Numerical Analysis of Turbulent Natural Convection in a Square Cavity using Large- Eddy Simulation in Lattice Boltzmann Method
In this paper Lattice Boltzmann simulation of
turbulent natural convection with large-eddy simulations (LES) in a
square cavity which is filled by water has been investigated. The
present results are validated by finds of other investigations which
have been done with different numerical methods. Calculations were
performed for high Rayleigh numbers of Ra=108 and 109. The results
confirm that this method is in acceptable agreement with other
verifications of such a flow. In this investigation is tried to present
Large-eddy turbulence flow model by Lattice Boltzmann Method
(LBM) with a clear and simple statement. Effects of increase in
Rayleigh number are displayed on streamlines, isotherm counters and
average Nusselt number. Result shows that the average Nusselt
number enhances with growth of the Rayleigh numbers.
[1] H. Tennekes, J.L. Lumley, "A First Course in Turbulence", MIT Press,
Cambridge, (1972).
[2] G. de Vahl Davis, Natural convection of air in a square cavity: a
benchmark numerical solution, Int. J. Numer. Meth. Fluids 3, (1983)
249-264.
[3] R.A.W.M. Henkes, C.J. Hoogendoorn, Scaling of the laminar naturalconvection
flow in a heated square cavity, Int. J. Heat Mass Transfer, 36
(1992) 2913-2925.
[4] N.C. Markatos, K.A. Pericleous, Laminar and turbulent natural
convection in an enclosed cavity, Int. J. Heat Mass Transfer, 27 (1984)
755-772.
[5] P. Le Que, Accurate solutions to the square thermally driven cavity at
high Rayleigh number, Comput. Fluids, 20 (1991) 29-41.
[6] Y. Peng, C. Shu, Y.T. Chew, Simplified thermal Lattice Boltzmann
model for incompressible thermal flows, Phys. Rev. E, 68 (2003).
[7] A. D._Orazio, M. Corcione, G.P. Celata, Application to natural
convection enclosed flows of a Lattice Boltzmann BGK model coupled
with a general purpose thermal boundary condition, Int. J. Therm. Sci,
43 (2004) 575-586.
[8] H. Liu, C. Zou, B. Shi, Z. Tian, L. Zhang, C. Zheng, Thermal Lattice-
BGK model based on large-eddy simulation of turbulent natural
convection due to internal heat generation, In. J. Heat and Mass
Transfer, 49 (2006) 4672-4680.
[9] U.Frisch, B.Hasslacher and Y.Pomeau, Lattice-Gas Automata For
Navier-Stokes Equation, Phys. Rev. Lett, 56 (1986) 1505-1508.
[10] G.McNamara, G.Zanetti, Use of the Boltzmann equation to simulate
the Lattice gas automata, Phys. Rev. Lett, 61 (1988) 2332-2335.
[11] F.J.Higuera, J.Jimenez, Boltzmann approach to Lattice-gas simulation,
Europhys. Ltt, 9 (1989) 663-668.
[12] J.A.V.M.Koelman, A simple Lattice Boltzmann Scheme for Navier-
Stokes Fluid Flow, Europhus. Lett, 15 (1991) 603-607.
[13] C.hudong, Recovery of Navier-Stokes equation using a Lattice-gas
Boltzmann equation method, Physical review A., 45(8) (1992) 5339-
5342.
[14] A. Horvat, I. Kljenak, J. Marn, Two-dimensional large-eddy simulation
of turbulent natural convection due to internal heat generation, Int. J.
Heat and Mass transfer 44 (2001) 3985-3995.
[15] S. Hou, J. Sterling, S. Chen, G.D. Doolen, A Lattice Boltzmann subgrid
model for high Reynolds number flows, Fields Inst. Comm, 6 (1996)
151-166.
[16] C.M. Teixeira, Incorporation turbulence models into the Lattice-
Boltzmann method, Int. J. Mod. Phys. C, 9 (1998) 1159-1175.
[17] M. Krafczyk, J. Tolke, L.S. Luo, Large-eddy simulations with a
multiple-relaxation-time LBE model, Int. J. Mod. Phys. B, 17 (2003)
33-39.
[18] G. Barakos, E. Mitsoulis, D. Assimacopoulos, Natural convection flow
in a square cavity revisited: laminar and turbulent models with wall
function, Int. J. Numerical Method in Fluids, 18 (1994) 695-719.
[19] H.N. Dixit, V. Babu, Simulation of high Rayleigh number natural
convection in a square cavity using the Lattice Boltzmann method, Int.
J. Heat and Mass Transfer, 46 (2006) 727-739.
[1] H. Tennekes, J.L. Lumley, "A First Course in Turbulence", MIT Press,
Cambridge, (1972).
