Numerical Solution of Three-Dimensional Unsteady Transonic Flow over Swept Wings

Abstract

An algorithm for the calculation of unsteady transonic flow over three-dimensional swept wings undergoing general unsteady motion has been developed. The equation considered is the transonic small-disturbance potential equation with second-order terms to insure proper swept shock jump conditions. An alternating direction-implicit approximate factorization difference scheme is employed. A shearing transformation of the coordinates is applied in order to map a swept-tapered planform onto a rectangle in the computational domain. Use of a rotated type-dependent differencing scheme provides computational stability as well as proper shock capture. Computed results for an infinite-yawed wing are found to agree with two-dimensional solutions when simple sweep theory is applied for both the steady and unsteady cases. Steady three-dimensional results compare favorably with existing steady methods. Unsteady results are presented for a swept wing undergoing sinusoidal pitching motion at M0.9. It is found that the shock position oscillates over about 16% of chord at the wing tip.