{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T19:21:27Z","timestamp":1774120887709,"version":"3.50.1"},"reference-count":83,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,6,22]],"date-time":"2023-06-22T00:00:00Z","timestamp":1687392000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Science and Higher Education of the Russian Federation","award":["FEUZ-2022-0030"],"award-info":[{"award-number":["FEUZ-2022-0030"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The requirements to switching the capacities of SF6 circuit breakers submitted by Russian Grid companies are difficult to satisfy. The first limitation is related to material and financial costs in order to create a new requirement-satisfying switching device. The second limitation is dictated by the necessity of calculating complex physical processes in a circuit braker interrupter during fault\u2013current making or breaking before creating a prototype. The latter task is reduced to the problem of simulating the processes of interaction between the switching arc and the SF6 gas flow. This paper deals with the solution of the problem both analytically by a special method and numerically by a numerical software package through the creation of a mathematical model of the interaction process. The switching arc is taken into account as a form of a temperature source, based on experimental data on measuring the temperature of the arc column. The key feature of the research is to use the finite element method based on a moving mesh\u2014the Arbitrary Lagrangian Eulerian (ALE) method. Such a problem statement allows us to take the contact separation curve of the circuit breaker into account as the input data of the model. The calculations were carried out during fault-current breaking by a 110 kV SF6 dead-tank circuit breaker. The calculations of pressure and mass flow in the under-piston volume change, gas flow speed, and temperature depending on the contact separation are given. The proposed model of the switching arc was used to simulate the process of 25 kA symmetrical fault\u2013current breaking and was compared with an experiment.<\/jats:p>","DOI":"10.3390\/axioms12070623","type":"journal-article","created":{"date-parts":[[2023,6,23]],"date-time":"2023-06-23T02:34:07Z","timestamp":1687487647000},"page":"623","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Fluid Dynamics Calculation in SF6 Circuit Breaker during Breaking as a Prerequisite for the Digital Twin Creation"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3327-2742","authenticated-orcid":false,"given":"Vladislav V.","family":"Popovtsev","sequence":"first","affiliation":[{"name":"Ural Power Engineering Institute, Ural Federal University Named after the First President of Russia B.N. Yeltsin, 620002 Ekaterinburg, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5327-6076","authenticated-orcid":false,"given":"Alexandra I.","family":"Khalyasmaa","sequence":"additional","affiliation":[{"name":"Ural Power Engineering Institute, Ural Federal University Named after the First President of Russia B.N. Yeltsin, 620002 Ekaterinburg, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yurii V.","family":"Patrakov","sequence":"additional","affiliation":[{"name":"Ural Power Engineering Institute, Ural Federal University Named after the First President of Russia B.N. Yeltsin, 620002 Ekaterinburg, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"K\u00fcchler, A. (2018). High Voltage Engineering. Fundamentals\u2014Technology\u2014Applications, Springer-Verlag GmbH Germany.","DOI":"10.1007\/978-3-642-11993-4_7"},{"key":"ref_2","unstructured":"(2007). Alternating-Current Circuit Breakers for Voltages from 3 to 750 kV (Standard No. GOST 52565-2006). (In Russian)."},{"key":"ref_3","unstructured":"(2008). High-Voltage Switchgear and Controlgear\u2014Part 100: Alternating-Current Circuit-Breakers (Standard No. IEC 62271-100)."