves.

Two other classic cases of gas or vapor flow are also presented. These are flows in cylindrical ducts, either irreversibly adiabatic (Fanno flow) or reversibly non-adiabatic (Rayleigh flow). The irreversible transition from supersonic to subsonic flow through a shock wave is presented.

Finally, the last part of the article is devoted to the study of the evolution of fluid characteristics during the passage of a shock wave, either straight or oblique.