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Some Finite Two-Dimensional Contractions

Published online by Cambridge University Press:  07 June 2016

R. D. Mills
R. D. Mills*
Affiliation:
Engineering Department, Cambridge University, †
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Summary

General solutions for two-dimensional incompressible potential flow occurring between two equipotential planes perpendicular to the x-axis are given. The first form is the two-dimensional analogue of Thwaites’s solution for axisymmetric flow and allows the calculation of the flow when the axial velocity distribution is specified as a Fourier cosine series in x. The second form of solution, obtained by “inverting” the first form, allows the calculation of the flow when the shape of the “boundary streamline” is specified by a similar series in the velocity potential ϕ.

It is shown how the second form of solution may be utilised to design contracting channels between equipotential planes. The computation of the contraction shapes and velocities is straightforward. In particular, contractions are derived from smoothing conditions similar to those used by Thwaites, and from a flow having a single (ϕ, y) step-discontinuity. It is shown in the Appendix that the latter flow possesses a closed form representation in terms of elliptic functions.

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Type
Research Article
Information
Aeronautical Quarterly , Volume 19 , Issue 1 , February 1968, pp. 91 - 104
Copyright
Copyright © Royal Aeronautical Society. 1968

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References

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