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A perturbation theory of unsteady hypersonic and supersonic flows

A perturbation theory of unsteady hypersonic and supersonic flows
A perturbation theory of unsteady hypersonic and supersonic flows
A general perturbation theory for hypersonic and supersonic flows past a wedge-like body is developed, which can be applied to both unsteady and steady flows for which the bow shock is attached to the body. It may be used to describe Inviscid and viscous flows over both slender and thick, rigid or flexible bodies performing either periodic or aperiodic motions. The exact (linearized) perturbation equations and boundary conditions are first derived, and the problem of finding the flow field reduced to that of solving a wave equation containing only one unknown function. Approximate formulae for the aerodynamic derivatives of a pitching wedge in inviscid flow are obtained in two forms of power series in the frequency parameter and in the reflection coefficient Which include McIntosh’s theory and Appleton's theory as special cases. Two sets of waves are shown to exist, the first is due to the disturbance at the body surface, the second is due to the motion of the bow shock and is found to be a factor strongly destabilizing the motion of thick bodies. Exact formulae in closed form are obtained for the stability derivatives of a pitching wedge of any thickness in inviscid hypersonic and supersonic flows« Also obtained is an exact general criterion for stability. It Includes the approximate theory and the theory of Carrier & Van Dyke as special cases. The effect of viscosity is included and closed form formulae for the stability derivatives of a wedge obtained which include the effects of wave reflection and thickness, and which appears to include Orlik-Ruchemann's theory as a special case. Finally, by extending the perturbation method previously mentioned, exact formulae for the stability derivatives of a pitching Nonweiler (caret) wing in hypersonic flow are obtained and shown to be independent of its aspect ratio. The three dimensional effect of the flow is shown to be dominant for the damping derivative.
University of Southampton
Hui, Wai How
8f7067a5-611f-42f6-a429-8f3d0fac3302
Hui, Wai How
8f7067a5-611f-42f6-a429-8f3d0fac3302
East, R.A.
c31d4581-0c23-43dd-9a1e-4281dd77e32e

Hui, Wai How (1968) A perturbation theory of unsteady hypersonic and supersonic flows. University of Southampton, Doctoral Thesis, 188pp.

Record type: Thesis (Doctoral)

Abstract

A general perturbation theory for hypersonic and supersonic flows past a wedge-like body is developed, which can be applied to both unsteady and steady flows for which the bow shock is attached to the body. It may be used to describe Inviscid and viscous flows over both slender and thick, rigid or flexible bodies performing either periodic or aperiodic motions. The exact (linearized) perturbation equations and boundary conditions are first derived, and the problem of finding the flow field reduced to that of solving a wave equation containing only one unknown function. Approximate formulae for the aerodynamic derivatives of a pitching wedge in inviscid flow are obtained in two forms of power series in the frequency parameter and in the reflection coefficient Which include McIntosh’s theory and Appleton's theory as special cases. Two sets of waves are shown to exist, the first is due to the disturbance at the body surface, the second is due to the motion of the bow shock and is found to be a factor strongly destabilizing the motion of thick bodies. Exact formulae in closed form are obtained for the stability derivatives of a pitching wedge of any thickness in inviscid hypersonic and supersonic flows« Also obtained is an exact general criterion for stability. It Includes the approximate theory and the theory of Carrier & Van Dyke as special cases. The effect of viscosity is included and closed form formulae for the stability derivatives of a wedge obtained which include the effects of wave reflection and thickness, and which appears to include Orlik-Ruchemann's theory as a special case. Finally, by extending the perturbation method previously mentioned, exact formulae for the stability derivatives of a pitching Nonweiler (caret) wing in hypersonic flow are obtained and shown to be independent of its aspect ratio. The three dimensional effect of the flow is shown to be dominant for the damping derivative.

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Published date: 1 April 1968

Identifiers

Local EPrints ID: 439426
URI: http://eprints.soton.ac.uk/id/eprint/439426
PURE UUID: 316a5f70-a0e4-4177-8f86-ae13f96dda02

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Date deposited: 22 Apr 2020 16:32
Last modified: 22 Apr 2020 16:32

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Contributors

Author: Wai How Hui
Thesis advisor: R.A. East

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