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A model for the effect of pressure gradient on turbulent axisymmetric wakes

Published online by Cambridge University Press:  04 January 2018

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

Turbulent axisymmetric wakes under pressure gradient have received little attention in the literature, in spite of their fundamental and practical importance, for example, in the case of wind turbine wakes over topography. In this paper, we develop an analytical framework to analyse turbulent axisymmetric wakes under different pressure gradient conditions. Specifically, we develop a model to predict how an arbitrary imposed pressure gradient perturbs the evolution of the zero-pressure-gradient wake. The starting point of the model is the basic mean conservation of the streamwise momentum equation. We take advantage of the self-similarity of the wake velocity deficit and the assumption that the ratio of the maximum velocity deficit to the wake width is independent of the pressure gradient; such an assumption is supported experimentally for planar wakes, and numerically for axisymmetric wakes in this study. Furthermore, an asymptotic solution for the problem is also derived. The problem is considered for both an axisymmetric strain and a planar strain. The inputs to the model are the imposed pressure gradient and the wake width in the zero-pressure-gradient case. To validate the model results, a set of large-eddy simulations (LES) are performed. Comparing the evolution of the maximum velocity deficit and the wake width, the model results and the LES data show good agreement. Similarly to planar wakes, it is observed that the axisymmetric wake recovers faster in the favourable pressure gradient compared with the adverse one.

JFM classification

Mathematical Foundations: General fluid mechanics Turbulent Flows: Turbulent Flows Wakes/Jets: Wakes
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 837 , 25 February 2018 , R3
Copyright
© 2018 Cambridge University Press 

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