The Predictive Method for the Submicron and Nano-Sized Particle Collection Efficiency of Multipoint-to-Plane Electrostatic Precipitators

The multipoint-to-plane electrostatic precipitator (ESP) is one type of ESP devices used for the sampling and control of nanoparticles and sub-micron particles, with the advantage of a low pressure drop and high particle collection efficiency. Several empirical equations for predicting the particle collection efficiency are available in the literature, but most of them are only applicable to wire-in-plate ESPs. For ESPs with different discharge electrodes, the empirical equations are different since the ion concentration and electric fields are different. In this paper, a predictive method is developed to calculate the particle migration velocity and the particle collection efficiency equation η(%) of multipoint-to-plane ESPs in the form of η(%) = {1 – exp{–[β1(NDe2) + β3(NDe) + β4]}} × 100%, in which β1, β2, β3 and β4 are regression coefficients and NDe is the Deutsch number determined by the particle migration velocity. Good agreement is obtained between the present model predictions and the experimental particle collection efficiencies obtained from the literature. It is expected that the present model can be used to facilitate the design of efficient multipoint-to-plane ESPs for nanoparticle and submicron particles removal in the future.


INTRODUCTION
Because of low pressure drop and high particle collection efficiency, electrostatic precipitators (ESPs) are widely used in the industry to remove particles suspended in the exhaust gas (Ruttanachot et al., 2011), in which the wire-to-plate ESP is the most commonly used.The multipoint-to-plane ESP, whose schematic diagram is shown in Fig. 1 is the other design type which has a low corona onset voltage and good resistance to mechanical shock and is often used in applications such as ozone generation and exhaust gas cleaning (Dasculescu et al., 1999).It is also used to enhance the particle collection efficiency of stainless steel (SS) filters (Kim et al., 2000;Mermelstein et al., 2002) and to sample particles (Sillanpää et al., 2008).
When a high voltage is applied to the point electrode in the multipoint-to-plane ESP, ionization, attachment and recombination between air ions and particles occur in a thin layer around the tip of the electrode, which is called the ionization region.The area outside the ionization region is called the drift region, in which unipolar charged ions with the same polarity as the discharge electrode are drifted to the grounded electrode and ion current is generated (Adamiak et al., 2005).The tips of the point discharge electrodes generate higher electric filed and current density than those in the wire-to-plate ESP, which lead to higher particle collection efficiency (Lin et al., 2012b).
Multipoint-to-plane ESPs has been studied for the current density distribution (Dascalescu et al., 1999), the V-I characteristic (Thanh, 1985;El-Mohandes et al., 1999;Kazlov and Solovyov, 2005) and particle collection efficiency (Kim et al., 2000;Huang and Chen, 2001;Mermelstein et al., 2002;Sillanpää et al., 2008;Kim et al., 2012).The particle collection efficiency of multipoint-to-plane ESPs was found to increase with an increasing particle residence time (Kim et al., 2000), an increasing applied voltage (Huang and Chen, 2001), an increasing length of the collection electrode, an increasing number of discharge electrodes and a decreasing gap spacing between the tip of the discharge and collection electrodes (El-Mohandes et al., 1999;Brocilo, 2003;Kazlov and Solovyov, 2005).However, only experimental data are presented in the previous literature for the collection efficiency.No mathematical models to explain the data are readily available, which are important to the design and scale-up of the efficient multipoint-toplane ESPs.In this study, a modified Deutsch-Anderson equation based on the work of Lin et al. (2013) is used to predict the collection efficiencies of multipoint-to-plane ESPs for nanoparticles and submicron particles and then the predictions are validated by previous experimental data of Kim et al. (2000) and Mermelstein et al. (2002).

PRESENT MODEL
The theoretical particle collection efficiency for the ESP is the following well-known Deutsch-Anderson derived which is based on many ideal assumptions (Matts and Öhnfeldt, 1964): where N De is the Deutsch number which can be calculated as: where A is the area of the collection electrode (m 2 ), Q is the air flow rate (m 3 /s), and W is the particle migration velocity (m/s).The Matts-Ohnfield equation (M-O) is a modified Deutsch-Anderson equation in which an additional exponent, k 1 , which ranges from 0.4 to 0.6, is used to provide a more conservative estimate of the removal efficiency (Matts and Öhnfeldt, 1964): Another modified Deutsch-Anderson equation was developed by Lin et al. (2013) to calculate the particle collection efficiency of a wet-electrocyclone in which sawtype discharge electrodes are used: where the regression coefficients are 6.122 for β 1 , 0.7289 for β 2 , -3.273 for β 3 , and 0.5821 for β 4 .This equation will be used in this study to predict the particle collection efficiency of the multipoint-to-plane ESP as it has multiple sharp-point discharge electrodes similar to the saw-type electrodes in the electrocyclone of Lin et al. (2013).To use Eq. ( 4) to calculate the collection efficiency, the particle migration velocity is needed.The method to calculate the particle migration velocity for determining the collection efficiency is the main focus of this study.

