Electrostatic Precipitators: Fundamentals
13.2.2.1 History of Electrostatic Precipitation
Electrostatic precipitation is one of the fundamental means of separating solid or liquid particles from gas streams. This technique has been utilized in numerous applications, including industrial gas-cleaning systems, air cleaning in general ventilation systems, and household room air cleaners.
The influence of the electrostatic forces on airborne particles has been known for centuries. The early discoveries are summarized in several books, including the classical book Industrial Electrostatic Precipitation by White10 And many others.11-14 An excellent historical review has been presented by White.10 This review’ includes information about the early steps in the development of electrostatic gas cleaning.
The earliest information dealing with this phenomenon dates back to 600 B. C. It was found that a piece of amber after it had been rubbed was able to attract small fibers. More recent observations are from the 17th century, when William Gilbert noticed that amber, sulfur, and other dielectrics charged by friction could attract smoke. Similar observations were made by Boyle (1675) and Otto von Guericke (1672). Francis Hauksbee (1709) reported that he had discovered a phenomenon which is now called ionic wind or electric wind. Ionic wind and the glow from the corona discharge was discussed by Isaac Newton (1718).
The early pioneers also include Benjamin Franklin and Charles de Coulomb. Franklin studied the effect of point electrodes in drawing electric currents. Coulomb discovered that a charged object gradually loses its charge;
I. E., he actually discovered the electrical conductivity of air. Coulomb’s importance for the development of electrostatic air-cleaning methods is great, mainly because the present theories about electric charges and electric fields are based on his work.
The first experiment with the electrostatic gas cleaning was made in 1824, when Hohlfeld show that a fog was cleared from a glass jar which contained an electrically charged point electrode. Similar demonstrations were published in the 19th century, an example being the precipitation of tobacco smoke in a glass cylinder by Guitard (1850).
The commercial utilization of electrostatic precipitation started at the end of 19th century and the beginning of the 20th century. The first gas-cleaning
Applications were realized by Lodge (in England), Cottrell (in the United States) And Mцller (in Germany). Lodge made experiments with an electrostatic PreCipitator starting in 1880, and in 1883 he published a paper in which he IndiCated the commercial possibilities of electrostatic precipitation. Together with Walker and Hutchinsson, he installed the first commercial electrostatic pn-cipi — tator at a lead smelter. This attempt failed, however, mainly because of the primitive high-voltage generator and the fact that particles from a lead smelter are very fine and their conductivity is low.
A person whose work has been of great importance for the development of electrostatic precipitators is F. G. Cottrell. He first aimed at collecting sulfuric acid mist with the aid of centrifuge, but after unsuccessful attempts he started experiments with electrostatic precipitation. Cottrell was able to utilize alternating current transformers and a mechanical rectifier to construct jn efficient high-voltage supply. He also invented a new type of discharge electrode, so — called pubescent wire, which increased the stability of the corona discharge,
Many of the typical features found in present-day electrostatic precipitators are based on work by W. A. Schmidt. One of his most important applications is the electrostatic precipitator that was installed at the Riverside Portland Cement Company in 1912. This plant handled a gas flow of 470 m/s at the temperature of 400-500 °C. This was the first precipitator in which thin wire was used as discharge electrode.
The development of electrostatic precipitators was based mostly on empirical work, and it has produced more than 1000 patents covering all aspects of electrostatic air cleaning. From the theoretical point of view, important milestones were papers published by Deutsch15 as well as White.16 These papers deal with the collection efficiency of the electrostatic precipitator. The most important early papers dealing with the electrical charging of particles are the ones published by Arendt And Kallmann,17 Pauthenier and Moreau-Hanot,18 and White.19
The development of electrostatic precipitators soon ted to new applications, including the separation of metal oxide fumes. This was followed by various metal manufacturing processes such as the lead blast furnace, ore roaster, and reverberatory furnace. Electrostatic gas cleaning was soon applied also in cement kilns and in several exotic applications, such as recovering valuable metals from exhaust gases.
The growth of the consumption of electric power led to the development of pulverized coal burning techniques, which were superior to earlier techniques. It Was, however, discovered that the fly ash in the exhaust gas caused a significant environmental problem. It was also found that an electrostatic precipitator is relatively efficient for the removal of fly ash, and the first power station precipitator was started in 1923. In the first phase, it was difficult to reach 90% efficiency, but gradually significant progress was made, leading to efficiencies as high as 99.9%.
In general, electrostatic precipitators have been shown to best suit those applications where high gas flows must be handled and relatively high efficiency is required. It must also be emphasized that the use of electrostatic precipitators is limited to those applications where the explosion risks are minimal.
Electrostatic gas cleaning is based on the electrostatic force which is applied directly to the particles. Thus, the separation energy is focused directly to
The particles and not to the entire gas flow. Therefore, the energy required to separate particles from a gas stream is normally lower than in those methods in which the separation energy must be applied primarily to the gas flow.
