Abstract: The design of efficient high-speed aircraft is of considerable interest for use in a multitude of applications including civil transport, access to low Earth orbit, and aero-assisted orbital transfer. The design of such vehicles is often accomplished with the aid of numerical methods. A new, numerical inverse-design method is developed for the principle lifting surface of such vehicles. Here the compressible, three-dimensional Euler equations are marched spatially away from a prescribed shock surface in a cross-stream direction to define the post-shock flowfield. The general three-dimensional problem is mathematically ill-posed; however, by marching within the local osculating plane, accurate and stable solutions are obtained.

The algorithm is applied to the design of a class of hypersonic vehicles called waveriders. The waverider's lower surface is defined as a streamsurface carved from the post-shock flowfield computed by this marching procedure. The waverider's upper surface is a parametrically-defined expansion surface, and the flowfield there is predicted by an approximation of the axisymmetric method of characteristics.

Comparisons with exact theory and direct Euler simulations demonstrate the validity and accuracy of the method. The algorithm's application to waverider design affords much greater flexibility in the choice of shock shapes than any previous studies, including here the possibility of nonaxisymmetric shocks with nonconstant shock strengths.

A summary of my thesis work was published as:

Jones, K.D., Sobieczky, H., Seebass, A.R. and Dougherty, F.C., "Waverider Design for Generalized Shock Geometries," Journal of Spacecraft and Rockets, Vol. 32, No. 6, 1995, pp. 957-963.