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A novel coupled lattice Boltzmann model for low Mach number combustion simulation. (English) Zbl 1193.80026

Summary: A novel coupled lattice Boltzmann model is developed for two- and three-dimensional low Mach number combustion simulations, in which the fluid density can bear sharp changes. Different to the hybrid lattice Boltzmann scheme [O. Filippova, D. Hänel, J. Comput. Phys. 158, No. 2, 139–160 (2000; Zbl 0963.76072)], this scheme is strictly pure lattice Boltzmann style (i.e., we solve the flow, temperature, and concentration fields using the lattice Boltzmann method only); different to the non-coupled lattice Boltzmann scheme [K. Yamamoto, X. He, G.D. Doolen, J. Stat. Phys. 107, No. 1–2, 367–383 (2002; Zbl 1007.82010)], the fluid density in this model is coupled directly with the temperature. In this model the time step and the fluid particle speed can be adjusted dynamically, depending on the “particle characteristic temperature”. And the algorithm is still a simple process of hopping from one grid point to the next, the same as the standard lattice Boltzmann method. Therefore the outstanding advantages of the standard lattice Boltzmann method are retained in this model besides better numerical stability. Excellent agreement between the present results and other numerical or experimental data shows that this scheme is an efficient numerical method for practical combustion simulations.

MSC:

80M25 Other numerical methods (thermodynamics) (MSC2010)
76M28 Particle methods and lattice-gas methods
76N15 Gas dynamics (general theory)
80A25 Combustion
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[1] Peters, N., Turbulent Combustion (2000), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0955.76002
[2] Poinsot, T.; Veynante, D., Theoretical and Numerical Combustion (2001), R.T. Edwards Inc.: R.T. Edwards Inc. Philadelphia
[3] Hua, J.; Wu, M.; Kumar, K., Numerical simulation of the combustion of hydrogenCair mixture in micro-scaled chambers Part II: CFD analysis for a micro-combustor, Chem. Eng. Sci., 60, 3507 (2005)
[4] Benzi, R.; Succi, S.; Vergassola, M., The lattice Boltzmann equation: theory and applications, Phys. Rep., 222, 145 (1992)
[5] Qian, Y.; Succi, S.; Orszag, S., Recent advances in lattice Boltzmann computing, Annu. Rev. Comput. Phys., 3, 195 (1995)
[6] Chen, S.; Dawson, S. P.; Doolen, G. D., Lattice method and their applications to reaction systems, Comput. Chem. Eng., 19, 617 (1995)
[7] Chen, S.; Doolen, G., Lattice Boltzmann method for fluid flows, Annu. Rev. Fluid Mech., 30, 329 (1998) · Zbl 1398.76180
[8] Succi, S., The Lattice Boltzmann Equation for Fluid Dynamics and Beyond (2001), Clarendon Press: Clarendon Press Oxford · Zbl 0990.76001
[9] Hazi, G.; Imre, A. R.; Mayer, G.; Farkas, I., Lattice Boltzmann methods for two-phase flow modeling, Ann. Nucl. Energy, 29, 1421 (2002)
[10] Yu, D.; Mei, R.; Luo, L. S.; Shyy, W., Viscous flow computations with the method of lattice Boltzmann equation, Prog. Aeosp. Sci., 39, 329 (2003)
[11] Martfnez, D.; Matthaeus, W. H.; Chen, S., Comparison of spectral method and lattice Boltzmann simulations of two-dimensional hydrodynamics, Phys. Fluids, 6, 1285 (1994) · Zbl 0826.76069
[12] Luo, L. S., Theory of the lattice Boltzmann method: lattice Boltzmann models for nonideal gases, Phys. Rev. E, 62, 4982 (2000)
[13] Guo, Z. L.; Zhao, T. S., Discrete velocity and lattice Boltzmann models for binary mixtures of nonideal fluids, Phys. Rev. E, 68, (R)035302 (2003)
[14] Chen, S.; Shi, B. C.; Liu, Z. H.; He, Z.; Guo, Z. L.; Zheng, C. G., Lattice-Boltzmann simulation of particle-laden flow over a backward-facing step, Chin. Phys., 13, 10, 1657 (2004)
[15] Spaid, M. A.A.; Phelan, F. R.J., Lattice Boltzmann methods for modeling microscale flow in fibrous porous media, Phys. Fluids, 9, 2468 (1997) · Zbl 1185.76888
[16] Guo, Z. L.; Zhao, T. S., Lattice Boltzmann model for incompressible flows through porous media, Phys. Rev. E, 66, 036304 (2002)
[17] Yoshino1, M.; Inamuro, T., Lattice Boltzmann model for incompressible flows through porous media, Int. J. Numer. Methods Fluids, 43, 183 (2003)
[18] Chen, S.; Chen, H.; Martinez, D.; Matthaeus, W., Lattice Boltzmann model for simulation of magnetohydrodynamics, Phys. Rev. Lett., 67, 3776 (1991)
[19] Dellar, P. J., Lattice kinetic schemes for magnetohydrodynamics, J. Comput. Phys., 179, 95 (2002) · Zbl 1060.76093