},{"key":"ref_4","unstructured":"(2017). High Voltage Switchgear and Controlgear\u2014Part 110: Inductive Load Switching, Ed. 2.0. (Standard No. IEC 62271-110)."},{"key":"ref_5","unstructured":"(2018). Guide for the Application of Shunt Reactor Switching (Standard No. IEEE Std C37.015\u20132017 (Revision of IEEE Std C37.015-2009))."},{"key":"ref_6","unstructured":"Zalesskiy, A. (1963). Electric Arc, Gosenergoizdat. (In Russian)."},{"key":"ref_7","unstructured":"Engelsht, V., Gurovich, V., and Desyatkov, G. (1990). Electric Arc Column Theory, AN USSR, Siberian department, Thermal physics institute. (In Russian)."},{"key":"ref_8","unstructured":"Agafonov, G., and Babkin, I. (2002). High Voltage Electrical Apparatus with SF6 Insulation, Energoatomizdat. (In Russian)."},{"key":"ref_9","unstructured":"Tonkonogov, E. (2008). The Design of Electrical Apparatus. High Voltage SF6 Circuit Breakers, Izdatelstvo of Peter the Great St. Petersburg Polytechnic University. (In Russian)."},{"key":"ref_10","unstructured":"Averyanova, S.A. (2015). Theory of Arc Extinguishing in Electrical Apparatuses. Interaction of the Electric Arc with the Gas Flow in High Voltage Circuit Breakers, Izdatelstvo of Peter the Great St. Petersburg Polytechnic University. (In Russian)."},{"key":"ref_11","unstructured":"Poltev, A. (1979). Design and Calculation of SF6 High Voltage Apparatus, Energiya, Leningrad department. (In Russian)."},{"key":"ref_12","unstructured":"Eroshenko, S. (2019). Calculation of Short Circuit Currents in Power Systems, Izdatelstvo of Ural Federal University. (In Russian)."},{"key":"ref_13","unstructured":"Khalyasmaa, A.I., Eroshenko, S.A., Zinovyev, K.A., and Bolgov, V. (2019). 2019 Electric Power Quality and Supply Reliability Conference and 2019 Symposium on Electrical Engineering and Mechatronics, PQ and SEEM 2019, IEEE."},{"key":"ref_14","unstructured":"Il\u2019in, A.S. (2012). Mathematical Modeling of Thermodynamic Processes of Arc Extinguishing in SF6 flow in Electrical Apparatus, Candidate of Technical Science Dissertation, Ural Federal University. (In Russian)."},{"key":"ref_15","unstructured":"Chunikhin, A., and Zhavoronkov, M. (1985). High Voltage Apparatus, Energoatomizdat. (In Russian)."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Smeets, R., Van Der Sluis, L., Kapetanovi\u0107, M., Peelo, D., and Janssen, A. (2015). Switching in Electrical Transmission and Distribution Systems, John Wiley & Sons, Ltd.. [1st ed.].","DOI":"10.1002\/9781118703618"},{"key":"ref_17","unstructured":"Kapetanovi\u0107, M. (2011). High Voltage Circuit Breakers, Faculty Electrotech. Eng., Univ. Sarajevo."},{"key":"ref_18","unstructured":"Kukekov, G. (1972). High Voltage AC Circuit Breakers, Energiya, Leningrad Department. [2nd ed.]. (In Russian)."},{"key":"ref_19","first-page":"588","article-title":"A new theory of rupture and circuit severity","volume":"102","author":"Cassie","year":"1939","journal-title":"CIGRE Rep."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"588","DOI":"10.1007\/BF02084317","article-title":"Beitrage zur Theorie des Statischen und des Dynamischen Lichtbogens","volume":"37","author":"Mayr","year":"1943","journal-title":"Arch. F\u00fcr Elektrotechnik"},{"key":"ref_21","first-page":"147","article-title":"A study of A-C. arc behavior near currents zero by means of mathematical models","volume":"67","author":"Browne","year":"1948","journal-title":"AIEE Trans."},{"key":"ref_22","first-page":"1508","article-title":"An Approach to Mathematical Analysis of A-C Arc Extinction in Circuit Breakers","volume":"77","author":"Browne","year":"1959","journal-title":"AIEE Trans."