THERMAL SCIENCE

International Scientific Journal

LATTICE BOLTZMANN SIMULATION OF MELTING PHENOMENON WITH NATURAL CONVECTION FROM AN ECCENTRIC ANNULUS

ABSTRACT
In the present study, a double-population thermal lattice Boltzmann was applied to solve phase change problem with natural convection in an eccentric annulus. The simulation of melting process from a concentrically and eccentrically placed inner hot cylinder inside an outer cold cylinder with Prandtl number of 6.2, Stefan number of 1 and Rayleigh number of 105 was carried out quantitatively. It was found that the position of the inner cylinder inside the outer cylinder significantly influence the flow patterns including the size and shape of two formed vortexes. It is also observed that the maximum of liquid fractions occurs where the inner cylinder is mounted at the bottom of outer cylinder.
KEYWORDS
PAPER SUBMITTED: 2011-05-10
PAPER REVISED: 2012-11-03
PAPER ACCEPTED: 2013-02-19
PUBLISHED ONLINE: 2013-04-13
DOI REFERENCE: https://doi.org/10.2298/TSCI110510012J
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2013, VOLUME 17, ISSUE 3, PAGES [877 - 890]
REFERENCES
  1. Benard, C., Gobin, D., Martinez, F., Melting in rectangular enclosures: experiments and numerical simulations, Journal of Heat Transfer, 107 (1985), 4, pp. 794-803
  2. Wolff, F., Viskanta, R., Melting of pure metal from a vertical wall, Experimental Heat Transfer, 1 (1987), 1, pp. 17-30
  3. Wang, Y., Amiri, A., Vafai, K., An experimental investigation of the melting process in a rectangular enclosure, International Journal of Heat and Mass Transfer, 42 (1999), 19, pp. 3659-3672
  4. Jany, P., Bejan, A., Scaling theory of melting with natural convection in an enclosure, International Journal of Heat and Mass Transfer, 31 (1988), 6, pp. 1221-1235
  5. Zhang, Z., Bejan, A., The problem of time-dependent natural convection melting with conduction in the solid, International Journal of Heat and Mass Transfer, 32 (1989), 12, pp. 2447-2457
  6. Usmani, A. S., Lewis, R. W., Seetharamu, K. N., Finite element modelling of natural-convection-controlled change of phase, International Journal for Numerical Methods in Fluids, 14 (1992), 9, pp. 1019-1036
  7. Javierre, E., et al., A comparison of numerical models for one-dimensional Stefan problems, Journal of Computational and Applied Mathematics, 192 (2006), 2, pp. 445-459
  8. Ng, K. W., Gong, Z. X., Mujumdar, A. S., Heat transfer in free convection-dominated melting of a phase change material in a horizontal annulus, International Communications in Heat and Mass Transfer, 25 (1998), 5, pp. 631-640
  9. Betzel, T., Beer, H., Solidification and melting heat transfer to an unfixed phase change material (PCM) encapsulated in a horizontal concentric annulus, Heat and Mass Transfer, 22 (1988), 6, pp. 335-344
  10. Khillarkar, D. B., Gong, Z. X., Mujumdar, A. S., Melting of a phase change material in concentric horizontal annuli of arbitrary cross-section, Applied Thermal Engineering, 20 (2000), 10, pp. 893-912
  11. Liu, Z., Sun, X., Ma, C., Experimental investigations on the characteristics of melting processes of stearic acid in an annulus and its thermal conductivity enhancement by fins, Energy Conversion and Management, 46 (2005), 6, pp. 959-969
  12. Dutta, R., Atta, A., Dutta, T. K., Experimental and numerical study of heat transfer in horizontal concentric annulus containing phase change material, The Canadian Journal of Chemical Engineering, 86 (2008), 4, pp. 700-710
  13. Tombarevic, E., Vusanovic, I., Modeling of Ice-Water Phase Change in Horizontal Annulus Using Modified Enthalpy Method, Advances in Applied Mathematics and Mechanics, 3 (2011), pp. 354-369
  14. Rabienataj Darzi, A. A., Farhadi, M., Sedighi, K., Numerical study of melting inside concentric and eccentric horizontal annulus, Applied Mathematical Modelling, 36, (2012), 9, pp. 4080-4086
