# A Study on the Improvement of Filter Performance to Remove Indoor Air Pollution
## 2 Simulation Method and Result
### Electric Dust Collector Simulation to Remove the Dust under PM2.5  
In the case of the previously simulated physical filter, it can be seen that the dust-collection efficiency is lowered for particles of 5 \(\upmu\)m or less. Therefore, it was simulated to collect particles of 0.1 \(\upmu\)m to 5 \(\upmu\)m or less using an electric dust-collection method. In order to calculate the dust-collection efficiency, a theoretical technology for the electric dust-collection method was secured. Dust particles require a high ion concentration in the electric field to be sufficiently charged. When a voltage higher than the starting voltage is applied between the electrode and the ground, dust in the air is charged by a strong electric field. The principle of dust collection of an electric dust collector is that (+) dust charged by (+) electrodes is attached to the ground under the influence of repulsion by the (+) polarity of the filter [22; 23; 24; 25; 26]. Although there are various equations, the amount of electric charge applied to a single dust particle was selected by referring to [PERSON] book. [PERSON] announced that there is both field charging and diffusion charging in electricity, and summarized it in an equation. This can be expressed by Equations (4) and (5). In the case of field charging, the larger the particles, the larger the charge, and in the case of diffusion charging, the smaller the particles, the larger the charge [22]. \[n_{1}(t)=\frac{d_{p}kT}{2K_{E}\epsilon^{2}}\ln\left[1+\frac{\pi K_{E}d_{p} \overline{c_{i}}e^{2}N_{i}t}{2 kT}\right] \tag{4}\]  
\[n_{2}(t)=\left[\frac{3\epsilon}{\epsilon+2}\right]\left[\frac{Ed^{2}}{4K_{E} \epsilon}\right]\left[\frac{\pi K_{E}\epsilon Z_{i}N_{i}t}{1+\pi K_{E}\epsilon Z _{i}N_{i}t}\right] \tag{5}\]  
The variables used here are: \(d_{p}\) is particle diameter, \(k\) is the Boltzmann constant, \(K_{E}\) is the electrical propositional constant, \(\overline{c}\) is the average thermal speed of ions (240 m/s at standard room condition), \(E\) is the intensity of the electric field, \(\epsilon\) is the relative permeability of KCl, \(Z_{i}\) is the mobility of ions, and \(N_{i}\) is the concentration of ions. Most are specified in units commonly used in the SI unit system among the variables; \(E\) and \(N_{i}\) can be inferred  
Figure 14: Comparison graph of filter with sub-filter applied. from the results of the electric field simulation. The study simulated a limited space, and the flow rate is 1 m/s, so the variable \(t\) is fixed. Here, \(t\) means the time during which the dust particles are charged. The charging number applied to one dust particle was obtained by using Equations (4) and (5), with the result values obtained from these variables and the simulation [22; 23]. If this electric charge is combined, a combined area can be seen, as illustrated in Figure 15, and it can be confirmed that a section of 0.3 \(\upmu\)m is the most extreme environment. These data are extracted from references and Hinds books [22; 27; 28]. This is currently the standard for setting the test particle to 0.3 \(\upmu\)m in the Korea Air Purifier Association's Indoor Air Purifier Standard (SPS-KACA002-132) [29]. Figure 16 shows the boundary conditions of the electric dust collector filter simulation. The simplified chevron filter mentioned in Figure 2 was used. Electrodes and grounding were added to the lower part of the filter to generate static electricity. Dust can be charged from the generated static electricity, and the flow escapes from the lower part of the filter to the upper part. A total of 8 kV was applied to the inlet electrode and 5 kV was applied to the dust filter to push the charged dust particles by repulsion. In this study, COMSOL Multiphysics v5.5 was used for the multi-physical analysis for the electric dust collector simulation. Flow analysis, electric field analysis, and particle tracking were performed simultaneously.