On changes of pressure center position of a sharp cone with small surface variations under hypersonic flow-around

Аuthors

Abstract

The problem of evaluating maximum possible changes in the position of the pressure center at small angles of attack and specified constrains on surface distortions of hypersonic vehicles in the form of sharp cones with small-parameter linearization is reduced to the math problem of a linear functional norm. The developed integral expression of linear functional, evaluating changes in the position of the pressure center for the shape variations is based on a semi-analytic method of differential locality hypothesis. The general integral expression of the preset functional norm in linear space of weak surface variations for the specified restrictive function is developed.

The validity of the developed analytical expressions being strictly in the class of sharp cones is confirmed by analyzing test examples for two possible types of linear surface variations and their linear combination. The first variation is related to a linear scale and the second one relates to a cone angle. The compliance of numerical results of analytical estimates of δx_ƒ to the exact result is taken as a criterion. The validity of the obtained analytical results for bodies close to a sharp cone shape is estimated by comparing with the results of numerical computations based on the solutions of inviscid Euler equations for models of perfect gas or equilibrium and dissociating air.

It is shown that the first variation of the sharp cone pressure center δx_ƒ at the specified weak variation of its surface under supersonic and hypersonic flows at small angles of attack depends only on two dimensionless parameters: a cone angle θ_k and relation of derivatives  of its surface pressure coefficient. The integral dependence of the first variation norm δx_ƒ for a sharp cone on the surface variation δy(x) and the above parameters is developed. The integral dependence of the first variation norm δx_ƒ for a sharp cone is developed at the specified restrictive norming function ψ(x) for a set of admissible variations of the cone surface δy(x), which allows of estimating a scale of probable variations δx_ƒ in indefinite-type conditions δy(x). The method to determine qualitative variation of the sharp cone surface, which is close to maximum possible variation δx_ƒ at the specified variation constrains δy(x), is pointed out.

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