Hostname: page-component-7bb8b95d7b-w7rtg Total loading time: 0 Render date: 2024-09-14T20:48:37.878Z Has data issue: false hasContentIssue false
  • English
  • Français

Computations of equilibrium and non-equilibrium turbulent channel flows using a nested-LES approach

Published online by Cambridge University Press:  22 March 2016

Yifeng Tang  and
Rayhaneh Akhavan
Yifeng Tang
Affiliation:
Department of Mechanical Engineering, The University of Michigan, Ann Arbor, MI 48109-2125, USA
Rayhaneh Akhavan*
Affiliation:
Department of Mechanical Engineering, The University of Michigan, Ann Arbor, MI 48109-2125, USA
*
†Email address for correspondence: raa@umich.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

A new nested-LES approach for computation of high Reynolds number, equilibrium, and non-equilibrium, wall-bounded turbulent flows is presented. The method couples coarse-resolution LES in the full computational domain with fine-resolution LES in a minimal flow unit to retain the accuracy of well-resolved LES throughout the computational domain, including in the near-wall region, while significantly reducing the computational cost. The two domains are coupled by renormalizing the instantaneous velocity fields in each domain dynamically during the course of the simulation to match the wall-normal profiles of single-time, ensemble-averaged kinetic energies of the components of ‘mean’ and fluctuating velocities in the inner layer to those of the minimal flow unit, and in the outer layer to those of the full domain. This simple renormalization procedure is shown to correct the energy spectra and wall shear stresses in both domains, thus leading to accurate turbulence statistics. The nested-LES approach has been applied to computation of equilibrium turbulent channel flow at $Re_{{\it\tau}}\approx 1000$, 2000, 5000, 10 000, and non-equilibrium, strained turbulent channel flow at $Re_{{\it\tau}}\approx 2000$. In both flows, nested-LES predicts the skin friction coefficient, first- and higher-order turbulence statistics, spectra and structure of the flow in agreement with available DNS and experimental data. Nested-LES can be applied to any flow with at least one direction of local or global homogeneity, while reducing the required number of grid points from $O(Re_{{\it\tau}}^{2})$ of conventional LES to $O(\log Re_{{\it\tau}})$ or $O(Re_{{\it\tau}})$ in flows with two or one locally or globally homogeneous directions, respectively.

JFM classification

Turbulent Flows: Turbulent Flows Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulence simulation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 793 , 25 April 2016 , pp. 709 - 748
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

