October  2015, 8(5): 833-846. doi: 10.3934/dcdss.2015.8.833

Numerical simulation of flow in fluidized beds

1. 

Institute of Thermomechanics, Czech Academy of Sciences, Dolejškova 5, 182 00 Prague, Czech Republic

2. 

Dept. of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 120 00 Prague, Czech Republic, Czech Republic, Czech Republic, Czech Republic, Czech Republic, Czech Republic, Czech Republic, Czech Republic, Czech Republic

3. 

Honeywell ACS AT Laboratory Prague, V Parku 2326/18, 148 00 Prague, Cyprus

Received  January 2014 Revised  June 2014 Published  July 2015

The article provides a brief overview of a one-dimensional model of two-phase flow in the geometry of a circulating fluidized bed combustor exhibiting vertical variability of cross-section. The model is based on numerical solution of conservation laws for mass, momentum and energy of gas and solid components of the fluidized-bed system by means of the finite-volume method in space and of a multistep higher-order solver in time. The presented computational results reproduce characteristic behavior of fluidized beds in the given geometry.
Citation: Petr Bauer, Michal Beneš, Radek Fučík, Hung Hoang Dieu, Vladimír Klement, Radek Máca, Jan Mach, Tomáš Oberhuber, Pavel Strachota, Vítězslav Žabka, Vladimír Havlena. Numerical simulation of flow in fluidized beds. Discrete and Continuous Dynamical Systems - S, 2015, 8 (5) : 833-846. doi: 10.3934/dcdss.2015.8.833
References:
[1]

J. D. Anderson, Computational Fluid Dynamics: The Basics with Applications, McGraw-Hill, 1995.

[2]

P. Basu, K. Cen and L. Jestin, Boilers and Burners: Design and Theory, Springer-Verlag, 2000

[3]

P. Basu, Combustion and Gasification in Fluidized Beds, CRC Press, 2006.

[4]

P. Bauer, A. Suzuki and Z. Jaňour, FEM for Flow and Pollution Transport in a Street Canyon. In: Numerical Mathematics and Advanced Applications 2009, Proceedings of ENUMATH 2009, the 8th European Conference on Numerical Mathematics and Advanced Applications, Uppsala, Sweden. Kreiss, G.; Lötstedt, P.; Malqvist, A.; Neytcheva, M. (Eds.), pp. 115-123.

[5]

M. Beneš, T. Oberhuber, P. Strachota, R. Straka and V. Havlena, Mathematical modelling of combustion and biofuel co-firing in industrial steam generators, RIMS Kokyuroku Bessatsu, B35 (2012), 141-157.

[6]

C. T. Bowman and D. J. Seery, Emissions from Continuous Combustion Systems, Plenum Press, New York, 1972.

[7]

M. Driscoll and D. Gidaspow, Wave Propagation and Granular Temperature in Fluidized Beds of Nano and FCC Particles, AIChE Journal, 53 (2007), 1718-1726.

[8]

R. Fučík and T. Oberhuber, Twophase Twodimensional Flow in Combustion Chamber Geometry, Functional Design Specification MMG 4-12, Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, 2012.

[9]

D. Gidaspow, Multiphase Flow and Fluidization: Continuum and Kinetic Theory Description, Academic Press, Inc., Boston, MA, 1994.

[10]

P. Lam and D. Gidaspow, Computational and Experimental Modelling of Slurry Bubble Column Reactors, U.S. DOE Annual Report No. DE-FG-98FT40117, National Energy Technology Laboratory, 2000.

[11]

J. Makovička and V. Havlena, Finite Volume Numerical Model of Coal Combustion, in: Beneš, M., Mikyška, J., Oberhuber, T. (Eds.), Proceedings of the Czech-Japanese Seminar in Applied Mathematics 2004, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, (2005), 106-116.

[12]

J. Makovička, M. Beneš and V. Havlena, Model of turbulent coal combustion, Proceedings of the Czech-Japanese Seminar in Applied Mathematics 2005, Kuju Training Center, Oita, Japan, (2006), 95-105.

[13]

M. F. Modest, Radiative Heat Transfer, 2nd ed., Academic Press, 2003.

[14]

K. Myöhänen, T. Hyppänen and A. Vepsäläinen, Modelling of circulating fluidized bed combustion with a semi-empirical three-dimensional model, In Juuso, E., ed., SIMS 2006: Proceedings of the 47th Conference on Simulation and Modelling, Helsinki: Finnish Society of Automation, (2006), 194-199.

[15]

W. E. Schiesser, The Numerical Method of Lines, Academic Press, New York, 1991.

[16]

J. C. Slattery, Momentum, Energy, and Mass Transfer in Continua, McGraw-Hill Book Company, New York, 1972.

[17]

L. D. Smoot and P. J. Smith, Coal Combustion and Gasification, Plenum Press, New York, 1985.

[18]

R. Straka and J. Makovička, Model of pulverized coal combustion in furnace, Kybernetika, 43 (2007), 879-891.

[19]

R. Straka, J. Makovička and M. Beneš, Numerical model of air-staging and OFA in PC boiler, in Algoritmy 2009, Proceedings of contributed papers and posters, ed. Handlovičová A., Frolkovič P., Mikula K. and Ševčovič D. Slovak University of Technology in Bratislava, Publishing House of STU, 2009.

