Plane transonic solution with shock by direct iteration

Abstract

Transonic reduced pressure distributions at thin symmetrical nonlifting profiles, with high subsonic free stream velocity are predicted by determining approximate solutions of the Oswatitsch integral equation by direct iteration scheme [1], which is extended here to include shocks. Converged solution with shock may be obtained if the starting solution contains a shock discontinuity or else, if with a continuous starting solution, the expansion shock which appearts at the accelerating sonic point be excluded at each iteration step. Computational results have been presented for a NACA 0012 profile and a parabolic arc profile and compared with other numerical results, which indicate good agreement, particularly for the shock position. A typical profile shape with shock converges in only 16 iteration steps, correct up to two decimal places requiring about 30 secs. of CPU time on a Burroughs B6700 computer system.