Hostname: page-component-7479d7b7d-qs9v7 Total loading time: 0 Render date: 2024-07-12T00:27:17.420Z Has data issue: false hasContentIssue false
  • English
  • Français

Direct simulations of a rough-wall channel flow

Published online by Cambridge University Press:  04 January 2007

TOMOAKI IKEDA  and
PAUL A. DURBIN
TOMOAKI IKEDA
Affiliation:
Department of Aeronautics and Astronautics, Stanford University, CA94305, USA
PAUL A. DURBIN
Affiliation:
Department of Aerospace Engineering, Iowa State University, IA 50011, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

In this study, we performed simulations of turbulent flow over rectangular ribs transversely mounted on one side of a plane in a channel, with the other side being smooth. The separation between ribs is large enough to avoid forming stable vortices in the spacing, which exhibits k-type, or sand-grain roughness. The Reynolds number Reτ of our representative direct numerical simulation case is 460 based on the smooth-wall friction velocity and the channel half-width. The roughness height h is estimated as 110 wall units based on the rough-wall friction velocity. The velocity profile and kinetic energy budget verify the presence of an equilibrium, logarithmic layer at y≳2h. In the roughness sublayer, however, a significant turbulent energy flux was observed. A high-energy region is formed by the irregular motions just above the roughness. Visualizations of vortical streaks, disrupted in all three directions in the roughness sublayer, indicate that the three-dimensional flow structure of sand-grain roughness is replicated by the two-dimensional roughness, and that this vortical structure is responsible for the high energy production. The difference in turbulence structure between smooth- and rough-wall layers can also be seen in other flow properties, such as anisotropy and turbulence length scales.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 571 , 25 January 2007 , pp. 235 - 263
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Akselvoll, K. & Moin, P. 1995 Large eddy simulation of turbulent confined coannular jets and turbulent flow over a backward facing step. Rep. TF-63, Thermosciences Division, Dept. of Mechanical Engineering, Stanford University.CrossRefGoogle Scholar
Arora, R., Kuo, K. K. & Razdan, M. K. 1982 Near-wall treatment for turbulent boudary-layer computations. AIAA J. 20, 1481–1482.CrossRefGoogle Scholar
Ashrafian, A. & Andersson, H. I. 2003 DNS of turbulent flow in a rod-roughened channel. In Proc. Third Intl Symp. on Turbulence and Shear Flow Phenomena, vol. 1, pp. 117–122. Sendai, Japan.CrossRefGoogle Scholar
Bandyopadhyay, P. R. 1985 Rough-wall turbulent boundary layers in the transition regime. J. Fluid Mech. 180, 231–266.CrossRefGoogle Scholar
Browne, L. W. B., Antonia, R. A. & Shah, D. A. 1987 Turbulent energy dissipation in a wake. J. Fluid Mech. 179, 307–326.CrossRefGoogle Scholar
Brunet, Y. & Irvine, M. R. 2000 The control of coherent eddies in vegetation canopies: streamwise structure spacing, canopy shear scale and atmospheric stability. Boundary-Layer Met. 94, 139–163.CrossRefGoogle Scholar
Butler, K. M. & Farrell, B. F. 1992 Three-dimensional optimal perturbations in viscous shear flow. Phys. Fluids 4 (8), 1637–1650.CrossRefGoogle Scholar
Cherukat, P., Na, Y., Hanratty, T. J. & McLaughlin, J. B. 1998 Direct numerical simulation of a fully developed turbulent flow over a wavy wall. Theoret. Comput. Fluid Dyn. 11, 109–134.CrossRefGoogle Scholar
