Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-12-01T06:08:13.771Z Has data issue: false hasContentIssue false
  • English
  • Français

On the anisotropy of a low-Reynolds-number grid turbulence

Published online by Cambridge University Press:  18 May 2012

L. Djenidi  and
S. F. Tardu
L. Djenidi*
Affiliation:
Discipline of Mechanical Engineering, School of Engineering, University of Newcastle, Newcastle, 2308 NSW, Australia
S. F. Tardu
Affiliation:
Laboratoires des Ecoulements Geophysiques et Industriels, LEGI BP 53 X Grenoble, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The anisotropy of a low-Reynolds-number grid turbulence is investigated through direct numerical simulations based on the lattice Boltzmann method. The focus is on the anisotropy of the Reynolds-stress () and Reynolds-stress dissipation-rate () tensors and the approach taken is that using the invariant analysis introduced by Lumley & Newman (J. Fluid Mech., vol. 82, 1977, pp. 161–178). The grid is made up of thin square floating elements in an aligned configuration.

The anisotropy is initially high behind the grid and decays quickly as the downstream distance increases. The anisotropy invariant map (AIM) analysis shows that the return-to-isotropic trend of both and is fast and follows a perfectly axisymmetic expansion, although just behind the grid there is an initial tendency toward a one-component state. It is found that the linear relation with is satisfied during the return-to-isotropy phase of the turbulence decay, although close to the grid a form , where is a nonlinear function of , is more appropriate. For large downstream distances, becomes almost independent of , suggesting that despite the absence of an inertial range, the (dissipative) small scales present a high degree of isotropy. It is argued that (i) the very small values of the mean strain rate and (ii) the weak anisotropy of the large scales are in fact responsible for this result.

JFM classification

Turbulent Flows: Homogeneous turbulence Turbulent Flows: Isotropic turbulence Turbulent Flows: Turbulence simulation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 702 , 10 July 2012 , pp. 332 - 353
Copyright
Copyright © Cambridge University Press 2012

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

1. Antonia, R. A., Djenidi, L. & Spalart, P. R. 1994 Anisotropy of the dissipation tensor in a turbulent boundary layer. Phys. Fluids 6, 2475–2479.CrossRefGoogle Scholar
2. Batchelor, G. K 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.Google Scholar
3. Burattini, P., Lavoie, P., Agrawal, A., Djenidi, L. & Antonia, R. A. 2006 On the power law of decaying homogeneous isotropic turbulence at low . Phys. Rev. E 73 (066304).CrossRefGoogle Scholar
4. Chasnov, J. R. 1995 The decay of axisymmetric homogeneous turbulence. Phys. Fluids 7, 600–605.CrossRefGoogle Scholar
5. Chen, S. & Doolen, G. D. 1998 Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30, 329–364.CrossRefGoogle Scholar
6. Comte-Bellot, G. & Corrsin, S. 1966 The use of a contraction to improve the isotropy of grid-generated turbulence. J. Fluid Mech. 25, 657–682.CrossRefGoogle Scholar
7. Corrsin, S. 1963 Turbulence: Experimental Methods, vol. 8. Springer.Google Scholar
8. Djenidi, L. 2006 Lattice Boltzmann simulation of grid-generated turbulence. J. Fluid Mech. 552, 13–35.CrossRefGoogle Scholar
9. Djenidi, L. 2008 Study of the structure of a turbulent crossbar near-wake by means of Lattice Boltzmann. Phys. Rev. E 77, 036310.CrossRefGoogle Scholar
10. Durbin, P. A. & Speziale, C. G. 1991 Local anisotropy in strained turbulence at high Reynolds numbers. Trans ASME: J. Fluids Engng 113, 707–709.Google Scholar
11. Ertunc, L., Ozyilmaz, N., Lienhart, H., Durst, F. & Beronov, K. 2010 Homogeneity of turbulence generated by static-grid structures. J. Fluid Mech. 654, 473–500.CrossRefGoogle Scholar
12. Frisch, U., Hasslacher, B. & Pomeau, Y. 1986 Lattice gas automata for the Navier–Stokes equations. Phys. Rev. Lett. 56, 1505–1508.CrossRefGoogle Scholar
13. Grant, H. L. & Nisbet, I. C. T 1957 The inhomogeneity of grid turbulence. J. Fluid Mech. 2, 263–272.CrossRefGoogle Scholar
14. Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
15. Jovanovic, J., Otic, L. & Bradshaw, P. 2003 On the anisotropy of axisymmetric strained turbulence in the dissipation range. Trans ASME: J. Fluids Engng 125, 401–413.Google Scholar
16. Lavoie, P., Djenidi, L. & Antonia, R. A. 2007 Effects of initial conditions in decaying turbulence generated by passive grids. J. Fluid Mech. 585, 395–420.CrossRefGoogle Scholar
17. Liu, K. & Pletcher, R. H. 2008 Anisotropy of a turbulent boundary layer. J. Turbul. 9, 1–18.CrossRefGoogle Scholar
18. Lumley, J. L. 1975 Prediction methods for turbulent flows – introduction. In Lecture Series, 76. Von Kármán Institute.Google Scholar
19. Lumley, J. L. 1978 Computational modelling of turbulent flow. Adv. Appl. Mech. 18, 123–176.CrossRefGoogle Scholar
20. Lumley, J. L. & Newman, G. R. 1977 The return to isotropy of homogeneous turbulence. J. Fluid Mech. 82, 161–178.CrossRefGoogle Scholar
21. Krogstad, P.-Å. & Davidson, P. A. 2011 Free decaying, homogeneous turbulence generated by multi-scale grids. J. Fluid Mech. 680, 417–434.CrossRefGoogle Scholar
22. Mansour, N. N., Kim, J. & Moin, P. 1988 Reynolds stress and dissipation rate budgets in a turbulent channel flow. J. Fluid Mech. 194, 15–44.CrossRefGoogle Scholar
23. Ozyilmaz, N., Beronov, K. N. & Delgado, A. 2008 Characterization of the Reynolds-stress and disspation-rate decay and anisotropy from DNS of grid-generated turbulence. Proc. Appl. Math. Mech. 8, 10585–10586.CrossRefGoogle Scholar
24. Ozyilmaz, N., Beronov, K. N. & Delgado, A. 2009 Characterization of the disspation tensor from DNS of grid-generated turbulence. In High Performance Computing in Science and Engineering, Garching/Munich 2007, Part IV (ed. Wagner, S., Steinmetz, M., Bode, A. & Brehm, M. ), pp. 315–323. Springler.CrossRefGoogle Scholar
25. Saffman, P. G. 1967 The large scale structure of homogeneous turbulence. J. Fluid Mech. 27, 581–593.CrossRefGoogle Scholar
26. Succi, S. 2001 The lattice Boltzmann equation for fluid dynamics and beyond. In Numerical Mathematics and Scientific Computation. Oxford University Press.Google Scholar
27. Taylor, G. I. 1935 Statistical theory of turbulence. Proc. R. Soc. Lond. A 151, 412–478.Google Scholar
28. Townsend, A. A. 1954 The uniform distortion of homogeneous turbulence. Q. J. Mech. Appl. Math. 7, 104–127.CrossRefGoogle Scholar