The operation of the electrostatic precipitator is based on three major factors:
• Particle charging
• Electrostatic collection of charged particles
• Removal of collected particles
The basic principle of single-stage electrostatic precipitation is shown in Fig. 13.5. Particle charging in an electrostatic precipitator is realized with a continuous flow of gas ions across the space between two electrodes. One of the electrodes is connected to a high-voltage power supply, while the other is connected to ground potential. Particles become charged when passing through this region. The electric field between the electrodes causes an electrostatic force on the charged particles, leading to particle drift toward grounded collection electrode.
Particle charging and collection can take place in different sections, as illustrated in Fig. 13.6. In this two-stage system, the collection of particles takes place in a region without gas ions, i. e., the electric field is generated by the high-voltage electrode only.
The electrostatic force is directly proportional to the net charge of an aerosol particle. Therefore, effective charging of the particles is of great importance. Airborne particles are normally charged either due to their birth processes or due to charge transfer from gas ions to particles. The natural charging of particles is normally so weak that it has no practical importance for electrostatic air cleaning.
Particle charging in electrostatic precipitators is caused by gas ions generated with high-voltage corona discharge. Corona discharge is utilized to create regions with a high concentration of unipolar gas ions. Ion concentration and electric field are the important parameters affecting the particle-charging process. Electrostatic force is proportional to the particle charge and the electric field. Thus, it is evident that a strong electric field is important for good performance of an electrostatic gas-cleaning system.
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I ligh-voltage electrode (ion source) I
Collection electrodc (ground potential) FIGURE 13.5 Principle of electrostatic precipitation. |
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• Corona discharge,
• Properties of gas ions,
• Electric field,
• Particle charging, and
» collection of particles.
For simplicity, the basic theoretical considerations of electrostatic precipitation are given in terms of cylindrical geometry, i. e., pipe-type electrostatic precipitation. This makes it possible to show most of the basic principles without numerical modeling.
As mentioned earlier, gas ions are essential for the charging of particles. In addition, gas ions play a very important role for the formation of the electric field inside the electrostatic precipitator. Thus, the controlled generation of ions is of major importance for the performance of the electrostatic precipitator. The most effective and practical means of generating gas ions is controlled corona discharge. A controlled corona discharge requires a nonuniform electric field, which is typically formed near a discharge electrode with small dimensions (e. g., needle or wire) compared with the rest of the system. By applying a high voltage to the discharge electrode, a sufficient electric field for the controlled corona discharge near the electrode can be created.
The corona discharge generates a glow, the form and the brightness of which vary depending on the discharge conditions. The light from the corona discharge can be seen as bright spots, brushes, streamers, or a steady glow. Positive corona discharge forms a steady glow, while a negative corona tends to form localized discharges, bright spots, and streamers. A typical feature of the phenomenon is a steep growth of the electric current with increasing voltage.
A gas which contains only neutral molecules or atoms does not conduct electric current. The natural background radiation (e. g., gamma radiation and cosmic radiation), however, continuously generate free electrons and positive ions. Electrons are rapidly captured with electronegative gas molecules, forming negative ions. Electrons and ions move under the influence of the electric field. Thus, a weak electrical conductivity of the gas is produced. If rhe voltage is increased, the electric field on the surface of the discharge electrode becomes high enough to initiate corona discharge. The voltage corresponding the critical electric field is called the onset voltage of the corona discharge. The critical electric field required to initiate the discharge depends on
• Gas composition,
• Gas pressure and temperature, and
• Diameter and roughness of the discharge electrode.
In a strong electric field, a free electron acquires enough kinetic energy to cause an impact ionization; i. e., an electron impacting on a neutral molecule causes an emission of a new electron, leading to the formation of new electron — ion pair. The new free electron is, in turn, accelerated to a velocity sufficient to cause further ionization. This leads to an avalanche-type generation of free electrons and ions. The electric field provides the necessary energy in such a way that the process can continue without the external radiation which was necessary for the onset of the process.
A negative discharge electrode attracts positive ions and forces them to impact on its surface. These impacts provide an additional source of electrons which contribute to the process. Ultraviolet light generated by the corona glow causes photoelectric emission of electrons from the electrode surfaces, which further enhances the formation of free electrons.
The lifetime of a free electron is normally very short; i. e., the electrons drifting toward the other electrode are captured by gas molecules, forming negative ions. As ions move toward the outer electrode, the electric field becomes so weak that corona discharge is not possible. Negative ions move in the electric field, but their velocity is much lower than the velocity of free electrons. Thus, a dense cloud of negative ions (order of magnitude: 107—10* ions/cm3) is formed in the region between the electrodes, and it is in this zone that the particles become charged. Negative ions form a space charge, which is of great importance for the electric current and the electric field between the electrodes.
