CHAPTER 2 LITERATURE REVIEW
2.2 Numerical studies of the corona unipolar chargers
Diffusion charging has been studied theoretically and various models are available.
Detailed overview on the diffusion charging models in all aerosol regimes can be seen from the literature (Romay and Pui 1992a; Biskos et al. 2004; Marquard 2007). In the transition regime (Knudsen number Kn1), the birth-and-death charging model (Boisdron and Brock 1970) with the ion-particle combination coefficient estimated by Fuchs diffusion charging theory (Fuchs 1963) was used to predict the charge distribution for the unipolar charger, assuming Ni t condition is given where Ni is the ion concentration (ions/m3) and t is the charging time (sec) (Biskos et al. 2005b; Marquard et al. 2005; Qi et al. 2007, 2009; Vivas et al. 2008; Li and Chen 2011). The model assumes that ion concentration in the charging region is spatially uniform, considering neither the transport of ions and particles nor particle loss in the charger. These assumptions which are difficult to validate, especially for charging devices with complicated geometrical, electrical, and hydrodynamic conditions (Marquard et al.
2006b), could lead to inaccurate predictions. By considering the transport effects of ions and particles, some numerical models (Aliat et al. 2008, 2009; Alonso et al. 2009) were able to simulate unipolar diffusion charging based on Fuchs theory in a tube flow with the simple plug flow assumption for the flow field. However, the models are not applicable to other unipolar chargers with more complicated geometry. Huang and Alonso (2011) obtained particle trajectories through the combined mechanisms of diffusion and field charging to calculate nanoparticle electrostatic loss in the corona-needle unipolar charger for particles ranging from 3–30 nm in diameter. But the charging efficiency was not calculated. Kimoto et al. (2010) developed a theoretical model based on Fuchs theory to predict the extrinsic charging efficiency of an efficient small mixing-type unipolar charger. The measured charging efficiency for particles
smaller than 10 nm was much higher than the theoretical results due to the well-mixed flow assumption.
Table 2.1 and 2.2 summarize the charging performances and numerical studies of the above mentioned corona-based unipolar aerosol chargers, respectively. In summary, the charger performance depends on the extrinsic charging efficiency. An efficient unipolar charger should be further designed and developed for charging nanoparticles. In addition, an accurate numerical model which can be used to facilitate the design of an efficient unipolar nanoparticle charger and predict charging efficiency is needed to develop.
Table 2.1 Charging performances of corona-based unipolar aerosol chargers.
Table 2.2 Numerical studies of the corona-based unipolar aerosol chargers.
Researcher Numerical method Particle
charging model Assumption / Limit Biskos et al. (2005b);
Alonso et al. (2009) Eulerian method Fuchs theory (1963)
Simple plug flow for the flow field in the charger.
Kimoto et al. (2010) Lagrangian method Fuchs theory (1963)
Complete mixing of particles with ions in the
charging chamber.
Huang and Alonso (2011) Lagrangian method Combined charging model
The charging efficiency is not available.
CHAPTER 3 METHODS
3.1 Experimental method
3.1.1 Design of unipolar charger with axial sheath air
Figure 3.1 shows the schematic diagram of the unipolar charger with axial sheath air which is a modification of the nanoparticle charger with multiple discharging wires developed by Tsai et al. (2010). The charger consists of a gold wire of 50 μm in diameter and 2 mm in length as the discharge electrode, on which a high D.C. voltage is applied from the top of the charger. The outer stainless steel cylindrical casing of 30 mm in diameter is grounded. The space between the gold wire and the stainless steel casing is the charging zone where aerosol charging takes place. The aerosol flow was introduced into the charger from the bottom and a filtered high-speed sheath air flow with the velocity of 0.9–7.1 m/s was introduced from an annular slit of 0.1 mm gap formed by the Teflon shroud and the outer casing to minimize charged particle loss. The charged particles were accelerated to exit the charger quickly through another annular slit of 0.1 mm gap after the charging zone.
Aerosol in
Sheath air Aerosol out Gold wire
Ø 30
Teflon
Copper Stainless steel 57
Figure 3.1 Schematic diagram of the charger with axial sheath air (unit: mm).