  15. Bertrand, O., et al., Melting driven by natural convection A comparison exercise: first results, International Journal of Thermal Sciences, 38 (1999), 1, pp. 5-26
  16. Tan, L., Zabaras, N., A level set simulation of dendritic solidification with combine features of front-tracking and fixed-domain methods, Journal of Computational Physics, 211 (2006), 1, pp. 36-63
  17. Jin, C., Xu, K., An adaptive grid method for two-dimensional viscous flows, Journal of Computational Physics, 218 (2006), 1, pp. 68-81
  18. Boettinger, W. J., et al., Phase-field simulation of solidification, Annual Review of Materials Research, 32 (2002), pp. 163-194
  19. Wang, C. -C., et al., Application of lattice Boltzmann method and field synergy principle to the heat transfer analysis of channel flow with obstacles inside, Thermal science, 15 (2011), 1, pp. 75-80
  20. Yan, Y. Y., Zu, Y. Q., Numerical simulation of heat transfer and fluid flow past a rotating isothermal cylinder - A LBM approach, International Journal of Heat and Mass Transfer, 51 (2008), 9-10, pp. 2519-2536
  21. Fattahi, E., Farhadi, M., Sedighi, K., Lattice Boltzmann simulation of natural convection heat transfer in eccentric annulus, International Journal of Thermal Sciences, 49 (2010), 12, pp. 2353-2362
  22. Azwadi, C. S. N., Shahrul O. A., Syahrullail, S., Lattice Boltzmann simulation of plume behaviour from an eccentric annulus cylinder, International Journal of Mechanical and Materials Engineering, 5 (2010), 2, pp. 129-135
  23. Fattahi, E., Farhadi, M., Sedighi, K., Lattice Boltzmann simulation of mixed convection heat transfer in eccentric annulus, International Communications in Heat and Mass Transfer, 38 (2011), 8, pp. 1135-1141
  24. Jourabian, M., et al., Melting of NEPCM within a Cylindrical Tube: Numerical Study Using the Lattice Boltzmann Method, Numerical Heat Transfer, Part A, 61 (2012), 12, pp. 929-948
  25. Nemati, H., et al., Lattice Boltzmann simulation of nanofluid in lid-driven cavity, International Communications in Heat and Mass Transfer, 37 (2010), 10, pp. 1528-1534
  26. Fattahi, E., et al., Lattice Boltzmann simulation of natural convection heat transfer in nanofluids, International Journal of Thermal Sciences, 52 (2012), pp. 137-144
  27. Semma, E., et al., Investigation of flows in solidification by using the lattice Boltzmann method, International Journal of Thermal Sciences, 47 (2008), 3, pp. 201-208
  28. Semma, E., Ganaoui, M. El., Bennacer, R., Lattice Boltzmann method for melting/solidification problems, Comptes Rendus Mécanique, 335 (2007), 5-6, pp. 295-303
  29. Ganaoui, M. El., Semma, E. A., A lattice Boltzmann coupled to finite volumes method for solving phase change problems, Thermal Science, 13 (2009), 2, pp. 205-216
  30. Gao, D., Chen, Z., Lattice Boltzmann simulation of natural convection dominated melting in a rectangular cavity filled with porous media, International Journal of Thermal Sciences, 50 (2011), 4, pp. 493-501
  31. Gong, ,S. Cheng, P., A lattice Boltzmann method for simulation of liquid-vapor phase-change heat transfer, International Journal of Heat and Mass Transfer, 55 (2012), 17-18, pp. 4923-4927
  32. Eshraghi, M., Felicelli, S. D., An implicit lattice Boltzmann model for heat conduction with phase change, International Journal of Heat and Mass Transfer, 55 (2012), 9-10, pp. 2420-2428
  33. Miller, W., Succi, S., Mansutti, D., Lattice Boltzmann model for anisotropic liquid-solid phase transition, Physical Review Letters, 86 (2001), 16, pp. 3578-3581
  34. Miller, W., Succi, S., A lattice Boltzmann model for anisotropic crystal growth from melt, Journal of Statistical Physics, 107 (2002), 1-2, pp. 173-186
  35. Rasin, I., Miller, W., Succi, S., Phase-field lattice kinetic scheme for the numerical simulation of dendritic growth, Physical Review E, 72 (2005), 6, pp. 1-10
  36. Medvedev, D., Kassner, K., Lattice Boltzmann scheme for crystal growth in external flows, Physical Review E, 72 (2005), 6, pp. 1-10
