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The minimal-span channel for rough-wall turbulent flows

  • M. MacDonald (a1), D. Chung (a1), N. Hutchins (a1), L. Chan (a2), A. Ooi (a1) and R. García-Mayoral (a3)...

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.

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Corresponding author

Email address for correspondence: michael.macdonald@unimelb.edu.au

References

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del Álamo, J. C., Jimenez, J., Zandonade, P. & Moser, R. D. 2006 Self-similar vortex clusters in the turbulent logarithmic region. J. Fluid Mech. 561, 329358.
Benedict, L. H. & Gould, R. D. 1996 Towards better uncertainty estimates for turbulence statistics. Exp. Fluids 22 (2), 129136.
Bernardini, M., Pirozzoli, S., Quadrio, M. & Orlandi, P. 2013 Turbulent channel flow simulations in convecting reference frames. J. Comput. Phys. 232 (1), 16.
Borrell, G.2015 Entrainment effects in turbulent boundary layers. PhD thesis, Universidad Politécnica de Madrid.
Busse, A. & Sandham, N. D. 2012 Parametric forcing approach to rough-wall turbulent channel flow. J. Fluid Mech. 712, 169202.
Chan, L., MacDonald, M., Chung, D., Hutchins, N. & Ooi, A. 2015 A systematic investigation of roughness height and roughness wavelength in turbulent pipe flow in the transitionally rough regime. J. Fluid Mech. 771, 743777.
Chin, C., Ooi, A. S. H., Marusic, I. & Blackburn, H. M. 2010 The influence of pipe length on turbulence statistics computed from direct numerical simulation data. Phys. Fluids 22 (11), 115107.
Choi, H. & Moin, P. 1994 Effects of the computational time step on numerical solutions of turbulent flow. J. Comput. Phys. 113 (1), 14.
Chung, D., Chan, L., MacDonald, M., Hutchins, N. & Ooi, A. 2015 A fast direct numerical simulation method for characterising hydraulic roughness. J. Fluid Mech. 773, 418431.
Chung, D., Monty, J. P. & Ooi, A. 2014 An idealised assessment of Townsend’s outer-layer similarity hypothesis for wall turbulence. J. Fluid Mech. 742, R3.
Dean, R. B. 1978 Reynolds number dependence of skin friction and other bulk flow variables in two-dimensional rectangular duct flow. J. Fluids Engng 100 (2), 215223.
Di Cicca, G. M. & Onorato, M. 2016 Roughness sub-layer investigation of a turbulent boundary layer. J. Turbul. 17 (1), 5174.
Flack, K. A., Schultz, M. P. & Shapiro, T. A. 2005 Experimental support for Townsend’s Reynolds number similarity hypothesis on rough walls. Phys. Fluids 17 (3), 035102.
Flores, O. & Jiménez, J. 2006 Effect of wall-boundary disturbances on turbulent channel flows. J. Fluid Mech. 566, 357376.
Flores, O. & Jiménez, J. 2010 Hierarchy of minimal flow units in the logarithmic layer. Phys. Fluids 22 (7), 071704.
Ham, F. & Iaccarino, G. 2004 Energy conservation in collocated discretization schemes on unstructured meshes. In Annual Research Briefs 2004, pp. 314. Center for Turbulence Research, Stanford University/NASA Ames.
Hama, F. R. 1954 Boundary-layer characteristics for smooth and rough surfaces. Trans. Soc. Nav. Archit. Mar. Engrs 62, 333358.
Hamilton, J. M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317348.
Handler, R. A., Saylor, J. R., Leighton, R. I. & Rovelstad, A. L. 1999 Transport of a passive scalar at a shear-free boundary in fully developed turbulent open channel flow. Phys. Fluids 11 (9), 26072625.
Hong, J., Katz, J. & Schultz, M. P. 2011 Near-wall turbulence statistics and flow structures over three-dimensional roughness in a turbulent channel flow. J. Fluid Mech. 667, 137.
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to Re 𝜏 = 2003. Phys. Fluids 18 (1), 011702.
Hoyas, S. & Jiménez, J. 2008 Reynolds number effects on the Reynolds-stress budgets in turbulent channels. Phys. Fluids 20 (10), 101511.
Hwang, Y. 2013 Near-wall turbulent fluctuations in the absence of wide outer motions. J. Fluid Mech. 723, 264288.
Hwang, Y. 2015 Statistical structure of self-sustaining attached eddies in turbulent channel flow. J. Fluid Mech. 767, 254289.
Hwang, Y. & Bengana, Y. 2016 Self-sustaining process of minimal attached eddies in turbulent channel flow. J. Fluid Mech. 795, 708738.
Jeong, J., Hussain, F., Schoppa, W. & Kim, J. 1997 Coherent structures near the wall in a turbulent channel flow. J. Fluid Mech. 332, 185214.
Jiménez, J. 2004 Turbulent flows over rough walls. Annu. Rev. Fluid Mech. 36, 173196.
Jiménez, J. 2015 Direct detection of linearized bursts in turbulence. Phys. Fluids 27 (1), 065102.
Jiménez, J., Kawahara, G., Simens, M. P., Nagata, M. & Shiba, M. 2005 Characterization of near-wall turbulence in terms of equilibrium and bursting solutions. Phys. Fluids 17 (1), 015105.
Jiménez, J. & Moin, P. 1991 The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213240.
