Minimum-Drag Axisymmetric Bodies in the Supersonic/Hypersonic Flow Regimes

A study of minimum-drag body shapes was conducted over a Mach range from 3 to 12. Numerical results show that power-law bodies result in low-drag shapes, where the power n = 0.69 (l/d = 3) or n = 0.70 (l/d = 5) shapes have lower drag than theoretical minimum results (« = 0.75 or 0.66, depending on the particular form of the theory). To evaluate the results, a numerical analysis was made, including viscous effects and the effect of a gas model. None of these considerations altered the conclusions. The Hayes minimum-drag body was analyzed and had a higher drag than the optimum power-law body. d i n r T rref x, y, 0 Nomenclature = drag coefficient based on the maximum cross-sectional area = skin-friction coefficient = pressure coefficient = body diameter at the base = marching plane index = unified supersonic-hypersonic similarity parameter, = body length = freestream Mach number = power-law exponent = body radius = temperature at the body surface = freestream temperature z - physical coordinates = circumferential angle

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