Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-23T09:14:58.777Z Has data issue: false hasContentIssue false
  • English
  • Français

Direct numerical simulation of the incompressible temporally developing turbulent boundary layer

Published online by Cambridge University Press:  05 May 2016

M. Kozul ,
D. Chung  and
J. P. Monty
M. Kozul*
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Victoria 3010, Australia
D. Chung
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Victoria 3010, Australia
J. P. Monty
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Victoria 3010, Australia
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We perform a direct numerical simulation (DNS) investigation of the incompressible temporally developing turbulent boundary layer. The approach is inspired by temporal simulations of flows which are generally thought of as developing in space, such as wakes and mixing layers. Compressible boundary layers have previously been studied in this manner yet the temporal approach appears to be under-exploited in the literature concerning incompressible boundary layers. The flow is the turbulent counterpart to the laminar Rayleigh problem or Stokes’ first problem, in which a fluid at rest is set into motion by a wall moving at constant velocity. An initial profile that models the effect of a wall-mounted trip wire is implemented and allows the characterisation of initial conditions by a trip Reynolds number. For the current set-up, a trip Reynolds number of 500 based on the trip-wire diameter successfully triggers transition yet only mildly perturbs the flow so it assumes a natural development at the lowest possible Reynolds number based on momentum thickness. A systematic trip study reveals that as the ratio of momentum thickness to trip-wire diameter approaches unity, our flow approaches a state free from the effects of its starting trip Reynolds number. The transport of a passive scalar by this flow is also simulated. The role played by domain size is investigated with two boxes, sized to accommodate two chosen final Reynolds numbers. Comparisons of the skin friction coefficient, velocity and scalar statistics demonstrate that the temporally developing boundary layer is a good model for the spatially developing boundary layer once initial conditions can be neglected. Analysis of similarity solutions suggests such a rapprochement of the spatial and temporal boundary layers may be expected at high Reynolds numbers given that the only terms that asymptotically persist are those common to both cases. If one seeks statistics for the turbulent boundary layer, the temporal boundary layer is therefore a viable method if modest convergence is sufficient. We suggest that such a temporal set-up could prove useful in the study of turbulence dynamics.

JFM classification

Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulent Flows Turbulent Flows: Turbulence simulation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 796 , 10 June 2016 , pp. 437 - 472
Check for updates
Copyright
© 2016 Cambridge University Press 