Jiménez, J. & Pinelli, A. 1999 The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389 (1), 335359.
Jones, M. B., Marusic, I. & Perry, A. E. 2001 Evolution and structure of sink-flow turbulent boundary layers. J. Fluid Mech. 428, 127.
Kim, J. 1989 On the structure of pressure fluctuations in simulated turbulent channel flow. J. Fluid Mech. 205, 421451.
Kim, K. C. & Adrian, R. J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11 (2), 417422.
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59 (2), 308323.
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30 (04), 741773.
Kozul, M., Chung, D. & Monty, J. P. 2016 Direct numerical simulation of the incompressible temporally developing turbulent boundary layer. J. Fluid Mech. 796, 437472.
Lee, M. & Moser, R. D. 2015 Direct numerical simulation of turbulent channel flow up to Re 𝜏 ≈ 5200. J. Fluid Mech. 774, 395415.
Lenaers, P., Schlatter, P., Brethouwer, G. & Johansson, A. V. 2014 A new high-order method for the simulation of incompressible wall-bounded turbulent flows. J. Comput. Phys. 272, 108126.
Leonardi, S. & Castro, I. P. 2010 Channel flow over large cube roughness: a direct numerical simulation study. J. Fluid Mech. 651, 519539.
Lozano-Durán, A. & Jiménez, J. 2014 Effect of the computational domain on direct simulations of turbulent channels up to Re 𝜏 = 4200. Phys. Fluids 26 (1), 011702.
Lundbladh, A., Berlin, S., Skote, M., Hildings, C., Choi, J., Kim, J. & Henningson, D. S.1999 An efficient spectral method for simulation of incompressible flow over a flat plate. Tech. Rep. TRITA-MEK 1999:11. Royal Institute of Technology, Stockholm.
MacDonald, M., Chan, L., Chung, D., Hutchins, N. & Ooi, A. 2016 Turbulent flow over transitionally rough surfaces with varying roughness density. J. Fluid Mech. 804, 130161.
Mahesh, K., Constantinescu, G. & Moin, P. 2004 A numerical method for large-eddy simulation in complex geometries. J. Comput. Phys. 197, 215240.
Marusic, I., Monty, J. P., Hultmark, M. & Smits, A. J. 2013 On the logarithmic region in wall turbulence. J. Fluid Mech. 716, R3.
Mizuno, Y. & Jiménez, J. 2013 Wall turbulence without walls. J. Fluid Mech. 723, 429455.
Munters, W., Meneveau, C. & Meyers, J. 2016 Shifted periodic boundary conditions for simulations of wall-bounded turbulent flows. Phys. Fluids 28 (2), 025112.
Nagib, H. M. & Chauhan, K. A. 2008 Variations of von Kármán coefficient in canonical flows. Phys. Fluids 20, 101518.
Nikuradse, J.1933 Laws of flow in rough pipes. English translation published 1950, NACA Tech. Mem. 1292.
Oliver, T. A., Malaya, N., Ulerich, R. & Moser, R. D. 2014 Estimating uncertainties in statistics computed from direct numerical simulation. Phys. Fluids 26 (3), 035101.
Patel, V. C. 1965 Calibration of the preston tube and limitations on its use in pressure gradients. J. Fluid Mech. 23 (01), 185208.
Perry, A. E. & Joubert, P. N. 1963 Rough-wall boundary layers in adverse pressure gradients. J. Fluid Mech. 17 (02), 193211.
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.
Raupach, M. R. 1981 Conditional statistics of Reynolds stress in rough-wall and smooth-wall turbulent boundary layers. J. Fluid Mech. 108, 363382.
Raupach, M. R., Antonia, R. A. & Rajagopalan, S. 1991 Rough-wall turbulent boundary layers. Appl. Mech. Rev. 44 (1), 125.
Schultz, M. P. & Flack, K. A. 2009 Turbulent boundary layers on a systematically varied rough wall. Phys. Fluids 21, 015104.
Seddighi, M., He, S., Vardy, A. E. & Orlandi, P. 2014 Direct numerical simulation of an accelerating channel flow. Flow Turbul. Combust. 92 (1–2), 473502.
Sekimoto, A., Dong, S. & Jiménez, J. 2016 Direct numerical simulation of statistically stationary and homogeneous shear turbulence and its relation to other shear flows. Phys. Fluids 28, 035101.
Spalart, P. R. & McLean, J. D. 2011 Drag reduction: enticing turbulence, and then an industry. Phil. Trans. R. Soc. Lond. A 369 (1940), 15561569.
Spalart, P. R., Moser, R. D. & Rogers, M. M. 1991 Spectral methods for the Navier–Stokes equations with one infinite and two periodic directions. J. Comput. Phys. 96 (2), 297324.
Toh, S. & Itano, T. 2005 Interaction between a large-scale structure and near-wall structures in channel flow. J. Fluid Mech. 524, 249262.
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.
Trenberth, K. E. 1984 Some effects of finite sample size and persistence on meteorological statistics. Part I: autocorrelations. Mon. Weath. Rev. 112 (12), 23592368.
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The minimal-span channel for rough-wall turbulent flows

  • M. MacDonald (a1), D. Chung (a1), N. Hutchins (a1), L. Chan (a2), A. Ooi (a1) and R. García-Mayoral (a3)...

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