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Ragaller, K. (1978). Current Interruption in High-Voltage Networks, Springer. [1st ed.].","DOI":"10.1007\/978-1-4757-1685-6"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1703","DOI":"10.1088\/0022-3727\/7\/12\/317","article-title":"Experimental and theoretical study of a stationary high-current arc in a supersonic nozzle flow","volume":"7","author":"Hermann","year":"1974","journal-title":"J. Phys. D (Appl. Phys.)"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1546","DOI":"10.1109\/T-PAS.1977.32483","article-title":"Theoretical description of the current interruption in HV gas blast breakers","volume":"96","author":"Hermann","year":"1977","journal-title":"IEEE Trans. Power Appar. Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3361","DOI":"10.1063\/1.322240","article-title":"Prediction of properties of arcs stabilized by forced convection","volume":"46","author":"Tuma","year":"1975","journal-title":"J. Appl. Phys."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3352","DOI":"10.1063\/1.322239","article-title":"A simple model for high-current arcs stabilized by forced convection","volume":"46","author":"Lowke","year":"1975","journal-title":"J. Appl. Phys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1784","DOI":"10.1109\/T-PAS.1977.32510","article-title":"Simulation of transient and zero current behavior of arcs stabilized by forced convection","volume":"96","author":"Tuma","year":"1977","journal-title":"IEEE Trans. Power Appar. Syst."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1697","DOI":"10.1109\/T-PAS.1977.32500","article-title":"Nozzle arc interruption in supersonic flow","volume":"96","author":"Swanson","year":"1977","journal-title":"IEEE Trans. Power Appar. Syst."},{"key":"ref_30","first-page":"140","article-title":"Numerical simulation of arc quenching processes in a high-voltage SF6 circuit breaker and comparison of results with real tests","volume":"5","year":"2011","journal-title":"Sci. Tech. Bull. Povolzhye"},{"key":"ref_31","first-page":"36","article-title":"Model of arc quenching processes in high voltage circuit breaker","volume":"12","year":"2011","journal-title":"Electrotekhnika"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1836","DOI":"10.1109\/TMAG.2009.2012805","article-title":"Evaluation on Short Line Fault Breaking Performance of SF6 Gas Circuit Breaker Considering Effects of Ablated Nozzle Vapor","volume":"45","author":"Park","year":"2009","journal-title":"IEEE Trans. Magn."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1109\/TPS.2013.2288102","article-title":"CFD Analysis of Arc-Flow Interaction in a High-Voltage Gas Circuit Breaker Using an Overset Method","volume":"42","author":"Park","year":"2014","journal-title":"IEEE Trans. Plasma Sci."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"580","DOI":"10.1109\/61.852988","article-title":"An Improved Mayr-Type Arc Model Based on Current-Zero Measurements","volume":"15","author":"Schavemaker","year":"2000","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1049\/ip-gtd:20000238","article-title":"Evaluation of High-Voltage Circuit Breaker Performance with a Validated Arc Model","volume":"147","author":"Smeets","year":"2000","journal-title":"IEEE Proc. Gener. Transm. Distrib."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1029","DOI":"10.1109\/TDEI.2011.5976092","article-title":"Linking a Physical Arc Model with a Black Box Arc Model and Verification","volume":"18","author":"Sokolija","year":"2011","journal-title":"IEEE Trans. Dielectr. Electr. Insul."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1835","DOI":"10.1109\/TPWRD.2017.2764108","article-title":"Novel Black-Box Arc Model Validated by High-Voltage Circuit Breaker Testing","volume":"33","author":"Ohtaka","year":"2018","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_38","unstructured":"Sinkevich, O.A., and Stahanov, I.P. (1991). Plasma Physics. Stationary Processes in a Partially Ionized Gas, Graduate school. (In Russian)."