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Research Papers: Evaporation, Boiling, and Condensation

Coupled Lattice Boltzmann and Meshless Simulation of Natural Convection in the Presence of Volumetric Radiation

[+] Author and Article Information
Kang Luo, Qing Ai

School of Energy Science and Engineering,
Harbin Institute of Technology,
Harbin 150001, China

Hong-Liang Yi

School of Energy Science and Engineering,
Harbin Institute of Technology,
Harbin 150001, China
e-mail: yihongliang@hit.edu.cn

He-Ping Tan

School of Energy Science and Engineering,
Harbin Institute of Technology,
Harbin 150001, China
e-mail: tanheping@hit.edu.cn

1Corresponding authors.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received September 6, 2014; final manuscript received May 7, 2015; published online July 21, 2015. Assoc. Editor: Zhuomin Zhang.

J. Heat Transfer 137(11), 111504 (Jul 21, 2015) (12 pages) Paper No: HT-14-1589; doi: 10.1115/1.4030904 History: Received September 06, 2014

In this work, the coupled lattice Boltzmann and direct collocation meshless (LB–DCM) method is introduced to solve the natural convection in the presence of volumetric radiation in irregular geometries. LB–DCM is a hybrid approach based on a common multiscale Boltzmann-type model. Separate particle distribution functions with multirelaxation time (MRT) and lattice Bhatnagar–Gross–Krook (LBGK) models are used to calculate the flow field and the thermal field, respectively. The radiation transfer equation is computed using the meshless method with moving least-squares (MLS) approximation. The LB–DCM code is first validated by the case of coupled convection–radiation flows in a square cavity. Comparisons show that this combined method is accurate and efficient. Then, the coupled convective and radiative heat transfer in two complex geometries are simulated at various parameters, such as eccentricity, Rayleigh number, and convection–radiation parameter. Numerical results show that the LB–DCM combination is a potential technique for the multifield coupling models, especially with the curved boundary.