del Alamo, J. C., Jimenez, J., Zandonade, P. & Moser, R. D. 2004 Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135–144.Google Scholar
Balakumar, B. J. & Adrian, R. J. 2007 Large- and very-large-scale motions in channel and boundary-layer flows. Phil. Trans. R. Soc. Lond. A 365 (1852), 665–681.Google Scholar
Balaras, E., Benocci, C. & Piomelli, U. 1996 Two-layer approximate boundary conditions for large-eddy simulations. AIAA J. 34 (6), 1111–1119.CrossRefGoogle Scholar
Cabot, W. & Moin, P. 1999 Approximate wall boundary conditions in the large-eddy simulation of high Reynolds number flow. Flow Turbul. Combust. 63 (1), 269–291.Google Scholar
Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. A. 1988 Spectral Methods in Fluid Dynamics. Springer.CrossRefGoogle Scholar
Chapman, D. R. 1979 Computational aerodynamics, development and outlook. AIAA J. 17 (12), 1293–1313.Google Scholar
Chung, D. & Pullin, D. I. 2009 Large-eddy simulation and wall modelling of turbulent channel flow. J. Fluid Mech. 631, 281–309.CrossRefGoogle Scholar
Coleman, G. N., Kim, J. & Le, A. T. 1996 A numerical study of three-dimensional wall-bounded flows. Intl J. Heat Fluid Flow 17 (3), 333–342.Google Scholar
Comte-Bellot, G.1963 Turbulent flow between two parallel walls. PhD thesis, University of Grenoble.Google Scholar
Dean, R. B. 1978 Reynolds number dependence of skin friction and other bulk flow variables in two-dimensional rectangular duct flow. Trans. ASME J. Fluids Engng 100 (2), 215–223.Google Scholar
Deardorff, J. W. 1970 A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. J. Fluid Mech. 41, 453–480.CrossRefGoogle Scholar
Driver, D. M. & Hebbar, S. K.1991 Three-dimensional turbulent boundary layer flow over a spinning cylinder. NASA Tech. Rep. TM-102240. AMES Research Center.Google Scholar
Flores, O. & Jimenez, J. 2010 Hierarchy of minimal flow units in the logarithmic layer. Phys. Fluids 22 (7), 071704.Google Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3 (7), 1760–1765.Google Scholar
Haliloglu, M. U. & Akhavan, R. 2004 A nonlinear interactions approximation model for LES. In Direct and Large-Eddy Simulation V (ed. Geurts, B., Metais, O. & Freidrich, R.), ERCOFTAC Series, vol. 9, p. 39. Kluwer.Google Scholar
Hoffmann, G. & Benocci, C. 1995 Approximate wall boundary conditions for large eddy simulations. In Advances in Turbulence V (ed. Benzi, R.), pp. 222–228. Kluwer.CrossRefGoogle Scholar
Hoyas, S. & Jimenez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to $Re_{{\it\tau}}=2003$ . Phys. Fluids 18 (1), 011702.Google Scholar
Hultmark, M., Vallikivi, M., Bailey, S. C. C. & Smits, A. J. 2013 Logarithmic scaling of turbulence in smooth- and rough-wall pipe flow. J. Fluid Mech. 728, 376–395.Google Scholar
Hutchins, N. & Marusic, I. 2007 Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. Lond. A 365 (1852), 647–664.Google ScholarPubMed
Hwang, Y. Y. 2013 Near-wall turbulent fluctuations in the absence of wide outer motions. J. Fluid Mech. 723, 264–288.Google Scholar
Jimenez, J. 2003 Computing high-Reynolds-number turbulence: will simulations ever replace experiments? J. Turbul. 4, N22.Google Scholar
Jimenez, J. & Hoyas, S. 2008 Turbulent fluctuations above the buffer layer of wall-bounded flows. J. Fluid Mech. 611, 215–236.CrossRefGoogle Scholar
Jimenez, 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
Jimenez, J. & Moin, P. 1991 The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213–240.Google Scholar
Kannepalli, C. & Piomelli, U. 2000 Large-eddy simulation of a three-dimensional shear-driven turbulent boundary layer. J. Fluid Mech. 423, 175–203.CrossRefGoogle Scholar
Kemenov, K. & Menon, S.2003 Two level simulation of high-Reynolds number non-homogeneous turbulent flows. AIAA Paper 2003-0084.Google Scholar
Knaepen, B., Debliquy, O. & Carati, D. 2002 Subgrid-scale energy and pseudo pressure in large-eddy simulation. Phys. Fluids 14 (12), 4235–4241.Google Scholar
Kosloff, D. & Talezer, H. 1993 A modified Chebyshev pseudospectral method with an $O(1/N)$ time step restriction. J. Comput. Phys. 104 (2), 457–469.Google Scholar
Kravchenko, A. G., Moin, P. & Moser, R. 1996 Zonal embedded grids for numerical simulations of wall-bounded turbulent flows. J. Comput. Phys. 127 (2), 412–423.Google Scholar
Lee, M. & Moser, R. D. 2015 Direct numerical simulation of turbulent channel flow up to $Re_{{\it\tau}}\approx 5200$ . J. Fluid Mech. 774, 395–415.CrossRefGoogle Scholar
Lilly, D. K. 1992 A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids A 4 (3), 633–635.Google Scholar
Marusic, I. & Heuer, W. D. C. 2007 Reynolds number invariance of the structure inclination angle in wall turbulence. Phys. Rev. Lett. 99 (11), 114504.Google Scholar
Marusic, I., Mathis, R. & Hutchins, N. 2010a Predictive model for wall-bounded turbulent flow. Science 329 (5988), 193–196.Google Scholar
