✍ Scribed by A.N. Kraiko
No coin nor oath required. For personal study only.
The structure of the one-dimensional steady spherically symmetric rarefaction flow of an ideal (inviscid and non-heat-conducting) gas in the neighbourhood of a reflection point of a "boundary" C--characteristic is investigated in principal order. The "boundary" C--characteristic separates the gas at rest from the flow due to the outward motion of a piston which confines the gas. In the rt plane, where r is the distance from the centre of symmetry and t is the time, the reflection point, which coincides with the point of arrival on the t axis of the boundary characteristic, coincides with the origin of coordinates. The initial velocity of the piston may be zero (for positive acceleration) or finite. When two symmetrical plane pistons advance, the "derived" derivatives of all the flow parameters on the C--characteristic at the origin of coordinates, which in this case lies on the plane of symmetry, are finite. When a cylindrical and spherical piston advance, the derived derivative of the pressure (velocity) of the gas on the C"-characteristic at the origin of coordinates becomes minus (plus)-infinity although without intersecting characteristics of the same family [1][2][3][4].
📜 SIMILAR VOLUMES
The image system for a velocity field of the Oseen tensor in a fluid region bounded by a rigid spherical container is derived. The Green's function and image system due to a nearby boundary constitute two themes explored in the pioneering (1896) paper by Lorentz. The special structure of our image s