American Institute of Mathematical Sciences

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

Numerical simulation of flow in fluidized beds

Petr Bauer 1, , Michal Beneš 2, , Radek Fučík 2, , Hung Hoang Dieu 2, , Vladimír Klement 2, , Radek Máca 2, , Jan Mach 2, , Tomáš Oberhuber 2, , Pavel Strachota 2, , Vítězslav Žabka 2, and  Vladimír Havlena 3,

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.
Keywords: multi-phase flow, turbulence, reactive flows., Navier-Stokes equations, combustion.
Mathematics Subject Classification: Primary: 35M10, 35Q79, 76V05; Secondary: 80A25, 65M0.
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 & 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).   Google Scholar

[2]

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

[3]

P. Basu, Combustion and Gasification in Fluidized Beds,, CRC Press, (2006).   Google Scholar

[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, (2009), 115.   Google Scholar

[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.   Google Scholar

[6]

C. T. Bowman and D. J. Seery, Emissions from Continuous Combustion Systems,, Plenum Press, (1972).   Google Scholar

[7]

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

[8]

R. Fučík and T. Oberhuber, Twophase Twodimensional Flow in Combustion Chamber Geometry,, Functional Design Specification MMG 4-12, (2012), 4.   Google Scholar

[9]

D. Gidaspow, Multiphase Flow and Fluidization: Continuum and Kinetic Theory Description,, Academic Press, (1994).   Google Scholar

[10]

P. Lam and D. Gidaspow, Computational and Experimental Modelling of Slurry Bubble Column Reactors,, U.S. DOE Annual Report No. DE-FG-98FT40117, (2000).   Google Scholar

[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, (2005), 106.   Google Scholar

[12]

J. Makovička, M. Beneš and V. Havlena, Model of turbulent coal combustion,, Proceedings of the Czech-Japanese Seminar in Applied Mathematics 2005, (2006), 95.   Google Scholar

[13]

M. F. Modest, Radiative Heat Transfer,, 2nd ed., (2003).   Google Scholar

[14]

K. Myöhänen, T. Hyppänen and A. Vepsäläinen, Modelling of circulating fluidized bed combustion with a semi-empirical three-dimensional model,, In Juuso, (2006), 194.   Google Scholar

[15]

W. E. Schiesser, The Numerical Method of Lines,, Academic Press, (1991).   Google Scholar

[16]

J. C. Slattery, Momentum, Energy, and Mass Transfer in Continua,, McGraw-Hill Book Company, (1972).   Google Scholar

[17]

L. D. Smoot and P. J. Smith, Coal Combustion and Gasification,, Plenum Press, (1985).   Google Scholar

[18]

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

[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, (2009).   Google Scholar

[20]

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

[21]

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

[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.   Google Scholar

show all references

References:
[1]

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

[2]

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

[3]

P. Basu, Combustion and Gasification in Fluidized Beds,, CRC Press, (2006).   Google Scholar

[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, (2009), 115.   Google Scholar

[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.   Google Scholar

[6]

C. T. Bowman and D. J. Seery, Emissions from Continuous Combustion Systems,, Plenum Press, (1972).   Google Scholar

[7]

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

[8]

R. Fučík and T. Oberhuber, Twophase Twodimensional Flow in Combustion Chamber Geometry,, Functional Design Specification MMG 4-12, (2012), 4.   Google Scholar

[9]

D. Gidaspow, Multiphase Flow and Fluidization: Continuum and Kinetic Theory Description,, Academic Press, (1994).   Google Scholar

[10]

P. Lam and D. Gidaspow, Computational and Experimental Modelling of Slurry Bubble Column Reactors,, U.S. DOE Annual Report No. DE-FG-98FT40117, (2000).   Google Scholar

[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, (2005), 106.   Google Scholar

[12]

J. Makovička, M. Beneš and V. Havlena, Model of turbulent coal combustion,, Proceedings of the Czech-Japanese Seminar in Applied Mathematics 2005, (2006), 95.   Google Scholar

[13]

M. F. Modest, Radiative Heat Transfer,, 2nd ed., (2003).   Google Scholar

[14]

K. Myöhänen, T. Hyppänen and A. Vepsäläinen, Modelling of circulating fluidized bed combustion with a semi-empirical three-dimensional model,, In Juuso, (2006), 194.   Google Scholar

[15]

W. E. Schiesser, The Numerical Method of Lines,, Academic Press, (1991).   Google Scholar

[16]

J. C. Slattery, Momentum, Energy, and Mass Transfer in Continua,, McGraw-Hill Book Company, (1972).   Google Scholar

[17]

L. D. Smoot and P. J. Smith, Coal Combustion and Gasification,, Plenum Press, (1985).   Google Scholar

[18]

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

[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, (2009).   Google Scholar

[20]

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

[21]

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

[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.   Google Scholar

[1]

José Luiz Boldrini, Luís H. de Miranda, Gabriela Planas. On singular Navier-Stokes equations and irreversible phase transitions. Communications on Pure & Applied Analysis, 2012, 11 (5) : 2055-2078. doi: 10.3934/cpaa.2012.11.2055
[2]