Marusic, I., Mckeon, B. J., Monkewitz, P. A., Nagib, H. M., Smits, A. J. & Sreenivasan, K. R. 2010b Wall-bounded turbulent flows at high Reynolds numbers: recent advances and key issues. Phys. Fluids 22 (6), 065103.Google Scholar
Marusic, I., Monty, J. P., Hultmark, M. & Smits, A. J. 2013 On the logarithmic region in wall turbulence. J. Fluid Mech. 716, R3.Google Scholar
Mathis, R., Hutchins, N. & Marusic, I. 2009 Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J. Fluid Mech. 628, 311–337.Google Scholar
Mathis, R., Hutchins, N. & Marusic, I. 2011 A predictive inner-outer model for streamwise turbulence statistics in wall-bounded flows. J. Fluid Mech. 681, 537–566.CrossRefGoogle Scholar
Meneveau, C. & Marusic, I. 2013 Generalized logarithmic law for high-order moments in turbulent boundary layers. J. Fluid Mech. 719, R1.CrossRefGoogle Scholar
Menter, F. R. & Egorov, Y.2005 A scale-adaptive simulation model using two-equation models. AIAA Paper 2005-1095.Google Scholar
Meyers, J. & Baelmans, M. 2004 Determination of subfilter energy in large-eddy simulations. J. Turbul. 5, N26.Google Scholar
Nikitin, N. V., Nicoud, F., Wasistho, B., Squires, K. D. & Spalart, P. R. 2000 An approach to wall modeling in large-eddy simulations. Phys. Fluids 12 (7), 1629–1632.CrossRefGoogle Scholar
Orszag, S. A. 1980 Spectral methods for problems in complex geometries. J. Comput. Phys. 37 (1), 70–92.Google Scholar
Pao, Y. H. 1965 Structure of turbulent velocity and scalar fields at large wavenumbers. Phys. Fluids 8 (6), 1063–1075.Google Scholar
Perry, A. E., Henbest, S. & Chong, M. S. 1986 A theoretical and experimental-study of wall turbulence. J. Fluid Mech. 165, 163–199.Google Scholar
Piomelli, U. 2008 Wall-layer models for large-eddy simulations. Prog. Aerosp. Sci. 44 (6), 437–446.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.Google Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601–639.Google Scholar
Sagaut, P. & Deck, S. 2009 Large eddy simulation for aerodynamics: status and perspectives. Phil. Trans. R. Soc. Lond. A 367 (1899), 2849–2860.Google Scholar
Sagaut, P. & Meneveau, C. 2006 Large Eddy Simulation for Incompressible Flows: An Introduction, 3rd edn. Springer.Google Scholar
Schlatter, P., Li, Q., Brethouwer, G., Johansson, A. V. & Henningson, D. S. 2010 Simulations of spatially evolving turbulent boundary layers up to $Re_{{\it\theta}}=4300$ . Intl J. Heat Fluid Flow 31 (3), 251–261.Google Scholar
Schumann, U. 1975 Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. J. Comput. Phys. 18 (4), 376–404.CrossRefGoogle Scholar
Shur, M. L., Spalart, P. R., Strelets, M. K. & Travin, A. K. 2008 A hybrid RANS-LES approach with delayed-DES and wall-modelled LES capabilities. Intl J. Heat Fluid Flow 29 (6), 1638–1649.Google Scholar
Sillero, J. A., Jimenez, J. & Moser, R. D. 2014 Two-point statistics for turbulent boundary layers and channels at Reynolds numbers up to ${\it\delta}^{+}\approx 2000$ . Phys. Fluids 26 (10), 105109.Google Scholar
Smits, A. J., Mckeon, B. J. & Marusic, I. 2011 High-Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353–375.Google Scholar
Spalart, P. R., Jou, W.-H., Strelets, M. & Allmaras, S. R. 1997 Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach. In Advances in DNS/LES (ed. Liu, C., Liu, Z. & Sakell, L.), pp. 137–147. Greyden.Google Scholar
Stevens, R. J. A. M., Wilczek, M. & Meneveau, C. 2014 Large-eddy simulation study of the logarithmic law for second- and higher-order moments in turbulent wall-bounded flow. J. Fluid Mech. 757, 888–907.Google Scholar
Talluru, K. M., Baidya, R., Hutchins, N. & Marusic, I. 2014 Amplitude modulation of all three velocity components in turbulent boundary layers. J. Fluid Mech. 746, R1.Google Scholar
Tang, Y.2015 A nested-LES approach for computation of high Reynolds number, equilibrium and non-equilibrium turbulent wall-bounded flows. PhD thesis, University of Michigan.Google Scholar
Tang, Y. & Akhavan, R. 2009 Recovery of subgrid-scale turbulence kinetic energy in LES of channel flow. In Advances in Turbulence XII (ed. Eckhardt, B.), Springer Proceedings in Physics, vol. 132, p. 949. Springer.Google Scholar
Townsend, A. A. 1958 The turbulent boundary layer. In Boundary Layer Research (ed. Görtler, H.), pp. 1–15. Springer.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.Google Scholar
Voelkl, T., Pullin, D. I. & Chan, D. C. 2000 A physical-space version of the stretched-vortex subgrid-stress model for large-eddy simulation. Phys. Fluids 12 (7), 1810–1825.Google Scholar
Winckelmans, G. S., Jeanmart, H. & Carati, D. 2002 On the comparison of turbulence intensities from large-eddy simulation with those from experiment or direct numerical simulation. Phys. Fluids 14 (5), 1809–1811.Google Scholar
Wu, Y. & Christensen, K. T. 2010 Spatial structure of a turbulent boundary layer with irregular surface roughness. J. Fluid Mech. 655, 380–418.Google Scholar
Yakhot, A., Orszag, S. A., Yakhot, V. & Israeli, M. 1989 Renormalization group formulation of large-eddy simulations. J. Sci. Comput. 4 (2), 139–158.Google Scholar