In some gases (e. g., nitrogen), the lifetime of free electrons can be very long; i. e., negative ions are not formed. Due to the high mobility of free electrons, the corona current rises very steeply with voltage, and therefore it is difficult to create a stable corona discharge. Thus, the presence of electronegative gases which effectively capture free electrons is necessary’ for the stable operation of negative corona discharge.
The corona discharge generated by positive voltage differs significantly from the negative corona. In a sufficiently strong electric field, the avalanche process takes place, but now the positive electrode attracts electrons, while positive ions drift toward the opposite electrode. Under these circumstances, new’ electron-ion pairs are nor produced as effectively as in the case of negative corona discharge.
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There are, however, also similarities between the two discharge types. Positive ions drifting toward the opposite electrode form a space charge that affects the electric field and the corona current principally in the same way as in a negative corona discharge. Also, the charging of particles takes place almost in the same way for both types of corona discharge.
A characteristic feature of the positive discharge is that a stable discharge is formed even though the gas does not contain electronegative components. The operation range, however, is more limited than in the case of negative corona; i. e., increasing the corona voltage leads to A Breakdown at a lower voltage level than in negative corona. In industrial applications, negative corona is normally used because it provides a higher collection efficiency.
The composition of the gas plays an important role in the electric. tl behavior of a corona discharge. The attachment of free electrons to gas molecules varies strongly, depending on the gas composition. Hydrogen, nitrogen, and argon have no electron affinity, and therefore negative ions are not formed. In most cases, however, electronegative gases {e. g., oxygen and sulfur dioxide! are present, and therefore negative ions are formed.
An increase in gas temperature normally means that sparking (from the grounded electrode) occurs at a lower voltage. Gas temperature and pressure affect both the onset voltage of the corona discharge and the mobility of ions. The mobility of a gas ion may change because of the change in gas density but also because of the change in the size of the ion. The decrease in gas density may cause an increase in the apparent ion mobility because of the longer free paths of electrons, which increase the velocity of the charge carriers. A high temperature may also cause thermal electron emission, which enhances the formation of free electrons.
The increase in the free path of electrons modifies the space charge between the electrodes. This produces a more unstable current-voltage relationship because the operation range of the negative corona becomes more limited; i. e., the breakdown voltage is closer to the onset voltage. This is especially important at high temperatures. The effect of gas density for a positive corona is less important because the electric current is transported by positive ions onlyw Thus, at high temperatures the positive corona discharge may produce more stable operation than a negative corona.
13.2.2.4 Properties of Gas Ions
The properties of gas ions are of great importance for the electrical performance of an electrostatic precipitator. They also are very important for particle-charging processes. The size of gas ions is normally such that they can be regarded as gas molecules carrying a single elementary charge. It can even be assumed that ions form a gas component with a very low partial pressure. Thus, the thermal motion of gas ions is assumed to be similar to that of gas molecules. The most important parameters describing the properties of gas ions are
• Mobility Z„
• Diffusion coefficient D;,
• Mean thermal speed Ct, and
• Mean free path A,.
The mobility of a gas ion, Z;, is defined as the ratio of ionic drift velocity V, to the electric field E, i. e.,
V, — Z;E
The relationship between the ion mobility and mass may be very complicated, mainly because the gas ions may form clusters, the size of which can vary depending on the gas composition and temperature. Empirical mobility values in standard conditions for several gases can be found in the literature.”1 NorMally, the mobility of a gas ion can be assumed to be in the range of 1.0 • 10’4 To 3.0 — 10~4 (m2/V s). According to Oglesby,20 it is beneficial for the operation of an electrostatic precipitator if the gas contains components with high electron affinity and the ion mobility is low. These factors produce circumstances for high voltages and intense electric field.
The random thermal motion or the diffusion of gas ions is characterized by the diffusion coefficient D,, which is related to the ion mobility Z. By
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Where K is the Boltzmann constant (k = 1.3807 ■ 10~23 J/K ), T is absolute temperature, and E is elementary charge ( E = 1.6021 • 10-iy As). Another factor which illustrates the random motion of gas ions is the mean thermal speed, Cp which is given by
Besides these parameters, the properties of a gas ion are sometimes characterized with mean free path A,-, which illustrates the mean distance between successive impacts with gas atoms or molecules. The mean free path of ions in air is in the range of 10~8 to 2 • 10~8 m.
13.2.2.5 Electrical Properties
Electric Field
The electric field between the discharge electrode and the collection electrode is of great importance for the particle-charging and — collection processes. Besides the dimensions of the electrode system, the electric field depends on the voltage which is applied between the electrodes and the space charge which is formed by gas ions and charged particles. Electric field and ion concentration can be modeled relatively easily by assuming a simple tubular geometry, i. e., a thin corona wire on the center line of the cylindrical collection tube (Fig. 13.7).
