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Turbulent planar wakes under pressure gradient conditions

Published online by Cambridge University Press:  05 October 2017

Sina Shamsoddin
École Polytechnique Fédérale de Lausanne (EPFL), Wind Engineering and Renewable Energy Laboratory (WIRE), EPFL-ENAC-IIE-WIRE, CH-1015 Lausanne, Switzerland
Fernando Porté-Agel*
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:


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.

© 2017 Cambridge University Press 

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Bastankhah, M. & Porté-Agel, F. 2014 A new analytical model for wind-turbine wakes. J. Renew. Energy 70, 116123; special issue on aerodynamics of offshore wind energy systems and wakes.CrossRefGoogle Scholar
Liu, X., Thomas, F. O. & Nelson, R. C. 2002 An experimental investigation of the planar turbulent wake in constant pressure gradient. Phys. Fluids 14 (8), 28172838.CrossRefGoogle Scholar
Nakayama, A. 1987 Curvature and pressure-gradient effects on a small-defect wake. J. Fluid Mech. 175, 215246.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Rogers, M. M. 2002 The evolution of strained turbulent plane wakes. J. Fluid Mech. 463, 53120.CrossRefGoogle Scholar
Rumsey, C. L. & Ying, S. X. 2002 Prediction of high lift: review of present CFD capability. Prog. Aerosp. Sci. 38 (2), 145180.CrossRefGoogle Scholar
Smith, A. M. O. 1975 High-lift aerodynamics. J. Aircraft 12 (6), 501530.CrossRefGoogle Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.Google Scholar
Thomas, F. O. & Liu, X. 2004 An experimental investigation of symmetric and asymmetric turbulent wake development in pressure gradient. Phys. Fluids 16 (5), 17251745.CrossRefGoogle Scholar
Wygnanski, I., Champagne, F. & Marasli, B. 1986 On the large-scale structures in two-dimensional, small-deficit, turbulent wakes. J. Fluid Mech. 168, 3171.CrossRefGoogle Scholar