Misha Perepelitsa. An ill-posed problem for the Navier-Stokes equations for compressible flows. Discrete & Continuous Dynamical Systems - A, 2010, 26 (2) : 609-623. doi: 10.3934/dcds.2010.26.609
[3]

Yong Hong Wu, B. Wiwatanapataphee. Modelling of turbulent flow and multi-phase heat transfer under electromagnetic force. Discrete & Continuous Dynamical Systems - B, 2007, 8 (3) : 695-706. doi: 10.3934/dcdsb.2007.8.695
[4]

Avetik Arakelyan, Henrik Shahgholian, Jyotshana V. Prajapat. Two-and multi-phase quadrature surfaces. Communications on Pure & Applied Analysis, 2017, 16 (6) : 2023-2045. doi: 10.3934/cpaa.2017099
[5]

Pavel I. Plotnikov, Jan Sokolowski. Compressible Navier-Stokes equations. Conference Publications, 2009, 2009 (Special) : 602-611. doi: 10.3934/proc.2009.2009.602
[6]

Jan W. Cholewa, Tomasz Dlotko. Fractional Navier-Stokes equations. Discrete & Continuous Dynamical Systems - B, 2018, 23 (8) : 2967-2988. doi: 10.3934/dcdsb.2017149
[7]

Shijin Ding, Zhilin Lin, Dongjuan Niu. Boundary layer for 3D plane parallel channel flows of nonhomogeneous incompressible Navier-Stokes equations. Discrete & Continuous Dynamical Systems - A, 2020, 40 (8) : 4579-4596. doi: 10.3934/dcds.2020193
[8]

Pavel I. Plotnikov, Jan Sokolowski. Optimal shape control of airfoil in compressible gas flow governed by Navier-Stokes equations. Evolution Equations & Control Theory, 2013, 2 (3) : 495-516. doi: 10.3934/eect.2013.2.495
[9]

Dieter Bothe, Jan Prüss. Modeling and analysis of reactive multi-component two-phase flows with mass transfer and phase transition the isothermal incompressible case. Discrete & Continuous Dynamical Systems - S, 2017, 10 (4) : 673-696. doi: 10.3934/dcdss.2017034
[10]

Hermenegildo Borges de Oliveira. Anisotropically diffused and damped Navier-Stokes equations. Conference Publications, 2015, 2015 (special) : 349-358. doi: 10.3934/proc.2015.0349
[11]

Hyukjin Kwean. Kwak transformation and Navier-Stokes equations. Communications on Pure & Applied Analysis, 2004, 3 (3) : 433-446. doi: 10.3934/cpaa.2004.3.433
[12]

Vittorino Pata. On the regularity of solutions to the Navier-Stokes equations. Communications on Pure & Applied Analysis, 2012, 11 (2) : 747-761. doi: 10.3934/cpaa.2012.11.747
[13]

C. Foias, M. S Jolly, I. Kukavica, E. S. Titi. The Lorenz equation as a metaphor for the Navier-Stokes equations. Discrete & Continuous Dynamical Systems - A, 2001, 7 (2) : 403-429. doi: 10.3934/dcds.2001.7.403
[14]

Igor Kukavica. On regularity for the Navier-Stokes equations in Morrey spaces. Discrete & Continuous Dynamical Systems - A, 2010, 26 (4) : 1319-1328. doi: 10.3934/dcds.2010.26.1319
[15]

Igor Kukavica. On partial regularity for the Navier-Stokes equations. Discrete & Continuous Dynamical Systems - A, 2008, 21 (3) : 717-728. doi: 10.3934/dcds.2008.21.717
[16]

Susan Friedlander, Nataša Pavlović. Remarks concerning modified Navier-Stokes equations. Discrete & Continuous Dynamical Systems - A, 2004, 10 (1&2) : 269-288. doi: 10.3934/dcds.2004.10.269
[17]

Eric Blayo, Antoine Rousseau. About interface conditions for coupling hydrostatic and nonhydrostatic Navier-Stokes flows. Discrete & Continuous Dynamical Systems - S, 2016, 9 (5) : 1565-1574. doi: 10.3934/dcdss.2016063
[18]

Fei Jiang, Song Jiang, Junpin Yin. Global weak solutions to the two-dimensional Navier-Stokes equations of compressible heat-conducting flows with symmetric data and forces. Discrete & Continuous Dynamical Systems - A, 2014, 34 (2) : 567-587. doi: 10.3934/dcds.2014.34.567
[19]

Jean-Pierre Raymond. Stokes and Navier-Stokes equations with a nonhomogeneous divergence condition. Discrete & Continuous Dynamical Systems - B, 2010, 14 (4) : 1537-1564. doi: 10.3934/dcdsb.2010.14.1537
[20]

Yoshikazu Giga. A remark on a Liouville problem with boundary for the Stokes and the Navier-Stokes equations. Discrete & Continuous Dynamical Systems - S, 2013, 6 (5) : 1277-1289. doi: 10.3934/dcdss.2013.6.1277

2019 Impact Factor: 1.233

Tools

Metrics

  • PDF downloads (76)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences