Investigation of spark breakdown paths in air by using an image processing technique

Abstract

Two simple but effective experimental set-ups were built to produce two orthogonal images of spark breakdown paths across short or long air gaps. These images were recorded simultaneously by a high-resolution video camera and subsequently processed by the computer image processing techniques to rebuild the spark breakdown paths in three dimensions. The experimental set-ups developed the investigations of spark breakdown paths from two dimensions to three dimensions. Up to 100 images were recorded for each of the experimental conditions investigated. The data of the three-dimensional spark breakdown paths with different experimental conditions were analysed by a statistical method to get the distributions of the geometrical parameters, which characterize the shapes of spark breakdown paths. The parameter distributions for the paths across different long air gaps indicate that as the length of air gaps increases, spark breakdown paths would change direction more and more violently during propagation, and therefore they become more tortuous. The same feature can be found in the parameter distributions as the input energy during spark breakdown increases meanwhile the air gap is kept unchanged. It is also observed from the statistical results that the average deviation of the first segments from the vertical axis increases as the inclined angle of the point electrode increases, and the mean length of the first segments decreases while the diameter of the rod electrode increases. These statistical results are compared with that obtained from the investigation of two-dimensional spark paths, it is found the two-dimensional parameter distributions only gave out part of the characteristics of the spark paths. The fractal method, as an alternative to the traditional statistical method in investigating the random complex phenomena, was also used in the thesis to analyse the spark breakdown paths from the point of engineering application. The mean fractal dimensions of spark breakdown paths are in the range of 1.03-1.23 and found to increase with the length of the air gap, the inclination of the pointed electrode, the diameter of the sphere electrode and the input energy during spark breakdown. An equivalent analysis has indicated the amplitude exponent and the time exponent, which describe the characteristic of the process of spark path forming, are about 2.55 and 1.25 respectively. They both stay nearly constant except for the input energy changing. The locations of spark breakdown paths on the plane electrode can be regarded as the ends of fractal random walks. The distribution exhibits power law behaviors. The dynamical mechanism of the spark breakdown path as a fractal phenomenon has been discussed in terms of a simple streamer model. The propagation of a spark breakdown path is a semi-random process. The analysis of the spark breakdown paths in point-plane gaps ranging from 45 to 400 mm section by section revealed that each leader channel section is consistently related to the previous section; and allowed the determination of the ratio of the mean angle to the vertical of the new leader channel section to that of the previous section. The ratio is about 0.7. This is true, regardless of gap width, when each path is divided up into equal steps. Thus the directional propagation probability in the leader channel formation is decomposed into a memory effect part and a random variation part. It is the directional probability function that determines the characteristic shape of spark paths. It is suggested that this directional propagation probability be closely related to the field distribution local to the leader tip. The numerical calculation of the field in three dimensions has provided some useful clues to determine the relationship between them. The direction of the maximum field nearly overlaps on the axis of the memory effect. The random variation imposed symmetrically on the memory axis can be described by a normal distribution. The results obtained from the analysis of the directional propagation probability were used to simulate spark breakdown paths. The simulated results show satisfactory agreements with the recorded paths.