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Turbulent planar wakes under pressure gradient conditions

Published online by Cambridge University Press:  05 October 2017

Sina Shamsoddin  and
Fernando Porté-Agel Open the ORCID record for Fernando Porté-Agel [Opens in a new window]
Sina Shamsoddin
Affiliation:
École Polytechnique Fédérale de Lausanne (EPFL), Wind Engineering and Renewable Energy Laboratory (WIRE), EPFL-ENAC-IIE-WIRE, CH-1015 Lausanne, Switzerland
Fernando Porté-Agel*
Affiliation:
École Polytechnique Fédérale de Lausanne (EPFL), Wind Engineering and Renewable Energy Laboratory (WIRE), EPFL-ENAC-IIE-WIRE, CH-1015 Lausanne, Switzerland
*
†Email address for correspondence: [email protected]
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Abstract

Accurate prediction of the spatial evolution of turbulent wake flows under pressure gradient conditions is required in some engineering applications such as the design of high-lift devices and wind farms over topography. In this paper, we aim to develop an analytical model to predict the evolution of a turbulent planar wake under an arbitrary pressure gradient condition. The model is based on the cross-stream integration of the streamwise momentum equation and uses the self-similarity of the mean flow. We have also made an experimentally supported assumption that the ratio of the maximum velocity deficit to the wake width is independent of the imposed pressure gradient. The asymptotic response of the wake to the pressure gradient is also investigated. After its derivation, the model is successfully validated against experimental data by comparing the evolution of the wake width and maximum velocity deficit. The inputs of the model are the imposed pressure gradient and the wake width under zero pressure gradient. The model does not require any parameter tuning and is deemed to be practical, computationally fast, accurate enough, and therefore useful for the scientific and engineering communities.

JFM classification

Mathematical Foundations: General fluid mechanics Mathematical Foundations: Mathematical Foundations Wakes/Jets: Wakes
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 830 , 10 November 2017 , R4
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Copyright
© 2017 Cambridge University Press 

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