3.1.2 Experimental setup
The experimental setup consisted of the aerosol generation section and performance evaluation section for measuring the charging efficiency and particle loss in the charger is shown in Figure 3.2 and similar to that described in Tsai et al. (2010). In the aerosol generation section, monodisperse Ag particles ranging from 2.5 to 20 nm in diameter were generated by the evaporation-condensation technique (Scheibel & Porstendorfer, 1983). First, silver powder was loaded in a ceramic boat placed in a tube furnace (Sunrise Co. Ltd., New Taipei City, Taiwan). Generated vapor was carried by clean air out of the furnace where polydisperse nanoparticles of high concentration were produced by quenching the hot vapor in a water-based cooler. The particles were neutralized by a TSI 3077A electrostatic charge neutralizer before being introduced into a Nano-DMA for classifying monodisperse test particles. Singly charged monodisperse particles were then neutralized and passed through a wire-in-tube electrostatic precipitator to remove all charged particles, allowing only uncharged particles to enter the unipolar charger for the charging efficiency experiments (performance evaluation section).
To generate the electric field and corona ions, high positive/negative voltage was supplied to the corona wire using a high-voltage D.C. power supplier (model SL P150/SL N30, Spellman High Voltage Electronic Corporation, NY, USA). The grounded stainless steel casing was connected to a picoammeter (model 6485, Keithley Instruments Inc., Cleveland, OH, USA) for measuring the corona current. The high-speed sheath air from the annular slit near the casing wall helped accelerate charged particles exit the charger. After charged aerosol flow to exit the charger, it passed through the second ESP for removing charged particles if the voltage was turned on. An ultrafine condensation particle counter (UCPC, model 3786, TSI Inc.) was used
to measure particle concentration downstream after the second ESP. For the experiment involving the measurement of particle charge distribution at the exit of the charger, the tandem-DMA method was used to measure the charge distribution of monodisperse particles of different sizes (Tsai et al. 2010).
Both particle charging efficiency and particle loss were measured at the sheath air flow rates (Qsh) from 0.5 to 4 L/min while the aerosol flow (Qa) was fixed at 1 L/min.
There are four parameters used for the performance evaluation of unipolar electrical aerosol chargers (Marquard et al. 2006b), including intrinsic charging efficiency (
int), extrinsic charging efficiency ext), electrostatic loss (Lel), and diffusion loss (L0d).The superscript "0" represents uncharged particles. The intrinsic charging efficiency, which is defined as the fraction of initial uncharged particles acquiring charge inside the charger regardless of charged particle loss, can be calculated as (Tsai et al. 2010):
where the dilution factor f is equal to the ratio of the total outlet aerosol flow rate to that at the inlet of the charger, PESP is the penetration of uncharged particles through the second ESP, Cin is the particle number concentration (particles/m3) measured
upstream of the charger, Cout OFF, is the particle number concentration measured downstream of the second ESP when no voltage is applied on the charger and the second ESP, and Cout0 is the particle number concentration measured downstream of the charger when the charger is on and sufficiently high voltage is applied on the second ESP to remove all charged particles.
The extrinsic charging efficiency is defined as the fraction of particles exiting the
charger which carries at least one elementary unit of charge:
0 ,
out ON out ext
ESP in
C C
f
P C
(3.2)
where Cout ON, is the particle number concentration measured downstream of the charger when the charger is on and the second ESP is off.
Experimental particle electrostatic loss, Lel , and diffusion loss, L0d , inside the charger can be calculated as
el out OFF, out ON,
ESP in
C C
L f
P C
(3.3)
0d 1 out OFF,
ESP in
f C
L P C (3.4)
Tube furnace Excess water
Figure 3.2 Schematic diagram of the experimental setup.
3.2 Numerical method 3.2.1 Flow field
A 2-D numerical simulation was conducted in this study. The calculation domain of 35 mm in length and 15 mm in width is shown in Figure 3.3, in which the hatched areas represent the solid region. The gap between the charger body and the wall is 0.1 mm for both sheath air and exiting aerosol flows.
