On the Subsonic Flow of a Compressible Fluid past an Axisymmetric Moderately Thick Body

抄録

We shall take the cylindrical coordinates o-xy, where x-axis is taken along the axis of revolution and y denotes the distance from the axis. Introducing new variables the fundamental equations for compressible fluid flow in the hodograph space are reduced to a form similar to that for incompressible fluid flow. Thus the flow of an incompressible fluid past a profile P₀ corresponds to the flow of a compressible fluid past a profile P, where the coordinates (x, y) and (x₀, y₀) of the profiles P and P₀ are related by the equations:
dx=(Q⁄q)dx₀,dy=(Q⁄q)dy₀,
and q and Q denote the magnitudes of velocity at corresponding points on the surface of the profiles in compressible and incompressible flows.
Also Q is a function of q defined as follows.
Q=\frac21+μ\left(\frac1+aμ1+a\ ight)^1⁄aq(1−a²q²)^1−a⁄2a,
μ=(1−q²⁄c²)^1⁄2=\left(\frac1−q²1−a²q²\ ight)^1⁄2,a²=\fracγ−1γ+1,
where c and γ denote respectively the local speed of sound and the ratio of the specific heats.
As examples the velocity distributions on the surface of a sphere and prolate spheroids with thickness ratio t=0.9 and 0.1 are calculated for various Mach numbers, and they are compared with the results obtained by the M²-expansion method, Meksyn-Imai’s method and the linear theory.