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References

Viskanta, R. , 1998, “Overview of Convection and Radiation in High Temperature Gas Flows,” Int. J. Eng. Sci., 36(12–14), pp. 1677–1699. [CrossRef]
Larson, D. W. , and Viskanta, R. , 1976, “Transient Combined Laminar Free Convection and Radiation in a Rectangular Enclosure,” J. Fluid Mech., 78(1), pp. 65–85. [CrossRef]
Kottke, P. A. , Ferguson, T. P. , and Fedorov, A. G. , 2004, “Scale Analysis of Combined Thermal Radiation and Convection Heat Transfer,” ASME J. Heat Transfer, 126(2), pp. 250–258. [CrossRef]
Banda, M. K. , Klar, A. , and Seaïd, M. , 2007, “A Lattice-Boltzmann Relaxation Scheme for Coupled Convection–Radiation Systems,” J. Comput. Phys., 226(2), pp. 1408–1431. [CrossRef]
Mezrhab, A. , Jami, M. , Bouzidi, M. , and Lallemand, P. , 2007, “Analysis of Radiation–Natural Convection in a Divided Enclosure Using the Lattice Boltzmann Method,” Comput. Fluids, 36(2), pp. 423–434. [CrossRef]
Bouali, H. , Mezrhab, A. , Amaoui, H. , and Bouzidi, M. , 2006, “Radiation–Natural Convection Heat Transfer in an Inclined Rectangular Enclosure,” Int. J. Therm. Sci., 45(6), pp. 553–566. [CrossRef]
Mondal, B. , and Mishra, S. C. , 2008, “Simulation of Natural Convection in the Presence of Volumetric Radiation Using the Lattice Boltzmann Method,” Numer. Heat Transfer, Part A, 55(1), pp. 18–41. [CrossRef]
Mondal, B. , and Li, X. , 2010, “Effect of Volumetric Radiation on Natural Convection in a Square Cavity Using Lattice Boltzmann Method With Non-Uniform Lattices,” Int. J. Heat Mass Transfer, 53(21–22), pp. 4935–4948. [CrossRef]
Lari, K. , Baneshi, M. , Gandjalikhan Nassab, S. A. , Komiya, A. , and Maruyama, S. , 2011, “Combined Heat Transfer of Radiation and Natural Convection in a Square Cavity Containing Participating Gases,” Int. J. Heat Mass Transfer, 54(23–24), pp. 5087–5099. [CrossRef]
Ansari, A. B. , and Nassab, S. A. G. , 2011, “Study of Laminar Forced Convection of Radiating Gas Over an Inclined Backward Facing Step Under Bleeding Condition Using the Blocked-Off Method,” ASME J. Heat Transfer, 133(7), p. 072702. [CrossRef]
Moufekkir, F. , Moussaoui, M. A. , Mezrhab, A. , Bouzidi, M. , and Laraqi, N. , 2013, “Study of Double-Diffusive Natural Convection and Radiation in an Inclined Cavity Using Lattice Boltzmann Method,” Int. J. Therm. Sci., 63, pp. 65–86. [CrossRef]
Moufekkir, F. , Moussaoui, M. A. , Mezrhab, A. , Fontaine, J. P. , and Bouzidi, M. , 2013, “Investigation of Double Diffusive Natural Convection in Presence of Gray Gas Radiation Within a Square Cavity Using Multiple Relaxation Time Lattice Boltzmann Method,” ASME J. Heat Transfer, 135(10), p. 102701. [CrossRef]
Luo, K. , Cao, Z. H. , Yi, H. L. , and Tan, H.-P. , 2014, “Convection–Radiation Interaction in 3-D Irregular Enclosures Using the Least Squares Finite Element Method,” Numer. Heat Transfer, Part A, 66(2), pp. 165–184. [CrossRef]
Luo, K. , Yi, H. L. , and Tan, H. P. , 2014, “Radiation Effects on Bifurcation and Dual Solutions in Transient Natural Convection in a Horizontal Annulus,” AIP Adv., 4(5), p. 057123. [CrossRef]
Luo, K. , Yi, H. L. , and Tan, H. P. , 2014, “Coupled Radiation and Mixed Convection in an Eccentric Annulus Using the Hybrid Strategy of Lattice Boltzmann-Meshless Method,” Numer. Heat Transfer, Part B, 66(3), pp. 243–267. [CrossRef]
Chen, S. , and Doolen, G. D. , 1998, “Lattice Boltzmann Method for Fluid Flows,” Annu. Rev. Fluid Mech., 30(1), pp. 329–364. [CrossRef]
Succi, S. , 2001, The Lattice Boltzmann Equation: For Fluid Dynamics and Beyond, Oxford University Press, Oxford, UK.
Aidun, C. K. , and Clausen, J. R. , 2009, “Lattice-Boltzmann Method for Complex Flows,” Annu. Rev. Fluid Mech., 42(1), pp. 439–472. [CrossRef]
Higuera, F. J. , Succi, S. , and Benzi, R. , 1989, “Lattice Gas Dynamics With Enhanced Collisions,” Europhys. Lett., 9(4), pp. 345–349. [CrossRef]
Jiaung, W. S. , Ho, J. R. , and Kuo, C. P. , 2001, “Lattice Boltzmann Method for the Heat Conduction Problem With Phase Change,” Numer. Heat Transfer, Part B, 39(2), pp. 167–187. [CrossRef]
Jeong, N. , Choi, D. H. , and Lin, C. L. , 2008, “Estimation of Thermal and Mass Diffusivity in a Porous Medium of Complex Structure Using a Lattice Boltzmann Method,” Int. J. Heat Mass Transfer, 51(15–16), pp. 3913–3923. [CrossRef]
Asinari, P. , Mishra, S. C. , and Borchiellini, R. , 2010, “A Lattice Boltzmann Formulation for the Analysis of Radiative Heat Transfer Problems in a Participating Medium,” Numer. Heat Transfer, Part B, 57(2), pp. 126–146. [CrossRef]
Fattahi, E. , Farhadi, M. , and Sedighi, K. , 2010, “Lattice Boltzmann Simulation of Natural Convection Heat Transfer in Eccentric Annulus,” Int. J. Therm. Sci., 49(12), pp. 2353–2362. [CrossRef]
Mohamad, A. A. , and Kuzmin, A. , 2010, “A Critical Evaluation of Force Term in Lattice Boltzmann Method, Natural Convection Problem,” Int. J. Heat Mass Transfer, 53(5–6), pp. 990–996. [CrossRef]
Mishra, S. C. , Lankadasu, A. , and Beronov, K. N. , 2005, “Application of the Lattice Boltzmann Method for Solving the Energy Equation of a 2-D Transient Conduction–Radiation Problem,” Int. J. Heat Mass Transfer, 48(17), pp. 3648–3659. [CrossRef]
Filippova, O. , Succi, S. , Mazzocco, F. , Arrighetti, C. , Bella, G. , and Hänel, D. , 2001, “Multiscale Lattice Boltzmann Schemes With Turbulence Modeling,” J. Comput. Phys., 170(2), pp. 812–829. [CrossRef]
Wallace, J. R. , Elmquist, K. A. , and Haines, E. A. , 1989, “A Ray Tracing Algorithm for Progressive Radiosity,” SIGGRAPH Comput. Graphics, 23(3), pp. 315–324. [CrossRef]
