Determination of the Parameters of a Normally Distributed Moving Surface Heat Source from Electric Arc Plasma to Predict the Object’s Thermal State
DOI:
https://doi.org/10.24160/1993-6982-2025-1-92-99Keywords:
moving heat source, heat transfer, infrared image monitoring, mathematical modelingAbstract
The article considers an approach to determining the parameters of a moving heat source during the thermal treatment of objects for subsequently predicting the thermal conditions. It is shown that under heat treatment conditions it is impossible to take into account all heat fluxes involved in the transfer of thermal energy from the source to the object. To take them into account, it is proposed to use an integral heat flux indicator in the form of a Gaussian function, the parameters of which (the maximum heat flux value at the contact spot center and the concentration coefficient) are determined on the basis of infrared image monitoring data and the heat transfer process mathematical model from the condition of the minimum standard deviation of the predicted data from the experimental ones. The mathematical model includes the object’s 3D geometric model, an unsteady equation of thermal conductivity in a continuous medium with coefficients depending on the local temperature. The phase transitions heat values are taken into account by an abrupt change in heat capacity in the thermal contact zone. On the object’s outer surface, complex heat transfer to the environment is specified, including convective and radiant mechanisms. The supply of thermal energy from a thermal source is specified by the surface heat flux, the distribution of which is specified in the boundary conditions. The mathematical model equations are integrated by the finite element method with an adaptive mesh, which ensures the condensation of elements in the thermal contact area. To illustrate the application of the proposed approach, computational and natural experiments were carried out. A steel structure and welding electrode electric arc plasma were selected as an object and a heat source. Control lines were identified on the object and its geometric model, along which a comparison was made between the object surface temperatures measured using the infrared imager and predicted using the mathematical model. The proposed methodology, which is based on infrared image monitoring data of the heat treatment zone and a mathematical model that specifies the relationship between the temperature fields in the treatment object and the moving distributed heat flux inducing them, makes it possible to identify the parameters of a moving heat source and predict the thermal conditions over the object’s volume.
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Для цитирования: Бирюков М.И., Хвостов А.А., Коновалов Д.А., Слюсарев М.И. Определение параметров движущегося нормально распределенного поверхностного источника теплоты от плазмы электрической дуги для прогнозирования теплового состояния объекта // Вестник МЭИ. 2025. № 1. С. 92—99. DOI: 10.24160/1993-6982-2025-1-92-99
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Конфликт интересов: авторы заявляют об отсутствии конфликта интересов
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3. Osman T., Boncheffa A. Analytical Solution for the 3D Study Conduction in a Solid Subjected to a Moving Rectangular Heat Source and Surface Cooling. C.R. Mecanique. 2009;337:107—111.
4. Hu Z., Liu Z. Heat Conduction Simulation of 2D Moving Heat Source Problems Using a Moving Mesh Method. Advances in Mathematical Phys. 2020:1—16.
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8. Anca A., Cardona A., Risso J., Fachinotti V.D. Finite Element Modeling of Welding Processes. Appl. Mathematical Modelling. 2011;35(2):688—707.
9. Eagar T., Tsai N. Temperature Fields Produced by Traveling Distributed Heat Sources. Welding J. 1983;62:346—355.
10. Das A. e. a. A Review of Heat Source and Resulting Temperature Distribution in Arc Welding. J Thermal Analysis and Calorimetry. 2022;147:12975—13010.
11. Çengel Y.A., Ghajar A.J. Heat and Mass Transfer: Fundamentals & Applications. N.-Y.: McGraw-Hill Education, 2015.
12. Alexiades V., Solomon A.D. Mathematical Modeling of Melting and Freezing Processes. Washington: Hemisphere Publ. Co, 1993.
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18. Bonacina C., Comini G., Fasano F., Primicerio V. Numerical Solution of Phase-change Problems. Intern. J. Heat Mass Transfer. 1973;16:1825—1832.
19. Kanwal R.P. Generalized Functions: Theory and Technique. Boston: Birkhäuser, 2004.
20. Zahedi S., Tornberg A.-K. Delta Function Approximations in Level Set Methods by Distance Function Extension. J. Computational Phys. 2010;229(6):2199—2219.
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22. Clain F.M., Teixeira P.R. de F., Araújo D.B. Two Heat Source Models to Simulate Welding Processes with Magnetic Deflection. Soldagem & Inspeção. 2017;22(1):99—113
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For citation: Biryukov M.I., Khvostov A.A., Konovalov D.A., Slyusarev M.I. Determination of the Parameters of a Normally Distributed Moving Surface Heat Source from Electric Arc Plasma to Predict the Object’s Thermal State. Bulletin of MPEI. 2025;1:92—99 13.05.2024. (in Russian). DOI: 10.24160/1993-6982-2025-1-92-99
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Conflict of interests: the authors declare no conflict of interest