[20] Vahala, L.; Vahala, G.; Yepez, J., Lattice Boltzmann and quantum lattice gas representations of one-dimensional magnetohydrodynamic turbulence, Phys. Lett. A, 306, 227 (2003) · Zbl 1006.76076
[21] Ladd, A., Numerical simulations of particulate suspensions via a discretized Boltzmann equation. 1. Theoretical foundation, J. Fluid Mech., 271, 285 (1994) · Zbl 0815.76085
[22] Aidun, C. K.; Lu, Y. N.; Ding, E. J., Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation, J. Fluid Mech., 373, 287 (1998) · Zbl 0933.76092
[23] Qi, D.; Luo, L. S., Transitions in rotations of a nonspherical particle in a three-dimensional moderate Reynolds number Couette flow, Phys. Fluids, 14, 4440 (2002) · Zbl 1185.76305
[24] Zhang, Y.; Qin, R.; Emerson, D., Lattice Boltzmann simulation of rarefied gas flows in microchannels, Phys. Rev. E, 71, 047702 (2005)
[25] Lee, T.; Lin, C., Rarefaction and compressibility effects of the lattice-Boltzmann-equation method in a gas microchannel, Phys. Rev. E, 71, 046706 (2005)
[26] Sofonea, V.; Sekerka, R., Diffuse-reflection boundary conditions for a thermal lattice Boltzmann model in two dimensions: Evidence of temperature jump and slip velocity in microchannels, Phys. Rev. E, 71, 066709 (2005)
[27] Succi, S.; Bella, G.; Papetti, F., Lattice kinetic theory for numerical combustion, J. Sci. Comput., 12, 395 (1997) · Zbl 0917.76099
[28] Filippova, O.; Hanel, D., Lattice-BGK model for low Mach number combustion, Int. J. Mod. Phys. C, 9, 1439 (1998)
[29] Filippova, O.; Hanel, D., A novel lattice BGK approach for low Mach number combustion, J. Comput. Phys., 158, 139 (2000) · Zbl 0963.76072
[30] Filippova, O.; Hanel, D., A novel numerical scheme for reactive flows at low Mach numbers, Comput. Phys. Commun., 129, 267 (2000) · Zbl 0974.76064
[31] Yamamoto, K.; He, X.; Doolen, G. D., Simulation of combustion field with lattice Boltzmann method, J. Stat. Phys., 107, 367 (2002) · Zbl 1007.82010
[32] Yu, H. D.; Luo, L. S.; Girimaji, S., Scalar mixing and chemical reaction simulations using lattice Boltzmann method, Int. J. Comput. Eng. Sci., 3, 73 (2002)
[33] Yamamoto, K., LB simulation on combustion with turbulence, Int. J. Mod. Phys. B, 17, 197 (2003)
[34] Yamamoto, K.; Takada, N.; Misawa, M., Combustion simulation with Lattice Boltzmann method in a three-dimensional porous structure, Proc. Combust. Inst., 30, 1509 (2005)
[35] Lallemand, P.; Luo, L. S., Theory of the lattice Boltzmann method: acoustic and thermal properties in two and three dimensions, Phys. Rev. E, 68, 036706 (2003)
[36] Inamuro, T.; Ogata, T.; Tajima, S.; Konishi, N., A lattice Boltzmann method for incompressible two-phase flows with large density differences, J. Comput. Phys., 198, 628 (2004) · Zbl 1116.76415
[37] Rehm, G. R.; Baum, H. R., The equations of motion for thermally driven, buoyant flows, J. Res. Natl. Bur. Standards, 83, 297 (1978) · Zbl 0433.76072
[38] Sivashinsky, G. J., Hydrodynamic theory of flame propagation in an enclosed volume, Acta Astronaut., 6, 631 (1979) · Zbl 0397.76062
[39] Tomboulides, A. G.; Lee, J. C.Y.; Orszag, S. A., Numerical simulation of low Mach number reactive flows, J. Sci. Comp., 12, 139 (1997) · Zbl 0905.76055
[40] He, X.; Luo, L. S., Lattice Boltzmann model for the incompressible Navier-Stokes equation, J. Stat. Phys., 88, 927 (1997) · Zbl 0939.82042
[41] Lee, T.; Lin, C. L.; Chen, L. D., Lattice Boltzmann simulation of laminar jet diffusion flames, (Proceedings of the 2002 Spring Technical Meeting (2002), Central Sates Section/The Combustion Institute: Central Sates Section/The Combustion Institute Knoxville, Tennessee)
[42] Lee, T.; Lin, C. L., A characteristic Galerkin method for discrete Boltzmann equation, J. Comput. Phys., 171, 336 (2001) · Zbl 1017.76043
[43] Watari, M.; Tsutahara, M., Two-dimensional thermal model of the finite-difference lattice Boltzmann method with high spatial isotropy, Phys. Rev. E, 67, 036306 (2003)
[44] Peng, Y.; Shu, C.; Chew, Y. T., Simplified thermal lattice Boltzmann model for incompressible thermal flows, Phys. Rev. E, 68, 026701 (2003)
[45] Williams, F. A., Combustion Theory (1985), Addison-Wesley: Addison-Wesley New York
[46] B.J. Boersma, Direct simulation of a jet diffusion flame, Annual Research Briefs 1998, Stanford University, Stanford, 1998.; B.J. Boersma, Direct simulation of a jet diffusion flame, Annual Research Briefs 1998, Stanford University, Stanford, 1998.
