Numerical study on the efficiency of an electrostatic precipitator having the shape of a truncated cone

Abstract

This paper presents a comprehensive numerical study of a truncated conical precipitator. The main objective was to enhance the efficiency of the precipitator by exploring the influence of several parameters on particle trajectories and the evolution of the collection efficiency. The studied parameters include the cone coefficient (D), flow velocity, applied voltage, conduit diameter and length, as well as relative permeability. For each parameter, analyses were conducted on the evolution of the collection efficiency for particles with various diameters, ranging from 0.01 to 10 μm. The results obtained from the numerical simulation on COMSOL Multiphysics^® indicate that, regardless of the value of D, the precipitator exhibits optimal efficiency in collecting particles with extreme diameters (0.01 and 10 μm) due to the dominance of the electrical force. In contrast, particles with intermediate diameters (0.1–1 μm) present a challenge, as the drag and electric forces are too weak to ensure effective particle collection. The study highlights that a sharper tip at the top of the precipitator significantly enhances its efficiency. Increasing the applied voltage and selecting lower inner radii of the collecting electrode reinforce the electrical force and enhance particle collection. Furthermore, increasing the height of the precipitator directs particle trajectories more effectively toward the collecting electrode. The results provide valuable insights for the design of more efficient precipitators and propose practical guidelines for improving their effectiveness. These contributions are particularly important for air pollution control technologies, offering significant advancements in this field.

Keywords

Numerical simulation electrostatic precipitator corona discharge particle collection efficiency particle trajectory

Introduction

Recently, uncontrolled emissions of polluting gases from industries and vehicle exhausts have led to the saturation of the atmosphere with harmful aerosol particles, posing risks to human and animal health, and causing environmental damage by exacerbating climate change and destabilizing natural ecosystems.^1,2 In this context, electrostatic precipitators (ESPs), which operate by capturing electrically charged particles via corona discharge,^3,4 emerge as a promising solution due to their particle collection efficiency exceeding 90%.⁵ ESPs are commonly used to capture particulate emissions from diesel engines, achieving a removal efficiency of up to 99% for certain types of particles.⁶ They are also utilized in biomass combustion installations, wood combustion, power plants, and biomass boilers to reduce emissions of fly ash resulting from combustion,^7–10 as well as in air purification and filtration systems,¹¹ and in livestock buildings such as pigsties, thereby improving the efficiency of these installations.^12–15

Improving particle collection efficiency and enhancing the effectiveness of electrostatic filters is of paramount importance, given the diversity of industrial applications previously mentioned using ESPs. In this context, several research efforts have been developed to predict the collection efficiency of ESPs. In addition to experimental work, the prediction of ESP collection efficiency is approached in two distinct ways. On the one hand, the simplest methods rely on one-dimensional studies based on the Deutsch-Anderson equation or its derivatives.^16,17 On the other hand, CFD simulations offer increased accuracy and reliability, regardless of the complexity of the equation system involved.^18–21 Dastoori et al.¹⁸ addressed the case of a wire-cylinder ESP in which some grounded baffles were introduced. The effect of these baffles on the collection percentage was numerically determined, showing a positive impact on collection efficiency. Skodras et al.¹⁹ developed a two-dimensional numerical study of a wire-plate ESP with several electrodes, demonstrating a satisfactory collection percentage for this precipitator. A 2-D axisymmetric numerical simulation of a wire-cylinder ESP was developed by Moody.²⁰ They demonstrated that the widespread use of the studied device can reduce PM2.5 emissions from the residential wood heating sector in Quebec by 64%.

