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

The Korean Society of Mechanical Engineers (대한기계학회)
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A Numerical Study of Natural Convection in a Square Enclosure with a Circular Cylinder at Different Vertical Locations

원형 실린더가 존재하는 사각형 실린더 내부의 자연대류에 관한 수치적 연구

  • 김병수 (부산대학교 대학원 기계공학과) ;
  • 이대성 (부산대학교 대학원 기계공학과) ;
  • 윤현식 (부산대학교 첨단조선공학연구센터) ;
  • 이현구 (부산대학교 기계공학부) ;
  • 하만영 (부산대학교 기계공학부)
  • Published : 2007.03.01
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Abstract

Numerical calculations are carried out for the natural convection induced by temperature difference between a cold outer square cylinder and a hot inner circular cylinder. A two-dimensional solution for unsteady natural convection is obtained, using the immersed boundary method (IBM) to model an inner circular cylinder based on finite volume method, for different Rayleigh numbers varying over the range of $10^4\;to\;10^6$. The study goes further to investigate the effect of an inner cylinder location on the heat transfer and fluid flow. The location of inner circular cylinder is changed vertically along the center-line of square enclosure. The number, size and formation of cell strongly depend on Rayleigh number and the position of inner circular cylinder. The changes in heat transfer quantities have been presented.

