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Numerical and experimental study of mechanisms responsible for turbulent secondary flows in boundary layer flows over spanwise heterogeneous roughness

Published online by Cambridge University Press:  06 March 2015

William Anderson ,
Julio M. Barros ,
Kenneth T. Christensen  and
Ankit Awasthi
William Anderson*
Affiliation:
Mechanical Engineering Department, University of Texas at Dallas, Richardson, TX 75080, USA
Julio M. Barros
Affiliation:
Department of Mechanical Engineering, United States Naval Academy, Annapolis, MD 21402, USA
Kenneth T. Christensen
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN 46556, USA International Institute for Carbon-Neutral Energy Research (WPI-I2CNER), Kyushu University, Nishi-ku, Fukuoka 819-0395, Japan
Ankit Awasthi
Affiliation:
Mechanical Engineering Department, University of Texas at Dallas, Richardson, TX 75080, USA
*
†Email address for correspondence: [email protected]
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Abstract

We study the dynamics of turbulent boundary layer flow over a heterogeneous topography composed of roughness patches exhibiting relatively high and low correlation in the streamwise and spanwise directions, respectively (i.e. the roughness appears as streamwise-aligned ‘strips’). It has been reported that such roughness induces a spanwise-wall normal mean secondary flow in the form of mean streamwise vorticity associated with counter-rotating boundary-layer-scale circulations. Here, we demonstrate that this mean secondary flow is Prandtl’s secondary flow of the second kind, both driven and sustained by spatial gradients in the Reynolds-stress components, which cause a subsequent imbalance between production and dissipation of turbulent kinetic energy that necessitates secondary advective velocities. In reaching this conclusion, we study (i) secondary circulations due to spatial gradients of turbulent kinetic energy, and (ii) the production budgets of mean streamwise vorticity by gradients of the Reynolds stresses. We attribute the secondary flow phenomena to extreme peaks of surface stress on the relatively high-roughness regions and associated elevated turbulence production in the fluid immediately above. An optimized state is attained by entrainment of fluid exhibiting the lowest turbulent stresses – from above – and subsequent lateral ejection in order to preserve conservation of mass.

JFM classification

Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulent Flows
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Papers
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Journal of Fluid Mechanics , Volume 768 , 10 April 2015 , pp. 316 - 347
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© 2015 Cambridge University Press 

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