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( |
At low voltages, i. e., below the onset of the corona discharge, the electric field E(r) depends on the voltage and the geometry of the system only. The electric field is given by
(13.42)
Where U is the voltage of the corona wire electrode, Rx is the radius of the corona wire, R2 is the radius of the collector tube, and R is the radial distance
from the centerline. This equation is based 011 the assumption of zero space charge between the electrodes.
The effect of space charge can be taken into account by means of the Poisson equation, which in the case of a cylindrical geometry is expressed in the form
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§-r№ir)r] |
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(13.43) |
[N{r) + n (r)] ,
Where E is the electric field, N is the ion concentration, E is the elementary charge, Nq is the charge concentration due to the charged particles, and e0 is the vacuum dielectric constant.
Corona current per unit length of the discharge electrode, JL, is given by
1.44)
1/2 |
Where I is corona current and L is the length of the discharge region. In the case of a zero particle-space-charge concentration (i. e., Nq — 0), one obtains the following solution for the electric field:
( V 11/2
E(r) = E ■ —1-^1 . (13.45)
For high corona currents and for R » rh electric field can be estimated by
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E(r): |
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;i3.46) |
LirenZ,
According to this equation, the electric field is constant in the region some distance from the corona wire.
A rough approximation for the relationship between corona current and voltage can be obtained from E(r) = -dU/dr. Solving this equation yields an approximation:
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U2. |
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JL’ |
(13.47)
According to this equation, corona current is proportional to the square of the corona voltage. The combination of Eqs. (13.46) and (13.47) produces a simple approximation for the electric field:
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(13.48) |
E ~ .
T ‘j
According to Eq. (13.48), the electric field should be a function of voltage and tube radius alone. Thus, the polarity of the corona discharge should have no influence. It must, however, be emphasized that these results are quite rough approximations which are not necessarily valid if the geometry of the system differs significantly from the wire-in-pipe configuration. Also, it must be noticed that these rough approximations do not take into account the effect of the onset voltage of the corona discharge.
These equations are based on the assumption of zero particle space charge. In practice, however, charged particles can significantly affect the electric field
Between the electrodes. The effect of charged particles on the performance of an electrostatic precipitator is a very complicated process. It can, however, be approximated relatively easily by assuming a constant particle — space-charge concentration, i. e., Dnq/dr = 0 .
Figure 13.10 illustrates the relationship between electric field and radial distance in various space-charge conditions. In the case of zero space charge (i. e., without ions and charged particles), the electric field decreases steeply with radial distance. If the space charge due to gas ions is included, the electric field is practically independent of the radial distance. If the space charge due ro ions and charged particles is included, the electric field increases with distance. It is worth noticing that, due to the particle space charge, the electric field at the surface of the collection electrode is higher than in the case of ionic space charge only. The particle space charge tends to decrease the electric field near the discharge electrode, leading to a decrease in the corona current.
The concentration of gas ions significantly influences the particle-charging process. The high ion concentration is essential for the effective charging of fine particles. The distribution of ion concentration in a pipe-type electrostatic precipitator can be approximated by using the equations presented in the previous section.
By combining Eqs. (13.44), (13.47), and (13.48), it is possible to give an expression for the ion concentration N(r). In the case of a thin wire electrode inside a large tube, the ion concentration can be approximated with
= (13.49)
Er1 r
According to these equations, ion concentration is directly proportional to the corona voltage and inversely proportional to the radial distance. Equation
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Radial distance FIGURE 13.10 Electric field as a function of radial distance (tubular geometry). |
(13.49) can also be used to estimate the mean ion concentration, wavf, between the electrodes, i. e.,
Er2
These solutions correspond to the idealized case; i. e., space charge due to aerosol particles is assumed to be zero.
13.2.2.6 Particle Charging
When the particles are exposed to either positive or negative gas ions, the unipolar particle-charging process causes the accumulation of electric charge on the particles. Due to the stochastic nature of the particle-charging process, the number of elementary charges carried by a particle is an integer. The prob ability that a particle carries a certain number of elementary charger, depends on several factors, including particle size and dielectric constant, ion concentration, electric field, and charging time.
In most practical applications, especially in the case of large particles, it is not necessary to know the charge distribution. Thus, the particle charging can be modeled by means of the average charge number. There are two basic mechanisms responsible for the charging of aerosol particles. These are referred to as field and diffusion charging. Particle charging in an electric field is assumed to be due to ordered motion of ions under the influence of the electric field. This approach is applicable predominantly for large particles (dp > 0.5 |xm). Diffusion charging is due to ion attachment to particles caused by the random motion of the ions. The diffusion charging model must be utilized especially if the charging of fine particles (D^ < 0.2 fim) is considered. Particle charging in an electrostatic air-cleaning system takes place in a strong electric field and high ion concentration; i. e., both charging mechanisms must be taken into account.