The laminar flow field model was used since the maximum flow Reynolds number based on the hydrodynamic diameter is 235.8, which is much smaller than 2000. The flow field in the charger was simulated by solving the following 2-D Navier-Stokes equations and continuity equation in the cylindrical coordinates:
2 governing equations were discretized using the finite volume method and solved by the SIMPLER algorithm (Semi-Implicit Method for Pressure Linked Equations) (Patankar 1980). When dealing with the boundary at the inclined wall surface, the concept of blocked-off region was applied to divide the control volumes into active and inactive regions, the later of which represent solid regions. At the inlets of aerosol and sheath
the experimental values. The outflow velocity at the exit of the charger was calculated based on the continuity equation.
A total of 49,600 (248 in r–direction × 200 in z–direction) non-uniform rectangular grids were used in the calculation domain. The average grid size was about 60.5 and 175 μm in r (radial) and z (axial) direction, respectively, while the smallest size of 0.54 and 1.34 μm was assigned near the wire and the wall surfaces, respectively. The shape of the wire tip was flat. In the test run, the number of grids was either 12,400 (124 × 100), 49,600 (248 × 200) or 198,400 (496 × 400). As the number of grids was increased from 12,400 to 49,600 or 198,400, the accuracy for the numerical diffusion loss of 5 nm particles at Qsh= 3 L/min was also changed from 20.1% to 18.6% or 18.4%. With the number of grids of 49,600 and the computation time for the flow field of about 3 hours, the calculated diffusion loss of 5 nm particles at Qsh= 3 L/min was found to be close to the experimental data of 17.9%. Further increase in the number of grids to 198,400, the diffusion loss only changed by about 0.2 % but the computation time for the flow field was increased to about 48 hours. Therefore, 49,600 grids were used in the simulation. The total number of iterations to reach convergence was about 10,000 for solving the flow field.
Charger wall
Gold wire Radius: 25 μm
5 2 2 5 3 5
13
15
0.1
11.9
1.325 1.675 35
Sheath air
Aerosol inlet r
z
Symmetric line
Figure 3.3 Calculation domain in the numerical simulation of the charger with axial sheath air (unit: mm).
3.2.2 Electric potential and ion concentration fields
The present methods for calculating corona discharge and ion concentration field were based on the work of Lin and Tsai (2010). The governing equation, Poisson’s equation, for the electric potential field in the charger can be written as
2 the permittivity of air (A·s/Volt·m).
The space charge density, ρi , in Equation (3.8) was calculated by the following convection-diffusion equation as
are the local electric field strengths in r and z direction (Volt/m), respectively, which can be calculated as
In Equation (3.8), ion quenching by particles was neglected because the predicted ion concentration was much higher than the particle number concentration in this study. For example, when the applied voltage was +2.1 and -2.1 kV, the average ion number concentration was calculated to be 9.0 10 14 and 9.3 10 14 ions/m3, respectively,
which was five orders of magnitude higher than the measured particle concentration. In Equation (3.9), the source term of the corona current generated by charged particles was neglected either. For the ion mobility, a value of 1.15 10 -4 m2/s·V for positive ions and 1.35 10 -4 m2/s·V for negative ions as suggested by Lin and Tsai (2010) was used in the simulation. To solve Equations (3.8) and (3.9), the ion density, i,0, at the discharge wire surface was calculated by the following equation:
,0 2 boundary condition at the wire surface followed the work of Aliat et al. (2009), in which the electric field on the corona wire surface, E , was assumed to be constant (Kaptzov w 1947) and the value was calculated from the following formula (Peek 1929):
1/ 2
3.2.3 Charged particle concentration field and particle charging efficiency
The governing equation for the concentration of particles carrying q elementary charges, Np,q, is
2
where ZP is the particle electrical mobility (m2/s·V), which is defined by
p coefficient for particles (m2/s), and Sc is the source term, which represents the generation of particles with q elementary charges. In equation (3.10), the boundary condition at the charger wall was assumed to be perfect absorption. The source term Sc
and sink term Sp are given by (Adachi et al. 1985; Aliat et al. 2009)
where αq is the combination coefficient of ions for particles carrying q elementary charges (m3/s) and can be calculated as (Fuchs 1963)
sphere (m), ξ is the striking probability, kb is the Boltzmann’s constant (J/K), is the electric potential between the particle and the ion (Volt) (Adachi et al. 1985), and a is the radius of particles (m). The ξ values shown in Table 1 of Hoppel and Frick (1986)were adopted to calculate the ion-particle combination coefficients. The parameters used in Equation (3.17) can be calculated as follows:
r
where r is the distance between particles and ions center (m), εp is the dielectric constant of particles (for Ag, p ), λi is the mean free path of ions (m), ra is the apsoidal distance (m), Mi is the molecular weight of ions (kg/mol), Mair is the molecular weight of air (kg/mol), and Na is the Avogadro number (6.023×1023 #/mol).