[20]

R. Straka, J. Makovička and M. Beneš, Numerical simulation of NO production in pulverized coal fired furnace, Environment Protection Engineering, 37 (2011), 13-22.

[21]

W.-C. Yang (ed.), Handbook of Fluidization and Fluid-Particle Systems, Marcel Dekker, 2003.

[22]

N. Zhang, B. Lu, W. Wang and J. Li, 3D CFD simulation of hydrodynamics of a 150MWe circulating fluidized bed boiler, Chemical Engineering Journal, 162 (2010), 821-828.

show all references

References:
[1]

J. D. Anderson, Computational Fluid Dynamics: The Basics with Applications, McGraw-Hill, 1995.

[2]

P. Basu, K. Cen and L. Jestin, Boilers and Burners: Design and Theory, Springer-Verlag, 2000

[3]

P. Basu, Combustion and Gasification in Fluidized Beds, CRC Press, 2006.

[4]

P. Bauer, A. Suzuki and Z. Jaňour, FEM for Flow and Pollution Transport in a Street Canyon. In: Numerical Mathematics and Advanced Applications 2009, Proceedings of ENUMATH 2009, the 8th European Conference on Numerical Mathematics and Advanced Applications, Uppsala, Sweden. Kreiss, G.; Lötstedt, P.; Malqvist, A.; Neytcheva, M. (Eds.), pp. 115-123.

[5]

M. Beneš, T. Oberhuber, P. Strachota, R. Straka and V. Havlena, Mathematical modelling of combustion and biofuel co-firing in industrial steam generators, RIMS Kokyuroku Bessatsu, B35 (2012), 141-157.

[6]

C. T. Bowman and D. J. Seery, Emissions from Continuous Combustion Systems, Plenum Press, New York, 1972.

[7]

M. Driscoll and D. Gidaspow, Wave Propagation and Granular Temperature in Fluidized Beds of Nano and FCC Particles, AIChE Journal, 53 (2007), 1718-1726.

[8]

R. Fučík and T. Oberhuber, Twophase Twodimensional Flow in Combustion Chamber Geometry, Functional Design Specification MMG 4-12, Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, 2012.

[9]

D. Gidaspow, Multiphase Flow and Fluidization: Continuum and Kinetic Theory Description, Academic Press, Inc., Boston, MA, 1994.

[10]

P. Lam and D. Gidaspow, Computational and Experimental Modelling of Slurry Bubble Column Reactors, U.S. DOE Annual Report No. DE-FG-98FT40117, National Energy Technology Laboratory, 2000.

[11]

J. Makovička and V. Havlena, Finite Volume Numerical Model of Coal Combustion, in: Beneš, M., Mikyška, J., Oberhuber, T. (Eds.), Proceedings of the Czech-Japanese Seminar in Applied Mathematics 2004, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, (2005), 106-116.

[12]

J. Makovička, M. Beneš and V. Havlena, Model of turbulent coal combustion, Proceedings of the Czech-Japanese Seminar in Applied Mathematics 2005, Kuju Training Center, Oita, Japan, (2006), 95-105.

[13]

M. F. Modest, Radiative Heat Transfer, 2nd ed., Academic Press, 2003.

[14]

K. Myöhänen, T. Hyppänen and A. Vepsäläinen, Modelling of circulating fluidized bed combustion with a semi-empirical three-dimensional model, In Juuso, E., ed., SIMS 2006: Proceedings of the 47th Conference on Simulation and Modelling, Helsinki: Finnish Society of Automation, (2006), 194-199.

[15]

W. E. Schiesser, The Numerical Method of Lines, Academic Press, New York, 1991.

[16]

J. C. Slattery, Momentum, Energy, and Mass Transfer in Continua, McGraw-Hill Book Company, New York, 1972.

[17]

L. D. Smoot and P. J. Smith, Coal Combustion and Gasification, Plenum Press, New York, 1985.

[18]

R. Straka and J. Makovička, Model of pulverized coal combustion in furnace, Kybernetika, 43 (2007), 879-891.

[19]

R. Straka, J. Makovička and M. Beneš, Numerical model of air-staging and OFA in PC boiler, in Algoritmy 2009, Proceedings of contributed papers and posters, ed. Handlovičová A., Frolkovič P., Mikula K. and Ševčovič D. Slovak University of Technology in Bratislava, Publishing House of STU, 2009.

[20]

R. Straka, J. Makovička and M. Beneš, Numerical simulation of NO production in pulverized coal fired furnace, Environment Protection Engineering, 37 (2011), 13-22.

[21]

W.-C. Yang (ed.), Handbook of Fluidization and Fluid-Particle Systems, Marcel Dekker, 2003.

[22]

N. Zhang, B. Lu, W. Wang and J. Li, 3D CFD simulation of hydrodynamics of a 150MWe circulating fluidized bed boiler, Chemical Engineering Journal, 162 (2010), 821-828.

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