The Mathematical Modelling of Heat Transfer in Electrical Cables
DOI:
https://doi.org/10.2478/ecce-2014-0007Keywords:
Power transmission, Numerical models, Finite element analysis, Finite volume methods, Convergence of numerical methodsAbstract
This paper describes a mathematical modelling approach for heat transfer calculations in underground high voltage and middle voltage electrical power cables. First of the all typical layout of the cable in the sand or soil is described. Then numerical algorithms are targeted to the two-dimensional mathematical models of transient heat transfer. Finite Volume Method is suggested for calculations. Different strategies of nonorthogonality error elimination are considered. Acute triangles meshes were applied in two-dimensional domain to eliminate this error. Adaptive mesh is also tried. For calculations OpenFOAM open source software which uses Finite Volume Method is applied. To generate acute triangles meshes aCute library is used. The efficiency of the proposed approach is analyzed. The results show that the second order of convergence or close to that is achieved (in terms of sizes of finite volumes). Also it is shown that standard strategy, used by OpenFOAM is less efficient than the proposed approach. Finally it is concluded that for solving real problem a spatial adaptive mesh is essential and adaptive time steps also may be needed.References
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Raim. Čiegis, Rem. Čiegis, M. Meilūnas, G. Jankevičiūtė, V. Starikovičius. Parallel numerical algorithm for optimization of electrical cables, Mathematical modelling and analysis, 13(4), 471-482 p., 2008.
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A. Ilgevicius. Analytical and numerical analysis and simulation of heat transfer in electrical conductors and fuses. Dissertation, Universität der Bundeswehr München, 2004.
A.A. Samarskii. The theory of difference schemes. Marcel Dekker, Inc., New York-Basel, 2001.
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LeVeque and Z. Li. Erratum: The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J. Numer. Anal, 32, 1704, 1995.
http://www.openfoam.com
Loudyi, D. Falconer, R.A. and Lin,B. Mathematical development and verification of a non-orthogonal finite volume model for groundwater flow applications. Adv. Water Res., 30:29-42, 2007
http://www.cise.ufl.edu/~ungor/aCute
F. Incropera, P. DeWitt, P. David, Introduction to heat transfer. John Willey & Sons, New Yourk, 1985.
A. Ilgevicius. Analytical and numerical analysis and simulation of heat transfer in electrical conductors and fuses. Dissertation, Universität der Bundeswehr München, 2004.
A. Ilgevicius and H.D. Liess. Calculation of the heat transfer in cylindrical wires and electrical fuses by implicit finite volume method. Mathematical Modelling and Analysis, 8, 217-228, 2003.
J. Taler and P. Duda. Solving Direct and Inverse Heat Conduction Problems. Springer, Berlin, 2006.
R. Čiegis, A. Ilgevičius, H. Liess, M. Meilūnas, O. Suboč. Numerical simulation of the heat conduction in electrical cables. Mathematical modelling and analysis, 12(4), 425-439 p., 2007.
Raim. Čiegis, Rem. Čiegis, M. Meilūnas, G. Jankevičiūtė, V. Starikovičius. Parallel numerical algorithm for optimization of electrical cables, Mathematical modelling and analysis, 13(4), 471-482 p., 2008.
R. Falk and J. Osborn. Remarks on mixed finite element methods for problems with rough coefficients. Math. Comp., 62, 1-19, 1994.
A. Ilgevicius. Analytical and numerical analysis and simulation of heat transfer in electrical conductors and fuses. Dissertation, Universität der Bundeswehr München, 2004.
A.A. Samarskii. The theory of difference schemes. Marcel Dekker, Inc., New York-Basel, 2001.
A.N. Tichonov and A.A. Samarskii. Homogeneous finite difference schemes. Zh. Vychisl. Mat. Mat. Fiziki, 1(1), 5-63, 1961.
V.P. Il'in. High order accurate finite volumes discretization for Poisson equation. Siberian Math. J., 37(1), 151-169, 1996.
LeVeque and Z. Li. Erratum: The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J. Numer. Anal, 32, 1704, 1995.
http://www.openfoam.com
Loudyi, D. Falconer, R.A. and Lin,B. Mathematical development and verification of a non-orthogonal finite volume model for groundwater flow applications. Adv. Water Res., 30:29-42, 2007
http://www.cise.ufl.edu/~ungor/aCute
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2014-05-01
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Copyright (c) 2014 Andrej Bugajev, Gerda Jankevičiūtė, Natalija Tumanova (Author)
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Bugajev, A., Jankevičiūtė, G., & Tumanova, N. (2014). The Mathematical Modelling of Heat Transfer in Electrical Cables. Electrical, Control and Communication Engineering, 5(1), 46-53. https://doi.org/10.2478/ecce-2014-0007