Field Charging
Electrostatic air-cleaning systems are normally based on particle charging by means of corona discharge. Thus, the charging takes place in a relatively strong electric field, and therefore the classical field charging theory10 can be successfully applied. The classical field charging theory assumes that the ions drift along the electric field lines as illustrated in Fig. 13.11.
According to the field charging theory, the external electric field drives ions to the aerosol particle until the repelling electric field prevents ions from reaching the surface of the particle. This condition corresponds to the saturation; i. e., the particle has reached a stable value which cannot be exceeded. The relationship between the net charge of the particle and charging time is given by
= (13.51)
Where the saturation charge number S0 is given by
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FIGURE 13.11 Field charging (ion paths in the vicinity of a charged particle in an electric field). |
And the time constant Ts is given by
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To* |
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= |
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NeZj’ |
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According to Eq. (13.52), saturation charge is directly proportional to the square of the particle diameter and the external electric field. Particle charging depends also on the composition of the particle, which is taken into account by the relative dielectric constant Er. It is worth noticing that the field charging model should not be applied for small particles (dp < 0.5 p. m).
Particle charging in a electrostatic gas-cleaning system should take place as quickly as possible. Therefore, the time constant Ts should be as low as possible. This requires that the ion concentration in the charging region be high.
Diffusion Charging
The direct effect of the external electric field on the particle charging decreases with particle size and electric field. Instead, the random thermal motion of ions starts to dominate the charging process; i. e., the ion attachment to aerosol particles is governed by the ion diffusion, as illustrated in Fig. 13.13. This charging process is called diffusion charging (see, e. g., Pui21), and it is a dominating process for small particle (d., < 0.2 |xm). It is worth noticing that in the case of low electric field, diffusion charging can play an important role in the charging of large particles as well. Due to diffusion charging, the saturation charge given by Eq. (13.52) is not an absolute maximum; i. e., the particle charge can slightly exceed the saturation charge due to the diffusion charging.
The traditional unipolar diffusion charging model is based on the kinetic theory of gases; i. e., ions are assumed to behave as an ideal gas, the properties of which can described by the kinetic gas theory. According to this theory, the particle-charging rate is a function of the square of the particle size Dp, particle charge numbers and mean thermal velocity of ions C,. The relationship between particle charge and time according White’s
White’s equation is widely used mainly because it is easy to use and because it gives values which are in reasonable agreement with the experimental ones. However, because this model is based on the kinetic theory of gases, it should be used for small particles only. This model (as many others) assumes that particle charge can be described with a continuous function. Especially in the case of small particles, only the lowest charge numbers (0, 1, 2) are possible, and therefore the model—which does not take into account the discrete charge numbers—is somewhat questionable.
Combining Field and Diffusion Charging
Particle charging by corona discharge normally requires that both charging mechanisms be taken into account. Thus, a model which combines the field charging model with the diffusion charging model is necessary. The sophisticated theoretical models which combine both charging mechanisms are relatively complicated, and they hardly produce significant benefit for the calculation of particle charging in electrostatic gas-cleaning systems.
The most straightforward approach is to assume that the field charging and diffusion charging are independent processes; i. e., particle charge can be presented as a sum of charges due to field (Sf) and diffusion {sd) charging. Another simple approach to estimating the combined effect is
S = sf+sd—^- . (13.56)
‘ Sf+sd
It is easy to see that this solution asymptotically approaches sy as particle size increases. On the other hand, this solution approaches Sd when particle size approaches zero.
13.2.2.7 Collection of Particles
Charged Particle in an Electric Field
The motion of a charged aerosol particle in a gas is governed by the electrostatic force and the aerodynamic forces. The theory dealing with the particle motion has been discussed in several books (see, e. g., Hinds22). The electrostatic force F caused by the electric field E is given by
Ft- = SeE, (13.57)
Where s is the particle charge number, E is the elementary charge (e — 1.6021 • 10-19A s ). This force causes a particle drift in the direction of the electric field. Electrostatic force is balanced by the gas resistance force or drag force. Normally, the particle drift velocity is low; i. e., the particle Reynolds number is small, and the drift velocity W due to the electrostatic force can be approximated by
E = ZnE . ! 13.58)
3 TTfjidp1"
In this equation, Zp is the electrical mobility of the particle. In the case of fine particles, the slip correction must be taken into account, and the mobility is given by
where A is the mean free path of the gas molecules (for air, A =
6. .53 • 10 8 m ). The values of the coefficients A, B, and C are: A = 2.154, B = 0.8, and C = 0.55.
