Transactions of the Korean Society of Mechanical Engineers B (대한기계학회논문집B)

The Korean Society of Mechanical Engineers (대한기계학회)
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Numerical Investigation of Mixing Characteristics in Cavity Flow at Various Aspect Ratios

종횡비에 따른 공동형상 내부에서의 혼합특성에 관한 수치적 연구

  • 신명섭 (동양미래대학교 기계공학부) ;
  • 양승덕 (한양대학교 기계공학과) ;
  • 윤준용 (한양대학교 기계공학과)
  • Received : 2014.07.24
  • Accepted : 2014.09.30
  • Published : 2015.01.01
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Abstract

This study numerically examined the mixing characteristics of rectangular cavity flows by using the hybrid lattice Boltzmann method (HLBM) applied to the finite difference method (FDM). Multi-relaxation time was used along with a passive scalar method which assumes that two substances have the same mass and that there is no interaction. First, we studied numerical results such as the stream function, position of vortices, and velocity profile for a square cavity and rectangular cavity with an aspect ratio of 2. The data were compared with previous numerical results that have been proven to be reliable. We also studied the mixing characteristics of a rectangular cavity flow such as the concentration profile and average Sherwood number at various Pe numbers and aspect ratios.

본 연구에서는 유한차분법(FDM)을 적용한 혼성 격자볼츠만 방법(HLBM)을 이용하여 직사각 형태를 갖는 공동형상 내 혼합특성에 대하여 수치적으로 연구하였다. 유동장은 다중 완화시간을 적용한 격자볼츠만 방법(LB-MRT)을 사용하였으며, 농도장은 두 물질의 질량은 같고 두 물질 사이의 상호작용이 없다고 가정한 Passive Scalar 방법을 사용하였다. 먼저, 정사각형과 종횡비가 2인 직사각형의 공동형상 내 유동해석 결과를 기존의 신뢰성 있는 연구결과와 비교하여 HLBM의 신뢰성을 검토하였다. 이를 토대로 다양한 종횡비를 갖는 공동형상에서 Pe수를 변화시키며 공동형상 내부에서의 혼합특성과 물질전달 형태에 대하여 파악하였다.

