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The Quarterly Journal of Mechanics and Applied Mathematics 1948 1(1):225-245; doi:10.1093/qjmam/1.1.225
© 1948 by Oxford University Press
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THE APPROXIMATE EXTERNAL AND INTERNAL FLOW PAST A QUASI-CYLINDRICAL TUBE MOVING AT SUPERSONIC SPEEDS

G. N. WARD

( Department of Mathematics, The University Manchester )

By using the Heaviside operational method applied to the linear perturbation theory for supersonic flow past a cylindrical tube of nearly constant radius at small incidence, the aerodynamic force and moment coefficients resulting from the fluid pressure have been calculated for the outside of the tube, and inside the tube for a length Formula times the diameter of the tube, where M0 is the Mach number of the undisturbed flow. The results are obtained in a form suitable for computation. The expressions for the drag, lift, and moment coefficients involve only the slope of the meridian section at any point, the angle of incidence, and certain auxiliary functions which are the same for all tube shapes.

The distribution of the velocity components inside the tube has been considered in linear theory; singularities and discontinuities occur in these velocity components, or in their derivatives, corresponding to a discontinuous change in the slope or curvature respectively of the meridian section of the tube, or, at entry, of the streamlines bounding the fluid entering the tube. The nature of these singularities is studied.


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