Simulation of Fluid Flow and Heat Transfer in Inclined Cavity using Lattice Boltzmann Method
In this paper, Lattice Boltzmann Method (LBM) is used to study laminar flow with mixed convection heat transfer inside a two-dimensional inclined lid-driven rectangular cavity with aspect ratio AR = 3. Bottom wall of the cavity is maintained at lower temperature than the top lid, and its vertical walls are assumed insulated. Top lid motion results in fluid motion inside the cavity. Inclination of the cavity causes horizontal and vertical components of velocity to be affected by buoyancy force. To include this effect, calculation procedure of macroscopic properties by LBM is changed and collision term of Boltzmann equation is modified. A computer program is developed to simulate this problem using BGK model of lattice Boltzmann method. The effects of the variations of Richardson number and inclination angle on the thermal and flow behavior of the fluid inside the cavity are investigated. The results are presented as velocity and temperature profiles, stream function contours and isotherms. It is concluded that LBM has good potential to simulate mixed convection heat transfer problems.
[1] Patil D.-V., Lakshmisha K.-N., Rogg B., Lattice Boltzmann simulation
of lid-driven flow in deep cavities, Computers & Fluids 35 (2006) 1116-
1125.
[2] D-Orazio A., Corcione M., Celata G.-P., Application to natural
convection enclosed flows of a lattice Boltzmann BGK model coupled
with a general purpose thermal boundary condition, Int. J. of Thermal
Sciences 43 (2004) 575-586.
[3] Chen S., Doolen G., Lattice Boltzmann method for fluid flows, Annual
Rev. Fluid Mech. 30 (1998) 329-364.
[4] Luo L., The lattice gas and lattice Boltzmann methods: Past, present, and
future, Appl. Comput. Fluid Dyn, Beijing (2000) 52-83.
[5] Succi S., The lattice Boltzmann equation for fluid dynamics and beyond,
Oxford, Oxford University Press (2001).
[6] Qian Y., Humie`res D., Lallemand P., Lattice BGK models for Navier-
Stokes equation, Europhys. Lett. 17 (1992) 479-484.
[7] He X., Luo L., Theory of the lattice Boltzmann equation: From the
Boltzmann equation to the lattice Boltzmann equation, Phys. Rev. 56
(1997) 6811-6817.
[8] Yu D., Mei R., Luo L., Shyy W., Viscous flow computations with the
method of lattice Boltzmann equation, Progress in Aerospace Sciences
39 (2003) 329-367.
[9] Guo Zh., Shi B., Wang N., Lattice BGK model for incompressible
Navier-Stokes equation, J. of Computational Physics 165 (2000) 288-
306.
[10] Hou Sh., Zou Q., Chen Sh., Doolen G.-D., Cogley A.-C., Simulation of
cavity flow by the lattice Boltzmann method, J. Comput. Phys. 118
(1995) 329-347.
[11] Wu J.-S., Shao Y.-L., Simulation of lid-driven cavity flows by parallel
lattice Boltzmann method using multi-relaxation-time scheme, Int. J.
Numer. Meth. Fluids 46 (2004) 921-937.
[12] He X., Chen Sh., Doolen G.-D., A novel thermal model for the lattice
Boltzmann method in incompressible limit, J. of Computational Physics
146 (1998) 282-300.
[13] Eggels J.-G.-M., Somers J.-A., Numerical simulation of free convective
flow using the lattice Boltzmann scheme, Int. J. Heat and Fluid Flow 16
(1995) 357-364.
[14] Dixit H.-N., Babu V., Simulation of high Rayleigh number natural
convection in a square cavity using the lattice Boltzmann method, Int. J.
of Heat and Mass Transfer 49 (2006) 727-739.
[15] Barrios G., Rechtman R., Rojas J., Tovar R., The lattice Boltzmann
equation for natural convection in a two-dimensional cavity with a
partially heated wall, J. Fluid Mech. 522 (2005) 91-100.
[16] Kao P.-H., Yang R.-J., Simulating oscillatory flows in Rayleigh Benard
convection using the lattice Boltzmann method, Int. J. of Heat and Mass
Transfer 50 (2007) 3315-3328.
