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On optimum profiles in Stokes flow

Published online by Cambridge University Press:  29 March 2006

O. Pironneau
O. Pironneau
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Abstract

In this paper, we obtain the first-order necessary optimality conditions of an optimal control problem for a distributed parameter system with geometric control, namely, the minimum-drag problem in Stokes flow (flow at a very low Reynolds number). We find that the unit-volume body with smallest drag must be such that the magnitude of the normal derivative of the velocity of the fluid is constant on the boundary of the body. In a three-dimensional uniform flow, this condition implies that the body with minimum drag has the shape of a pointed body similar in general shape to a prolate spheroid but with some differences including conical front and rear ends of angle 120°.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 59 , Issue 1 , 5 June 1973 , pp. 117 - 128
Copyright
© 1973 Cambridge University Press

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References

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