Wang, A. , Modest, M. F. , Haworth, D. C. , and Wang, L. , 2008, “Monte Carlo Simulation of Radiative Heat Transfer and Turbulence Interactions in Methane/Air Jet Flames,” J. Quant. Spectrosc. Radiat. Transfer, 109(2), pp. 269–279. [CrossRef]
Mishra, S. C. , and Lankadasu, A. , 2005, “Transient Conduction–Radiation Heat Transfer in Participating Media Using the Lattice Boltzmann Method and the Discrete Transfer Method,” Numer. Heat Transfer, Part A, 47(9), pp. 935–954. [CrossRef]
Ismail, K. A. R. , and Salinas, C. S. , 2004, “Application of Multidimensional Scheme and the Discrete Ordinate Method to Radiative Heat Transfer in a Two-Dimensional Enclosure With Diffusely Emitting and Reflecting Boundary Walls,” J. Quant. Spectrosc. Radiat. Transfer, 88(4), pp. 407–422. [CrossRef]
Kim, C. , Kim, M. Y. , Yu, M. J. , and Mishra, S. C. , 2010, “Unstructured Polygonal Finite-Volume Solutions of Radiative Heat Transfer in a Complex Axisymmetric Enclosure,” Numer. Heat Transfer, Part B, 57(3), pp. 227–239. [CrossRef]
Liu, L. H. , Zhang, L. , and Tan, H. P. , 2006, “Finite Element Method for Radiation Heat Transfer in Multi-Dimensional Graded Index Medium,” J. Quant. Spectrosc. Radiat. Transfer, 97(3), pp. 436–445. [CrossRef]
Tan, J. Y. , Zhao, J. M. , Liu, L. H. , and Wang, Y. Y. , 2009, “Comparative Study on Accuracy and Solution Cost of the First/Second-Order Radiative Transfer Equations Using the Meshless Method,” Numer. Heat Transfer, Part B, 55(4), pp. 324–337. [CrossRef]
Wang, C. A. , Sadat, H. , Ledez, V. , and Lemonnier, D. , 2010, “Meshless Method for Solving Radiative Transfer Problems in Complex Two-Dimensional and Three-Dimensional Geometries,” Int. J. Therm. Sci., 49(12), pp. 2282–2288. [CrossRef]
Luo, K. , Cao, Z. H. , Yi, H. L. , and Tan, H. P. , 2014, “A Direct Collocation Meshless Approach With Upwind Scheme for Radiative Transfer in Strongly Inhomogeneous Media,” J. Quant. Spectrosc. Radiat. Transfer, 135, pp. 66–80. [CrossRef]
Tan, J. Y. , Liu, L. H. , and Li, B. X. , 2006, “Least-Squares Radial Point Interpolation Collocation Meshless Method for Radiative Heat Transfer,” ASME J. Heat Transfer, 129(5), pp. 669–673. [CrossRef]
Lallemand, P. , and Luo, L. S. , 2003, “Lattice Boltzmann Method for Moving Boundaries,” J. Comput. Phys., 184(2), pp. 406–421. [CrossRef]
Luo, L. S. , Liao, W. , Chen, X. , Peng, Y. , and Zhang, W. , 2011, “Numerics of the Lattice Boltzmann Method: Effects of Collision Models on the Lattice Boltzmann Simulations,” Phys. Rev. E, 83(5), p. 056710. [CrossRef]
Lallemand, P. , and Luo, L. S. , 2000, “Theory of the Lattice Boltzmann Method: Dispersion, Dissipation, Isotropy, Galilean Invariance, and Stability,” Phys. Rev. E, 61(6), pp. 6546–6562. [CrossRef]
Mishra, S. C. , and Roy, H. K. , 2007, “Solving Transient Conduction and Radiation Heat Transfer Problems Using the Lattice Boltzmann Method and the Finite Volume Method,” J. Comput. Phys., 223(1), pp. 89–107. [CrossRef]
Zhao, J. M. , Tan, J. Y. , and Liu, L. H. , 2013, “A Second Order Radiative Transfer Equation and Its Solution by Meshless Method With Application to Strongly Inhomogeneous Media,” J. Comput. Phys., 232(1), pp. 431–455. [CrossRef]
Nayroles, B. , Touzot, G. , and Villon, P. , 1992, “Generalizing the Finite Element Method: Diffuse Approximation and Diffuse Elements,” Comput. Mech., 10(5), pp. 307–318. [CrossRef]
Wendland, H. , 1995, “Piecewise Polynomial, Positive Definite and Compactly Supported Radial Functions of Minimal Degree,” Adv. Comput. Math., 4(1), pp. 389–396. [CrossRef]
Gallivan, M. A. , Noble, D. R. , Georgiadis, J. G. , and Buckius, R. O. , 1997, “An Evaluation of the Bounce-Back Boundary Condition for Lattice Boltzmann Simulations,” Int. J. Numer. Methods Fluids, 25(3), pp. 249–263. [CrossRef]
Yu, D. , Mei, R. , Luo, L. S. , and Shyy, W. , 2003, “Viscous Flow Computations With the Method of Lattice Boltzmann Equation,” Prog. Aerosp. Sci., 39(5), pp. 329–367. [CrossRef]
Guo, Z. , Zheng, C. , and Shi, B. , 2002, “An Extrapolation Method for Boundary Conditions in Lattice Boltzmann Method,” Phys. Fluids, 14(6), pp. 2007–2010. [CrossRef]
Dixit, H. N. , and Babu, V. , 2006, “Simulation of High Rayleigh Number Natural Convection in a Square Cavity Using the Lattice Boltzmann Method,” Int. J. Heat Mass Transfer, 49(3–4), pp. 727–739. [CrossRef]
Fattahi, E. , Farhadi, M. , and Sedighi, K. , 2011, “Lattice Boltzmann Simulation of Mixed Convection Heat Transfer in Eccentric Annulus,” Int. Commun. Heat Mass Transfer, 38(8), pp. 1135–1141. [CrossRef]
Kim, B. S. , Lee, D. S. , Ha, M. Y. , and Yoon, H. S. , 2008, “A Numerical Study of Natural Convection in a Square Enclosure With a Circular Cylinder at Different Vertical Locations,” Int. J. Heat Mass Transfer, 51(7–8), pp. 1888–1906. [CrossRef]
Hussain, S. H. , and Hussein, A. K. , 2010, “Numerical Investigation of Natural Convection Phenomena in a Uniformly Heated Circular Cylinder Immersed in Square Enclosure Filled With Air at Different Vertical Locations,” Int. Commun. Heat Mass Transfer, 37(8), pp. 1115–1126. [CrossRef]
Lee, J. M. , Ha, M. Y. , and Yoon, H. S. , 2010, “Natural Convection in a Square Enclosure With a Circular Cylinder at Different Horizontal and Diagonal Locations,” Int. J. Heat Mass Transfer, 53(25–26), pp. 5905–5919. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Schematic of the LB–DCM system: (a) D2Q9 LB model for convection with the lattice cells as the basic computational units in which the fluid particles undergo collision and streaming steps, (b) the arrangement of lattices and collocation points, and (c) DCM method with MLS approximation for radiation where the lattice nodes are taken as collocation points for MLS approximation

