Swirling-strength based large eddy simulation of turbulent flow around single square cylinder at low Reynolds numbers

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• 作者：Zuo-jin Zhu (1) (2)
  Jian-lei Niu (2)
  Ying-lin Li (1)
  
• 关键词：large scale vortex ; lift and drag coefficient ; turbulence intermittency ; swirling strength ; O29 ; O35 ; 76D17 ; 76D05 ; 65P99
• 刊名：Applied Mathematics and Mechanics
• 出版年：2014
• 出版时间：August 2014
• 年：2014
• 卷：35
• 期：8
• 页码：959-978
• 全文大小：821 KB
• 参考文献：1. Zhu, Z. J. / Numerical Study of Flows Around Rectangular Cylinders (in Chinese), Ph. D. dissertation, Shanghai Jiaotong University, 1-2 (1990)
  2. Vickery, B. J. Fluctuating lift and drag on a long cylinder of square cross-section in a smooth and in a turbulent stream. / Journal of Fluid Mechanics, 25, 481-94 (1966) CrossRef
  3. Okajima, A. Strouhal numbers of rectangular cylinders. / Journal of Fluid Mechanics, 123, 379-98 (1982) CrossRef
  4. Bearman, P. W. and Trueman, D. M. An investigation of the flow around rectangular cylinders. / Aeronautical Quarterly, 23, 229-37 (1972)
  5. Courchesne, J. and Laneville, A. An experimental evaluation of drag coefficient for rectangular cylinders exposed to grid turbulence. / Journal of Fluids Engineering, 104, 523-28 (1982) CrossRef
  6. Nakamura, Y. and Tomonari, Y. The effect of turbulence on the drags of rectangular prisms. / Japan Society of Aeronautical Space Sciences Transactions, 19, 82-6 (1976)
  7. Davis, R. W., Moore, E. F., and Purtell, L. P. A numerical-experimental study on confined flow around rectangular cylinders. / Physics of Fluids, 23, 46-9 (1984) CrossRef
  8. Lyn, D. A. and Rodi, W. The flapping shear layer formed by flow separation from the forward corner of a square cylinder. / Journal of Fluid Mechanics, 267, 353-76 (1994) CrossRef
  9. Gu, Z. F. and Sun, T. F. On interference between two circular cylinders in staggered arrangement at high subcritical Reynolds numbers. / Journal of Wind Engineering and Industrial Aerodynamics, 80, 287-09 (1999) CrossRef
  10. Gu, Z. F. and Sun, T. F. Classifications of flow pattern on three circular cylinders in equilateraltriangular arrangements. / Journal of Wind Engineering and Industrial Aerodynamics, 89, 553-68 (2001) CrossRef
  11. Luo, S. C., Chew, Y. T., and Ng, Y. T. Characteristics of square cylinder wake transition flows. / Physics of Fluids, 15, 2549-559 (2003) CrossRef
  12. So, R. M. C., Wang, X. Q., Xie, W. C., and Zhu, J. Free-stream turbulence effects on vortexinduced vibration and flow-induced force of an elastic cylinder. / Journal of Fluids and Structures, 24, 481-95 (2008) CrossRef
  13. Zhou, Y. Vortical structures behind three side-by-side. / Experiments in Fluids, 34, 68-6 (2003) CrossRef
  14. Wang, H. F. and Zhou, Y. The finite-length square cylinder near wake. / Journal of Fluid Mechanics, 638, 453-90 (2009) CrossRef
  15. Alam, M. M., Zhou, Y., Zhao, J. M., Flamand, O., and Boujard, O. Classification of the tripped cylinder wake and bi-stable phenomenon. / International Journal of Heat and Fluid Flow, 31, 545-60 (2010) CrossRef
  16. Alam, M. M., Zhou, Y., and Wang, X. W. The wake of two side-by-side square cylinders. / Journal of Fluid Mechanics, 669, 432-71 (2011) CrossRef
  17. Kelkar, K. M. and Patankar, S. V. Numerical prediction of vortex shedding behind a square cylinder. / International Journal for Numerical Methods in Fluids, 14, 327-41 (1992) CrossRef
  18. Robichaux, J., Balachandar, S., and Vanka, S. P. Three-dimensional Floquet instability of the wake of square cylinder. / Physics of Fluids, 11, 560-78 (1999) CrossRef
  19. Williamson, C. H. K. Vortex dynamics in the cylinder wake. / Annual Review of Fluid Mechanics, 28, 477-25 (1996) CrossRef
  20. Bosch, G. and Rodi, W. Simulation of vortex shedding past a square cylinder with different turbulence models. / International Journal for Numerical Methods in Fluids, 28, 601-16 (1998) CrossRef
  21. Kato, M. and Launder, B. E. The modelling of turbulent flow around stationary and vibrating square cylinders. / Proceeding of 9 / th Symposium Turbulent Shear Flows, Kyoto, 10-4-1 (1993)
  22. Sohankar, A., Norberg, C., and Davidson, L. Simulation of three-dimensional flow around a square cylinder at moderate Reynolds numbers. / Physics of Fluids, 11, 288-06 (1999) CrossRef
  23. Tao, W. Q. / Numerical Heat Transfer (in Chinese), Xi’an Jiantong University Press, Xi’an (1988)
  24. Patankar, S. V. / Numerical Heat Transfer and Fluid Flow, Hemisphere, New York (1980)
  25. Saha, A. K., Biswas, G., and Muralidhar, K. Three-dimensional study of flow past a square cylinder at low Reynolds numbers. / International Journal of Heat and Fluid Flow, 24, 54-6 (2003) CrossRef
