General Conclusion
The field of compressible aerodynamics, or gas dynamics, is not only that of planes, missiles, space launchers, and projectiles flying at supersonic velocities, that of planetary probes entering into the atmosphere at hypersonic Mach numbers, but also that of present transonic transport aircraft. In the domain of propulsion, it concerns air intakes, turbomachines, propulsive nozzle, or supersonic diffusers. Unsteady propagation mechanism and shock wave formation directly pertain to gas dynamics. The application field of unsteady theory is particularly vast. It includes the propagation of waves generated by a sudden energy release (explosion), supersonic boom, or shock wave formation due to the entering into a tunnel of a high-speed train, to cite a few examples. We should also mention auto-induced fluctuations in a flow, like transonic buffeting or air-intake buzz. Such phenomena, which are the source of numerous inconveniences (noise, vibrations, loss of control, etc.) are the subject of special attention from aerodynarnicists. Acoustics belongs to these domains; however this discipline by itself is a science justifying separate developments; this is only evoked in this treatise.
The presented notions constitute the theoretical basis for the study of flows reaching speeds high enough to induce substantial variations of the density. This fact requires us to take into account, in the formulation of the problem, the energy equation, and hence a strong coupling ...
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