[17] Bhatnagar P. L., Gross E. P., Krook M., A model for collision process in
gases. I. Small amplitude processes in charged and neutral onecomponent
system, Phys. Rev. 94 (1954) 511-1954.
[18] Cercignani C., The Boltzmann equation and its applications, Applied
Mathematical Sciences, Springer-Verlag, New York 61 (1988).
[19] He X., Luo L., A priori derivation of the lattice Boltzmann equation,
Phys. Rev. E 55 (6) (1997) R6333-R6336.
[20] Zou Q., He X., On pressure and velocity boundary conditions for the
lattice Boltzmann BGK model, Phys. Fluids 9 (6) (1997) 1591-1596.
[21] Ziegler DP., Boundary conditions for lattice Boltzmann simulations. J.
Stat. Phys. 71 (1993) 1171-1177.
[22] Ginzbourg I., Alder PM., Boundary flow condition analysis for the
three-dimensional lattice Boltzmann model. J Phys. II France 4 (1994)
191-214.
[23] D-Orazio A., Succi S., Simulating two-dimensional thermal channel
flows by means of a lattice Boltzmann method with new boundary
conditions, Future Generation Computer Systems 20 (2004) 935-944.
[24] Kuznik F., Vareilles J., Rusaouen G., Krauss G., A double-population
lattice Boltzmann method with non-uniform mesh for the simulation of
natural convection in a square cavity, Int. J. of Heat and Fluid Flow 28
(2007) 862-870.
[25] Iwatsu R., Hyun J.-M., Kuwahara K., Mixed convection in a driven
cavity with a stable vertical temperature gradient, Int. J. Heat Mass
Transfer 36 (1993) 1601-1608.
[26] Prasad Y.-S., Das M.-K., Hopf bifurcation in mixed convection flow
inside a rectangular cavity, Int. J. of Heat and Mass Transfer 50 (2007)
3583-3598.
[1] Patil D.-V., Lakshmisha K.-N., Rogg B., Lattice Boltzmann simulation
of lid-driven flow in deep cavities, Computers & Fluids 35 (2006) 1116-
1125.
[2] D-Orazio A., Corcione M., Celata G.-P., Application to natural
convection enclosed flows of a lattice Boltzmann BGK model coupled
with a general purpose thermal boundary condition, Int. J. of Thermal
Sciences 43 (2004) 575-586.
[3] Chen S., Doolen G., Lattice Boltzmann method for fluid flows, Annual
Rev. Fluid Mech. 30 (1998) 329-364.
[4] Luo L., The lattice gas and lattice Boltzmann methods: Past, present, and
future, Appl. Comput. Fluid Dyn, Beijing (2000) 52-83.
[5] Succi S., The lattice Boltzmann equation for fluid dynamics and beyond,
Oxford, Oxford University Press (2001).
[6] Qian Y., Humie`res D., Lallemand P., Lattice BGK models for Navier-
Stokes equation, Europhys. Lett. 17 (1992) 479-484.
[7] He X., Luo L., Theory of the lattice Boltzmann equation: From the
Boltzmann equation to the lattice Boltzmann equation, Phys. Rev. 56
(1997) 6811-6817.
[8] Yu D., Mei R., Luo L., Shyy W., Viscous flow computations with the
method of lattice Boltzmann equation, Progress in Aerospace Sciences
39 (2003) 329-367.
[9] Guo Zh., Shi B., Wang N., Lattice BGK model for incompressible
Navier-Stokes equation, J. of Computational Physics 165 (2000) 288-
306.
[10] Hou Sh., Zou Q., Chen Sh., Doolen G.-D., Cogley A.-C., Simulation of
cavity flow by the lattice Boltzmann method, J. Comput. Phys. 118
(1995) 329-347.
[11] Wu J.-S., Shao Y.-L., Simulation of lid-driven cavity flows by parallel
lattice Boltzmann method using multi-relaxation-time scheme, Int. J.
Numer. Meth. Fluids 46 (2004) 921-937.
[12] He X., Chen Sh., Doolen G.-D., A novel thermal model for the lattice
Boltzmann method in incompressible limit, J. of Computational Physics
146 (1998) 282-300.
