Hostname: page-component-745bb68f8f-hvd4g Total loading time: 0 Render date: 2025-01-09T23:44:17.833Z Has data issue: false hasContentIssue false
  • English
  • Français

A dynamic multi-scale approach for turbulent inflow boundary conditions in spatially developing flows

Published online by Cambridge University Press:  22 February 2011

GUILLERMO ARAYA ,
LUCIANO CASTILLO ,
CHARLES MENEVEAU  and
KENNETH JANSEN
GUILLERMO ARAYA*
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
LUCIANO CASTILLO
Affiliation:
Department of Mechanical, Aeronautical and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
CHARLES MENEVEAU
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
KENNETH JANSEN
Affiliation:
Department of Mechanical, Aeronautical and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A dynamic method for prescribing realistic inflow boundary conditions is presented for simulations of spatially developing turbulent boundary layers. The approach is based on the rescaling–recycling method proposed by Lund, Wu & Squires (J. Comput. Phys, vol. 140, 1998, pp. 233–258) and the multi-scale method developed by Araya, Jansen & Castillo (J. Turbul., vol. 10, no. 36, 2009, pp. 1–33). The rescaling process requires prior knowledge about how the velocity and length scales are related between the inlet and recycle stations. Here a dynamic approach is proposed in which such information is deduced dynamically by involving an additional plane, the so-called test plane located between the inlet and recycle stations. The approach distinguishes between the inner and outer regions of the boundary layer and enables the use of multiple velocity scales. This flexibility allows applications to boundary layer flows with pressure gradients and avoids the need to prescribe empirically the friction velocity and other flow parameters at the inlet of the domain. The dynamic method is tested in direct numerical simulations of zero, favourable and adverse pressure gradient flows. The dynamically obtained scaling exponents for the downstream evolution of boundary layer parameters are found to fluctuate in time, but on average they agree with the expected values for zero, favourable and adverse pressure gradient flows. Comparisons of the results with data from experiments, and from other direct numerical simulations that use much longer computational domains to capture laminar-to-turbulence transition, demonstrate the suitability of the proposed dynamic method.

JFM classification

Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulence simulation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 670 , 10 March 2011 , pp. 581 - 605
Copyright
Copyright © Cambridge University Press 2011