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References

  1. Ha, M.Y., Kim, I.K., Yoon, H.S. and Lee, S.S., 2002, 'Unsteady Fluid Flow and Temperature Fields in a Horizontal Enclosure with an Adiabatic Body,' Physics of Fluids, Vol. 14, No. 9, pp. 3189-3202 https://doi.org/10.1063/1.1497168
  2. Ha, M.Y., Yoon, H.S., Balachandar, S., Kim, I., Lee, J.R. and Chun, H.H., 2002, 'Two-Dimensional and Unsteady Natural Convection in a Horizontal Enclosure with a Square Body,' Numerical Heat Transfer, Vol. 41, pp. 183-210 https://doi.org/10.1080/104077802317221393
  3. Lee, J.R. and Ha, M.Y., 2005, 'A Numerical Study of Natural Convection in a Horizontal Enclosure with a Conducting Body,' Int. J. Heat and Mass Transfer, Vol. 48, pp. 3308-3318 https://doi.org/10.1016/j.ijheatmasstransfer.2005.02.026
  4. Lee, J.R. and Ha, M.Y., 2005, 'Numerical Simulation of Natural Convection in Horizontal Enclosure with Heat-Generating Conducting Body,' Trans. of the KSME B, Vol. 29, No. 4, pp. 441-452 https://doi.org/10.3795/KSME-B.2005.29.4.441
  5. Lee, J.R., Ha, M.Y., Balachandar, S., Yoon, H.S. and Lee, S.S., 2004, 'Natural Convection in a Horizontal Layer of Fluid with a Periodic Array of Square Cylinders in the Interior,' Physics of Fluids, Vol. 16, pp. 1273-1286 https://doi.org/10.1063/1.1649989
  6. Hyun, J.M. and Lee, J.W., 1989, 'Numerical Solutions for Transient Natural Convection in a Square Cavity with Different Sidewall Temperatures,' Int. J. Heat & Fluid Flow, Vol. 10, pp. 146-151 https://doi.org/10.1016/0142-727X(89)90009-X
  7. Misra, D. and Sarkar, A., 1997, 'Finite Element Analysis of Conjugate Natural Convection in a Square Enclosure with a Conducting Vertical Wall,' Comput. Methods Appl. Mech. Engrg., Vol. 141, pp. 205-219 https://doi.org/10.1016/S0045-7825(96)01109-7
  8. Wright, J.L., Jin, H., Hollands, K.G.T. and Naylor, D., 2006, 'Flow Visualization of Natural Convection in a Tall, Air-Filled Vertical Cavity,' Int. J. Heat and Mass Transfer, Vol. 49, pp. 889-904 https://doi.org/10.1016/j.ijheatmasstransfer.2005.06.045
  9. McBain, G.D., 1997, 'Natural Convection with Unsaturated Humid Air in Vertical Cavities,' Int. J. Heat and Mass Transfer, Vol. 40, pp. 3005-3012 https://doi.org/10.1016/S0017-9310(96)00371-7
  10. Jami, M., Mezrhab, A., Bouzidi, M. and Lallemand, P., 2006, 'Lattice Boltzmann Method Applied to the Laminar Natural Convection in an Enclosure with a Heat-Generating Cylinder Conducting Body,' Int. J. Thermal Sci., Available online
  11. Ha, M.Y. and Jung, M.J., 2000, 'A Numerical Study on Three-Dimensional Conjugate Heat Transfer of Natural Convection and Conduction in a Differentially Heated Cubic Enclosure with a Heat-Generating Cubic Conducting Body,' Int. J. Heat and Mass Transfer, Vol. 43, pp. 4229-4248 https://doi.org/10.1016/S0017-9310(00)00063-6
  12. Asan, H., 2000, 'Natural Convection in an Annulus Between Two Isothermal Concentric Square Ducts,' Int. Comm. Heat Mass Transfer, Vol. 27, pp. 367-376 https://doi.org/10.1016/S0735-1933(00)00117-2
  13. Kumar De, A. and Dalal, A., 2006, 'A Numerical Study of Natural Convection around a Square, Horizontal, Heated Cylinder Placed in an Enclosure,' Int. J. Heat and Mass Transfer, Available online
  14. Ghaddar, N.K., 1992, 'Natural Convection Heat Transfer Between a Uniformly Heated Cylindrical Element and Its Rectangular Enclosure,' Int. J. Heat and Mass Transfer, Vol. 35, pp. 2327-2334 https://doi.org/10.1016/0017-9310(92)90075-4
  15. Cesini, G., Paroncini, M., Cortella, G. and Manzan, M., 1999, 'Natural Convection from a Horizontal Cylinder in a Rectangular Cavity,' Int. J. Heat and Mass Transfer, Vol. 42, pp. 1801-1811 https://doi.org/10.1016/S0017-9310(98)00266-X
  16. Moukalled, F. and Acharya, S., 1996, 'Natural Convection in the Annulus Between Concentric Horizontal Circular and Square Cylinders,' Journal of Thermophysics and Heat Transfer, Vol. 10, No. 3, pp. 524-531 https://doi.org/10.2514/3.820
  17. Shu, C. and Zhu, Y.D., 2002, 'Efficient Computation of Natural Convection in a Concentric Annulus between an Outer Square Cylinder and an Inner Circular Cylinder,' Int. J. Numer. Meth. Fluids, Vol. 38, pp. 429-445 https://doi.org/10.1002/fld.226
  18. Shu, C., Xue, H. and Zhu, Y. D., 2000, 'Numerical Study of Natural Convection in an Eccentric Annulus Between a Square Outer Cylinder and a Circular Inner Cylinder Using DQ Method,' Int. J. Heat and Mass Transfer, Vol. 44, pp. 3321-3333 https://doi.org/10.1016/S0017-9310(00)00357-4
  19. Kim, J. and Moin, P., 1985, 'Application of a Fractional Step Method to Incompressible Navier-Stokes Equations,' J. Comp. Physics, Vol. 59, pp. 308-323 https://doi.org/10.1016/0021-9991(85)90148-2
  20. Zang, Y., Street, R.L. and Koseff, J.R., 1994, 'A Non-Staggered Grid, Fractional Step Method for Time-Dependent Incompressible Navier-Stokes Equations in Curvilinear Coordinates,' J. Comp. Physics, Vol. 114, pp. 18-33 https://doi.org/10.1006/jcph.1994.1146
  21. Kim, J.W., Kim, D.J. and Choi, H.C., 2001, 'An Immersed-Boundary Finite-Volume Method for Simulations of Flow in Complex Geometries,' J. Comp. Physics, Vol. 171, pp. 132-150 https://doi.org/10.1006/jcph.2001.6778
  22. Kim, J.W. and Choi, H.C., 2004, 'An Immersed-Boundary Finite-Volume Method for Simulation of Heat Transfer in Complex Geometries,' KSME Int. J., Vol. 18, No. 6, pp. 1026-1035