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Solution of the flow over a non-uniform heavily loaded ducted actuator disk

Published online by Cambridge University Press:  05 July 2013

R. Bontempo  and
M. Manna
R. Bontempo
Affiliation:
Dipartimento di Meccanica ed Energetica, Università degli Studi di Napoli Federico II, Via Claudio 21, 80125 Naples, Italy
M. Manna*
Affiliation:
Dipartimento di Meccanica ed Energetica, Università degli Studi di Napoli Federico II, Via Claudio 21, 80125 Naples, Italy
*
†Email address for correspondence: [email protected]
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Abstract

The paper presents an extension to ducted rotors of the nonlinear actuator disk theory of Conway (J. Fluid Mech., vol. 365, 1998, pp. 235–267) and it is exact for incompressible, axisymmetric and inviscid flows. The solution for the velocities and the Stokes stream function results from the superposition of ring vortices properly arranged along the duct surface and the wake region. Using a general analytical procedure the flow fields are given as a combination of one-dimensional integrals of expressions involving complete as well as incomplete elliptic integrals. The solution being exact, the proper shape of the slipstream whether converging or diverging is naturally accounted for, even for heavy loads. A semi-analytical method has been developed that enables the flow induced by an actuator disk housed in a contoured duct to be solved duly accounting for the nonlinear mutual interaction between the duct and the rotor. Non-uniform load distributions, rotor wake rotation and ducts of general shapes and thickness distribution can be dealt with. Thanks to its reduced numerical cost, the method is well suited for the design and/or analysis of ducted rotors for marine, wind and aeronautical applications.

JFM classification

Aerodynamics: Aerodynamics Mathematical Foundations: General fluid mechanics Mathematical Foundations: Mathematical Foundations
Type
Papers
Information
Journal of Fluid Mechanics , Volume 728 , 10 August 2013 , pp. 163 - 195
Copyright
©2013 Cambridge University Press 

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