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Solution of the wedge entry problem by numerical conformal mapping

Published online by Cambridge University Press:  29 March 2006

O. F. Hughes
O. F. Hughes
Affiliation:
School of Mechanical and Industrial Engineering, The University of New South Wales
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Abstract

An accurate quasi-analytic method of solution is presented for the classical hydrodynamics problem of the constant-velocity entry of a prismatic wedge into a weightless incompressible inviscid fluid. The method uses the Wagner function W, which reduces the problem to the determination of a mapping function Λ = [Lscr ](W) for the hodograph. [Lscr ](W) is constructed by using the hodograph for an unsymmetric diamond together with a modifying or ‘preparatory’ trans-formation. A computer method of conformal mapping is developed and is used to obtain this latter transformation. Results are presented for the case of a 90° wedge and show that the solution is both more accurate than previous solutions, having an error of less than 1 %, and more complete, as it portrays the entire flow field and furnishes information about the functional dependence among the variables.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 56 , Issue 1 , 14 November 1972 , pp. 173 - 192
Copyright
© 1972 Cambridge University Press

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