[13] Eggels J.-G.-M., Somers J.-A., Numerical simulation of free convective
flow using the lattice Boltzmann scheme, Int. J. Heat and Fluid Flow 16
(1995) 357-364.
[14] Dixit H.-N., Babu V., Simulation of high Rayleigh number natural
convection in a square cavity using the lattice Boltzmann method, Int. J.
of Heat and Mass Transfer 49 (2006) 727-739.
[15] Barrios G., Rechtman R., Rojas J., Tovar R., The lattice Boltzmann
equation for natural convection in a two-dimensional cavity with a
partially heated wall, J. Fluid Mech. 522 (2005) 91-100.
[16] Kao P.-H., Yang R.-J., Simulating oscillatory flows in Rayleigh Benard
convection using the lattice Boltzmann method, Int. J. of Heat and Mass
Transfer 50 (2007) 3315-3328.
[17] Bhatnagar P. L., Gross E. P., Krook M., A model for collision process in
gases. I. Small amplitude processes in charged and neutral onecomponent
system, Phys. Rev. 94 (1954) 511-1954.
[18] Cercignani C., The Boltzmann equation and its applications, Applied
Mathematical Sciences, Springer-Verlag, New York 61 (1988).
[19] He X., Luo L., A priori derivation of the lattice Boltzmann equation,
Phys. Rev. E 55 (6) (1997) R6333-R6336.
[20] Zou Q., He X., On pressure and velocity boundary conditions for the
lattice Boltzmann BGK model, Phys. Fluids 9 (6) (1997) 1591-1596.
[21] Ziegler DP., Boundary conditions for lattice Boltzmann simulations. J.
Stat. Phys. 71 (1993) 1171-1177.
[22] Ginzbourg I., Alder PM., Boundary flow condition analysis for the
three-dimensional lattice Boltzmann model. J Phys. II France 4 (1994)
191-214.
[23] D-Orazio A., Succi S., Simulating two-dimensional thermal channel
flows by means of a lattice Boltzmann method with new boundary
conditions, Future Generation Computer Systems 20 (2004) 935-944.
[24] Kuznik F., Vareilles J., Rusaouen G., Krauss G., A double-population
lattice Boltzmann method with non-uniform mesh for the simulation of
natural convection in a square cavity, Int. J. of Heat and Fluid Flow 28
(2007) 862-870.
[25] Iwatsu R., Hyun J.-M., Kuwahara K., Mixed convection in a driven
cavity with a stable vertical temperature gradient, Int. J. Heat Mass
Transfer 36 (1993) 1601-1608.
[26] Prasad Y.-S., Das M.-K., Hopf bifurcation in mixed convection flow
inside a rectangular cavity, Int. J. of Heat and Mass Transfer 50 (2007)
3583-3598.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:51641", author = "Arash Karimipour and A. Hossein Nezhad and E. Shirani and A. Safaei", title = "Simulation of Fluid Flow and Heat Transfer in Inclined Cavity using Lattice Boltzmann Method", abstract = "In this paper, Lattice Boltzmann Method (LBM) is used to study laminar flow with mixed convection heat transfer inside a two-dimensional inclined lid-driven rectangular cavity with aspect ratio AR = 3. Bottom wall of the cavity is maintained at lower temperature than the top lid, and its vertical walls are assumed insulated. Top lid motion results in fluid motion inside the cavity. Inclination of the cavity causes horizontal and vertical components of velocity to be affected by buoyancy force. To include this effect, calculation procedure of macroscopic properties by LBM is changed and collision term of Boltzmann equation is modified. A computer program is developed to simulate this problem using BGK model of lattice Boltzmann method. The effects of the variations of Richardson number and inclination angle on the thermal and flow behavior of the fluid inside the cavity are investigated. The results are presented as velocity and temperature profiles, stream function contours and isotherms. It is concluded that LBM has good potential to simulate mixed convection heat transfer problems.
", keywords = "gravity, inclined lid driven cavity, lattice Boltzmannmethod, mixed convection.", volume = "5", number = "4", pages = "751-8", }
