## 4 Results and Discussion
### Effects of Pulsed Corona Discharge Field on Particle Number Concentration  
The discharge characteristic is an important criterion to measure the discharge energy of different pulsed power supplies, and the pulse energy directly affects the concentration of electrons and ions in the reactor. The monopulse energy calculation formula is as follows:  
\[E_{s}=\int V(t)I(t)dt. \tag{11}\]  
The total energy injected into the reactor per unit time can be obtained by multiplying the pulse frequency with the monopulse energy,  
\[E_{t}=E_{s}f_{i}, \tag{12}\]  
where \(V(t)\) and \(I(t)\) are the instantaneous pulse voltage and pulse current recorded by the oscilloscope respectively, and \(f_{i}\) is the pulse frequency. The monopulse energy and the total pulse energy of the pulse corona discharge under different pulse voltages and pulse frequencies are shown in Figure 11. When the input pulse voltage increased, both the monopulse energy and the total pulse energy increased, indicating that the ion and electron concentration in the reactor increased. When the pulse frequency was adjusted to 100 Hz and the input pulse voltage was 20 kV, the monopulse energy and the total pulse energy per unit time were only 28.4 mJ and 2.8 J, while they were as high as 193.6 mJ and 19.4 J when the input pulse voltage was 50 kV. In addition, it can be clearly observed from the figure that the monopulse energy decreased with the  
Figure 10: Reduction ratios of 4-\(\upmu\)m particles under different acoustic conditions. increase in pulse frequency, while the total pulse energy increased with the increase in pulse frequency. When the pulse voltage was 50 kV and the pulse frequency was 300 Hz, the corresponding monopulse energy was 165.9 mJ, which was lower than that at 100 Hz, while the total pulse energy was 49.8 J, which was much higher than the 19.4 J corresponding to 100 Hz. In this agglomeration experiment, the selected input voltages were 30, 40, and 50 kV, while 300 Hz was selected as the pulse frequency. Figure 12 shows that when 0.5-\(\upmu\)m particles were generated, the pulsed corona discharge effect on the PNC was not evident; when voltage input was increased, the PNC gradually decreased. The increase in the pulse input voltage improved the input energy, which charged the particles. This facilitated the aggregation of particles into larger ones because of the Coulomb force. There are two mechanisms in the process of particle charging: field charge (by high-energy free electrons) and diffusion charge (by positive ions) in the pulsed electric field. Particles larger than 0.2 \(\upmu\)m are dominated by field charge, and they become more charged with increasing size, while particles smaller than 0.2 \(\upmu\)m are dominated by diffusion charge and they become more charged with decreasing size [22]. Particles with critical size are hard to charge and 0.5 \(\upmu\)m is near the critical size; thus, the charge effect is relatively weak, which reduces particle collision. The probability of particle collision is also decreased. Figure 13 indicates the change in the number concentration of the 2-\(\upmu\)m particles in the pulsed corona discharge field. Compared with the 0.5-\(\upmu\)m particles, the reduction ratio of 2-\(\upmu\)m PNC was more significant with the increase in input voltage. When the input voltage was 50 kV, the reduction ratio reached 38.5%. This also proved that the 2-\(\upmu\)m particles were more easily charged. Under the same parameters, the migration velocity of particles to the plate significantly increases, particle collisions become increasingly frequent, and the particle agglomeration efficiency similarly increases because of the presence of Coulomb coagulation. Figure 11: Pulse energy input at different pulse voltages and pulse frequencies. As demonstrated in Figure 14, when the particle diameter was adjusted to 4 \(\upmu\)m, the input voltages (30, 40, and 50 kV) could contribute to particle reduction with reduction ratios of 52%, 69.5%, and 79.4%, respectively.