Numerical simulation of resistance furnaces by using distributed and lumped models

  1. Bermúdez, A. 12
  2. Gómez, D. 12
  3. González, D. 1
  1. 1 Department of Applied Mathematics, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Spain
  2. 2 Galician Centre for Mathematical Research and Technology (CITMAga), E-15782 Santiago de Compostela, Spain
Revista:
Advances in Computational Mathematics

ISSN: 1019-7168,  1572-9044

Ano de publicación: 2024

Volume: 50

Número: 2

Tipo: Artigo

DOI: 10.1007/S10444-024-10120-Z GOOGLE SCHOLAR lock_openAcceso aberto editor

Outras publicacións en: Advances in Computational Mathematics

Resumo

This work proposes a methodology that combines distributed and lumped models tosimulate the current distribution within an indirect heat resistance furnace and, inparticular, to calculate the current to be supplied for achieving a desired power output. The distributed model is a time-harmonic eddy current problem, which is solvednumerically using the finite element method. The lumped model relies on calculatinga reduced impedance associated with an equivalent circuit model. Numerical simulations and plant measurements demonstrate the effectiveness of this approach. Thegood correlation between the results indicates that this approximation is well-suitedto support the design and improve the efficiency of the furnace in a short time

€ Ver financiamento

Información de financiamento

Financiadores

Referencias bibliográficas

  • Adachi, M., Yonemori, H.: Considerations of configurations on induction heating type indirect heating system. In: Proceedings of the IEEE region 10 humanitarian technology conference 2014, vol. 2015–Jan, pp. 88–93 (2015)
  • Alonso-Rodríguez, A., Valli, A.: Eddy current approximation of Maxwell equations: theory. Algorithms and Applications. Springer, Milan (2010)
  • Amrouche, C., Bernardi, C., Dauge, M., Girault, V.: Vector potentials in three-dimensional non-smooth domains. Math. Methods Appl. Sci. 21(9), 823–864 (1998)
  • Balabanian, N., Bickart, T.: Electrical network theory. Wiley, New York (1969)
  • Bermúdez, A., Rodríguez R., Salgado, P.: Numerical solution of eddy current problems in bounded domains using realistic boundary conditions. Comput. Methods Appl. Mech. Eng. 194(2), 411–426 (2005)
  • Bermúdez, A., Gómez, D., Muñiz, M.C., Salgado, P.: Transient numerical simulation of a thermoelectrical problem in cylindrical induction heating furnaces. Adv. Comput. Math. 26(1–3), 39–62 (2007)
  • Bermúdez, A., Gómez, D., Salgado, P.: Mathematical models and numerical simulation in electromagnetism. Springer, New York (2014)
  • Bossavit, A.: Computational electromagnetism: variational formulations, complementarity. Edge Elements. Academic Press series in electromagnetism. Academic Press, San Diego, CA (1998)
  • Bossavit, A.: Most general “non-local” boundary conditions for the Maxwell equation in a bounded region. COMPEL - Int. J. Comput. Math. Electr. Electron. Eng. 19(2), 239–245 (2000)
  • Callegaro, L.: Electrical impedance. Measurements and Applications. Taylor & Francis, Boca Raton, Principles (2013)
  • Edgerley, C., Smith, L., Wilford, C.F.: Electric metal melting - a review. Power Eng. J. 2(2), 83–92 (1988)
  • Fletcher, S.: The two-terminal equivalent network of a three-terminal electrochemical cell. Electrochem. Commun. 3, 692–696 (2001)
  • Gross, P.W., Kotiuga, P.R.: Electromagnetic theory and computation: a topological approach, 1st edn. No. 48 in Mathematical Sciences Research Institute Publications. Cambridge University Press, Cambridge (2004)
  • Grzella, J., Sturm, P., Krüger, J., Reuter, M.A., Kögler, C., Probst, T.: Metallurgical furnaces. In: Ullmann’s Encyclopedia of Industrial Chemistry. Wiley-VCH Verlag GmbH & Co. KGaA (2003)
  • Jankowski, T.A., Pawley, N.H., Gonzales, L.M., Ross, C.A., Jurney, J.D.: Approximate analytical solution for induction heating of solid cylinders. Appl. Math. Model. 40(4), 2770–2782 (2016)
  • Kawashima, R., Mishima, T., Ide, C.: Three-phase to single-phase multiresonant direct AC-AC converter for metal hardening high-frequency induction heating applications. IEEE Trans. Power Electron. 36(1), 639–653 (2021)
  • Kettunen, L.: Fields and circuits in computational electromagnetism. IEEE Trans. Magn. 37(5), 3393–3396 (2001)
  • Nguyen, B.A., Phan, Q.D., Nguyen, D.M., Nguyen, K.L., Durrieu, O., Maussion, P.: Parameter identification method for a three-phase induction heating system. IEEE Trans. Ind. Appl. 51(6), 4853–4860 (2015)
  • Puckett, T.: A note on the admittance and impedance matrices of a n-terminal network. IRE Transactions - Circuit Theory CT-3, 70–75 (1956)
  • Ramírez, M., Trapaga, G.: Mathematical modeling of a direct current electric arc: part I. Analysis of the characteristics of a direct current arc. Metallurgical and Materials Transactions B: Process Metallurgy and Materials Processing Science 35(2), 363–372 (2004)
  • Redondo, R.C., Melchor, N.R., Redondo, M., Quintela, F.R.: Electrical power and energy systems instantaneous active and reactive powers in electrical network theory: a review of some properties. Int. J. Electr. Power Energy Syst. 53, 548–552 (2013)
  • Tan, Y., Wen, S., Shi, S., Jiang, D., Dong, W., Guo, X.: Numerical simulation for parameter optimization of silicon purification by electron beam melting. Vacuum 95, 18–24 (2013)
  • Tarhasaari, T., Kettunen, L., Bossavit, A.: Some realizations of a discrete Hodge operator: a reinterpretation of finite element techniques [for EM field analysis]. IEEE Trans. Magn. 35(3), 1494–1497 (1999)
  • Tellegen, B.: A general network theorem, with applications. Philips Res. Rep. 7, 259–269 (1952)
  • Touzani, R., Rappaz, J.: Mathematical models for eddy currents and magnetostatics. Scientific Computation. Springer, Dordrecht (2014)
  • Vutova, K., Donchev, V.: Non-stationary heat model for electron beam melting and refining - an economic and conservative numerical method. Appl. Math. Model. 40(2), 1565–1575 (2016)
  • Walton, R.R.: Furnaces, electric, resistance furnaces, p. 12. Wiley, Ltd, New Jersey (2000)
  • Yermekova, M., Galunin, S.A.: Numerical simulation and automatic optimization of the disk induction heating system. In: Proceedings of the 2017 IEEE Russia section young researchers in electrical and electronic engineering conference, ElConRus 2017, pp. 1085–1090 (2017)
  • Zadeh, L.A.: Multipole analysis of active networks. IRE Trans. Circ. Theory 4(3), 97–105 (1957)
  • Zhang, X.K., He, Y.L., Tang, S.Z., Wang, F.L., Xie, T.: An electromagnetics-temperature-component multi-physical coupled model for electric furnace in calcium carbide smelting process. Appl. Therm. Eng. 165, 114552 (2020)