These equations are valid for spherical particles. For nonspherical particles, a more detailed model must be used; i. e., the effect of the irregular shape of the particles must be taken into account by means of shape factors. -1-‘
Figure 13.14 shows examples of particle drift velocities calculated b> different charging models. These curves clearly indicate that the drift velocity of large particles is almost totally due to field charging, while in the case of small particles, diffusion charging dominates. Figure 13.14 also illustrates that the minimum of the drift velocity is in the particle size range between 0.1 and 3 m.
If particle charging and collection take place in the same electric field E, The drift velocity of large particles can be estimated by
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DpE2 |
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(13.60) |
W~ — —
H er+2
According to this approximation, the drift velocity is proportional to the square of the electric field. This is a clear indication of the importance of the electric field inside an electrostatic precipitator. Equation (13.60} is a valid approximation for large particles (dp > 0.5 m), provided that particle charge is close to the saturation level. In the case of small particles, the effect of diffusion charging must be taken into account.
There are two basic approaches to handling the particle collection in an electrostatic gas-cleaning system. The first approach is based on the assump —
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Hs ‘u -a |
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Particle size (|im) |
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FIGURE 13.14 Particle velocities in an electric field based on different charging models (E ; 2500 V/cm, Nt = 10® s/cm3). |
Tion of laminar gas flow, while the other assumes a turbulent flow. In the case of laminar airflow between two parallel plate electrodes, the particle collection efficiency T]L can be presented with a simple equation:
Vi = Zp~E- = ^ (0 < 1.0), (13.61)
Where A is the area of the collection surface and Q is the volumetric flow rate. According to this model, the collection efficiency is directly proportional to the drift velocity and the collection area and inversely proportional to the flow rate. In practice, laminar gas flow requires that the distance between the electrodes be short. A typical example is a two-stage electrostatic precipitator in which particle collection is realized with a large number of parallel plate electrodes. The right side of the equation represents the Deutsch number, De = WA/q,Which is frequently used when discussing the removal efficiency of an electrostatic precipitator.
In most cases, laminar gas flow is an unrealistic assumption. A more realistic alternative is to assume a complete mixing of air in the collection system. The collection efficiency in the case of turbulent flow T]t is given by
7)T = 1 — EwA/q = 1 — e-De. (13.62)
This equation, which is called the Deutsch equation, has been shown to be a useful tool for estimating the performance of electrostatic precipitators. An interesting detail in the Deutsch equation is the exponent, which is equal to the collection efficiency of a laminar flow system. The equations based on laminar flow and turbulent flow can be assumed to be the extreme conditions, and the true situation is somewhere in between these two cases (see Fig. 13.15).
These simple models are based on the assumption of constant drift velocity; i. e., particles are assumed to achieve their final charge instantaneously. This is a reasonable assumption in the case of large particles, the charging of which is governed by field-driven ion motion. The characteristic distance X. Corresponding to the time constant Ts in Eq. (13.53) is given by
X. = Vt( = . (13.63!
— NeZ,
It is easy to see that, under normal circumstances, the characteristic distance is much shorter than the effective length of the precipitation system.
Advanced Modeling of Particle Collection
Particle collection in an electrostatic air-cleaning system can be modeled with more sophisticated methods, such as
• modifying the Deutsch equation,
• solving the particle trajectories in certain flow field and electric field conditions,
• solving the convective diffusion equation, or
• utilizing effective migration velocities.
A relatively simple modification of the Deutsch equation is obtained by assuming that the particle concentration near the collection surface is linearly
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1- 1———— J —— ……. J — — — 1 — —^ ————- — “J’~……. 0 1 2 3 4 5 Deutsch number, De (-) FIGURE 13.15 Particle penetration as a function of the Deutsch number. |
Dependent on the mean concentration at that location of the electrostatic precipitator. This leads to a modified Deutsch equation:
7}T = L-e h De, (13.64)
Where H is the concentration ratio (h = csurface/cave). Unfortunately, there is no good model for the coefficient H. It is reasonable to assume that its value depends on several factors, including the turbulent mixing inside the collection system as well as the electric field and particle size.
Particle trajectories can be calculated by utilizing the modern CFD (computational fluid dynamics) methods. In these calculations, the flow field is determined with numerical means, and particle motion is modeled by combining a deterministic component with a stochastic component caused by the air turbulence. This technique is probably an effective means for solving particle collection in complicated cleaning systems. Computers and computational techniques are being developed at a fast pace, and one can expect that practical computer programs for solving particle collection in electrostatic precipitators will become available in the future.