},{"key":"ref_39","unstructured":"Cherednichenko, V.S., Anshakov, A.S., and Kuzmin, M.G. (2009). Plasma Electrotechnological Installations, Izdatelstvo of Novosibirsk State University. (In Russian)."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Boulos, M.I., Fauchais, P.L., and Pfender, E. (2020). Handbook of Thermal Plasmas, Springer.","DOI":"10.1007\/978-3-319-12183-3"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1835","DOI":"10.1109\/TPS.2019.2898696","article-title":"Evaluation of Arc Quenching Ability for a Gas by Combining 1-D Hydrokinetic Modeling and Boltzmann Equation Analysis","volume":"47","author":"Zhong","year":"2019","journal-title":"IEEE Trans. Plasma Sci."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"103507","DOI":"10.1063\/1.5127274","article-title":"An Improved Method for Fast Evaluating Arc Quenching Performance of a Gas Based on 1D Arc Decaying Model","volume":"26","author":"Zhong","year":"2019","journal-title":"Phys. Plasmas."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"085122","DOI":"10.1063\/1.5043516","article-title":"Comparison of Dielectric Breakdown Properties for Different Carbon-Fluoride Insulating Gases as SF6 Alternatives","volume":"8","author":"Zhong","year":"2018","journal-title":"AIP Adv."},{"key":"ref_44","unstructured":"Ivanov, M.F., and Galburt, V.A. (2000). Numerical Simulation of Gas and Plasma Dynamics by Particle Methods, Izdatelstvo of Moscow Institute of Physics and Technology. (In Russian)."},{"key":"ref_45","unstructured":"Klimontonovich, Y.L. (1975). Kinetic Theory of Non-Ideal Gas and Non-Ideal Plasma, Science. (In Russian)."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Fridman, A., and Kennedy, L.A. (2021). Plasma Physics and Engineering, CRC Press. [3rd ed.].","DOI":"10.1201\/9781315120812"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Muratovi\u0107, M., Kapetanovi\u0107, M., Ahmethodzi\u0107, A., Delic, S., and Suh, W.B. (July, January 30). Nozzle Ablation Model: Calculation of Nozzle Ablation Intensity and Its Influence on State of SF6 Gas in Thermal Chamber. Proceedings of the 2013 IEEE International Conference on Solid Dielectrics (ICSD), Bologna, Italy.","DOI":"10.1109\/ICSD.2013.6619901"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"4506","DOI":"10.1109\/TPWRD.2022.3150111","article-title":"Experimental and Numerical Studies of Nozzle Ablation and Geometric Change in Real Gas Circuit Breakers","volume":"37","author":"Park","year":"2022","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Kuroda, M., Urai, H., Terada, M., Ishii, T., Kojima, Y., and Yokomizu, Y. (2019, January 13\u201316). Evaluation of Dielectric Interruption Performance in Gas Circuit Breaker with Ablated PTFE\/BN Vapor. Proceedings of the 2019 5th International Conference on Electric Power Equipment\u2014Switching Technology: Frontiers of Switching Technology for a Future Sustainable Power System, ICEPE-ST 2019, Kitakyushu, Japan.","DOI":"10.1109\/ICEPE-ST.2019.8928849"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"496","DOI":"10.1002\/tee.23322","article-title":"Research on Parameters Optimization of High Voltage Circuit Breaker Nozzle Based on Image Recognition and Deep Learning","volume":"16","author":"Jianying","year":"2021","journal-title":"IEEJ Trans. Electr. Electron. Eng."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Kwak, C.S., Kim, H.K., and Lee, S.H. (2017, January 22\u201325). Bezier Curve-Based Shape Optimization of SF6 Gas Circuit Breaker to Improve the Dielectric Withstanding Performance for Both Medium and Maximum Arcing Time. Proceedings of the ICEPE-ST 2017\u20144th International Conference on Electric Power Equipment-Switching Technology, Xi\u2019an, China.","DOI":"10.1109\/ICEPE-ST.2017.8188797"},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Bang, B.H., Lee, Y.S., Choi, J.U., Ahn, H.S., and Park, S.W. (2013, January 20\u201323). Prediction and Improvement of