title: Radiation Transfer Calculations in Three-Dimensional Switching Arcs Based on Discrete Ordinates Method (DOM)
Creators: name: Esmaeili, Saro
Publisher: name: University of Liverpool Repository
Year: 2025

description: The present work is concerned with radiation transfer calculation in three-dimensional switching arcs based on the Discrete Ordinates Method (DOM). The complexity of arc simulation using numerical methods in specialised software (such as Phoenics or Ansys Fluent) restricts the calculation time for radiation transfer to less than a value of a few millisecond (such as 5 ms) per iteration. So far, none of the existing methods of radiation transfer calculation, except the Net Emission Coefficient (NEC) based model, has been able to meet a trade-off between the computation time and the accuracy required for commercial applications. In the thesis, definitive information regarding the radiation transfer calculations in the actual arc conditions is gathered, aiming at establishing a procedure to compute the radiated energy in a commercially-affordable model for switching arcs. The study mainly focuses on the SF_6 medium. Meanwhile the radiation transfer parameters of the C_4 F_7 N+CO_2+PTFE mixture are calculated and analysed for the first time. The information extracted from this work can be a baseline for future research on different mediums. A 3-D cylindrical radiation transfer model of an actual arc is developed and implemented in C++ programming language. The temperature and pressure profiles at an instant towards the end of the high-current stage (I = 15 kA) of a switching duty, simulated in Phoenics, are used to build a real arc case with variable temperature and pressure in all directions. The test object of the switching duty is a 245 kV/50 kA self-blast circuit breaker with an initial filling pressure of 6 bar (absolute). Furthermore, different case studies are presented based on the data from the literature to verify the radiation model. The radiation flux divergence and the NEC of the two mentioned gases are the subjects of calculations. At first, the factors involved in the numerical method are studied to find the sensitivity of response and the minimum required value of each factor. It is found that a minimum number of 200 intervals over 1 cm for integration over a radiation line, 25 discrete directions in half-cylinder, and 10,000 uniform wavelength points for integration over the frequency spectrum are required. It turned out that a 20% change in the flux divergence leads to less than a 5% change in the temperature. The spatial and spectral distribution of the flux divergence and NEC are studied in detail, and the contribution of different parts of the frequency spectrum and space to each of the two parameters is determined. It is found that most of the photons of the infrared and visible spectra (&lt; 1015 Hz) can escape the arc and reach the nozzle surface. As the frequency increases, despite having a high emission at the mid-ultraviolet and far-ultraviolet regions, the high rate of self-absorption inside the arc lowers the probability of escape for the emitted photons. The study of the attenuation coefficient and optical depth also reaches the same conclusions. It is shown that the calculation of the flux divergence at a point in an arc cylinder only needs to consider a segment of 2.4 cm in thickness to produce results with less than 7% deviation from the results by considering the entire cylinder (8 cm). In all cases for both gases, the absorption region starts at a temperature ranging from 0.73Tmax to 0.83Tmax. The results provide important references to a crucial factor in the NEC-based semi-empirical radiation model that is widely used for radiation transfer calculation in industrial switching arc simulations. The absorption ratio extracted from the results provides verification to another important parameter in the NEC based radiation model. The absorption ratio in SF6 arcs varies between 50% and 71%. This ratio for the C4F7N+CO2+PTFE mixture is between 35% and 77%. Results from the present work provide novel quantitative information with a deep impact on our understanding of the radiation phenomenon in switching arcs. They can be used in the arc simulation process and can also help circuit breaker design since the phenomena involved in the switching process, such as nozzle ablation or arc cooling of high current arcs, are directly related to radiation transfer. In addition to the above work, a new method that is based on the concept of the so- called Absorption Potential is introduced for calculating the radiation transfer. This method is based on the DOM formulation and the Partial Characteristics Method (PCM) technique and provides results more than 90% close to the DOM results in a much shorter time with a saving in computational time of 60%-90%.