Rotation body of minimal aerodynamic drag in hypersonic rarefied gas flow


DOI: 10.34759/TRD-2020-113-04

Аuthors

Gorelov S. L.1*, Nguyen V. L.2**

1. Central Aerohydrodynamic Institute named after N.E. Zhukovsky (TsAGI), 1, Zhukovsky str., Zhukovsky, Moscow Region, 140180, Russia
2. Moscow Institute of Physics and Technology (National Research University), 9, Institutskiy per., Dolgoprudny, Moscow region, 141701, Russia

*e-mail: gorelovsl@yandex.ru
**e-mail: lamvqtc1990@gmail.com

Abstract

Equations obtained from local models gained wide proliferation for assessed calculations of forces acting on a body while its high-speed motion in a gas. The basis of these models is the assumption that each element of the body surface interacts with the gas flow independently from the other segments of the body, and the force acting on it depends only upon the element orientation relative to the motion direction. Such representation of the forces acting on the bodies in the hypersonic flow allows rather simple solution of variation problem on searching for the shapes of the bodies of minimal drag.

The drag force in the hypersonic rarefied gas flow for a rotation body with power-law generatrix is being computed based on several local models.

In this case, the drag factor value is being computed analytically. The variation problem is being reduced to the problem on the extreme value of the one-variable function, i.e. the degree of the rotation body generatrix.

Apart from the classical Newton aerodynamic problem, the problem of a rotation body with minimal drag for a free-molecular hypersonic gas flow is beings also solved as well. To determine the degree in the rotation body generatrix at the arbitrary Reynolds numbers the well-known local model for the approximate determination of pressure and friction on the body surface in a hypersonic rarefied gas flow is being used. In all cases, the problem is being solved for bodies of arbitrary elongation.

At Reynolds numbers tending to zero and for large elongations, the degree in generatrix of the rotation bodies of minimal drag tends to 2/3, and for Reynolds numbers tending to the infinity it tends to ¾. This is consistent with the well-known results for the free-molecular flow mode, as well as for the continuous medium (Newton formula), respectively.

Keywords:

hypersonic flow, local models, aerodynamic drag of a rotational body, variation problem

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