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The minimal-span channel for rough-wall turbulent flows

Published online by Cambridge University Press:  28 February 2017

M. MacDonald Open the ORCID record for M. MacDonald [Opens in a new window] ,
D. Chung Open the ORCID record for D. Chung [Opens in a new window] ,
N. Hutchins ,
L. Chan Open the ORCID record for L. Chan [Opens in a new window] ,
A. Ooi  and
R. García-Mayoral
M. MacDonald*
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Victoria 3010, Australia
D. Chung
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Victoria 3010, Australia
N. Hutchins
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Victoria 3010, Australia
L. Chan
Affiliation:
Department of Mechanical Engineering, Universiti Tenaga Nasional, Kajang 43000, Malaysia
A. Ooi
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Victoria 3010, Australia
R. García-Mayoral
Affiliation:
Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK
*
†Email address for correspondence: michael.macdonald@unimelb.edu.au
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Abstract

Roughness predominantly alters the near-wall region of turbulent flow while the outer layer remains similar with respect to the wall shear stress. This makes it a prime candidate for the minimal-span channel, which only captures the near-wall flow by restricting the spanwise channel width to be of the order of a few hundred viscous units. Recently, Chung et al. (J. Fluid Mech., vol. 773, 2015, pp. 418–431) showed that a minimal-span channel can accurately characterise the hydraulic behaviour of roughness. Following this, we aim to investigate the fundamental dynamics of the minimal-span channel framework with an eye towards further improving performance. The streamwise domain length of the channel is investigated with the minimum length found to be three times the spanwise width or 1000 viscous units, whichever is longer. The outer layer of the minimal channel is inherently unphysical and as such alterations to it can be performed so long as the near-wall flow, which is the same as in a full-span channel, remains unchanged. Firstly, a half-height (open) channel with slip wall is shown to reproduce the near-wall behaviour seen in a standard channel, but with half the number of grid points. Next, a forcing model is introduced into the outer layer of a half-height channel. This reduces the high streamwise velocity associated with the minimal channel and allows for a larger computational time step. Finally, an investigation is conducted to see if varying the roughness Reynolds number with time is a feasible method for obtaining the full hydraulic behaviour of a rough surface. Currently, multiple steady simulations at fixed roughness Reynolds numbers are needed to obtain this behaviour. The results indicate that the non-dimensional pressure gradient parameter must be kept below 0.03–0.07 to ensure that pressure gradient effects do not lead to an inaccurate roughness function. An empirical costing argument is developed to determine the cost in terms of CPU hours of minimal-span channel simulations a priori. This argument involves counting the number of eddy lifespans in the channel, which is then related to the statistical uncertainty of the streamwise velocity. For a given statistical uncertainty in the roughness function, this can then be used to determine the simulation run time. Following this, a finite-volume code with a body-fitted grid is used to determine the roughness function for square-based pyramids using the above insights. Comparisons to experimental studies for the same roughness geometry are made and good agreement is observed.

JFM classification

Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 816 , 10 April 2017 , pp. 5 - 42
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© 2017 Cambridge University Press 

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