Global Existence of a Shock for the Supersonic Flow Past a Curved Wedge

In this paper, we establish the global existence and stability of a multidimensional conic shock wave for three-dimensional steady supersonic flow past an infinite cone. The flow is assumed to be hypersonic and described by a steady potential flow equation. Under an appropriate boundary condition on the curved cone, we show that a pointed shock attached at the vertex of the cone will exist globally in the whole space.

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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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Global existence of shock for the supersonic Euler flow past a curved 2-D wedge

Journal of Differential Equations ◽

10.1016/j.jde.2012.11.014 ◽

2013 ◽

Vol 254 (5) ◽

pp. 2076-2127 ◽

Cited By ~ 1

Author(s):

Dian Hu

Keyword(s):

Global Existence ◽

Euler Flow ◽

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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