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Effect of small roughness elements on thermal statistics of a turbulent boundary layer at moderate Reynolds number

Published online by Cambridge University Press:  08 December 2015

Ali Doosttalab ,
Guillermo Araya ,
Jensen Newman ,
Ronald J. Adrian ,
Kenneth Jansen  and
Luciano Castillo
Ali Doosttalab
Affiliation:
Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79409, USA
Guillermo Araya*
Affiliation:
Department of Mechanical Engineering, University of Puerto Rico – Mayagüez, PR 00681, USA
Jensen Newman
Affiliation:
Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79409, USA
Ronald J. Adrian
Affiliation:
School for Engineering of Matter, Transport and Energy, Arizona State University, P.O. Box 876106, Tempe, AZ 85287-6106, USA
Kenneth Jansen
Affiliation:
Department of Aerospace Engineering Sciences, University of Colorado at Boulder, Boulder, CO 80309, USA
Luciano Castillo
Affiliation:
Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79409, USA
*
†Email address for correspondence: araya@mailaps.org
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Abstract

A zero-pressure-gradient turbulent boundary layer flowing over a transitionally rough surface (24-grit sandpaper) with $k^{+}\approx 11$ and a momentum-thickness Reynolds number of approximately 2400 is studied using direct numerical simulation (DNS). Heat transfer between the isothermal rough surface and the turbulent flow with molecular Prandtl number $Pr=0.71$ is simulated. The dynamic multiscale approach developed by Araya et al. (J. Fluid Mech., vol. 670, 2011, pp. 581–605) is employed to prescribe realistic time-dependent thermal inflow boundary conditions. In general, the rough surface reduces mean and fluctuating temperature profiles with respect to the smooth surface flow when normalized by Wang & Castillo (J. Turbul., vol. 4, 2003, 006) inner/outer scaling. It is shown that the Reynolds analogy does not hold for $y^{+}<9$. In this region the value of the turbulent Prandtl number departs substantially from unity. Above this region the Reynolds analogy is only approximately valid, with the turbulent Prandtl number decreasing from 1 to 0.7 across the boundary layer for rough and smooth walls. In comparison with the smooth-wall case, the turbulent transport of heat per unit mass, $\overline{v^{\prime }v^{\prime }{\it\theta}^{\prime }}$, towards the wall is enhanced in the buffer layer, but the transport of $\overline{v^{\prime }v^{\prime }{\it\theta}^{\prime }}$ away from the wall is reduced in the outer layer for the rough case; similar behaviour is found for the vertical transport of turbulent momentum per unit mass, $\overline{v^{\prime }u^{\prime }v^{\prime }}$. Above the roughness sublayer (3$k$–5$k$) it is found that most of the temperature field statistics, including higher-order moments and conditional averages, are highly similar for the smooth and rough surface flow, showing that the Townsend’s Reynolds number similarity hypothesis applies for the thermal field as well as the velocity field for the Reynolds number and $k^{+}$ considered in this study.

JFM classification

Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 787 , 25 January 2016 , pp. 84 - 115
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© 2015 Cambridge University Press 

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