The Application of Meksyn-Imai’s Method to the Subsonic Flow past an Axisymmetric Body

抄録

For the axisymmetric subsonic now of a compressible fluid we shall develop an analogous procedure to Meksyn-Imai’s method, which was offered for the two-dimensional irratational now of a compressible fluid. And then it will be proved that the final results obtained in the two-dimensional case can also be immediately used in the present three-dimensional case.
Namely, the ratio of the velocity of a compressible fluid past an obstacle to that of an incompressible fluid past the same obstacle, denoted by (q⁄q₀), can be given by solving the following algebraic equation of fifth degree:
(q⁄q₀)=1+M₁²(q⁄q₀)³\left{1−\fracγ−12M₁²\ ight}K(α,β)+M₁⁴(q⁄q₀)⁵L(α,β),
where M₁ and γ are respectively the Mach number of the main flow and the ratio of the specific heats, and K and L are functions determined merely by the form of the obstacle.
Also K and L can be related with the coefficients of the series of the M²-expansion method as follows:
K=Q₁⁄q₀,
L=(Q₂⁄q₀)+\fracγ−12(Q₁⁄q₀)−3(Q₁⁄q₀)²,
where
q=q₀+M₁²Q₁+M₁⁴Q₂+···.
As an example the flow past a sphere is discussed.