Investigation of Flow Around Simple Bodies in Hypersonic Flow

Abstract

A theoretical analysis of the flow around slender blunt-nosed bodies was made by applying the flow similarity concept to the hypersonic small- disturbance equations. The flow field around a class of bodies of the form r_b ~ x^m exhibits a certain similarity in the sense that the pressure, density and transverse velocity are described by relations of the form Q(x, r)/Q(R) = f(r/R), where R is the distance from the axis to the shock wave. This similarity holds when the Mach number is infinitely large, and when the exponent in the equation defining the body shape lies in the range 1/2 < m ≤ 1 for axially-symmetric bodies and in the range 2/3 < m ≤ 1 for two-dimensional bodies. For large but finite Mach numbers a second approximation was obtained by expanding solutions in series of powers of x^((1-m))/M_∞^ δ^2. An experimental investigation of the flow around "similar-flow" bodies of revolution was conducted at Mach number 7.7 in the GALCIT hypersonic wind tunnel. The surface pressure distributions agreed closely with the theoretical predictions, after a simplified correction was made for the boundary-layer displacement effect. The results indicated that the boundary layer interaction effect needs a further investigation.

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