  37. Jiaung, W. S., Ho, J. R., Kuo, C. P., Lattice-Boltzmann method for the heat conduction problem with phase change, Numerical Heat Transfer: Part B, 39 (2001), 6, pp. 167-187
  38. Chatterjee, D., Chakraborty, S., An enthalpy-based lattice Boltzmann model for diffusion dominated solid-liquid phase transformation, Physics Letters A, 341 (2005), 1-4, pp. 320-330
  39. Chatterjee, D., Chakraborty, S., An enthalpy-source based lattice Boltzmann model for conduction dominated phase change of pure substances, International Journal of Thermal Sciences, 47 (2008), 5, pp. 552-559
  40. Huber, C., et al., Lattice Boltzmann model for melting with natural convection, International Journal of Heat and Fluid Flow, 29 (2008), 5, pp. 1469-1480
  41. Bodenschatz, E., Pesch, W., Ahlers, G., Recent Developments in Rayleigh-Bénard Convection, Annual Review of Fluid Mechanics, 32 (2000), pp. 709-778
  42. Benzi, R., Succi, S., Vergassola, M., The lattice Boltzmann equation: Theory and applications, Physics Reports, 222 (1992), 3, 145-197
  43. Chen, S., Doolen, G. D., Lattice Boltzmann method for fluid flows, Annual Review of Fluid Mechanics, 30 (1998), pp. 329-364
  44. Succi, S., Lattice Boltzmann Method for Fluid Dynamics and Beyond, Oxford, London, 2001
  45. Djebali, R., et al., Some benchmarks of a side wall heated cavity using lattice Boltzmann approach, Fluid Dynamics & Material Processing (FDMP), 5 (2009), 3, pp. 261-282
  46. Mohamad, A. A., Ganaoui, M. El., Bennacer, R., Lattice Boltzmann simulation of natural convection in an open ended cavity, International Journal of Thermal Sciences, 48 (2009), 10, pp. 1870-1875
  47. Rabienataj Darzi A. A., et al., Mixed convection simulation of inclined lid driven cavity using lattice Boltzmann method, Iranian Journal of Science and Technology, Transection B, 35 (2011), (M1), pp. 209-219
  48. He, X., Chen, S., Doolen, G. D., A novel thermal model for the lattice Boltzmann method incompressible limit, Journal of Computational Physics, 146 (1998), 6, pp. 282-300
  49. Lallemand, P., Luo, L. S., Lattice Boltzmann method for moving boundaries, Journal of Computational Physics, 184 (2003), 2, pp. 406-421
  50. Hou, S., et al., Simulation of cavity flow by the lattice Boltzmann method, Journal of Computational Physics, 118 (1995), 2, pp. 329-347
  51. Shan, X., Simulation of Rayleigh-Benard convection using a lattice Boltzmann method, Physical Review E, 55 (1997), 2, pp. 2780-2788
  52. Guo, Z., Shi, B., Zheng, C., A coupled lattice BGK model for the Boussinesq equations, International Journal for Numerical Methods in Fluids, 39 (2002), 4, pp. 325-342
  53. Guo, Z., Zhao, T. S., A lattice Boltzmann model for convection heat transfer in porous media, Numerical Heat Transfer, Part B, 47 (2005), 2, pp. 157-177
  54. Guo, Z. L., Zheng, Ch., Shi, B. C., An Extrapolation Method for Boundary Conditions in Lattice Boltzmann Method, Physics of Fluids, 14 (2002), 6, pp. 2007-2010
  55. Mei, R., et al., Force evaluation in the lattice Boltzmann method involving curved geometry, Physical Review E, 65 (2002), 4, pp. 1-14
  56. Yu, D., et al., Viscous flow computations with the method of lattice Boltzmann equation, Progress in Aerospace Sciences, 39 (2003), 5, pp. 329-367
  57. Glapke, E. K., Watkins, C. B., Cannon, J. N., Constant heat flux solutions for natural convection between concentric and eccentric horizontal cylinders, Numerical Heat Transfer, 10 (1986), 3, pp. 279-295
  58. Yuan, P., Laura, S., A Thermal Lattice Boltzmann Two-Phase Flow Model and its Application to Heat Transfer Problems—Part 1. Theoretical Foundation, Journal of Fluids Engineering, 128 (2006), 1, pp. 142-150
  59. Vahl Davis, G. D., Natural convection of air in a square cavity: a benchmark numerical solution, International Journal for Numerical Methods in Fluids, 3 (1983), 4, pp. 249-264lattice Boltzmann method, melting, solid liquid phase change, BGK collision, natural convection, phase change material

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