The theory of Marlow and Brock (1975), which was found to be more appropriate
than Fuchs theory for predicting particle charging for particles with dp 20 nm (Pui et al. 1988; Romay and Pui 1992a; Lin and Tsai 2010), was applied to predict the charging efficiency in the present simulation. The combination coefficient between an ion and an uncharged particle, , was calculated as 0
2
In Equation (3.25), GIN is the first iteration correction to the flux, which was calculated to be 0.26 (Marlow and Brock 1975).
The charging theory of Fuchs (1963) requires five ion properties including the mobility, molecular weight, diffusion coefficient, mean thermal velocity, and mean free path to calculate the combination coefficient of ions for particles. Only two of these five properties are independent. The ion mobility and molecular weight are used to derive the other three properties (Romay and Pui 1992a). A wide range of the values of the ion mobility and molecular weight in the aerosol charging literature summarized in Table 1 of Lin and Tsai (2010) is a constraint for the use of the present model. Moreover, at the negative applied voltage charging contribution from electrons was ignored in the simulation because of their lower concentration than negative ions. Some researchers speculated that electrons might play an important role in the negative charging for
nanoparticles because of high combination coefficient as compared with that of negative ions (Romay and Pui 1992b; Marquard et al. 2007; Aliat et al. 2008, 2009). However, this issue remains to be studied when the theory of Marlow and Brock (1975) is considered for particles with dp 20 nm.
Equations (3.8), (3.9), and (3.14) were also discretized by using the finite volume method and solved by the same computer code used in the flow field simulation. The extrinsic charging efficiency, electrostatic loss, and convection-diffusion loss ( c
-con dif
L ) of charged particles in the charger were then calculated as (Marquard et al. 2006b):
inlet of the charger, the rate of charged particles exiting the charger, electrostatic deposition rate of charged particles, and convection-diffusion deposition rate of charged particles (number of particles/s), respectively. From the above equations, the simulated intrinsic charging efficiency can be calculated as follows:
In the above equations, the superscript "c" in the variables represents charged
CHAPTER 4
RESULTS AND DISCUSSION
4.1 Experimental results for the charging efficiency of the charger with axial sheath air
4.1.1 Characteristics of the V-I curve
Figure 4.1 shows the corona current as a function of applied voltage in the charger with axial sheath air. The corona current varies from 0.001 to 1.817 and -0.004 to -2.087 μA at the applied voltage of +1.6 to + 2.4 and -1.6 to -2.4 kV, respectively. For an aerosol charger based on the ion attachment technique, the Ni t product is the key parameter when the charging mechanism is dominated by ion diffusion. A greater Ni t product will lead to higher intrinsic charging efficiency. Numerical results show that the maximum ion concentration occurs at the discharge wire surface, which ranged 1.10 10 13~1.49 10 16 ions/m3 at the positive applied voltage of +1.6 ~ +2.4 kV and
3.04 10 13~1.47 10 16 ions/m3 at the negative applied voltage of -1.6 ~ -2.4 kV, respectively. The average charging time in the charging zone is calculated to be 0.222 to 0.067 sec when the sheath air flow rate varies from 0.5 to 4 L/min at the fixed aerosol flow rate of 1 L/min. Therefore, both sheath air flow rate and applied voltage will influence the intrinsic charging efficiency. A smaller flow rate and higher applied voltage will lead to a higher Ni t product and hence a higher intrinsic charging efficiency.
But for the extrinsic charging efficiency, the loss of charged particles inside the charger also has to be considered.
