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Reverse-flow integral methods for second-order supersonic flow theory

Published online by Cambridge University Press:  28 March 2006

Joseph H. Clarke
Joseph H. Clarke
Affiliation:
Division of Engineering, Brown University, Providence, Rhode Island
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Abstract

A general reverse-flow relation is obtained within the framework of second-order (in surface deflexion) supersonic flow theory. From this it is shown that the second-order increment in the drag of an arbitrary quasi-cylindrical body can be expressed as surface and volume integrals of the first-order solutions corresponding to forward and reverse flow past the body. Analogous results are obtained for second-order transverse forces and moments on an arbitrary quasi-planar wing, where the first-order reverse flow must correspond to certain zero-thickness wings. Other similar results are possible. Thus, second-order aerodynamic forces on bodies may be obtained from first-order solutions by quadrature. It is also shown that the reverse-flow integral relation can yield the pressure distribution on the surface by inversion of an integral equation constructed therefrom. It is thought that these results should be particularly useful for the Machnumber range between that of linearized theory and that of full hypersonic small-disturbance theory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 18 , Issue 2 , February 1964 , pp. 209 - 224
Copyright
© 1964 Cambridge University Press

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References

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