  26. Harlow, F. H. and Welch, J. E. Numerical calculation of time dependent viscous incompressible flow of fluid with free surfaces. / Physics of Fluids, 8, 2182-188 (1965) CrossRef
  27. Niu, J. L. and Zhu, Z. J. Numerical study of three-dimensional flows around two identical square cylinders in staggered arrangements. / Physics of Fluids, 18, 044106 (2006) CrossRef
  28. Niu, J. L., Zhu, Z. J., and Huang, S. H. Numerical study of convective heat transfer from two identical square cylinders submerged in a uniform cross flow. / Numerical Heat Transfer, / Part A, 50, 21-4 (2006) CrossRef
  29. Hanjalic, K. One-point closure model for buoyancy-driven turbulent flows. / Annual Review of Fluid Mechanics, 34, 321-47 (2002) 35" target="_blank" title="It opens in new window">CrossRef
  30. Groetzbach, G. Direct numerical simulation of laminar and turbulent Benard convection. / Journal of Fluid Mechanics, 119, 27-3 (1982) CrossRef
  31. Manhart, M. A zonal grid algorithm for DNS of turbulent boundary layers. / Computers and Fluids, 33, 435-61 (2004) CrossRef
  32. Holmes, P., Lumley, J. L., and Berkooz, G. / Turbulence, / Coherent Structures, / Dynamicsal Systems and Symmetry, Cambridge University Press, Cambridge (1996)
  33. Friedrich, R. and Su, M. D. Large eddy simulation of a turbulent wall-bounded shear layer with longitudinal curvature. / Lecture Notes in Physics, 170, 196-02 (1982) CrossRef
  34. McMillan, O. J. and Ferziger, J. H. Direct testing of subgrid-scale models. / AIAA Journal, 17, 1340-346 (1979) CrossRef
  35. Smagorinsky, J. S. General circulation experiments with the primitive equations, the basic experiment. / Monthly Weather Review, 91, 99-64 (1963) CrossRef
  36. Moin, P. and Kim, J. Numerical investigation of turbulent channel flow. / Journal of Fluid Mechanics, 118, 341-77 (1982) CrossRef
  37. Madabhushi, R. K. and Vanka, S. P. Large eddy simulation of turbulence-driven secondary flow in a square duct. / Physics of Fluidss A: / Fluid Dynamics, 3, 2734-745 (1991) CrossRef
  38. Su, M. D. and Friedrich, R. Investigation of fully developed turbulent flow in a straight duct with large eddy simulation. / Journal of Fluids Engineering, 116, 677-84 (1994) 35" target="_blank" title="It opens in new window">CrossRef
  39. Vázquez, M. S. and Métais, O. Large-eddy simulation of the turbulent flow through a heated square duct. / Journal of Fluid Mechanics, 453, 201-38 (2002) CrossRef
  40. Métais, O. and Lesieur, M. New trend in large eddy simulation of turbulence. / Annual Review of Fluid Mechanics, 28, 45-2 (1996) CrossRef
  41. Pallares, J. and Davidson, L. Large-eddy simulations of turbulent flow in a rotating square duct. / Physics of Fluids, 12, 2878-894 (2000) CrossRef
  42. Pallares, J. and Davidson, L. Large-eddy simulations of turbulent heat transfer in stationary and rotating square ducts. / Physics of Fluids, 14, 2804-816 (2002) CrossRef
  43. Germano, M., Piomelli, U., Moin, P., and Cabot, W. H. A dynamic subgrid-scale eddy viscosity model. / Physics of Fluidss A: / Fluid Dynamics, 3, 1760-765 (1991) CrossRef
  44. Lilly, D. K. A proposed modification of the Germano subgrid-scale closure model. / Physics of Fluidss A: / Fluid Dynamics, 4, 633-35 (1992) CrossRef
  45. Cui, G. X., Zhou, H. B., Zhang, Z. S., and Shao, L. A new subgrid eddy viscosity model and its application (in Chinese). / Chinese Journal of Computer Physics, 21, 289-93 (2004)
  46. Cui, G. X., Xu, C. X., and Zhang, Z. S. Progress in large eddy simulation of turbulent flows (in Chinese). / Acta Aerodynamica Sinica, 22, 121-29 (2004)
  47. Vreman, A. W. An eddy-viscosity subgrid-scale model for turbulent shear flow: algebraic theory and applications. / Physics of Fluids, 16, 3670-681 (2004) CrossRef
  48. Verma, A. and Mahesh, K. A Lagrangian subgrid-scale model with dynamic estimation of Lagrangian time scale for large eddy simulation of complex flows. / Physics of Fluids, 24, 085101 (2012)
  49. Holm, D. D. Fluctuation effects on 3D Lagrangian mean and Eulerian mean fluid motion. / Physica D, 133, 215-69 (1999) CrossRef
  50. Cheskidov, A., Holm, D. D., Olson, E., and Titi, E. S. On a Leray- / α model of turbulence. / Proceedings of the Royal Society, 461, 629-49 (2005) CrossRef
  51. Geurts, B. J. and Holm, D. D. Regularization modeling for large-eddy simulation. / Physics of Fluids, 15, 13-6 (2003) CrossRef
  52. van Reeuwijk, M., Jonker, H. J. J., and Hanjalic, K. Wind and boundary layers in Rayleigh-Bénard convection I, analysis and modelling. / Physical Review E, 77, 036311 (2008)
  53. van Reeuwijk, M., Jonker, H. J. J., and Hanjalic, K. Leray- / α simulations of wall-bounded turbulent flows. / International Journal of Heat and Fluid Flow, 30, 1044-053 (2009) CrossRef