Another approach to modeling the particle-collection process is based on the convective diffusion equation
| = DV2c-V-(w) = 0, (13.65)
Where D is the diffusion coefficient, which takes into account the eddy diffusion. Velocity V is the combination of fluid velocity and the migration velocity due to the electrostatic force. The diffusion equation can be solved numerically, provided that the diffusion coefficient is known. Unfortunately, the turbulent mixing of air inside an electrostatic precipitator is a very complicated phenomenon which depends on the flow conditions, including the ionic wind,
I. e., air movements caused by the repulsion of gas ions.
The efficiency of an electrostatic precipitator is influenced by several factors (e. g., reentrainment of collected particles and gas sneakage around precipitation sections) which are difficult to include in simple theories. Therefore, the performance of electrostatic precipitators is often characterized with effective migration velocities, which are often derived from field experiences. Thus, effective migration velocity can be regarded as a semiempirical parameter which characterizes the mass transfer in electrostatic precipitation. Effective migration velocity is a practical tool because it can used for estimating the total mass efficiencies. This is of great importance, because the total mass emission is a key parameter when designing and operating electrostatic precipitators today. A widely used equation which illustrates the relationship between mass efficiency tj„, and effective migration velocity Wk is
-[{A/q)Vk]k
TJm = 1 — E , s I,.>.66)
Where K is a parameter having a value around Ґ2.
13.2.2.8 Effects of Dust Layer
Most of the results presented in the previous chapters are based 011 idealized conditions. In practice, the performance of an electrostatic precipitator can be significantly influenced by the dust layers on discharge and collection electrodes; i. e., dust layers may alter the electrical properties of the system. It is also possible that dust layers are not stable; i. e., collected particles become loose, increasing the particle concentration in the outlet of the precipitator. These problems play a much smaller role if the surface collection electrode is continuously flushed with water. These wet electrostatic precipitators, however, cannot be used in all applications.
Electric Field and Voltage
A layer of high-resistivitv dust on the collection surface may significantly affect the performance of the electrostatic gas-cleaning system. In practice, the effect of a dust layer affects the performance and operation of an electrostatic precipitator in a very complicated way. The corona current flowing through the dust layer generates a voltage which tends to decrease the effective voltage between the electrodes. The electric field Ed in the dust layer and the voltage Ud across the dust layer are given by
Ed = &c = //lP’ (13.67)
Where JA is the corona current density (I/A), p is the resistivity of the dust, and Ax is the thickness of the dust layer. Depending on the density of corona current and the resistivity of the collected dust, the electric field inside the dust layer may even grow so high that it initiates sparkover or back corona.
Back corona is caused by the electrical breakdown of gas in the dust layer. This breakdown produces positive ions, which drift toward the negative discharge electrode. The presence of ions with opposite polarity causes a reduction in the particle-charge and — collection efficiency. To avoid this problem, several methods are used. These include
• Good electrode geometry (i. e., even current-density distribution)
• Adjustment of corona current
• Utilization of pulsed high-voltage supplies
• Gas conditioning (i. e., injection of S03 or NH3 into the flue gas)
• Temperature and humidity control (e. g., reducing resistivity with the aid of reduced gas temperature)
Thus, the corona voltage is normally adjusted to compensate for the adverse effects of a dust layer; i. e., the operating conditions of the electrostatic precipitator are kept as ideal as possible.
The stability of the collected dust is of great importance for the overall performance of the electrostatic precipitator. The behavior of the collected dust layer is governed by electrical, molecular, and mechanical forces. Molecular forces (e. g., van der Waals forces) tend to keep particles together. 1 hese forces depend on the properties of particle surfaces. Mechanical forces are due to the interlocking of particles and to interparticle friction. Electrostatic force that affects the dust layer depends on two components. The electric field between the discharge electrode and the surface of the dust layer creates a force Fc that tends to extract particles from the surface, while the electric field inside the dust layer creates a force Fj that tends to compress the dust layer and prevent particles from escaping.
The net electric force per unit area is given by
F = Fd-Fc = e^riAP)2-EP-]. (13.68)
In this equation, e0 is the vacuum dielectric constant, er is the dielectric constant of the dust and E is the electric field in the gas adjacent to the dust layer. According to Eq. (13.68), the electrostatic force due to the electric field in the dust layer increases with increasing dust resistivity. If the dust resistivity decreases below a certain limit, the total electrostatic force becomes negative,
I. e., electrostatic force no longer holds the dust layer on the collection surface. Thus, the probability of dust reentrainment to the gas flow increases. The dust layer is, however, influenced by chemical and mechanical holding forces, which normally significantly diminish particle reentrainment. On the other hand, if the resistivity of the collected dust is very high, the electrostatic force may be so strong that the removal of dust may become very difficult.
Electrostatic precipitators have been used in various gas-cleaning applications almost for a century. During the past decades, a large number of modifi cations to electrostatic precipitators have been developed, the most common being duct and pipe types. The utilization of electrostatic precipitation extends from small household air cleaners up to huge industrial gas-cleaning systems.