Particle Migration Velocity
The particle migration velocity (m/s) can be calculated as (Lin et al., 2012a): where d p is the particle diameter (m), C(d p ) is the slip correction factor for the particle with the diameter d p , µ is the air dynamic viscosity (N-s/m 2 ), n p (t) is the total number of elemental units of charge (#) as a function of particle charging time (or the resident time of particles in the ESP) t (sec), e is the elementary charge (C), and E ave is the average electric field strength (V/m) given by: in which d is the point-to-plane spacing (m) and the axial electric field distribution from the tip to the collection electrode, E y (y) (V/m), is given by (Abdel-Salam et al., 2007): where V a is the applied voltage (V), a is the tip radius of discharge electrode (m), and y is the distance from the tip of discharge electrode (m).The particle electrostatic charge as a function of time, n p (t) (#, number of elementary units of charges), is given by (Lin et al., 2012a): where In the above equations, δ 1 is 1.91588, δ 2 is -0.1425, δ 3 is 1.296 × 10 -5 , and δ 4 is -1.2671, i c is the mean thermal speed of ion (m/s), ε is the relative permittivity of the particle, k is the Boltzmann constant (1.38 × 10 -23 J/K), K E is the constant of proportionality (9.0 × 10 9 N-m/C 2 ), and N i is the average ion concentration (#/m 3 ) which can be determined as follows (Lin et al., 2012a): where A is the drift region on the plane (m 2 ), and I t , the total ion current (A), can be calculated as follows (Kazlov and Solovyov, 2005): where N is the number of point discharge electrodes, I is the ion current of a single electrode (A) which can be calculated as follows (Adamiak and Atten, 2004): In the above equation, ε 0 is the gas permittivity (C 2 /Nm 2 ), Z i is the ion mobility (m 2 /V-s), and V 0 is the breakdown voltage (V), and α i is the empirical coefficient which can be obtained by the following equation: where S is the point-to-point spacing (m) and γ 1 and γ 2 are regression coefficients which are 1.16 and 0.55, respectively, obtained in this work by fitting Eq. ( 14) to the experimental data of El-Mohandes et al. (1992), in which the S/d ratio ranges from 0.074 to 3. The breakdown voltage is expressed as (Adamiak and Atten, 2004): in which the breakdown electric filed (V/m) is : where a is in cm, and the constant δ is 0 0 where P 0 is the standard pressure (bar), T is the air temperature (°K), and T 0 is the standard temperature (°K).
The circular drift region, A (m 2 ) can be calculated from the radius of the drift region on the collection electrode surface, R (m), as A = πR 2 , where R can be determined as (Sigmond, 1985;Allibone et al., 1993): where in which m is the Warburg's parametric index for the cosine power law, which is 4.82 for positive and 4.65 for negative corona, and θ is semi-apex angle of corona discharge (Allibone et al., 1993).

Calculation Procedure
Fig. 2 shows the calculation procedure for the average electric field, ion current, particle migration velocity and particle collection efficiency in the present model.The empirical coefficient (α i ) and the breakdown voltage (V 0 ) are first obtained from Eq. ( 14) and Eqs.(15-17), respectively.Then the total ion current (I t ) and the drift region on the plane (A) are then calculated by Eqs.(12-13) and Eqs.(18-19), respectively while and the average electric field (E ave ) are calculated by Eqs.(6-7) followed by the calculation of the ion concentration (N i ) by Eq. ( 11).Subsequently, the particle electrostatic charge (n p (t)) are obtained by Eqs.(8-10).The particle migration velocity (W) is then calculated by Eq. ( 5) and then the Deutsch number (N De ) is obtained by Eq. (2).Finally, the particle collection efficiency in the multipoint-to-plane ESP is calculated by using Eq.(4).

Voltage-Current Characteristic
Fig. 3 shows the fitted curve obtained by fitting Eq. ( 14) to the experimental data of El-Mohandes et al. (1992) resulting in the regression coefficients of 1.16 for γ 1 and 0.55 for γ 2 .Based on these regression coefficients, the total ion current (I t ) were calculated by Eq. ( 12) for different applied voltages (V a ).The calculated V-I curves compare very well with the experimental data of El-Mohandes et al. (1992) with six sewing needles (N = 6, a = 13-17 µm) and the point-to-plane spacing (d) and point-to-point spacing (S) ranging from 2.7-6.9 cm and 0.5-8.0cm, respectively.Figs.4(a) and 4(b) show only two examples for the comparison of the V-I curves between the present model predictions and the experimental data with d = 5 cm, S = 0.5, 2, 4, 6, and 8 cm and V a = -5 to -26 kV for negative corona (Fig. 4(a)) and V a = +5 to +19 kV positive corona (Fig. 4(b)).The deviation of the predicted total ion current from the experimental data is less than ± 20% when the negative ion mobility value of 2.3 × 10 -4 m 2 /V-s suggested by Adamiak and Atten (2004) is used (Fig. 4(a)), and is less than ± 21% when the positive ion mobility value of 1.4 × 10 -4 m 2 /V-s suggested by Lin and Tsai (2010) is used (Fig. 4(b)).The predicted V-I curves also agree with the experimental data of Thanh (1985) as shown in Fig. 5 for the multipointto-plane ESP with three needle-type discharge electrodes (a = 10 µm), the point-to-point spacing (S) of 2 cm, and the point-to-plane spacing (d) of 1.0-1.5 cm.Good agreement is obtained with a deviation of ± 18% when the applied voltage (V a ) ranges from -5 to -29 kV and the ion mobility is 2.3 × 10 -4 m 2 /V-s for negative ions (Adamiak and Atten, 2004).The above results suggest that Eq. ( 12) can be used to predict the ion current of the multipoint-to-plane ESPs with needle-type discharge electrodes with a good accuracy.