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

Abe, H., Kawamura, H. & Choi, H. 2004 Very large-scale structures and their effects on the wall shear-stress fluctuations in a turbulent channel flow up to Re 𝜏 = 640. Trans. ASME: J. Fluids Engng 126, 835–843.Google Scholar
Adrian, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19, 041301.Google Scholar
Bernardini, M., Pirozzoli, S. & Orlandi, P. 2014 Velocity statistics in turbulent channel flow up to Re 𝜏 = 4000. J. Fluid Mech. 742, 171–191.Google Scholar
Brereton, G. J. & Reynolds, W. C. 1991 Dynamic response of boundary-layer turbulence to oscillatory shear. Phys. Fluids A 3, 178–187.Google Scholar
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.Google Scholar
Coles, D. 1954 The problem of the turbulent boundary layer. Z. Angew. Math. Phys. 5 (3), 181–203.Google Scholar
Coles, D. 1956 The law of the wake in the turbulent boundary layer. J. Fluid Mech. 1, 191–226.Google Scholar
Crow, S. 1968 Turbulent Rayleigh shear flow. J. Fluid Mech. 32, 113–130.CrossRefGoogle Scholar
Eggels, J. G. M., Unger, F., Weiss, M. H., Westerweel, J., Adrian, R. J., Friedrich, R. & Nieuwstadt, F. T. M. 1994 Fully developed turbulent pipe flow: a comparison between direct numerical simulation and experiment. J. Fluid Mech. 268, 175–210.Google Scholar
Erm, L. P. & Joubert, P. N. 1991 Low-Reynolds-number turbulent boundary layers. J. Fluid Mech. 230, 1–44.Google Scholar
Esmaili, H. & Piomelli, U. 1992 Temporal development of turbulent boundary layers with embedded streamwise vortices. Theor. Comput. Fluid Dyn. 3, 369–380.Google Scholar
Falco, R. E. 1977 Coherent motions in the outer region of turbulent boundary layers. Phys. Fluids Suppl. 20, 124–132.CrossRefGoogle Scholar
Ferrante, A. & Elghobashi, S. E. 2004 A robust method for generating inflow conditions for direct simulations of spatially-developing turbulent boundary layers. J. Comput. Phys. 198, 372–387.Google Scholar
Ferrante, A. & Elghobashi, S. E. 2005 Reynolds number effect on drag reduction in a microbubble-laden spatially developing turbulent boundary layer. J. Fluid Mech. 543, 93–106.Google Scholar
Gaster, M. & Grant, I. 1975 An experimental investigation of the formation and development of a wave packet in a laminar boundary layer. Proc. R. Soc. Lond. A 347, 253–269.Google Scholar
Hutchins, N., Nickels, T. B., Marusic, I. & Chong, M. S. 2009 Hot-wire spatial resolution issues in wall-bounded turbulence. J. Fluid Mech. 635, 103–136.CrossRefGoogle Scholar
Jiménez, J., Hoyas, S., Simens, M. P. & Mizuno, Y. 2010 Turbulent boundary layers and channels at moderate Reynolds numbers. J. Fluid Mech. 657, 335–360.Google Scholar
Jones, M. B., Nickels, T. B. & Marusic, I. 2008 On the asymptotic similarity of the zero-pressure-gradient turbulent boundary layer. J. Fluid Mech. 616, 195–203.Google Scholar
Jonker, H. J. J., van Reeuwijk, M., Sullivan, P. P. & Patton, E. G. 2013 On the scaling of shear-driven entrainment: a DNS study. J. Fluid Mech. 732, 150–165.Google Scholar
Kader, B. A. & Yaglom, A. M. 1972 Heat and mass transfer laws for fully turbulent wall flows. Intl J. Heat Mass Transfer 15, 2329–2351.CrossRefGoogle Scholar
Kays, W. M. & Crawford, M. E. 1993 Convective Heat and Mass Transfer, 3rd edn. McGraw-Hill.Google Scholar
Kim, J. & Moin, P.1987 Transport of passive scalars in a turbulent channel flow. NASA Tech. Mem. TM-89463.Google Scholar
Kong, H., Choi, H. & Lee, J. 2000 Direct numerical simulation of turbulent thermal boundary layers. Phys. Fluids 12 (10), 2555–2568.CrossRefGoogle Scholar
Kozul, M. & Chung, D. 2014 Direct numerical simulation of the incompressible temporally developing turbulent boundary layer. In Proceedings of 19th Australasian Fluid Mechanics Conference, 8th–11th December 2014 (ed. Chowdhury, H. & Alam, F.). Australasian Fluid Mechanics Society.Google Scholar
Laurien, E. & Kleiser, L. 1989 Numerical simulation of boundary-layer transition and transition control. J. Fluid Mech. 199, 403–440.Google Scholar
Lee, J. H., Kwon, Y. S., Monty, J. P. & Hutchins, N. 2014 Time-resolved PIV measurement of a developing zero pressure gradient turbulent boundary layer. In Proceedings of 19th Australasian Fluid Mechanics Conference, 8th–11th December 2014 (ed. Brandner, P. A. & Pearce, B. W.). Australasian Fluid Mechanics Society.Google Scholar