1.2 1.6 2 2.4 Corona voltage (kV)
0 0.5 1 1.5 2 2.5
C or ona c u rr ent ( A)
Lines: fitted curve Positive Negative
Figure 4.1 Corona current versus applied voltage.
4.1.2 Effect of sheath air flow rate
The effect of the sheath air flow rate on the extrinsic charging efficiency was obtained experimentally. Figure 4.2a shows the experimental extrinsic charging efficiency of 20 nm particles as a function of corona voltage and sheath air flow rate. At all sheath air flow rates, there is a corresponding maximum extrinsic charging efficiency occurs at +1.8kV. In general, the extrinsic charging efficiency of 20 nm particles increases with increasing sheath air flow rate from 0.5 to 3 L/min due to a decrease in the charging time and the reduction of charged particle loss. For example, at the applied voltage of +1.8 kV, the extrinsic charging efficiency of 20 nm particles increases from 61.2% to 71.1% when Qsh is increased from 0.5 to 3 L/min. However, further increase of Qsh from 3 to 4 L/min does not increase the extrinsic charging efficiency any further. For example, at +1.8 kV, the extrinsic charging efficiency is 70.1% at Qsh= 4 L/min, which is very close to 71.1% at Qsh= 3 L/min. As also shown in Figure 4.2b, the electrostatic loss of 20 nm charged particles is decreased with an increasing Qsh from 0.5 to 3 L/min at the applied voltage from +1.7 to +2.2 kV. The electrostatic loss in the charger is effectively reduced at Qsh= 3 L/min, but does not change very much when
Qsh is increased to 4 L/min. However, by increasing Qsh to 4 L/min, electrostatic loss does not decrease further for the applied voltage below +1.9 kV. The loss is increased instead when the applied voltage is greater than +1.9 kV. The highest extrinsic charging efficiency for 20 nm particles is thus obtained at 3 L/min.
The maximum extrinsic charging efficiency of the charger with axial sheath air operating at Qsh= 3 L/min is compared with that of the previous corona-based chargers and shown in Figure 4.3. The best extrinsic charging efficiency of the charger with axial sheath air is 3.1%–71.1% (dp = 2.5–20 nm) at the positive applied voltages of +1.8 to
+2.1 kV, and 14.7%–66.4% (dp = 5–20 nm) at the negative applied voltages of -1.8 to -2.1 kV. The extrinsic charging efficiency of the charger with axial sheath air is seen to be higher than that of other corona-based unipolar chargers, but lower than that of Kimoto et al. (2010) for particles smaller than 10 nm in diameter. The charger developed by Kimoto et al. (2010) consisted of a high-pressure corona ionizer to generate unipolar ions and a small charging chamber (0.5 cm3 volume) where the ions were mixed with nanoparticles without an external electric field.
1.6 1.8 2 2.2
Figure 4.2 (a) Experimental extrinsic charging efficiency and (b) electrostatic loss of 20 nm particles versus corona voltage at different sheath air flow rates.
1 10 100 d
p(nm)
1 10 100
E x tr in si c char gi n g ef fi ci en cy ( % )
Buscher et al. (1994) Kruis and Fissan (2001) Hernandez et al. (2003) Alonso et al. (2006) Qi et al. (2007) Qi et al. (2008) Kimoto et al. (2010) Li and Chen (2011)
Charger with axial sheath air Qsh = 3 L/min, Positive HV Charger with axial sheath air Qsh = 3 L/min, Negative HV Fitted curve, Positive HV
Figure 4.3 Comparison of the experimental extrinsic charging efficiency of the charger with axial sheath air with that of previous corona-based chargers.
4.2 Numerical results for the charging efficiency of the charger with axial sheath air
4.2.1 Flow streamlines, electric potential, ion concentration, and charged particle concentration fields
The flow, electric potential and ion concentration fields were calculated first before the charged particle concentration could be calculated. An example of the calculated flow filed (plotted as flow streamlines), electric potential, and ion number concentration
The flow, electric potential and ion concentration fields were calculated first before the charged particle concentration could be calculated. An example of the calculated flow filed (plotted as flow streamlines), electric potential, and ion number concentration