[47] Shan, X. W.; Chen, H. D., Lattice Boltzmann model for simulating flows with multiple phases and components, Phys. Rev. E, 47, 1815 (1993)
[48] Shan, X., Simulation of Rayleigh-Bnard Convection using a lattice-Boltzmann Method, Phys. Rev. E, 55, 2780 (1997)
[49] Qian, Y. H., Simulating thermohydrodynamics with lattice BGK models, J. Sci. Comput., 8, 231 (1993) · Zbl 0783.76004
[50] Alexander, F. J.; Chen, S.; Sterling, J. D., Lattice Boltzmann thermohydrodynamics, Phys. Rev. E, 47, R2249 (1993)
[51] Soe, M.; Vahala, G.; Pavlo, P.; Vahala, L.; Chen, H., Thermal lattice Boltzmann simulations of variable Prandtl number turbulent flows, Phys. Rev. E, 57, 4227 (1998)
[52] Palmer, B. J.; Rector, D. R., Lattice Boltzmann algorithm for simulating thermal flow in compressible fluids, J. Comput. Phys., 161, 1 (2000) · Zbl 0969.76075
[53] Guo, Z. L.; Zheng, C. G.; Li, Q.; Wang, N. C., Lattice Boltzmann Method for Hydrodynamics (2002), Hubei Science and Technology Press: Hubei Science and Technology Press Hubei
[54] Guo, Z. L.; Shi, B. C.; Zheng, C. G., A lattice BGK model for the Bouessinesq equation, Int. J. Numer. Fluids, 39, 325 (2002)
[55] Guo, Z. L.; Shi, B. C.; Wang, N. C., Lattice BGK model for incompressible Navier-Stokes equation, J. Comput. Phys., 165, 288 (2000) · Zbl 0979.76069
[56] Qian, Y.; d’Humieres, D.; Lallemand, P., Lattice BGK models for Navier-Stokes equation, Europhys. Lett., 17, 479 (1992) · Zbl 1116.76419
[57] Deng, B.; Shi, B.; Wang, G., A new lattice Bhatnagar-Gross-Krook model for the convection-diffusion equation with a source term, Chin. Phys. Lett., 22, 267 (2005)
[58] Lee, T.; Lin, C., A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio, J. Comput. Phys., 206, 16 (2005) · Zbl 1087.76089
[59] Cao, N.; Chen, S.; Jin, S.; Martinez, D., Physical symmetry and lattice symmetry in the lattice Boltzmann method, Phys. Rev. E, 55, R21 (1997)
[60] He, X.; Doolen, G. D.; Clark, T., Comparison of the lattice Boltzmann method and the artificial compressibility method for Navier-Stokes equations, J. Comput. Phys., 179, 439 (2002) · Zbl 1130.76397
[61] He, X.; Chen, S.; Doolen, G. D., A novel thermal model for the lattice Boltzmann method in incompressible limit, J. Comput. Phys., 146, 282 (1998) · Zbl 0919.76068
[62] Landau, L. D.; Lifshitz, E. M., Fluid Mechanics (1987), McGraw-Hill: McGraw-Hill Oxford · Zbl 0146.22405
[63] Bosschaart, K. J.; Goey, L. P.H., The laminar burning velocity of flames propagating in mixtures of hydrocarbons and air measured with the heat flux method, Combust. Flame, 136, 261 (2004)
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