Keywords

References

  1. Burggraf, O. R., 1966, "Analytical and Numerical Studies of the Structure of Steady Separated Flows," Journal of Fluid Mechanics, Vol. 24, pp. 113-151. https://doi.org/10.1017/S0022112066000545
  2. Pan, F. and Acrivos, A., 1967, "Steady Flows in Rectangular Cavities," Journal of Fluid Mechanics, Vol. 28, pp. 643-655. https://doi.org/10.1017/S002211206700237X
  3. Ghia, U., Ghia, K. N. and Shin, C. T., 1982, "High-Re Solutions for Incompressible Flow Using the Navier-Stokes Equations and a Multigrid Method," Journal of Computational Physics, Vol. 48, pp. 387-411. https://doi.org/10.1016/0021-9991(82)90058-4
  4. Shankar, P. N. and Deshpande, M. D., 2000, "Fluid Mechanics in the Driven Cavity," Annual Review of Fluid Mechanics, Vol. 32, pp. 93-136. https://doi.org/10.1146/annurev.fluid.32.1.93
  5. Mehta, U. B. and Lavan Z., 1969, "Flow in a Two-Dimensional Channel With a Rectangular Cavity," Journal of Applied Mechanics, Vol. 36, pp. 897-901. https://doi.org/10.1115/1.3564799
  6. Shen, C. and Floryan, J. M., 1985, "Low Reynolds Number Flow Over Cavities," Physics of Fluids, Vol. 28, pp. 3191-3202 https://doi.org/10.1063/1.865366
  7. Alkire, R. C., Deligianni, H. and Ju, J. B., 1990, "Effect of Fluid Flow on Convective Transport in Small Cavities," Journal of the Electrochemical Society, Vol. 139, pp. 2845-2855.
  8. Occhialini, J. M. and Higdon, J. J. L., 1992, "Convective Mass Transport from Rectangular Cavities in Viscous Flow," Journal of the Electrochemical Society, Vol. 139, pp. 2845-2855. https://doi.org/10.1149/1.2068991
  9. Trevelyan, P. M. J., Kalliadasis, S., Merkin, J. H. and Scott, S. K., 2001, "Circulation and Reaction Enhancement of Mass Transport in a Cavity," Chemical Engineering Science, Vol. 56, pp. 5177-5188. https://doi.org/10.1016/S0009-2509(01)00179-8
  10. Shin., M. S., Jeon, S. Y. and Yoon, J. Y., 2013, "Numerical Investigation of Mixing Characteristics in a Cavity Flow by Using Hybrid Lattice Boltzmann Method," Trans. Korean Soc. Mech. Eng. B, Vol. 37, No. 7, pp. 683-693. https://doi.org/10.3795/KSME-B.2013.37.7.683
  11. Shin, M. S., Byun, S. J. and Yoon, J. Y., 2010, "Numerical Investigation of Effect of Surface Roughness in a Microchannel," Trans. Korean Soc. Mech. Eng. B, Vol. 34, No. 5, pp. 539-546. https://doi.org/10.3795/KSME-B.2010.34.5.539
  12. Shin, M. S., Byun, S. J., Kim, J. H. and Yoon, J. Y., 2011, "Numerical Investigation of Pollutant Dispersion in a Turbulent Boundary Layer by Using Lattice Boltzmann-Subgrid Model," Trans. Korean Soc. Mech. Eng. B, Vol. 35, No. 2, pp. 169-178. https://doi.org/10.3795/KSME-B.2011.35.2.169
  13. Chen, S. and Doolen, G. D., 1998, "Lattice Boltzmann Method for Fluid Flows," Annual Review of Fluid Mechanics, Vol. 30, pp. 329-364. https://doi.org/10.1146/annurev.fluid.30.1.329
  14. Shan, X., 1997, "Simulation of Rayleigh-Benard Convection Using a Lattice Boltzmann Method," Physical Review E, Vol. 55, pp. 2780-2788.
  15. Lallemand, P. and Luo, L. S., 2003, "Hybrid Finite-Difference Thermal Lattice Boltzmann Equation," International Journal of Medern Physics, Vol. 17, pp 41-47.
  16. McNamara, G. and Alder, B., 1993, "Analysis of the Lattice Boltzmann Treatment of Hydrodynamics," Physica A, Vol. 194, pp. 218-228. https://doi.org/10.1016/0378-4371(93)90356-9
  17. Bhatnagar, P. L., Gross, E. P. and Krook, M., 1954, "A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems," Physical Review, Vol. 94, No. 5, pp. 511-525. https://doi.org/10.1103/PhysRev.94.511
  18. Lallemand, P. and Luo, L. S., 2000, "Theory of the Lattice Boltzmann method: Dispersion, Dissipation, Isotropy, Galilean Invariance, and Stability," Physical Review E, Vol. 61, pp. 6546-6562. https://doi.org/10.1103/PhysRevE.61.6546
  19. d'Humieres, D., 1992, "Generalized Lattice Boltzmann Equation," in Rarefied Gas Dynamics: Theory and Simulations, ed. by Shizgal, D, and Weaver, D.P, Progress in Astronautics and Aeronautics, Vol. 159, AIAA, Washington DC, pp. 450-458.
  20. Treek, C. V., Rank, E., Krafczyk, M., Tolke, J. and Nachtwey, B., 2006, "Extension of a Hybrid Thermal LBE Scheme for Large-eddy Simulations of Turbulent Convective Flow," Computers & Fluids, Vol. 35, pp. 863-871. https://doi.org/10.1016/j.compfluid.2005.03.006
  21. Hou, S., Zou, Q., Chen, S., Doolen, G. and Cogley, A. C., 1995, "Simulation of Cavity Flow by Lattice Boltzmann Method," Journal of Computational Physics, Vol. 118, pp. 329-347. https://doi.org/10.1006/jcph.1995.1103
  22. Gupta, M. M. and Kalita, J. C., 2005, "A New Paradigm for Solving Navier-Stokes Equations: Streamfunction-velocity Formulation," Journal of Computational physics, Vol. 207, pp. 52-68. https://doi.org/10.1016/j.jcp.2005.01.002
  23. Bruneau, C. H. and Jouron, C., 1990, "An Efficient Scheme for Solving Steady Incompressible Navier-Stokes Equations," Journal of Computational physics, Vol. 89, pp. 389-413. https://doi.org/10.1016/0021-9991(90)90149-U
  24. Antonini, G., Gelus, M., Guiffant, G. and Zoulalian, A., 1981, "Simultaneous Momentum and Mass Transfer Characteristics in Surface-Driven Recirculating Flows," International Journal of Heat and Mass Transfer, Vol. 24, pp. 1313-1323. https://doi.org/10.1016/0017-9310(81)90182-4