Dielectric Breakdown between Arc Contacts in Gas Circuit Breaker. Proceedings of the 2013 2nd International Conference on Electric Power Equipment\u2014Switching Technology, ICEPE-ST 2013, Matsue, Japan.","DOI":"10.1109\/ICEPE-ST.2013.6804354"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"105385","DOI":"10.1016\/j.ijepes.2019.105385","article-title":"Prestrike Modeling in SF6 Circuit Breakers","volume":"114","author":"Homaee","year":"2020","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Zhang, H., Yao, Y., Wang, Z., Zhang, B., Hao, X., Liu, Y., and Du, Y. (2020, January 2\u20133). Application of Arc Breaking Simulation in Development of Extra High Voltage SF6 Circuit Breaker. Proceedings of the 16th IET International Conference on AC and DC Power Transmission (ACDC 2020), Online.","DOI":"10.1049\/icp.2020.0405"},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Dhotre, M.T., Ye, X., Seeger, M., Schwinne, M., and Kotilainen, S. (2017, January 11\u201314). CFD Simulation and Prediction of Breakdown Voltage in High Voltage Circuit Breakers. Proceedings of the 2017 IEEE Electrical Insulation Conference, EIC 2017, Baltimore, MD, USA.","DOI":"10.1109\/EIC.2017.8004627"},{"key":"ref_56","unstructured":"Ha, M.J., Kim, J., Yeo, C.H., and Kweon, K.Y. (2009). Transmission and Distribution Conference and Exposition: Asia and Pacific, T and D Asia 2009, IEEE."},{"key":"ref_57","unstructured":"Iordanidis, A.A., and Franck, C.M. (2008). GD 2008\u201417th International Conference on Gas Discharges and Their Applications, IEEE."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1109\/TPWRD.2013.2287380","article-title":"Influence of DC Component of Short-Circuit Current on Arc Characteristics during the Arcing Period","volume":"29","author":"Zhang","year":"2014","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"1314","DOI":"10.1109\/TDEI.2011.5976133","article-title":"Computer Simulation of High-Voltage SF6 Circuit Breakers: Approach to Modeling and Application Results","volume":"18","year":"2011","journal-title":"IEEE Trans. Dielectr. Electr. Insul."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"1663","DOI":"10.1109\/TPWRD.2015.2403413","article-title":"Arc Gas-Flow Simulation Algorithm Considering the Effects of Nozzle Ablation in a Self-Blast GCB","volume":"30","author":"Choi","year":"2015","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"135206","DOI":"10.1088\/0022-3727\/41\/13\/135206","article-title":"Self-Consistent Radiation-Based Simulation of Electric Arcs: II. Application to Gas Circuit Breakers","volume":"41","author":"Iordanidis","year":"2008","journal-title":"J. Phys. D Appl. Phys."},{"key":"ref_62","first-page":"1720","article-title":"Investigation of the Effects of Pressure Ratios on Arc Behavior in a Supersonic Nozzle","volume":"28","author":"Zhang","year":"2000","journal-title":"IEEE Trans. Plasma Sci."},{"key":"ref_63","doi-asserted-by":"crossref","unstructured":"Park, Y., and Song, T. (2022, January 15\u201318). Plasma Arc Simulation of High Voltage Circuit Breaker with a Hybrid 2D\/3D Model. Proceedings of the 2022 6th International Conference on Electric Power Equipment-Switching Technology (ICEPE-ST), Seoul, Republic of Korea.","DOI":"10.1109\/ICEPE-ST51904.2022.9757101"},{"key":"ref_64","unstructured":"Golovin, S.V. (2009). Partially Invariant Solutions of the Magnetohydrodynamics Equations. [Doctor of Physical-Mathematical Science Dissertation, Novosibirsk State University]. (In Russian)."},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Lie, S. (1893). Vorlesungen \u00fcber Continuierliche Gruppen mit Geometrischen und Anderen Anwendungen, B.G. Teubner. (In German).","DOI":"10.5962\/bhl.title.18549"},{"key":"ref_66","unstructured":"Ovsyannikov, L.V. (1962). Group Properties of Differential Equations, AN USSR, Siberian department. (In Russian)."