The enhancement of particle collection efficiency and the heightened effectiveness of electrostatic filters hold paramount significance, given the diverse array of previously mentioned industrial applications that employ ESPs. The improvement in efficiency depends not only on the ESP design but also on electrode geometry, particle size, flow velocity, and various other parameters. Several comprehensive research initiatives, encompassing both experimental and numerical methodologies, have been undertaken to delve into this subject matter. Kim et al.²² focused on wet ESPs, which are prone to deterioration or corrosion caused by water on the collection electrode. The effectiveness of such a filter may decrease due to this corrosion issue. To address this, Kim et al.²² attempted to install a PVC dust precipitator. The collection efficiency significantly improved following this modification, demonstrating that it could reach 99.7%. Berhardt et al.²³ experimentally developed an ESP integrated into a heat source. Their experimental model demonstrated that the collection efficiency reached 89% when using wood chip fuel. Rodriguez et al.’s work focuses on studying a condensing heat exchanger with electrical charging.²⁴ The primary role of this heat exchanger is to both remove fine particles and recover heat from combustion gases in a biomass boiler. The developed model resulted in an 80% reduction in fine particle emissions and an improvement in heat recovery efficiency. Hu et al.¹² numerically and experimentally investigated the evolution of the efficiency of a wire-plate ESP with the aim of improving air quality in pig houses. They demonstrated that the collection efficiency of PM2.5 particles (diameter <2.5 μm) increases with the decrease in airflow velocity and the increase in applied voltage. Notably, they found that the collection efficiency of particles with a diameter of 2 μm is 100% at an airflow velocity of 1 m/s and an applied voltage of 50 kV.

To our knowledge, and based on the literature review, researchers have not explored the use of a truncated conical collector electrode. This work presents a comprehensive numerical study of a truncated conical precipitator conducted using COMSOL Multiphysics. The objective of this study is to enhance the precipitator’s efficiency by examining the influence of several factors on particle trajectories and the evolution of the collection efficiency. These factors include the cone inclination percentage (D), flow velocity (u₀), applied voltage (V), conduit diameter (R_ex) and length (H), and relative permeability (Er). For each parameter, a detailed analysis of the collection efficiency will be conducted for particles with various diameters d_p, ranging from 0.01 to 10 µm. This innovative approach aims to provide crucial insights, opening new possibilities to enhance particle capture in various industrial and environmental applications.

Numerical modeling

Problem formulation

The electrostatic precipitator under study is depicted in Figure 1. It is primarily composed of two electrodes: the active electrode, also known as the discharge electrode, which has a cylindrical shape with a height H of 0.5 m and a radius R_in of 0.5 mm. The collecting electrode is in the form of a truncated cone with a height H of 0.5 m and radii R_ex-out and R_{ex_in} = 75 mm.

Figure 1.

Schematic diagram of the truncated conical electrostatic precipitator geometry.

We have defined the coefficient D as a relative measure of the differences in the radii of the collecting electrode as a function of the height of the precipitator. This coefficient normalizes the difference between the upper and lower radii of the cone relative to its height:

D = \frac{R_{e x_o u t} - R_{e x_i n}}{H} \times 100 .

An upward flow of dusty air enters the precipitator with a velocity u₀ of 1 m/s, an inlet pressure P₀ = 1 atm, and an inlet temperature T₀ = 20°C. A voltage of 20 kV is applied to the active electrode, while the collecting electrode is grounded. The potential difference between the two electrodes triggers an electrical discharge, which, in turn, charges the particles present in the air. Under the combined effect of the electric force and the air drag force, the particles are captured by the collecting electrode. The collection efficiency depends not only on the discharge intensity and particle velocity but also on several geometric parameters, such as the distance between the electrodes, their length, particle diameter, etc. While there are no strict limitations regarding the dimensions of the frustum of the cone, it is important to note that very tall heights and large radii may not be advantageous. In fact, very tall heights would result in particle collection occurring predominantly on the lower part of the precipitator, rendering the upper part less effective. Similarly, large radii could slow down the corona effect, potentially reducing the particle collection efficiency. The impact of these parameters on the properties of the precipitator and its efficiency will be explored in the following sections of this paper.