Cui, J., Patel, V. C. & Lin, C.-L. 2003 Large-eddy simulation of turbulent flow in a channel with rib roughness. Intl J. Heat Fluid Flow 24, 372–388.CrossRefGoogle Scholar
De Angelis, V., Lombardi, P. & Banerjee, S. 1997 Direct numerical simulation of turbulent flow over a wavy wall. Phys. Fluids 9, 2429–2442.CrossRefGoogle Scholar
Djenidi, L., Elavarasan, R. & Antonia, R. A. 1999 The turbulent boundary layer over transverse square cavities. J. Fluid Mech. 395, 271–294.CrossRefGoogle Scholar
Durbin, P. A. 1991 Near-wall turbulence closure modeling without ‘damping functions’. Theoret. Comput. Fluid Dyn. 3, 1–13.CrossRefGoogle Scholar
Durbin, P. A. 1995 Separated flow computations with the k–ϵ–v 2 model. AIAA J. 33, 659–664.CrossRefGoogle Scholar
Durbin, P. A., Medic, G., Seo, J.-M., Song, S. & Eaton, J. K. 2001 Rough wall modification of two-layer k–ϵ. Trans. ASME I: J. Fluids Engng 123, 16–21.Google Scholar
Finnigan, J. 2000 Turbulence in plant canopies. Annu. Rev. Fluid Mech. 32, 519–571.CrossRefGoogle Scholar
Hanjalić, K. & Launder, B. E. 1972 Fully developed asymmetric flow in a plane channel. J. Fluid Mech. 51, 301–335.CrossRefGoogle Scholar
Ikeda, T. & Durbin, P. A. 2002 Direct simulations of a rough-wall channel flow. Rep. TF-81, Flow Physics and Computation Division, Dept. of Mechanical Engineering, Stanford University.Google Scholar
Ikeda, T. & Durbin, P. A. 2004 Mesh stretch effects on convection in flow simulations. J. Comput. Phys. 123, 110–125.CrossRefGoogle Scholar
Jackson, P. S. 1981 On the displacement height in the logarithmic velocity profile. J. Fluid Mech. 111, 15–25.CrossRefGoogle Scholar
Judd, M. J., Raupach, M. R. & Finnigan, J. J. 1996 A wind tunnel study of turbulent flow around single and multiple windbreaks; Part I: Velocity fields. Boundary-Layer Met. 80, 127–165.CrossRefGoogle Scholar
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308–323.CrossRefGoogle Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.CrossRefGoogle Scholar
Krogstad, P.-M. & Antonia, R. A. 1994 Structure of turbulent boundary layers on smooth and rough walls. J. Fluid Mech. 277, 1–21.CrossRefGoogle Scholar
Krogstad, P.-M., Antonia, R. A. & Browne, L. W. B. 1992 Comparison between rough- and smooth-wall turbulent boundary layers. J. Fluid Mech. 245, 599–617.CrossRefGoogle Scholar
Lee, J. 1996 Modeling boundary layer flows over rough surfaces using a modified Chien k–ϵ turbulence model. AIAA-96-0384.CrossRefGoogle Scholar
Leonardi, S., Orlandi, P., Djenidi, L. & Antonia, R. A. 2003a Structure of turbulent channel flow with square bars on one wall. In Proc. Third Intl Symp. on Turbulence and Shear Flow Phenomena, vol. 1, pp. 123–128. Sendai, Japan.CrossRefGoogle Scholar
Leonardi, S., Orlandi, P., Smalley, R. J., Djenidi, L. & Antonia, R. A. 2003b Direct numerical simulations of turbulent channel flow with transverse square bars on the wall. J. Fluid Mech. 491, 229–238.CrossRefGoogle Scholar
Ligrani, P. M. & Moffat, R. J. 1986 Structure of transitionally rough and fully rough turbulent boundary layers. J. Fluid Mech. 162, 69–98.CrossRefGoogle Scholar
Miyake, Y., Tsujimoto, K. & Nakaji, M. 2001 Direct numerical simulation of rough-wall heat transfer in a turbulent channel flow. Intl J. Heat Fluid Flow 22, 237–244.CrossRefGoogle Scholar
Moser, R. D., Kim, J. & Mansour, N. N. 1999 Direct numerical simulation of turbulent channel flow up to Re τ=590. Phys. Fluids 11 (4), 943–945.CrossRefGoogle Scholar
