Bodies Having Minimum Pressure Drag in Supersonic Flow: Investigating Nonlinear Effects

Abstract

T HE life cycle of engineering design involves innovating to introduce a product, and when that is done, looking for ways to make itwork better. Supersonic aerodynamics can be looked atwith a similar perspective. Man has always wanted to fly faster. While the basicmechanics of supersonic flightwas laid out in the 1950s, people are yet to find ways in which to make Supersonic flight more efficient. One of the classic research problems in supersonic flight has been that of finding two-dimensional and axisymmetric profiles that have minimum pressure drag in supersonic flow. The two-dimensional sections are used as wing-profile sections, and the axisymmetric profiles are useful in that the distribution of the cross-sectional area is made to follow the optimumdistribution (the area rule). This problem becomes redundant without suitable constraints. The minimum drag shape is a flat plate in two-dimensional flow and a needle-like profile in axisymmetric flow. This, however, is not a meaningful result. To make the problem more meaningful, the enclosed area/volume should be kept constant. The ends should also be kept pointed. This is to anchor the shocks firmly to the leading and trailing edges. This problem has been solved in the fifties using a linear flow model. However, recent advances in computational fluid dynamics and aerodynamic shape optimization have made it possible for this problem to be analyzed using a nonlinear flow model. The results of this exercise are discussed in this paper.