Investigation of the slip boundary condition in wall-modeled LES (original) (raw)

Abstract

The near-wall resolution requirement to accurately resolve the boundary layer in wall-bounded flows remains one of the largest obstacles in large-eddy simulation (LES) of high-Reynolds-number engineering applications. Chapman (1979) estimated that the number of grid points necessary for a wall-resolved (WR) LES scales as N W R ∼ Re 9/5 , where Re is the characteristic Reynolds number of the problem. A more recent study by Choi & Moin (2012), using more accurate correlations for the skin friction coefficients, concluded that N W R ∼ Re 13/7 , which is far too expensive for many practical engineering applications and not very different from the N DN S ∼ Re 37/14 scaling required for direct numerical simulation (DNS) where all the relevant scales of motion are resolved. By modeling the near-wall flow such that only the outer layer of the boundary layer is resolved, the grid point requirements for wall-modeled (WM) LES scale at most linearly with increasing Reynolds number, N W M ∼ Re. Therefore, wall-modeling stands as the most feasible approach for most engineering applications. Several strategies for modeling the near-wall region have been explored in the past. The most popular and well-known wall-models are the traditional wall-stress models (or approximate boundary condition) and detached eddy simulation (DES) and its variants. Approximate boundary condition models compute the wall stress using either the law of the wall (Schumann 1975; Deardorff 1970; Piomelli et al. 1989) or the solution obtained by solving a simplified version of the boundary layer equations close to the wall, e.g., the Reynolds-averaged Navier-Stokes (RANS) equations (Balaras et al. 1996; Cabot & Moin 1999; Kawai & Larsson 2010). DES (Spalart et al. 1997) combines RANS equations close to the wall and LES in the outer layer, with the interface between RANS and LES domains enforced implicitly through the change in the turbulence model. In order to reduce the computational cost, all above models assume a simplified state of the local near-wall boundary layer, including the shape of the velocity profile, the relative significance of the different terms in the equations solved, and the alignment of the subgrid velocity field with respect to local strain. Furthermore, models involving RANS equations close to the wall are sensitive to the choice of the particular closure and its associated coefficients, as well as the location of the RANS/LES interface. The above wall-model techniques may not be accurate in flow regimes where these assumptions are no longer valid as in transitional or separated flows. Moreover, sensitivities to model parameters or RANS/LES interface locations can limit the predictive capabilities of wall-modeled LES, and their computational complexity may make their implementation a difficult and time-consuming task. Recently, Bose & Moin (2014) showed promising results using a dynamic slip boundary condition that does not require any prior knowledge of the local boundary layer. However, the computed slip length is sensitive to changes in grid resolution, Reynolds number and subgrid scale (SGS) model. Our goal is to investigate the effects of the slip

Loading...

Loading Preview

Sorry, preview is currently unavailable. You can download the paper by clicking the button above.

References (23)

  1. Balaras, E., Benocci, C. & Piomelli, U. 1996 Two-layer approximate boundary conditions for large-eddy simulations. AIAA J. 34, 1111-1119.
  2. Bose, S. T. & Moin, P. 2014 A dynamic slip boundary condition for wall-modeled large-eddy simulation. Phys. Fluids. 26, 015104.
  3. Cabot, W. H. & Moin, P. 1999 Approximate wall boundary conditions in the large- eddy simulation of high Reynolds number flows. Flow Turbul. Combust. 63, 269-291.
  4. Chapman, D. R. 1979 Computational aerodynamics development and outlook. AIAA J. 17, 1293-1313.
  5. Choi, H. & Moin, P. 2012 Grid-point requirements for large eddy simulation: Chap- man's estimates revisited. Phys. Fluids. 24, 011702.
  6. Deardorff, J. W. 1970 A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. J. Fluid Mech. 41, 453-480.
  7. del Álamo, J. C., Jiménez, J., Zandonade, P. & Moser, R. D. 2004 Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135-144.
  8. Germano, M. 1986 Differential filters for the large eddy numerical simulation of turbu- lent flows. Phys. Fluids. 29, 1755-1757.
  9. Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid- scale eddy viscosity model. Phys. Fluids. 3, 1760-1765.
  10. Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to Re τ = 2003. Phys. Fluids. 18, 011702.
  11. Jiménez, J. & Moser, R. D. 2000 Large-eddy simulations: Where are we and what can we expect? AIAA J. 38 605-612.
  12. Kawai, S. & Larsson, J. 2010 A dynamic wall-model for large-eddy simulation of high Reynolds number compressible flows. Annual Research Briefs, Center for Turbulence Research, Stanford University, pp. 25-37.
  13. Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier-Stokes equations. J. Comput. Phys. 59, 308-323.
  14. Lilly, D. K. 1991 A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids 4, 633-635.
  15. 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, 011702.
  16. Meyers, J. & Sagaut, P. 2007 Is plane-channel flow a friendly case for the testing of large-eddy simulation subgrid-scale models? Phys. Fluids 19, 048105.
  17. Millikan, C. M. 1938 A critical discussion of turbulent flows in channels and circular tubes. In Proceedings of the Fifth International Congress for Applied Mechanics, Harvard and MIT, 12-26 September. Wiley.
  18. Orlandi, P. 2000 Fluid flow phenomena: a numerical toolkit. Kluwer.
  19. Piomelli, U., Moin, P., Ferziger, J. H. & Kim, J. 1989 New approximate boundary conditions for large-eddy simulations of wall-bounded flows. Phys. Fluids 1, 1061- 1068.
  20. Schumann, U. 1975 Subgrid-scale model for finite difference simulation of turbulent flows in plane channels and annuli. J. Comput. Phys. 18, 376-404.
  21. Smagorinsky, J. 1963 General circulation experiments with the primitive equations. Mon. Weather Rev.. 91, 99--164.
  22. 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. C Liu, Z Liu, pp.137-148.
  23. Wray, A. A. 1990 Minimal-storage time advancement schemes for spectral methods. NASA Tech. Rep. #MS 202 A-1.