Nagano, Y., Hattori, H. & Houra, T. 2004 DNS of velocity and thermal fields in turbulent channel flow with transverse-rib roughness. Intl J. Heat Fluid Flow 25, 393–403.CrossRefGoogle Scholar
Nikuradse, J. 1933 Strömungsgesetze in rauhen Rohren. Forschungsheft Arb. Ing.-Wes. 361.Google Scholar
Novak, M. D., Warland, J. S., Orchansky, A. L., Ketler, R. & Green, S. 2000 Comparison between wind tunnel and field measurements of turbulent flow. Part I: Uniformly thinned forests. Boundary-Layer Met. 95, 457–495.CrossRefGoogle Scholar
Perry, A. E. & Joubert, P. N. 1963 Rough-wall boundary layers in adverse pressure gradients. J. Fluid Mech. 17, 193–211.CrossRefGoogle Scholar
Perry, A. E., Schofield, W. H. & Joubert, P. N. 1969 Rough wall turbulent boundary layers. J. Fluid Mech. 37, 383–413.CrossRefGoogle Scholar
Perry, A. E., Henbest, S. M. & Chong, M. S. 1986 A theoretical and experimental study of wall turbulence. J. Fluid Mech. 165, 163–199.CrossRefGoogle Scholar
Poggi, D., Porporato, A., Ridolfi, L., Albertson, J. D. & Katul, G. G. 2004b The effect of vegetation density on canopy sub-layer turbulence. Boundary-Layer Met. 111, 565–587.CrossRefGoogle Scholar
Poggi, D., Katul, G. G. & Albertson, J. D. 2004b Momentum transfer and turbulent kinetic energy budgets within a dense model canopy. Boundary-Layer Met. 111, 589–614.CrossRefGoogle Scholar
Raupach, M. R. 1981 Conditional statistics of Reynolds stress in rough-wall and smooth-wall turbulent boundary layers. J. Fluid Mech. 108, 363–382.CrossRefGoogle Scholar
Raupach, M. R. & Shaw, R. H. 1982 Averaging procedures for flow within vegetation canopies. Boundary-Layer Met. 22, 79–90.CrossRefGoogle Scholar
Raupach, M. R., Antonia, R. A. & Rajagopalan, S. 1991 Rough-wall turbulent boundary layers. Appl. Mech. Rev. 44, 1–25.CrossRefGoogle Scholar
Raupach, M. R., Finnigan, J. J. & Brunet, Y. 1996 Coherent eddies and turbulence in vegetation canopies: the mixing layer analogy. Boundary-Layer Met. 78, 351–382.CrossRefGoogle Scholar
Rogers, S. E. & Kwak, D. 1990 Upwind differencing scheme for the time-accurate incompressible Navier–Stokes equations. AIAA J. 28, 253–262.CrossRefGoogle Scholar
Schlichting, H. 1979 Boundary-Layer Theory, 7th edn. McGraw–Hill.Google Scholar
Seo, J.-M. 2004 Closure modeling and numerical simulation for turbulent flows: wall roughness model, realizability and turbine blade heat transfer. PhD thesis, Stanford University.Google Scholar
Shafi, H. S. & Antonia, R. A. 1997 Small-scale characteristics of a turbulent boundary layer over a rough wall. J. Fluid Mech. 342, 263–293.CrossRefGoogle Scholar
Shah, K. B. & Ferziger, J. H. 1998 Large eddy simulations of flow past a cubic obstacle. PhD thesis, Stanford University.Google Scholar
Spalart, P. R. 1987 Hybrid RKW3 + Crank–Nicolson scheme. Internal Rep. NASA-Ames Research Center, Moffett Field, CA.Google Scholar
Spalart, P. R. & Allmaras, S. R. 1994 A one-equation turbulence model for aerodynamic flows. Rech. Aérosp. 1, 5–21.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.CrossRefGoogle Scholar
Wilson, N. R. & Shaw, R. H. 1977 A higher order closure model for canopy flow. J. Appl. Met. 16, 1198–1205.2.0.CO;2>CrossRefGoogle Scholar
Yang, K. & Ferziger, J. H. 1993 Large-eddy simulation of turbulent obstacle flow using a dynamic subgrid-scale model. AIAA J. 31, 1406–1413.CrossRefGoogle Scholar
Zhuang, Y. & Wilson, J. D. 1994 Coherent motions in windbreak flow. Boundary-Layer Met. 70, 151–169.CrossRefGoogle Scholar