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

Araya, G. 2008 DNS of turbulent wall bounded flows with a passive scalar. PhD thesis, Rensselaer Polytechnic Institute, Troy, NY.Google Scholar
Araya, G., Jansen, K. & Castillo, L. 2009 Inlet condition generation for spatially-developing turbulent boundary layers via multi-scale similarity. J. Turbul. 10 (36), 1–33.CrossRefGoogle Scholar
Balakumar, B. J. & Adrian, R. 2007 Large- and very-large-scale motions in channel and boundary-layer flows. Phil. Trans. R. Soc. A 365, 665–681.CrossRefGoogle ScholarPubMed
Castillo, L. & George, W. K. 2001 Similarity analysis for turbulent boundary layer with pressure gradient: outer flow. AIAA J. 39 (1), 41–47.CrossRefGoogle Scholar
DeGraaff, D. B. & Eaton, J. K. 2000 Reynolds-number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319–346.CrossRefGoogle Scholar
Ferrante, A. & Elghobashi, S. 2004 A robust method for generating inflow conditions for direct simulations of spatially-developing turbulent boundary layers. J. Comput. Phys. 198, 372–387.CrossRefGoogle Scholar
Ferrante, A. & Elghobashi, S. 2005 Reynolds number effect on drag reduction in a microbubble-laden spatially developing turbulent boundary layer. J. Fluid Mech. 543, 93–106.CrossRefGoogle Scholar
George, W. K. & Castillo, L. 1997 Zero-pressure-gradient turbulent boundary layer. Appl. Mech. Rev. 50, 689–729.CrossRefGoogle Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3, 1760–1765.CrossRefGoogle Scholar
Guala, M., Hommema, S. E. & Adrian, R. 2006 Large-scale and very-large-scale motions in turbulent pipe flow J. Fluid Mech. 554, 521–542.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 a Evidence of very long meandering structures in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 b Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. A 365, 647–664.CrossRefGoogle ScholarPubMed
Jansen, K. E. 1999 A stabilized finite element method for computing turbulence. Comput. Meth. Appl. Mech. Engng 174, 299–317.CrossRefGoogle Scholar
Jones, W. P. & Launder, B. E. 1972 Some properties of sink-flow turbulent boundary layers. J. Fluid Mech. 56, 337–351.CrossRefGoogle Scholar
Kays, W. M. & Crawford, M. E., 1993 Convective Heat and Mass Transfer, 3rd edn. McGraw-Hill.Google Scholar
Keating, A., Piomelli, U., Balaras, E. & Kaltenbach, H. 2004 A priori and a posteriori tests of inflow conditions for large-eddy simulation. Phys. Fluids 16 (12), 4696–4712.CrossRefGoogle Scholar
Kempf, A., Klein, M. & Janicka, J. 2005 Efficient generation of initial- and inflow-conditions for transient turbulent flows in arbitrary geometries. Flow Turbul. Combust. 74, 67–84.CrossRefGoogle Scholar
Khujadze, G. & Oberlack, M. 2004 DNS and scaling laws from new symmetry groups of ZPG turbulent boundary layer flow. Theor. Comput. Fluid Dyn. 18, 391–411.CrossRefGoogle Scholar
Kim, J. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 129, 133–166.CrossRefGoogle Scholar
Klein, M., Sadiki, A. & Janicka, J. 2002 A digital filter based generation of inflow data for spatially developing direct numerical or large eddy simulations. J. Comput. Phys. 186, 652–665.CrossRefGoogle Scholar
Kong, H., Choi, H. & Lee, J. 2000 Direct numerical simulation of turbulent thermal boundary layers. Phys. Fluids 12 (10), 2555–2568.CrossRefGoogle Scholar
Le, H. & Moin, P. 1994 Direct numerical simulation of turbulent flow over a backward-facing step. Rep. TF-58. Thermosciences Division, Department of Mechanical Engineering, Stanford University.Google Scholar
Lee, J. & Sung, H. 2008 Effects of an adverse pressure gradient on a turbulent boundary layer. Intl J. Heat Fluid Flow 29 (3), 568–578.CrossRefGoogle Scholar
Lee, S., Lele, S. & Moin, P. 1992 Simulation of spatially evolving turbulence and the applicability of Taylor's hypothesis in compressible flow. Phys. Fluids A 4, 1521–1530.CrossRefGoogle 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.CrossRefGoogle 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, pp. 311–337.CrossRefGoogle Scholar
Moin, P. & Mahesh, K. 1998 Direct numerical simulation: a tool in turbulence research. Annu. Rev. Fluid Mech. 30, 539–578.Google Scholar
Na, Y. & Moin, P. 1998 The structure of wall-pressure fluctuations in turbulent boundary layers with adverse pressure gradient and separation. J. Fluid Mech. 377, 347–373.CrossRefGoogle Scholar
Osterlund, J. M. 1999 Experimental studies of zero pressure-gradient turbulent boundary-layer flow. PhD thesis, Royal Institute of Technology, Stockholm, Sweden.Google Scholar
Park, J. & Choi, H. 1999 Effects of uniform blowing or suction from a spanwise slot on a turbulent boundary layer flow. Phys. Fluids 11 (10), 3095–3105.CrossRefGoogle Scholar
Perry, A. E., Marusic, I. & Jones, M. B. 2002 On the streamwise evolution of turbulent boundary layers in arbitrary pressure gradients. J. Fluid Mech. 461, 61–91.CrossRefGoogle Scholar
Rai, M. & Moin, P. 1993 Direct numerical simulation of transition and turbulence in a spatially evolving boundary layer. J. Comput. Phys. 109, 169–192.CrossRefGoogle Scholar
Schlatter, P., Orlu, 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 (5), 1070–6631.CrossRefGoogle Scholar
Simens, M. P., Jimenez, J., Hoyas, S. & Mizuno, Y. 2009 A high-resolution code for turbulent boundary layers. J. Comput. Phys. 228 (11), 4218–4231.CrossRefGoogle Scholar
Skote, M. 2001 Studies of turbulent boundary layer flow through direct numerical simulation. PhD thesis, Royal Institute of Technology, Stockholm, Sweden.Google Scholar
Smith, C. R. & Metzler, S. P. 1983 The characteristics of low-speed streaks in the near-wall region of a turbulent boundary layer. J. Fluid Mech. 129, 27–54.CrossRefGoogle Scholar
Smits, A. J., Matheson, N. & Jourbert, P. N. 1983 Low-Reynolds-number turbulent boundary layers in zero and favorable pressure gradients. J. Ship Res. 27 (3), 147–157.CrossRefGoogle Scholar
Spalart, P. R. 1986 Numerical study of sink-flow boundary layers. J. Fluid Mech. 172, 172–307.CrossRefGoogle Scholar
Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to Re θ = 1410. J. Fluid Mech. 187, 61–98.CrossRefGoogle Scholar
Spalart, P. R. & Leonard, A. 1985 Direct numerical simulation of equilibrium turbulent boundary layers. In Proceedings of the 5th Symposium on Turbulent Shear Flows, Pennsylvania State University, University Park, PA (ed. Durst, F., Launder, B. E., Lumley, J. L., Schmidt, F. W. & Whitelaw, J. H.), pp. 935–940. Springer.Google Scholar
Tejada-Martinez, A. E. & Jansen, K. E. 2005 On the interaction between dynamic model dissipation and numerical dissipation due to streamline upwind/Petrov—Galerkin stabilization. Comput. Meth. Appl. Mech. Engng 194, 1225–1248.CrossRefGoogle Scholar
Tejada-Martinez, A. E. & Jansen, K. E. 2006 A parameter-free dynamic subgrid-scale model for large-eddy simulation. Comput. Meth. Appl. Mech. Engng 195, 2919–2938.CrossRefGoogle Scholar
Trofima, A. V., Tejada-Martinez, A. E., Jansen, K. E. & Lahey, R. T. 2009 Direct numerical simulation of turbulent channel flows using a stabilized finite element method. Comput. Fluids 38, 924–938.CrossRefGoogle Scholar
White, F. M. 1974 Viscous Fluid Flow, 1st edn. McGraw-Hill.Google Scholar
Whiting, C. H. & Jansen, K. E. 2001 A stabilized finite element method for the incompressible Navier–Stokes equations using a hierarchical basis. Intl J. Numer. Meth. Fluids 35, 93–116.3.0.CO;2-G>CrossRefGoogle 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.CrossRefGoogle Scholar
Xu, S. & Martin, M. P. 2004 Assessment of inflow boundary conditions for compressible turbulent boundary layers. Phys. Fluids 16 (7), 2623–2639.CrossRefGoogle Scholar