DOI QR코드

DOI QR Code

LARGE EDDY SIMULATION OF TURBULENT CHANNEL FLOW USING ALGEBRAIC WALL MODEL

MALLIK, MUHAMMAD SAIFUL ISLAM;UDDIN, MD. ASHRAF

  • 투고 : 2015.12.21
  • 심사 : 2016.03.03
  • 발행 : 2016.03.25

초록

A large eddy simulation (LES) of a turbulent channel flow is performed by using the third order low-storage Runge-Kutta method in time and second order finite difference formulation in space with staggered grid at a Reynolds number, $Re_{\tau}=590$ based on the channel half width, ${\delta}$ and wall shear velocity, $u_{\tau}$. To reduce the calculation cost of LES, algebraic wall model (AWM) is applied to approximate the near-wall region. The computation is performed in a domain of $2{\pi}{\delta}{\times}2{\delta}{\times}{\pi}{\delta}$ with $32{\times}20{\times}32$ grid points. Standard Smagorinsky model is used for subgrid-scale (SGS) modeling. Essential turbulence statistics of the flow field are computed and compared with Direct Numerical Simulation (DNS) data and LES data using no wall model. Agreements as well as discrepancies are discussed. The flow structures in the computed flow field have also been discussed and compared with LES data using no wall model.

키워드

Large Eddy simulation;Turbulent channel flow;Algebraic wall model

참고문헌

  1. J. Kim, P. Moin, and R. Moser, Turbulence statistics in fully developed channel flow at low Reynolds number, Journal of Fluid Mechanics, 177 (1987), 133-166. https://doi.org/10.1017/S0022112087000892
  2. R.D. Moser, J. Kim, and N.N. Mansour, Direct numrical simulation of turbulent channel flow up to $Re_{\tau}$ = 590, Physics of Fluids, 11(4) (1999), 943-945. https://doi.org/10.1063/1.869966
  3. P. Moin and J. Kim, Numerical Investigation of Turbulent Channel Flow, Journal of Fluid Mechanics, 118 (1982), 341-377. https://doi.org/10.1017/S0022112082001116
  4. F. Yang, H.Q. Zhang, C.K. Chan, and X.L. Wang, Large Eddy Simulation of Turbulent Channel Flow with 3D Roughness Using a Roughness Element Model, Chinese Physics Letters, 25(1) (2008), 191-194. https://doi.org/10.1088/0256-307X/25/1/052
  5. M.A. Uddin and M.S.I. Mallik, Large Eddy Simulation of Turbulent Channel Flow using Smagorinsky Model and Effects of Smagorinsky Constants, British Journal of Mathematics & Computer Science, 7(5) (2015), 375-390. https://doi.org/10.9734/BJMCS/2015/15962
  6. M.S.I. Mallik, M.A. Uddin, and M.A. Meah, Large Eddy Simulation of Turbulent Channel Flow at $Re_{\tau}$ = 590, IOSR - Journal of Mathematics, 10(6) (2014), 41-50.
  7. Z. Xie, B. Lin, and R.A. Falconer, Large-eddy simulation of the turbulent structure in compound open-channel flows, Advances in Water Resources, 53 (2013), 66-75. https://doi.org/10.1016/j.advwatres.2012.10.009
  8. G. GrOtzbach, Direct numerical and large eddy simulation of turbulent channel flows. Encyclopedia of Fluid Mechanics, Cheremisinoff, N. P. ed., Gulf Pub. Co., Chap. 34, (1987), 1337-1391.
  9. H. Werner and H. Wengle, Large eddy simulation of turbulent flow around a cube in a plane channel, Selected Papers from the 8th Symposium on Turbulent Shear Flows, ed. F Durst, R Friedrich, BE Launder, U Schumann, JH Whitelaw, Springer, New York (1993).
  10. U. Piomelli and E. Balaras, Wall-Layer Models for Large-Eddy Simulations, Annual Review of Fluid Mechanics, 34 (2002), 349-374. https://doi.org/10.1146/annurev.fluid.34.082901.144919
  11. G. Kalitzin, G. Medic, G. Iaccarino, and P. Durbin, Near-wall behavior of RANS turbulence models and implications for wall functions, Journal of Computational Physics, 204 (2005), 265-291. https://doi.org/10.1016/j.jcp.2004.10.018
  12. U. Schumann, Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli, Journal of Computational Physics, 18 (1975), 376-404. https://doi.org/10.1016/0021-9991(75)90093-5
  13. U. Piomelli, J. Ferziger, P. Moin, and J. Kim, New approximate boundary conditions for large-eddy simulations of wall-bounded flows, Physics of Fluids, 1 (1989), 1061-1068. https://doi.org/10.1063/1.857397
  14. D.B. Spalding, A single formula for the law of the wall, Journal of Applied Mechanics, 28, Ser. E (1961), 455-458. https://doi.org/10.1115/1.3641728
  15. F.E. Ham, F.S. Lien, and A.B. Strong, A Fully Conservative Second-Order Finite Difference Scheme for Incompressible Flow on Nonuniform Grids, Journal of Computational Physics, 177 (2002), 117-133. https://doi.org/10.1006/jcph.2002.7006
  16. Y. Morinishi, Skew-symmetric form of convective terms and fully conservative finite difference schemes for variable density low-Mach number flows, Journal of Computational Physics, 229 (2010), 276-300. https://doi.org/10.1016/j.jcp.2009.09.021
  17. Y.M. Han, J.S. Cho, and H.S. Kang, Analysis of a one-dimensional fin using the analytic method and the finite difference method, Journal of Korean Society for Industrial and Applied Mathematics, 9(1) (2005), 91-98.
  18. M.Y. Kim and Y.K. Choi, Efficient Numerical Methods for the KDV Equation, Journal of Korean Society for Industrial and Applied Mathematics, 15(4) (2011), 291-306.
  19. B. Sanderse and B. Koren, Accuracy analysis of explicit Runge-Kutta methods applied to the incompressible Navier-Stokes equations, Journal of Computational Physics, 231 (2012), 3041-3063. https://doi.org/10.1016/j.jcp.2011.11.028
  20. J.H. Williamson, Low-storage Runge-Kutta schemes, Journal of Computational Physics, 35 (1980), 48-56. https://doi.org/10.1016/0021-9991(80)90033-9
  21. P. Sagaut, Large Eddy Simulation for Incompressible Flows: An Introduction, Springer-Verlag, Berlin Heidelberg, (2001).
  22. C.A. Kennedy, M.H. Carpenter, and R.M. Lewis, Low-storage, explicit Runge-Kutta schemes for the compressible Navier-Stokes equations, Applied Numerical Mathematics, 35 (2000), 177-219. https://doi.org/10.1016/S0168-9274(99)00141-5
  23. D.B. Johnson, P.E. Raad, and S. Chen, Simulation of impacts of fluid free surfaces with solid boundaries, International Journal for Numerical Methods in Fluids, 19 (1994), 153-176. https://doi.org/10.1002/fld.1650190205
  24. H.K. Versteeg and W. Malalasekera, An introduction to computational fluid dynamics, Longman Group Limited, England, (1995).
  25. J.D. Anderson, Computational Fluid Dynamics, McGraw-Hill, New York, (1995).