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Fig. 2

Layout of the regularly spaced lattices and curved wall boundary: lattice and boundary nodes are taken as collocation points

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Fig. 3

General flow chart of LB–DCM method

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Fig. 4

Geometries of (a) a square cavity, (b) eccentric annulus, and (c) a square cavity with an internal cylinder

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Fig. 5

Total Nusselt number along inner cylinder for Rc = 1 and τ = 10 at different Ra: comparison of LB–DCM and FVM–DOM

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Fig. 6

Isotherms (top) and streamlines (bottom) in eccentric annulus at different eccentricities for Ra=104, Rc=1, and τ=10: (a) ɛ=(0.5,0), (b) ɛ=(0.5,π/2), (c) ɛ=(0.5,π), and (d) ɛ=(0.5,3π/2)

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Fig. 7

Isotherms (top) and streamlines (bottom) in eccentric annulus at different Rayleigh numbers for ɛ=(0.5,0), Rc=1, and τ=10: (a) Ra=103, (b) Ra=104, (c) Ra=3×104, and (d) Ra=105

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Fig. 8

Isotherms (top) and streamlines (bottom) in eccentric annulus at different convection–radiation parameters for ɛ=(0.5,0), Ra=104, and τ=10: (a) Rc=0.1, (b) Rc=0.5, (c) Rc=1, and (d) Rc=5

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Fig. 9

The distributions of total Nusselt number along the inner cylinder of eccentric annulus at different parameters: (a) effect of ε, (b) effect of Ra, (c) effect of Rc, and (d) effect of τ

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Fig. 10

Nondimensional temperature (left) and incident radiation (right) in a square cavity with an internal cylinder at different Rayleigh numbers for Rc=1 and τ=10: (a) Ra=103, (b) Ra=104, (c) Ra=3×104, and (d) Ra=105

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Fig. 11

The distributions of Nusselt number along the inner cylinder immersed in a square cavity at different Rayleigh numbers for Rc=1 and τ=10: (a) convective, (b) radiative, and (c) total Nusselt number

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