  54. Trias, F. X., Verstappen, R. W. C. P., Gorobets, A., Soria, M., and Oliva, A. Parameter-free symmetry-preserving regularization modeling of a turbulent differentially heated cavity. / Computers and Fluids, 39, 1815-831 (2010) CrossRef
  55. Verstappen, R. On restraining the production of small scales of motion in a turbulent channel flow. / Computers and Fluids, 37, 887-97 (2008) CrossRef
  56. Chandrasekhar, S. / Hydrodynamic and Hydromagnetic Stability, Oxford University Press, Cambridge (1961)
  57. Zhou, J., Adrian, R. J., Balachandar, S., and Kendall, T. M. Mechanisms of generating coherent packets of Hairpin vortices in channel flow. / Journal of Fluid Mechanics, 387, 353-96 (1999) CrossRef
  58. Ganapathisubramani, B., Longmire, E. K., and Marusic, I. Experimental investigation of vortex properties in a turbulent boundary layer. / Physics of Fluids, 18, 155105 (2006) CrossRef
  59. Lin, C. and Zhu, Z. Direct numerical simulation of incompressible flows in a zero-pressure gradient turbulent boundary layer. / Advances in Applied Mathematics and Mechanics, 2, 503-17 (2010)
  60. Orlanski, I. A simple boundary condition for unbounded flows. / Journal of Computational Physics, 21, 251-69 (1976) CrossRef
  61. Yang, H. X., Chen, T. Y., and Zhu, Z. J. Numerical study of forced turbulent heat convection in a straight square duct. / International Journal of Heat and Mass Transfer, 52, 3128-136 (2009) CrossRef
  62. Khanafer, K., Vafai, K., and Lightstone, M. Mixed convection heat transfer in two dimensional open-ended enclosures. / International Journal of Heat and Mass Transfer, 45, 5171-190 (2002) CrossRef
  63. Papanicolaou, E. and Jaluria, Y. Transition to a periodic regime in mixed convection in a square cavity. / Journal of Fluid Mechanics, 239, 489-09 (1992) CrossRef
  64. Nikitin, N. Finite-difference method for incompressible Navier-Stokes equations in arbitrary orthogonal curvilinear coordinates. / Journal of Computational Physics, 217, 759-81 (2006) CrossRef
  65. Ni, M. J. and Abdou, M. A. A bridge between projection methods and simple type methods for incompressible Navier-Stokes equations. / International Journal of Numerical Methods in Engineering, 72, 1490-512 (2007) CrossRef
  66. Tian, Z. F., Liang, X., and Yu, P. X. A higher order compact finite difference algorithm for solving the incompressible Navier-Stokes equations. / International Jouranl of Numerical Methods in Engineering, 88, 511-32 (2011) CrossRef
  67. Brown, D. L., Cortez, R., and Minion, M. L. Accurate projection methods for the incompressible Navier-Stokes equations. / Journal of Computational Physics, 168, 464-99 (2001) CrossRef
  68. Zhu, Z. J., Yang, H. X., and Chen, T. Y. Numerical study of turbulent heat and fluid flow in a straight square duct at higher Reynolds numbers. / International Jouranal of Heat Mass Transfer, 53, 356-64 (2010) CrossRef
  69. Baker, T. J., Potential flow calculation by the approximate factorization method. / Journal of Computational Physics, 42, 1-9 (1981) CrossRef
  70. van der Vorst, H. A. BiCGSTAB: a fast and smoothly converging variant of BICG for the solution of non-symmetric linear system. / Journal on Scientific and Statistical Computing, 13, 631-44 (1992) 35" target="_blank" title="It opens in new window">CrossRef
  71. Zhu, Z. J. and Yang, H. X. Numerical investigation of transient laminar natural convection of air in a tall cavity. / Heat and Mass Transfer, 39, 579-87 (2003) CrossRef
  72. Zhu, Z. J. and Yang, H. X. Discrete Hilbert transformation and its application to estimate the wind speed in Hong Kong. / Journal of Wind Engineering and Industrial Aerodynamics, 90, 9-8 (2002) CrossRef
  73. Wu, F. / Nonstandard Picture of Turbulence, 2nd ed., 1-0 (2004) http://arXiv:physics/0308012
  74. Wu, F. Some key concepts in nonstandard analysis theory of turbulence. / Chinese Physics Letters, 22, 2604-607 (2005) CrossRef
  75. Wu, F. Mathematical concepts and their physical foundation in the nonstandard analysis theory of turbulence. / Chinese Physics, 16, 1186-196 (2007) CrossRef
  76. Shraiman, B. I. and Siggia, D. E. Scalar turbulence. / nature, 405, 639-46 (2000) 35015000" target="_blank" title="It opens in new window">CrossRef
  77. Adrian, R. J., Meinhart, C. D., and Tomkins, C. D. Vortex organization in the outer region of the boundary layer. / Journal of Fluid Mechanics, 422, 1-4 (2000) CrossRef
  78. Natrajan, V. K., Wu, Y., and Christensen, K. T. Spatial signatures of retrograde spanwise vortices in wall turbulence. / Journal of Fluid Mechanics, 574, 155-67 (2007) CrossRef
  79. Tennekes, H. and Lumley, J. L. / A First Course in Turbulence, MIT Press, Cambridge, 146-95 (1974)
  80. Frisch, U. / The Legacy of A. N. Kolmogorov in Turbulence, Cambridge University Press, Cambrigde, 81-8 (1995)
  
