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
THERMAL SCIENCE YEAR
2013, VOLUME
17, ISSUE
Issue 3, PAGES [877 - 890]
- Benard, C., Gobin, D., Martinez, F., Melting in rectangular enclosures: experiments and numerical simulations, Journal of Heat Transfer, 107 (1985), 4, pp. 794-803
- Wolff, F., Viskanta, R., Melting of pure metal from a vertical wall, Experimental Heat Transfer, 1 (1987), 1, pp. 17-30
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Jin, C., Xu, K., An adaptive grid method for two-dimensional viscous flows, Journal of Computational Physics, 218 (2006), 1, pp. 68-81
- Boettinger, W. J., et al., Phase-field simulation of solidification, Annual Review of Materials Research, 32 (2002), pp. 163-194
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Fattahi, E., et al., Lattice Boltzmann simulation of natural convection heat transfer in nanofluids, International Journal of Thermal Sciences, 52 (2012), pp. 137-144
- 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
- Semma, E., Ganaoui, M. El., Bennacer, R., Lattice Boltzmann method for melting/solidification problems, Comptes Rendus Mécanique, 335 (2007), 5-6, pp. 295-303
- 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
- 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
- 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
- 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
- Miller, W., Succi, S., Mansutti, D., Lattice Boltzmann model for anisotropic liquid-solid phase transition, Physical Review Letters, 86 (2001), 16, pp. 3578-3581
- 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
- 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
- Medvedev, D., Kassner, K., Lattice Boltzmann scheme for crystal growth in external flows, Physical Review E, 72 (2005), 6, pp. 1-10
- 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
- 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
- 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
- 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
- Bodenschatz, E., Pesch, W., Ahlers, G., Recent Developments in Rayleigh-Bénard Convection, Annual Review of Fluid Mechanics, 32 (2000), pp. 709-778
- Benzi, R., Succi, S., Vergassola, M., The lattice Boltzmann equation: Theory and applications, Physics Reports, 222 (1992), 3, 145-197
- Chen, S., Doolen, G. D., Lattice Boltzmann method for fluid flows, Annual Review of Fluid Mechanics, 30 (1998), pp. 329-364
- Succi, S., Lattice Boltzmann Method for Fluid Dynamics and Beyond, Oxford, London, 2001
- 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
- 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
- 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
- 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
- Lallemand, P., Luo, L. S., Lattice Boltzmann method for moving boundaries, Journal of Computational Physics, 184 (2003), 2, pp. 406-421
- Hou, S., et al., Simulation of cavity flow by the lattice Boltzmann method, Journal of Computational Physics, 118 (1995), 2, pp. 329-347
- Shan, X., Simulation of Rayleigh-Benard convection using a lattice Boltzmann method, Physical Review E, 55 (1997), 2, pp. 2780-2788
- 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
- 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
- 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
- Mei, R., et al., Force evaluation in the lattice Boltzmann method involving curved geometry, Physical Review E, 65 (2002), 4, pp. 1-14
- Yu, D., et al., Viscous flow computations with the method of lattice Boltzmann equation, Progress in Aerospace Sciences, 39 (2003), 5, pp. 329-367
- 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
- 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
- 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