Application of the Thin-Wing-Expansion Method to the Compressible Flow past Profiles of Arbitrary Shape

Abstract

The formulae for the velocity distribution over the surface of an obstacle of arbitrary shape are given to the transonic third approximation by the use of Imai’s thin-wing-expansion method. These formulae are applied to the flow past an elliptic cylinder and it has been found that the results are in accord with the other authors’s results within the order of the approximation used. Further, these formulae, together with the Ψ- and the ΦΨ-procedures, are applied to the flow past Tomotika-Tamada’s profiles. Calculated velocity distributions are compared with Tomotika-Tamada’s exact solutions as well as with Takami’s numerical results obtained by various approximate methods.
These formulae seem to be very useful, because their convergency and accuracy are very good up to considerably high Mach numbers.