• 作者单位：Zuo-jin Zhu (1) (2)
  Jian-lei Niu (2)
  Ying-lin Li (1)
  
  1. Faculty of Engineering Science, University of Science and Technology of China, Hefei, 230026, P. R. China
  2. Faculty of Construction and Environment, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, P. R. China
  
• ISSN：1573-2754

文摘

In view of the fact that large scale vortices play the substantial role of momentum transport in turbulent flows, large eddy simulation (LES) is considered as a better simulation model. However, the sub-grid scale (SGS) models reported so far have not ascertained under what flow conditions the LES can lapse into the direct numerical simulation. To overcome this discrepancy, this paper develops a swirling strength based the SGS model to properly model the turbulence intermittency, with the primary characteristics that when the local swirling strength is zero, the local sub-grid viscosity will be vanished. In this paper, the model is used to investigate the flow characteristics of zero-incident incompressible turbulent flows around a single square cylinder (SC) at a low Reynolds number range Re [103, 104]. The flow characteristics investigated include the Reynolds number dependence of lift and drag coefficients, the distributions of time-spanwise averaged variables such as the sub-grid viscosity and the logarithm of Kolmogorov micro-scale to the base of 10 at Re = 2 500 and 104, the contours of spanwise and streamwise vorticity components at t = 170. It is revealed that the peak value of sub-grid viscosity ratio and its root mean square (RMS) values grow with the Reynolds number. The dissipation rate of turbulent kinetic energy is larger near the SC solid walls. The instantaneous factor of swirling strength intermittency (FSI) exhibits some laminated structure involved with vortex shedding.