A mathematical model of a direct-fired continuous strip annealing furnace

Abstract A mathematical model of a direct-fired continuous strip annealing furnace is developed. The first-principle model uses the heat balance to describe the dynamic behavior of the strip and the rolls. The mass and the enthalpy balance are employed to calculate the mass, the composition, and the temperature of the flue gas. The heat conduction equation of the furnace wall is discretized by means of the Galerkin method. Furthermore, the convective and radiative heat transfer interconnect all submodels of the furnace. For the calculation of the radiative heat transfer, the zone method is utilized. Finally, the assembled model is reduced by applying the singular perturbation method. A comparison of simulation results with measurement data from a real plant demonstrates the accuracy of the reduced model. Moreover, due to the moderate computational effort, the model is suitable for real-time applications in control and dynamic optimization.

[1]  B. Porter,et al.  Singular pertubation methods in the synthesis of control policies for production-inventory systems , 1982 .

[2]  S. Turns.  Introduction to Combustion , 1995, Aerothermodynamics and Jet Propulsion.

[3]  David O Marlow.  Modelling direct-fired annealing furnaces for transient operations , 1996 .

[4]  Qingdong Zhang,et al.  FEM analysis of large thermo-deflection of strips being processed in a continuous annealing furnace , 2007 .

[5]  M. J. Moran,et al.  Fundamentals of Engineering Thermodynamics: SI Version (6th edition) , 2010 .

[6]  Yun Chao,et al.  Dynamic modeling of reheat-furnace using neural network based on PSO algorithm , 2009, 2009 International Conference on Mechatronics and Automation.

[7]  Thomas A. Adams,et al.  A dynamic two-dimensional heterogeneous model for water gas shift reactors , 2009 .

[8]  O. Zienkiewicz,et al.  Finite elements and approximation , 1983 .

[9]  W. Kays,et al.  Convective Heat and Mass Transfert , 1980 .

[10]  M. Modest.  Radiative heat transfer , 1993 .

[11]  P. Raviart,et al.  Numerical Approximation of Hyperbolic Systems of Conservation Laws , 1996, Applied Mathematical Sciences.

[12]  A. Abdel-azim.  Fundamentals of Heat and Mass Transfer , 2011 .

[13]  N. Yoshitani.  Modelling and parameter estimation for strip temperature control in continuous annealing processes , 1993, Proceedings of IECON '93 - 19th Annual Conference of IEEE Industrial Electronics.

[14]  J. Sacadura,et al.  The Zone Method: A New Explicit Matrix Relation to Calculate the Total Exchange Areas in Anisotropically Scattering Medium Bounded by Anisotropically Reflecting Walls , 2002 .

[15]  Frederick C. Munchmeyer,et al.  Radiant heat transmission from gases in tubes , 1948 .

[16]  Martin Kozek,et al.  Modeling and Control of an Industrial Continuous Furnace , 2009, 2009 International Conference on Computational Intelligence, Modelling and Simulation.

[17]  Gilmar Guimaraes,et al.  A mathematical and computational model of furnaces for continuous steel strip processing , 2006 .

[18]  H. C. Hottel,et al.  Radiant heat exchange in a gas-filled enclosure: Allowance for nonuniformity of gas temperature , 1958 .

[19]  J. Strikwerda.  Finite Difference Schemes and Partial Differential Equations , 1989 .

[20]  J. Stoer,et al.  Introduction to Numerical Analysis , 2002 .

[21]  J. Bowles,et al.  Fourier Analysis of Numerical Approximations of Hyperbolic Equations , 1987 .

[22]  Andreas Kugi,et al.  Nonlinear model predictive control of a continuous slab reheating furnace , 2013 .

[23]  M. Pinar Mengüç,et al.  Thermal Radiation Heat Transfer , 2020 .

[24]  Andreas Kugi,et al.  A fast simulation method for 1D heat conduction , 2011, Math. Comput. Simul..

[25]  Yu-Chu Tian,et al.  Mathematical Model of a Continuous Galvanizing Annealing Furnace , 2000 .

[26]  C.D. Kelly,et al.  Application of modern control to a continuous anneal line , 1988, IEEE Control Systems Magazine.

[27]  Dipankar Sanyal,et al.  A methodology to control direct-fired furnaces , 2004 .

[28]  P. Boineau,et al.  Heat transfer modelling using advanced zone model based on a CFD code , 2002 .

[29]  Karl Stephan,et al.  Convective heat and mass transfer. Flows with phase change , 2006 .

[30]  A. Kugi,et al.  A mathematical model of a slab reheating furnace with radiative heat transfer and non-participating gaseous media , 2010 .

[31]  Mark P. Taylor,et al.  Development and validation of models for annealing furnace control from heat transfer fundamentals , 2010, Comput. Chem. Eng..

[32]  Andreas Kugi,et al.  Modelling and experimental model validation for a pusher-type reheating furnace , 2009 .

[33]  Harvey G. Stenger,et al.  Water gas shift reaction kinetics and reactor modeling for fuel cell grade hydrogen , 2003 .

[34]  T. N. Stevenson,et al.  Fluid Mechanics , 2021, Nature.

[35]  R. J. Tucker,et al.  Modelling of Gas-Fired Furnaces and Boilers and Other Industrial Heating Processes , 1992 .

[36]  Dipankar Sanyal,et al.  Process modeling for control of a batch heat treatment furnace with low NOx radiant tube burner , 2005 .

[37]  C. Fletcher.  Computational Galerkin Methods , 1983 .

[38]  Tei-Chen Chen,et al.  3-D temperature and stress distributions of strip in preheating furnace of continuous annealing line , 2010 .

[39]  H. Hottel,et al.  The effect of gas flow patterns on radiative transfer in cylindrical furnaces , 1965 .

[40]  Mark H. Holmes,et al.  Introduction to Numerical Methods in Differential Equations , 2006 .

[42]  J. M. Moe.  Design of water-gas shift reactors , 1962 .

[43]  M. J. Moran,et al.  Fundamentals of Engineering Thermodynamics , 2014 .

[44]  J. Lienhard.  A heat transfer textbook , 1981 .