Evaluation of two lattice Boltzmann methods for fluid flow simulation in a stirred tank

Document Type : English


Department of mechanical engineering, Islamic Azad university, Isfahan,Iran


In the present study, commonly used weakly compressible lattice Boltzmann method and Guo incompressible lattice Boltzmann method have been used to simulate fluid flow in a stirred tank. For this purpose a 3D Parallel code has been developed in the framework of the lattice Boltzmann method. This program has been used for simulation of flow at different geometries such as 2D channel fluid flow and 3D stirred tank fluid flow. It has been shown that in addition to elimination of compressibility error, the Guo incompressible method eliminates mass leakage error from the fluid flow simulations although its implementation is as easy as the weakly compressible Lattice Boltzmann method. By the way, comparison between results of the two methods shows that differences in local flow quantities are negligible in both methods; however, for overall flow quantities, the results of Guo incompressible method are more accurate than those of weakly compressible method.


[1]   Eggels, J. G. M., "Direct and large-eddy simulation of turbulent fluid flow using the lattice-boltzmann scheme," International journal of heat and fluid flow, vol. 17, pp. 307-323, 1996.
[2]   Musavi, S. H. and Ashrafizaadeh, M., "On the simulation of porous media flow using a new meshless lattice boltzmann method," in Mathematical and computational approaches in advancing modern science and engineering: Springer, pp. 469-480, 2016.
[3]   Musavi, S. H. and Ashrafizaadeh, M., "A mesh-free lattice boltzmann solver for flows in complex geometries," International journal of heat and fluid flow, vol. 59, pp. 10-19, 2016.
[4]   Oulaid, O. and Zhang, J., "On the origin of numerical errors in the bounce-back boundary treatment of the lattice boltzmann method: A remedy for artificial boundary slip and mass leakage," European Journal of Mechanics-B/Fluids, vol. 53, pp. 11-23, 2015.
[5]   Musavi, S. H. and Ashrafizaadeh, M., "Meshless lattice boltzmann method for the simulation of fluid flows," Physical Review E, vol. 91, p. 023310, 2015.
[6]   Khazaeli, R., Mortazavi, S., and Ashrafizaadeh, M., "Application of an immersed boundary treatment in simulation of natural convection problems with complex geometry via the lattice boltzmann method," Journal of Applied Fluid Mechanics, vol. 8, pp. 309-321, 2015.
[7]   Khazaeli, R., Ashrafizaadeh, M., and Mortazavi, S., "A ghost fluid approach for thermal lattice boltzmann method in dealing with heat flux boundary condition in thermal problems with complex geometries," Journal of Applied Fluid Mechanics, vol. 8, pp. 439-452, 2015.
[8]   Zadehgol, A., Ashrafizaadeh, M., and Musavi, S. H., "A nodal discontinuous galerkin lattice boltzmann method for fluid flow problems," Computers & Fluids, vol. 105, pp. 58-65, 2014.
[9]   Zadehgol, A. and Ashrafizaadeh, M., "Introducing a new kinetic model which admits an h-theorem for simulating the nearly incompressible fluid flows," Journal of Computational Physics, vol. 274, pp. 803-825, 2014.
[10] Xiong, Q., Madadi-Kandjani, E., and Lorenzini, G., "A lbm dem solver for fast discrete particle simulation of particle fluid flows," Continuum Mechanics and Thermodynamics, vol. 26, pp. 907-917, 2014.
[11] Walther, E., Bennacer, R., and Desa, C., "Lattice boltzmann method applied to diffusion in restructured heterogeneous media," Defect and Diffusion Forum, pp. 237-242, 2014.
[12] Viggen, E. M., "The lattice boltzmann method: Fundamentals and acoustics," 2014.
[13] Rahmati, A. R. and Niazi, S., "Entropic lattice boltzmann method for microflow simulation," Nanomechanics Science and Technology: An International Journal, vol. 5, 2014.
[14] Rahmani, G. M. and Ashrafizaadeh, M., "Simulation of pressurization step of a psa process using the multi-component lattice boltzmann method," 2014.
[15] Naghavi, S. M. and Ashrafizaadeh, M., "A comparison of two boundary conditions for the fluid flow simulation in a stirred tank," JCME, vol. 33, pp. 15-30, 2014.
[16] Zhuo, C., Zhong, C., Guo, X., and Cao, J., "Mrt-lbm simulation of four-lid-driven cavity flow bifurcation," Procedia Engineering, vol. 61, pp. 100-107, 2013.
[17] Yang, F. L., Zhou, S. J., Zhang, C. X., and Wang, G. C., "Mixing of initially stratified miscible fluids in an eccentric stirred tank: Detached eddy simulation and volume of fluid study," Korean Journal of Chemical Engineering, vol. 30, pp. 1843-1854, 2013.
