Supersonic Flow Past Axially Symmetric Bodies

SummaryThe supersonic flow past an elliptic cone of small eccentricity is treated as a pertubation of the axially-symmetric conical flow. The perturbation is singular; a uniformly valid solution is constructed by formulating the problem in sphero-conal coordinates (in which the cone surface is always a level surface of one of the coordinates) and by using the method of matched asymptotic expansions. This formulation enables first-order results to be obtained economically. In a numerical example for the flow past a cone of quite large eccentricity at incidence, it is shown that the present first-order solution (of three terms) agrees as well with experiment as a ten-term approximation obtained by Martellucci using the method of linearised characteristics.

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The Supersonic Flow Past a Slender Ducted Body of Revolution with an Annular Intake

Aeronautical Quarterly ◽

10.1017/s0001925900000214 ◽

1950 ◽

Vol 1 (4) ◽

pp. 305-318

Author(s):

G. N. Ward

Keyword(s):

Supersonic Flow ◽

Velocity Potential ◽

Operational Calculus ◽

The Body ◽

Body Of Revolution ◽

Internal Flows ◽

Flow Past ◽

External Forces ◽

Internal Pressures ◽

Slender Body Of Revolution

SummaryThe approximate supersonic flow past a slender ducted body of revolution having an annular intake is determined by using the Heaviside operational calculus applied to the linearised equation for the velocity potential. It is assumed that the external and internal flows are independent. The pressures on the body are integrated to find the drag, lift and moment coefficients of the external forces. The lift and moment coefficients have the same values as for a slender body of revolution without an intake, but the formula for the drag has extra terms given in equations (32) and (56). Under extra assumptions, the lift force due to the internal pressures is estimated. The results are applicable to propulsive ducts working under the specified condition of no “ spill-over “ at the intake.

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An approximate solution of the problem of separated flow past an axially symmetric body

Journal of Applied Mathematics and Mechanics ◽

10.1016/0021-8928(59)90137-6 ◽

1959 ◽

Vol 23 (5) ◽

pp. 1351-1355 ◽

Cited By ~ 4

Author(s):

S.S. Grigorian

Keyword(s):

Approximate Solution ◽

Separated Flow ◽

Symmetric Body ◽

Axially Symmetric ◽

Flow Past

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Study on Supersonic Flow Past a Pointed Body

Hyperbolic Problems: Theory, Numerics, Applications ◽

10.1007/978-3-0348-8370-2_25 ◽

2001 ◽

pp. 237-245

Author(s):

Shuxing Chen

Keyword(s):

Supersonic Flow ◽

Flow Past ◽

Pointed Body

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The behaviour of supersonic flow past a body of revolution, far from the axis

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1950.0045 ◽

1950 ◽

Vol 201 (1064) ◽

pp. 89-109 ◽

Cited By ~ 43

Keyword(s):

Supersonic Flow ◽

General Theory ◽

Body Of Revolution ◽

Flow Past ◽

Physical Importance ◽

Special Case ◽

Pointed Body ◽

Asymptotic Forms

A theory is developed of the supersonic flow past a body of revolution at large distances from the axis, where a linearized approximation is valueless owing to the divergence of the characteristics at infinity. It is used to find the asymptotic forms of the equations of the shocks which are formed from the neighbourhoods of the nose and tail. In the special case of a slender pointed body, the general theory at large distances is used to modify the linearized approximation to give a theory which is uniformly valid at all distances from the axis. The results which are of physical importance are summarized in the conclusion (§ 9) and compared with the results of experimental observations.

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