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Airscrews† at Supersonic Forward Speeds

Published online by Cambridge University Press:  07 June 2016

J. C. Burns
J. C. Burns*
Affiliation:
Department of Mathematics, The University, Manchester
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Summary

The flow past an airscrew rotating with uniform angular velocity in a uniform supersonic stream is considered from the point of view of axes fixed in the airscrew, the motion relative to these axes being steady. A linearised equation and boundary conditions are found for the potential of the disturbance flow caused by airscrews which produce only small perturbations in the main stream. This equation is solved by expanding the potential in powers of the ratio, χ, of the tip speed of the airscrew to the speed of sound in the undisturbed stream. Equations and boundary conditions are found for the coefficients of each term of the series and it is seen that the term independent of χ satisfies the ordinary linearised potential equation for fixed axes. By subtracting suitable special integrals, the more complicated equations for the coefficients of the various powers of χ can be reduced to this ordinary potential equation. Hadamard's methods have been applied by Puckett, Evvard and, finally, Ward to the problem of finding the flow past a thin wing fixed in a supersonic stream and their methods are applied to find the terms of the series in our case. The first two terms are found explicitly for a particular type of windmill. Approximate expressions are then developed for the torque and the drag on such a windmill and the results applied in special cases. The best working conditions for windmills of this type are found by considering the effect on efficiency and power of varying the shape and the speed of rotation, within the limits imposed by the strength of the material of the airscrew.

Type
Research Article
Information
Aeronautical Quarterly , Volume 3 , Issue 1 , May 1951 , pp. 23 - 50
Copyright
Copyright © Royal Aeronautical Society. 1951

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Footnotes

†

The word airscrew is used in this paper in its general sense, referring to any type of screw designed to rotate in air. Although the theory can be modified to deal with propellers, it is applied here to windmills.—Ed.

References

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