[2] G. de Vahl Davis, Natural convection of air in a square cavity: a
benchmark numerical solution, Int. J. Numer. Meth. Fluids 3, (1983)
249-264.
[3] R.A.W.M. Henkes, C.J. Hoogendoorn, Scaling of the laminar naturalconvection
flow in a heated square cavity, Int. J. Heat Mass Transfer, 36
(1992) 2913-2925.
[4] N.C. Markatos, K.A. Pericleous, Laminar and turbulent natural
convection in an enclosed cavity, Int. J. Heat Mass Transfer, 27 (1984)
755-772.
[5] P. Le Que, Accurate solutions to the square thermally driven cavity at
high Rayleigh number, Comput. Fluids, 20 (1991) 29-41.
[6] Y. Peng, C. Shu, Y.T. Chew, Simplified thermal Lattice Boltzmann
model for incompressible thermal flows, Phys. Rev. E, 68 (2003).
[7] A. D._Orazio, M. Corcione, G.P. Celata, Application to natural
convection enclosed flows of a Lattice Boltzmann BGK model coupled
with a general purpose thermal boundary condition, Int. J. Therm. Sci,
43 (2004) 575-586.
[8] H. Liu, C. Zou, B. Shi, Z. Tian, L. Zhang, C. Zheng, Thermal Lattice-
BGK model based on large-eddy simulation of turbulent natural
convection due to internal heat generation, In. J. Heat and Mass
Transfer, 49 (2006) 4672-4680.
[9] U.Frisch, B.Hasslacher and Y.Pomeau, Lattice-Gas Automata For
Navier-Stokes Equation, Phys. Rev. Lett, 56 (1986) 1505-1508.
[10] G.McNamara, G.Zanetti, Use of the Boltzmann equation to simulate
the Lattice gas automata, Phys. Rev. Lett, 61 (1988) 2332-2335.
[11] F.J.Higuera, J.Jimenez, Boltzmann approach to Lattice-gas simulation,
Europhys. Ltt, 9 (1989) 663-668.
[12] J.A.V.M.Koelman, A simple Lattice Boltzmann Scheme for Navier-
Stokes Fluid Flow, Europhus. Lett, 15 (1991) 603-607.
[13] C.hudong, Recovery of Navier-Stokes equation using a Lattice-gas
Boltzmann equation method, Physical review A., 45(8) (1992) 5339-
5342.
[14] A. Horvat, I. Kljenak, J. Marn, Two-dimensional large-eddy simulation
of turbulent natural convection due to internal heat generation, Int. J.
Heat and Mass transfer 44 (2001) 3985-3995.
[15] S. Hou, J. Sterling, S. Chen, G.D. Doolen, A Lattice Boltzmann subgrid
model for high Reynolds number flows, Fields Inst. Comm, 6 (1996)
151-166.
[16] C.M. Teixeira, Incorporation turbulence models into the Lattice-
Boltzmann method, Int. J. Mod. Phys. C, 9 (1998) 1159-1175.
[17] M. Krafczyk, J. Tolke, L.S. Luo, Large-eddy simulations with a
multiple-relaxation-time LBE model, Int. J. Mod. Phys. B, 17 (2003)
33-39.
[18] G. Barakos, E. Mitsoulis, D. Assimacopoulos, Natural convection flow
in a square cavity revisited: laminar and turbulent models with wall
function, Int. J. Numerical Method in Fluids, 18 (1994) 695-719.
[19] H.N. Dixit, V. Babu, Simulation of high Rayleigh number natural
convection in a square cavity using the Lattice Boltzmann method, Int.
J. Heat and Mass Transfer, 46 (2006) 727-739.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:64164", author = "H. Sajjadi and M. Gorji and GH.R. Kefayati and D. D. Ganji and M. Shayan Nia", title = "Numerical Analysis of Turbulent Natural Convection in a Square Cavity using Large- Eddy Simulation in Lattice Boltzmann Method", abstract = "In this paper Lattice Boltzmann simulation of
turbulent natural convection with large-eddy simulations (LES) in a
square cavity which is filled by water has been investigated. The
present results are validated by finds of other investigations which
have been done with different numerical methods. Calculations were
performed for high Rayleigh numbers of Ra=108 and 109. The results
confirm that this method is in acceptable agreement with other
verifications of such a flow. In this investigation is tried to present
Large-eddy turbulence flow model by Lattice Boltzmann Method
(LBM) with a clear and simple statement. Effects of increase in
Rayleigh number are displayed on streamlines, isotherm counters and
average Nusselt number. Result shows that the average Nusselt
number enhances with growth of the Rayleigh numbers.", keywords = "Turbulent natural convection, Large Eddy
Simulation, Lattice Boltzmann Method", volume = "6", number = "1", pages = "357-5", }