Li, Q., Schlatter, P., Brandt, L. & Henningson, D. S. 2009 DNS of a spatially developing turbulent boundary layer with passive scalar transport. Intl J. Heat Fluid Flow 30, 916–929.Google Scholar
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.Google Scholar
Lund, T. S., Wu, X. & Squires, K. D. 1998 Generation of turbulent inflow data for spatially-developing boundary layer simulations. J. Comput. Phys. 140, 233–258.Google Scholar
Martin, M. P. 2007 Direct numerical simulation of hypersonic turbulent boundary layers. Part 1. Initialization and comparison with experiments. J. Fluid Mech. 570, 347–364.Google Scholar
Mellado, J. P. 2012 Direct numerical simulation of free convection over a heated plate. J. Fluid Mech. 712, 418–450.Google 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, 943–945.Google Scholar
Nagib, H. M., Chauhan, K. A. & Monkewitz, P. A. 2007 Approach to an asymptotic state for zero pressure gradient turbulent boundary layers. Phil. Trans. R. Soc. Lond. A 365, 755.Google Scholar
Narasimha, R. 1985 The laminar-turbulent transition zone in the boundary layer. Prog. Aeronaut. Sci. 22, 29–80.Google Scholar
Pirozzoli, S., Bernardini, M. & Orlandi, P. 2016 Passive scalars in turbulent channel flow at high Reynolds number. J. Fluid Mech. 788, 614–639.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.Google Scholar
Redford, J. A., Castro, I. P. & Coleman, G. N. 2012 On the universality of turbulent axisymmetric wakes. J. Fluid Mech. 710, 419–452.Google Scholar
van Reeuwijk, M. & Holzner, M. 2014 The turbulence boundary of a temporal jet. J. Fluid Mech. 739, 254–275.Google Scholar
Rist, U. & Fasel, H. 1995 Direct numerical simulation of controlled transition in a flat-plate boundary layer. J. Fluid Mech. 298, 211–248.Google Scholar
Rogers, M. M. & Moser, R. D. 1994 Direct simulation of a self-similar turbulent mixing layer. Phys. Fluids 6, 903–923.CrossRefGoogle Scholar
Sayadi, T., Hamman, C. W. & Moin, P. 2013 Direct numerical simulation of complete H-type and K-type transitions with implications for the dynamics of turbulent boundary layers. J. Fluid Mech. 724, 480–509.Google Scholar
Schlatter, P. & Örlü, R. 2010 Assessment of direct numerical simulation data of turbulent boundary layers. J. Fluid Mech. 659, 116–126.CrossRefGoogle Scholar
Schlatter, P. & Örlü, R. 2012 Turbulent boundary layers at moderate Reynolds numbers: inflow length and tripping effects. J. Fluid Mech. 710, 5–34.Google Scholar
Schlatter, P., Örlü, R., Li, Q., Brethouwer, G., Fransson, J. H. M., Johansson, A. V., Alfredsson, P. H. & Henningson, D. S. 2009 Turbulent boundary layers up to Re 𝜃 = 2500 studied through simulation and experiment. Phys. Fluids 21, 051702.Google Scholar
Sillero, J. A., Jiménez, J. & Moser, R. D. 2013 One-point statistics for turbulent wall-bounded flows at Reynolds numbers up to 𝛿+ ≈ 2000. Phys. Fluids 25, 105102.Google Scholar
Sillero, J. A., Jiménez, J. & Moser, R. D. 2014 Two-point statistics for turbulent boundary layers and channels at Reynolds numbers up to 𝛿+ ≈ 2000. Phys. Fluids 26, 105109.Google Scholar
da Silva, C. B. & Pereira, J. C. F. 2008 Invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors across the turbulent/nonturbulent interface in jets. Phys. Fluids 20, 055101.Google Scholar
Skote, M.2001 Studies of turbulent boundary layer flow through direct numerical simulation, PhD Thesis, Royal Institute of Technology, Stockholm, Sweden.Google Scholar
Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to Re 𝜃 = 1410. J. Fluid Mech. 187, 61–98.Google Scholar
Spalart, P. R. & Yang, K. 1987 Numerical study of ribbon-induced transition in Blasius flow. J. Fluid Mech. 178, 345–365.Google Scholar
Stanley, S. & Sarkar, S. 1997 Simulations of spatially developing two-dimensional shear layers and jets. Theor. Comput. Fluid Dyn. 9 (2), 121–147.Google Scholar
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow, 1st edn. Cambridge University Press.Google Scholar
Wray, A. & Hussaini, M. Y. 1984 Numerical experiments in boundary-layer stability. Proc. R. Soc. Lond. A 392, 373–389.Google Scholar
Wu, X. & Moin, P. 2009 Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer. J. Fluid Mech. 630, 5–41.Google Scholar
Wu, X. & Moin, P. 2010 Transitional and turbulent boundary layer with heat transfer. Phys. Fluids 22, 085105.Google Scholar
Yaglom, A. M. 1979 Similarity laws for constant-pressure and pressure-gradient turbulent wall flows. Annu. Rev. Fluid Mech. 11, 505–540.Google Scholar