},{"key":"ref_67","unstructured":"Versteeg, H.K., and Malalasekera, W. (2007). An Introduction to Computational Fluid Dynamics, Pearson Education Ltd.. [2nd ed.]."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1146\/annurev.fluid.010908.165248","article-title":"Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics","volume":"41","author":"Najm","year":"2009","journal-title":"Annu. Rev. Fluid Mech."},{"key":"ref_69","unstructured":"Loycanskiy, L.G. (2003). Fluid and Gas Mechanics, Drofa. [7th ed.]. (In Russian)."},{"key":"ref_70","unstructured":"Batchelor, G.K. (2012). An Introduction to Fluid Dynamics, Cambridge University Press."},{"key":"ref_71","unstructured":"Averyanova, S.A. (2005). Numerical Simulation of Gas Flow in the Arcing Device of a High-Voltage Circuit Breaker, Candidate of Physical-Mathematical Science Dissertation, Peter the Great St. Petersburg Polytechnic University. (In Russian)."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1109\/TPAS.1972.293219","article-title":"Thermal Analysis of an SF6 Circuit Breaker ARC","volume":"PAS-91","author":"Swanson","year":"1971","journal-title":"IEEE Trans. Power Appar. Syst."},{"key":"ref_73","unstructured":"Pei, Y. (2014). Computer Simulation of Fundamental Processes in High Voltage Circuit Breakers Based on an Automated Modelling Platform. [Ph.D. Thesis, The University of Liverpool]."},{"key":"ref_74","unstructured":"Liu, J. (2016). Modelling and Simulation of Air and SF6 Switching Arcs in High Voltage Circuit Breakers. [Ph.D. Thesis, The University of Liverpool]."},{"key":"ref_75","unstructured":"Wilcox, D.C. (2006). Turbulence Modeling for CFD, DCW Industries. [3rd ed.]."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"2120","DOI":"10.1109\/TPS.2018.2834735","article-title":"Arc Shape and Arc Temperature Measurements in SF6 High-Voltage Circuit Breakers Using a Transparent Nozzle","volume":"46","author":"Bai","year":"2018","journal-title":"IEEE Trans. Plasma Sci."},{"key":"ref_77","unstructured":"Chernoskutov, D., Popovtsev, V., and Sarapulov, S. (2020). 2020 Ural Smart Energy Conference (USEC), IEEE."},{"key":"ref_78","unstructured":"Chernoskutov, D., Popovtsev, V., and Sarapulov, S. (2020). 2020 Ural Smart Energy Conference (USEC), IEEE."},{"key":"ref_79","unstructured":"Thomas, R. (2007). Three Phase Controlled Fault Interruption Using High Voltage SF6 Circuit Breakers. [Ph.D. Thesis, The University of Liverpool]."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1115\/1.2911398","article-title":"Turbulent Pratidtl Number\u2014Where Are We?","volume":"116","author":"Kays","year":"1994","journal-title":"J. Heat Transfer."},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1016\/j.ijthermalsci.2004.03.004","article-title":"On the Judicious Use of the k-\u03b5 Model, Wall Functions and Adaptivity","volume":"43","author":"Lacasse","year":"2004","journal-title":"Int. J. Therm. Sci."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"2703","DOI":"10.1109\/TPS.2015.2450536","article-title":"PTFE Vapor Contribution to Pressure Changes in High-Voltage Circuit Breakers","volume":"43","author":"Gonzalez","year":"2015","journal-title":"IEEE Trans. Plasma Sci."},{"key":"ref_83","unstructured":"Chernoskutov, D.V. (2017). Increasing the Switching Capacity of High-Voltage Electrical Equipment, Candidate of Technical Science Dissertation, Ural Federal University. (In Russian)."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/7\/623\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:58:29Z","timestamp":1760126309000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/7\/623"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,22]]},"references-count":83,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2023,7]]}},"alternative-id":["axioms12070623"],"URL":"https:\/\/doi.org\/10.3390\/axioms12070623","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,6,22]]}}}