The two-stage electrostatic precipitators used in light-industry applications are compact devices which can be fitted into the ventilation system. These air cleaners are normally used to clean air from dusts, smokes, and fumes in industrial workplaces. The basic features of these devices are the separate sections for particle charging and collection. The charging section consists of thin metal wires installed between grounded metal plates. The distance between the discharge wire and grounded plate electrodes is typically in the range of 1.5-3 cm. The collection section consists of a set of parallel metal plates installed in a such way that every second plate is connected to the high voltage, while every second plate is connected to the ground potential. The separation between the plates is typically 5-10 mm.
Positive corona discharge is normally used, mainly because of lower ozone production than with negative corona discharge. The corona voltage is in the range of 9-13 kV. The collection voltage is typically half of the corona voltage. In some constructions the collection voltage equals the corona voltage. The length of the collection section is typically 10-30 cm, and the airflow velocities are in the range of 0.5-3 m/s.
The most important application of electrostatic precipitation is, however, the solving of environmental pollution problems caused by many heavy-indus — try processes. The dimensions, corona voltages, and currents of these gas — cleaning systems are much larger than for ventilation electrostatic precipitators. Typical applications of industrial electrostatic precipitators are
• collection of fly ash from electric power boilers,
• particle collection from furnace operations in metallurgical processes,
• particle collection from black-liquor recovery furnaces in paper mills,
• particle collection from cement and gypsum manufacturing processes, and
• cleaning of stack emissions in municipal incinerators.
Pipe-type electrostatic precipitators are used to collect liquid aerosols (e. g., mists and fogs). They are also used in applications which require water flushing of collection electrodes. The diameter of precipitator pipes is typically in the range of 15—40 cm, and the length is in the range of 3-6 m. The number of pipes depends on the total gas flow. The gas-flow rates in pipe-type electro static precipitators is normally much lower than in duct-type precipitators.
Duct-type electrostatic precipitators are the most important electrostatic gas-cleaning devices today. Duct-type electrostatic precipitators are made of vertically mounted collection plate electrodes, with discharge electrodes placed midway between plates. The width of the collection plates in a large electrostatic precipitator can be several meters and the height up to 15 m. An electrostatic precipitator system may include several sections energized from separate high-voltage supplies. The spacing between the plates is typically in the range of 20^10 cm. The gas-flow velocity is typically 0.5-2 m/s. The ratio of collection area to the volumetric gas flow is in the range of 20-150 (m/s)-1. The corona voltages of large electrostatic precipitator systems are typically in the range of 40-100 kV, and the corresponding corona current densities (i. e., corona current divided by collection area) are in the range of 0.05-1 mA/m2. It is worth noticing that the corona voltage is normally generated by means of a thyristor-controlled transformer/rectifier system. Thus, a cyclic corona voltage and current are applied to a precipitator section.
Electrostatic precipitators are operated near the sparking limit; i. e., corona voltage is continuously adjusted to maximize the collection efficiency. This is normally achieved at the sparking rate of 10-50 sparks per minute. Sparking occurs mostly in the front section(s) of an electrostatic precipitator. In the case of high-resistivity (>1010 fi cm) dust, special techniques must be
Used to avoid the formation of back corona. This requires sophisticated systems for controlling corona voltage and current. The formation of back corona can also be reduced with intermittent or low-frequency energization. This technique is based on the extension of the time period between corona current bursts. Thus, much higher current bursts can be used without cruising back corona. Pulse energization is a more elaborate technique, which i-. nasid on current bursts of microsecond duration.
Besides optimal energization of an electrostatic precipitator, several other factors must be controlled to achieve a good performance. The gas velocity profile should be even to fully utilize the capacity of an electrostatic precipitutor. Also, the gas flow outside the active collection sections (sneakagei should be minimized. Keeping the electrodes clean is also of great importance, especially when eliminating the harmful effects of high-resistivity dust. The collected dust is normally removed by rapping forces, which are generated by mechanical impacts or by vibration of electrodes. Collection plates are normally cleaned with either a magnetic-impulse rapper or a rotating-hammer rapper. Adjustment of the rapping frequency and intensity is of great importance for the controlled removal of collected dust without excessive particle reentrainment.
The design and operation of a large electrostatic precipitator requires lot of practical knowledge about the general properties of electrostatic particle separation. In addition, the properties of the dust must be known, and correct techniques (e. g., altering dust resistivity by means of gas conditioning) must be utilized. Depending on the application, the performance of an electrostatic precipitator can be affected by several factors in a rather complicated way. Therefore, practical work with electrostatic precipitators often requires empirical information about the separation process. Thus, the experimental results from existing installations are of great importance when designing new ones. Even though theoretical calculations provide less feasible information for design purposes, they still help to understand the basic factors influencing the overall performance of the electrostatic precipitator.
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