Thermo-Hydrodynamic Analysis of Duct Flow using Lattice Boltzmann Method

Author

Abstract

In this paper, the thermo-hydrodynamic analysis of incompressible fluid flow in conjunction with cell-centered finite volume-lattice Boltzmann method is developed. To demonstrate the temperature field, the double distribution function model was used. Since, instability is the most severe problem of the thermal lattice Boltzmann methods to handle flows; a stable and accurate cell-centered scheme is presented. For this purpose, the pressure and temperature based upwind biasing factors are used as flux correctors. Also, additional lattices at the edge of each boundary cell are introduced, which allow a much better description of the actual geometrical shape. The unknown energy distribution at the boundary cells were decomposed into its equilibrium and non-equilibrium parts. This treatment enlarges the domain stability and leads to faster convergence. In addition of calculating numerical viscosity, The method is applied to two dimensional incompressible thermal plane duct flow. The results show a very good accuracy and agreement with the exact solution and previous numerical results.

References

[1]  Succi S (2001) The lattice Boltzmann equation for fluid dynamics and beyond. Clarendon, Oxford.
[2]  Benzi R, Succi S, Vergassola M (1992) The lattice Boltzmann equation: theory and applications. Phys Rep 222: 145–197.
[3]  Bella G, Ubertini S, Bertolino M (2003) Computational fluid dynamics for low and moderate Reynolds numbers through the lattice Boltzmann method. Int J Comp Num Analy Appl 3(1): 83–115.
[4]  Rothman DH, Zaleski S (1994) Lattice-gas model of phase separation: interfaces, phase transitions, and multiphase flow. Rev Mod Phys 66(4): 1417–1479.
[5]  Chen S, Doolen G (1998) Lattice Boltzmann method for fluid flows. Ann Rev Fluid Mech 30: 329–364.
[6]  Zarghami A, Maghrebi MJ, Ghasemi  J (2011) Finite volume-lattice Boltzmann modeling of viscous flows. Majlesi J Mech Eng 4(2): 11–19.
[7]   Barth TJ, Jespersen DC (1989) The design and application of upwind schemes on unstructured meshes. AIAA Paper 89:0366.
[8]   Tamamidis P (1995) A new upwind scheme on triangular meshes using the finite volume method. Comput Methods Appl Mech Eng 124: 15–21.
[9]    Sofonea V, Sekerka RF (2005) Boundary conditions for the upwind finite difference lattice Boltzmann model: evidence of slip velocity in micro-channel flow. J Comput Phys 207: 639–659.
[10] Patil DV, Lakshmisha KN (2009) Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh. J Comput Phys 228: 5262–5279.
[11] Premnath KN, Pattison MJ, Banerjee S (2009) Dynamic subgrid scale modeling of turbulent flows using lattice-Boltzmann method. Physica A 338: 2640–2658.
[12] He X, Chen S,  Doolen GD (1998) A novel thermal model for the lattice Boltzmann method in incompressible limit. J Comput Phys 146: 282-289.
[13] Alexanders F, Chen S, Sterling J (1993) Lattice Boltzmann thermo-hydrodynamics. Phys Rev E 47: 2249–2252.
[14] Pavlo P, Vahala G, Vahala L (1998) Linear stability analysis of thermo-lattice Boltzmann models. J Comput Phys 1391: 79–91.
[15] Piaud B, Blanco S, Fournier R, Clifton MJ (2005) Energy conserving of lattice Boltzmann thermal model in two dimensions. J Stat Phys 121(1-2:119–131.
[16] Peng Y, Shu C, Chew YT (2003) Simplified thermal lattice Boltzmann model for incompressible thermal flows. Phys Rev E 68: 026701.
[17] Shi Y, Zhao TS, Guo ZL (2004) Thermal lattice Bhatnagar-Gross-Krook model for flows with viscous heat dissipation in the incompressible limit. Phys Rev E 70: 066310.
[18] Van der Sman RGM (1997) Lattice Boltzmann scheme for natural convection in Porous media. Int J Modern Phys C 8:879–888.
[19] Palmer BJ, Rector DR (2000) Lattice Boltzmann algorithm for simulating thermal flow in compressible fluids. J Comput Phys 161: 1–20.
[20]  Onishi J, Chen Y, Ohashi H (2001) Lattice Boltzmann simulation of natural convection in a square cavity. JSME Int J Ser B 44: 53–62.
[21] Zheng L, Guo Z, Shi B, Zheng C (2010) Kinetic theory based lattice Boltzmann equation with viscous dissipation and pressure work for axisymmetric thermal flows. J Comput  Physics 229(16): 5843–5856.
[22] Bhatnagar PL, Gross EP, Krook M (1954) A model for process in gases, Phys Rev 94: 511–525.
[23]  Peng Y, Shu C, Chew YT (2003) Simplified thermal lattice Boltzmann model for incompressible thermal flows. Phys Rev E 68: 026701.
[24] Ubertini S, Succi S (2005) Recent advances of lattice Boltzmann techniques on unstructured grids. Prog Comput Fluid Dyn 5: 85–96.
[25] Hirsch C, (1998) Numerical Computation of Internal and External Flows, Vol. I: Fundamentals of Numerical Discretization, Wiley, Chichester.
[26] Stiebler M, Tolke J, Krafczyk M (2006) An upwind discretization schem for the finite volume lattice boltzamnn method. Computer Fluids 35: 814–819.
[27] Ghasemi J, Razavi SE (2010) On the finite volume lattice boltzmann modeling of thermo-hydrodynamics. Comput Math Appl 60: 1135–1144.
[28] Xi H, Peng G, Chou SH (1999) Finite-volume lattice Boltzmann method. Phys Rev E 59(5): 6202–6205.
[29] Tanehill JC, Anderson DA, Pletcher RH (1997) Computational Fluid Mechanics and Heat Transfer. 2nd Edition. Taylor & Francis.
[30] Zou Q, He X (1997) On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Phys Fluids 9: 1591–1598.
[31] Guo Z, Zheng C, Shi B (2002) An extrapolation method for boundary conditions in lattice Boltzmann method. Phys Fluids 14(6): 2007–2010.
[32] Tang GH, Tao WQ, He YL (2005) Thermal boundary condition for the thermal lattice Boltzmann equation. Phys Rev E 72:016703.
[33] Chen CK, Tzu-Shuang Y, Yue-Yzu Y (2006) Lattice Boltzmann method of backward facing step on convective heat transfer with field synergy principle. Int J Heat Mass Trans 49: 1195–1204.
[34] Schlichting H (2005) Boundary Layer Theory. 3rd Ed. Springer-Verlag.
[35] Chen RY (1973) Flow in the entrance region at low Reynolds numbers. J Fluid Eng 95: 153–158.
Journal of Solid and Fluid Mechanics
Volume 1, Issue 2 - Serial Number 2
September and October 2011
Pages 81-90

Files

Share

How to cite

Statistics