Particle Collection Efficiency
The regression coefficients of 6.122 for β 1 , 0.7289 for β 2 , -3.Thanh (1985).Fig. 6.The comparison of predicted particle collection efficiencies with the experimental data of Kim et al. (2000) for PSL particles.The comparison of predicted particle collection efficiencies by the present model and the experimental data of Kim et al. (2000) are shown in Fig. 6 for polystyrene latex (PSL) particles with 0.05 ≤ d p ≤ 1 μm at the fixed applied voltage of +14 kV and the air flow rate ranging from 20 to 100 L/min.The multipoint-to-plate ESP used a fibrous SS filter as the grounded electrode (pore size: 20 μm).The predicted values agree reasonably with experimental data with a deviation of 2.68-7.9% at 20 L/min, 5.81-14.98%at 40 L/min, 0.81-12.91%at 80 L/min and 2.62-11.36%at 100 L/min when the positive ion mobility is 1.4 × 10 -4 m 2 /V-s (Lin and Tsai, 2010).In comparison, the deviation of particle collection efficiencies calculated by the M-O equation (k 1 = 0.4) from the experimental data at 20 L/min, 40 L/min, 80 L/min and 100 L/min is much larger, which is 37.17-48.44%, 47.95-57.52%, 50.83-60.86% and 49.14 applied voltage was +14 kV.The data also refer to the ESP efficiencies only, which are obtained from the original figures of Mermelstein et al. (2002) who showed both the filtration efficiencies of the filters and total combined efficiencies of the ESP and the filters.The predictions are seen to agree well with the experimental data with a deviation of 2.3-6.52% at 10 L/min (Fig. 7(a)), 2.71-12.12%at 20 L/min (Fig. 7(b)) and 0.19-12.27%at 50 L/min (Fig. 7(c)) for the fibrous filter electrodes.For the porous SS electrodes, the deviation is smaller, which is 0.09-1.72%(10 L/min, Fig. 7(a)), 1.51-7.47%(20 L/min, Fig. 7(b)) and 1.97-8.5% (50 L/min, Fig. 7(c)).The reason why the agreement is better for the porous SS electrodes as compared to the fibrous SS electrodes is not known but is suspected to be due to smoother surface and more uniform electric field of the former than the later, which deserves further investigation in the future.Similar agreement between model predictions and experimental data are also obtained for the fibrous and porous filter grounded electrodes of other pore sizes (6, 7 and 16 µm-fibrous, 40 and 100 µm-porous) (data are not shown).The deviation of the particle collection efficiencies calculated by the M-O equation (k 1 = 0.4) and the experimental data at the flow rate of 10 L/min, 20 L/min and 50 L/min is again larger, which is 13.07-30.51%,respectively, for the porous SS filters, respectively.If the Deutsch-Anderson equation is used (or k 1 = 1.0 in the M-O equation), again even a larger deviation occurs (data are not shown).

CONCLUSIONS
This study developed a predictive model to calculate the particle migration velocity and particle collection efficiency of the multipoint-to-plane ESP for nanoparticles and submicron particles.The particle migration velocity is first calculated based on the empirical voltage-current relationship and particle electrostatic charge, and then the particle collection efficiency equation is calculated as η(%) = {1 -exp{-[β 1 (N De β 2 ) +β 3 (N De ) + β 4 ]}} × 100% in which regression coefficients β 1 = 6.221, β 2 = 0.7289, β 3 = -3.273,and β 4 = 0.5821 and N De is the Deutsch number ranging from 0.13-4.69.Good agreement is obtained with a deviation smaller than 20% between the predicted collection efficiencies and the experimental data in the literature.The present model is able to facilitate the design and scale-up efficient multipoint-to-plane ESPs for controlling emissions of nanoparticles as well as sub-micron particles.Future study can be aimed at investigating the particle loading effect of different materials on the collection efficiency and conducting field validation of the present model using a pilot-scale ESP.

Fig. 2 .
Fig. 2. The calculation procedure for the particle collection efficiency of multipoint-to-plane ESPs.

Fig. 4 .
Fig. 4. The comparison of V-I curves between the present predictions and the experimental data of El-Mohandes et al. (1985) with d = 5 cm.(a) negative corona.(b) positive corona.

Fig. 5 .
Fig. 5.The comparison of V-I curve between the present predictions and the experimental data of Thanh (1985).

Fig. 7 .
Fig. 7.The comparison of predicted particle collection efficiencies with the experimental data of Mermelstein et al. (2002) for NaCl particles at the aerosol flow rate of (a) 10 L/min (b) 20 L/min and (c) 50 L/min.