Analysis and Design of Supersonic Aircraft Based on Inviscid Nonlinear Eulerian Equations. Part I. Rotational Euler Solutions with Explicit Shock Fitting

摘要

A computer program has been developed to compute the inviscid supersonic flow over delta wings and smooth wing-body configurations. A second-order accurate predictor-corrector finite-difference scheme is used to integrate the three dimensional Euler equations in regions of continuous flow. Bow shock and crossflow-induced embedded shocks are explicitly computed as discontinuities which simultaneously satisfy the characteristic and the Rankine-Hugoniot conditions. In computing the flow about complex wing cross sections, the use of appropriate conformal mappings were an important factor in developing a computational mesh capable of resolving the large flow gradients that are inevitable in the vicinity of wing leading edges. Geometry programs were developed to supply the appropriate geometric boundary conditions necessary to compute complex wing cross sections. New starting solutions were developed that were more appropriate to thin-wing cross sections. In the initial stage of development, the flow about conical wings was computed for a two-fold purpose. Conical Euler solutions would be used as starting conditions for conical wing-bodies and three dimensional wings and the conical problem would uncover potential problem areas in the computation of these flows without the added complexity of geometrical variations. The conical problem led to the development of special techniques to resolve the vortical layer that inevitably develops on the body surface. Typical results are shown for subsonic and supersonic leading edge delta wings and wing-body combinations.