[18] Wang, L., Zhang, B., Wang, X., Ge, W., and Li, J., "Lattice boltzmann based discrete simulation for gas–solid fluidization," Chemical engineering science, vol. 101, pp. 228-239, 2013.
[19] Wang, L., Zhang, B., Wang, X., Ge, W., and Li, J., "Lattice boltzmann based discrete simulation for gas-solid fluidization," Chemical engineering science, vol. 101, pp. 228-239, 2013.
[20] Derksen, J. and Van den Akker, H. E. A., "Large eddy simulations on the flow driven by a rushton turbine," AIChE Journal, vol. 45, pp. 209-221, 1999.
[21] Guha, D., Ramachandran, P. A., Dudukovic, M. P., and Derksen, J. J., "Evaluation of large eddy simulation and euler-euler cfd models for solids flow dynamics in a stirred tank reactor," AIChE Journal, vol. 54, pp. 766-778, 2008.
[22] Derksen, J. J., "Solid particle mobility in agitated bingham liquids," Industrial & Engineering Chemistry Research, vol. 48, pp. 2266-2274, 2009.
[23] Derksen, J. J., "Agitation and mobilization of thixotropic liquids," AIChE Journal, vol. 56, pp. 2236-2247, 2010.
[24] Derksen, J. J., "Direct flow simulations of thixotropic liquids in agitated tanks," The Canadian Journal of Chemical Engineering, vol. 89, pp. 628-635, 2011.
[25] Derksen, J. J., "Simulations of mobilization of bingham layers in a turbulently agitated tank," Journal of Non-Newtonian Fluid Mechanics, vol. 191, pp. 25-34, 2013.
[26] Guo, Z., Shi, B., and Wang, N., "Lattice bgk model for incompressible navier-stokes equation," Journal of Computational Physics, vol. 165, pp. 288-306, 2000.
[27] Yu, D., Mei, R., Luo, L. S., and Shyy, W., "Viscous flow computations with the method of lattice boltzmann equation," Progress in Aerospace Sciences, vol. 39, pp. 329-367, 2003.
[28] Du, R. and Liu, W., "A new multiple-relaxation-time lattice boltzmann method for natural convection," Journal of Scientific Computing, vol. 56, pp. 122-130, 2013.
[29] He, X. and Luo, L. S., "Lattice boltzmann model for the incompressible navier stokes equation," Journal of Statistical Physics, vol. 88, pp. 927-944, 1997.
[30] Dellar, P. J., "Incompressible limits of lattice boltzmann equations using multiple relaxation times," Journal of Computational Physics, vol. 190, pp. 351-370, 2003.
[31] Du, R., Shi, B., and Chen, X., "Multi-relaxation-time lattice boltzmann model for incompressible flow," Physics Letters A, vol. 359, pp. 564-572, 2006.
[32] Bao, J., Yuan, P., and Schaefer, L., "A mass conserving boundary condition for the lattice boltzmann equation method," Journal of Computational Physics, vol. 227, pp. 8472-8487, 2008.
[33] Chun, B. and Ladd, A. J. C., "Interpolated boundary condition for lattice boltzmann simulations of flows in narrow gaps," Physical Review E, vol. 75, p. 66705, 2007.
[34] Krüger, T., Varnik, F., and Raabe, D., "Shear stress in lattice boltzmann simulations," Physical Review E, vol. 79, p. 46704, 2009.
[35] Schaefer, M., Turek, S., Durst, F., Krause, E., and Rannacher, R., "Benchmark computations of laminar flow around a cylinder," Notes on numerical fluid mechanics, vol. 52, pp. 547-566, 1996.
[36] Peng, Y. and Luo, L. S., "A comparative study of immersed-boundary and interpolated bounce-back methods in lbe," Progress in Computational Fluid Dynamics, an International Journal, vol. 8, pp. 156-167, 2008.
[37] Mei, R., Yu, D., Shyy, W., and Luo, L. S., "Force evaluation in the lattice boltzmann method involving curved geometry," Physical Review E, vol. 65, p. 041203, 2002.
[38] Wu, H. and Patterson, G. K., "Laser doppler measurements of turbulent flow parameters in a stirred mixer," Chemical engineering science, vol. 44, pp. 2207-2221, 1989.
[39] Chapple, D., Kresta, S. M., Wall, A., and Afacan, A., "The effect of impeller and tank geometry on power number for a pitched blade turbine," Trans ICheme, vol. 80, pp. 364-372, 2002.
[40] Rutherford, K., Mahmoudi, S. M. S., Lee, K. C., and Yianneskis, M., "The influence of rushton impeller blade and disk thickness on the mixing characteristics of stirred vessels," Trans ICheme, vol. 74, pp. 369-378, 1996.
[41] Costes, J. and Couderc, J. P., "Study by laser doppler anemometry of the turbulent flow induced by a rushton turbine in a stirred tank: Influence of the size of the units i. Mean flow and turbulence," Chemical engineering science, vol. 43, pp. 2751-2764, 1988.