Effect of Fineness Ratio on Minimum-Drag Shapes in Hypersonic Flows

Abstract

The importance of fineness ratio in determining the aerodynamic shapes of minimum-drag, zero-lift axisymmetric bodies in inviscid hypersonic flows is investigated using a shape optimization framework. The framework employs modified Newtonian theory for surface pressure computation, Bezier curves for geometric parameterization and a steepest-descent approach for minimization of the wave-drag coefficient. Studies are performed on axisymmetric bodies of a given length for fineness ratios varying from 1 to 6 and Mach numbers ranging from 6 to 12. It is shown that the optimal axisymmetric body for a given freestream Mach number is blunt-nosed for smaller fineness ratios but becomes sharp-nosed at larger fineness ratios. The fineness ratio at which the optimal body of revolution transitions from blunt-nosed to sharp-nosed is found to be nearly constant at hypersonic speeds and is around 3. Results indicate that the optimal bodies derived from the framework are superior in terms of wave drag to the von Kármán ogive but comparable to the 0.7 power-law body. High-resolution Euler simulations of these optimal forebodies demonstrate that, while the modified Newtonian theory underpredicts the wave drag for lower values of the similarity parameter, the derived configurations remain “near-optimal” for the entire range of the similarity parameter in the hypersonic regime. The study hints at the possibility of multiple near-optimal configurations in inviscid hypersonic flows and affirms the utility of the present framework as a low-fidelity approach for the design of minimum-drag configurations.