## 3 Results and Discussion  
Numerical simulations were done with the geometry while varying the discharge voltage, particle size, gas flow velocity and corona charge wire diameter to investigate the influence of these parameters on collection efficiency. The operating parameters of the modelled ESP are summarised in Table 2. Three supply voltages as 35, 45, and 55 kV, three corona wire diameters as 0.3, 1, and 2 mm, two inlet velocity values as 1 and 2 m/s, and two different distances between the wire and plate electrodes as 90 and 115 mm are considered in this study. Consequently, thirty-six operating conditions for the computational simulations are performed. In addition to that, the collection efficiencies for the particle diameters between 0.02 and 10 um are obtained and compared. This means that about six-hundred fifty different three-dimensional CFD simulations with an electric field and particle transport are conducted in the present study. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Collection plate length (\(L\)) & 900 mm \\ Collection plate height (\(H\)) & 300 mm \\ Distance between wires and plates (\(S_{y}\)) & 90.0–115.0 mm \\ Distance between wire electrodes (\(S_{x}\)) & 150 mm \\ Number of wires & 5 \\ Wire electrode diameter (\(d_{w}\)) & 0.3–1–2 mm \\ Air flow inlet velocity (\(U_{in}\)) & 1–2 m/s \\ Supply voltage (\(\phi\)) & 35–45–55 kV \\ Pressure (\(p\)) & 101.3 kPa \\ Inlet temperature of air (\(T\)) & 293 K \\ Ion mobility (\(b_{ion}\)) & 0.00015 m\({}^{2}\)/Vs \\ Particles mass flow rate & \(20\times 10^{-20}\) kg/s \\ Relative permittivity of particles (\(\varepsilon_{p}\)) & 3 \\ Diameter of particles (\(d_{p}\)) & 0.02–10 μm \\ Charge on an electron (\(e\)) & 1.6 \(\times\) 10\({}^{-19}\) C \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Geometric dimensions and operating parameters of the modelled ESP. Particles are injected into the computational domain from the inlet surface, and the motions and charging process of particles were calculated once through the domain. Collection efficiency as a function of the particle diameter can be obtained by using Equation (23). Figure 10 shows the particle tracking pathlines with respect to residence time for the case of 1 mm wire diameter, 55 kV, and \(U_{in}\) = 1 m/s in the 230 mm wide channel. It can be seen that when particle diameters are large, most of the particles are trapped close to the inlet in a very short residence time. However, residence time increases with decreasing particle diameter, and particles may travel along the ESP channel. On the other hand, the nano-size particles such as \(d_{p}\) = 0.02 m have smaller residence time than the one micrometre (\(d_{p}\) = 1 m) particles. Figure 11 shows the comparison of collection efficiency values obtained with analytic and CFD models for \(S_{y}\) = 115 mm, applied potential 55 kV, and corona wire diameters \(d_{w}\) = 0.3 mm and \(d_{w}\) = 1 mm. It can be seen that the present numerical and the analytic models have a good agreement. The discrepancies are less than 10 percent for all particle diameters range. It is noted that the horizontal axis is given on a logarithmic scale. It can be seen that a higher corona wire diameter results in better collection efficiencies compared to a smaller diameter one. In addition to that, the inlet velocity significantly affects the efficiency. Smaller velocity (\(U_{in}\) = 1 m/s) results in better efficiency values than a higher one (\(U_{in}\) = 2 m/s) for all cases. It can be said that the analytic model can be used confidently for further evaluations of the collection efficiencies for the wire-plate type ESPs. Figure 8: Distribution of current density (J) magnitude at the midplanes in the case of d\({}_{w}\) = 1 mm, 45 kV, and U\({}_{in}\) = 2 m/s in the 230 mm wide channel. Figure 9: Distribution of electric field (E) magnitude at the midplanes in the case of d\({}_{w}\) = 1 mm, 45 kV, and U\({}_{in}\) = 2 m/s in the 230 mm wide channel.