Assumptions and governing equations

Corona discharge

Two main assumptions have been made to simplify our model. Firstly, we have disregarded the magnetic field generated by the corona cylinder. Additionally, we assumed that the influence of fluid flow on the distribution of the electric field is negligible. The governing equations of the particle migration caused by corona discharge are then as follows¹²:

\nabla . J = 0,

(1)

J = z_{q} γ ρ_{q} E + ρ_{q} u,

(2)

ε_{0} \nabla^{2} V = - ρ_{q} .

(3)

Where J is the current density, z_q is the charge number, γ is the electrophoretic mobility, ρ_q is the space charge density, E is the electric field intensity, u is the flow velocity, V is the electric potential, ε₀ is the vacuum dielectric constant.

Laminar airflow

Considering the airflow as a Newtonian fluid with incompressible and laminar flow, and disregarding the effect of particles on airflow displacement, the governing equations at steady state are written in the cylindrical coordinate system (r, z) as follows²⁵:

\frac{1}{r} \frac{\partial (r u_{r})}{\partial r} + \frac{\partial (u_{z})}{\partial z} = 0,

(4)

\begin{matrix} ρ u_{r} \frac{\partial u_{r}}{\partial r} + ρ u_{z} \frac{\partial u_{r}}{\partial z} = - \frac{\partial P}{\partial r} + μ \frac{1}{r} \frac{\partial}{\partial r} (r \frac{\partial u_{r}}{\partial r}) \\ + μ \frac{\partial}{\partial z} (\frac{\partial u_{r}}{\partial z}) + F_{r}, \end{matrix}

(5)

\begin{matrix} ρ u_{r} \frac{\partial u_{z}}{\partial r} + ρ u_{z} \frac{\partial u_{z}}{\partial z} = - \frac{\partial P}{\partial r} + μ \frac{1}{r} \frac{\partial}{\partial r} (r \frac{\partial u_{z}}{\partial r}) \\ + μ \frac{\partial}{\partial z} (\frac{\partial u_{z}}{\partial z}) + F_{z}, \end{matrix}

(6)

F_{r} = ρ_{q} E_{r},

(7)

F_{z} = ρ_{q} E_{z} .

(8)

ρ is the airflow density, P is the pressure, and μ is the dynamic viscosity. (F_r, F_z) are the components of the body force in the cylindrical coordinate system, and the expressions for its components in the cylindrical coordinate system are given in equations (7) and (8).

Particle tracking

To simplify the numerical problem, we neglect any interaction between particles, and we assume that particles, upon reaching the collecting electrode (the truncated cone), can be fully adsorbed, and there is no rebounding of particles. According to these hypotheses, the position of the particles can be calculated using the following equations¹²:

m_{p} \frac{d V_{r}}{dt} = F_{t_r},

(9)

m_{p} \frac{d V_{z}}{dt} = F_{t_z} .

(10)

Here (V_r, V_z) are the particle velocity components in the cylindrical coordinate system, m_p is the particle mass, and (F_{t_r}, F_{t_z}) denote the components of the total force F_t applied to particle.

The composite force F_t acting on the particles encompasses the drag force (F_D) influenced by the airflow within the precipitator, and the electric force (F_e) generated by particle charge and electrical field.

The drag force F_D is calculated using Cunningham Millikan Davis equations.²⁶ Its components in cylindrical coordinate system are as follows:

F_{D_r} = \frac{m_{p}}{τ_{t} S} (u_{r} - V_{r}),

(11)

F_{D_z} = \frac{m_{p}}{τ_{t} S} (u_{z} - V_{z}) .

(12)

Where τ_{t} = \frac{16 ρ_{p} R_{p}^{2}}{3 μ C_{t} R e_{relative}},

(13)

and R e_{relative} = \frac{2 ρ R_{p} | | \vec{u} - \vec{V} | |}{μ} .

(14)

Here, τ_t represents the velocity response time of particle, ρ_p denotes the particle density, R_p stands for the particle radius, C_t is the drag coefficient, Re_relative represents the relative Reynolds number, and S is the correction coefficient of drag force.

The components of the electrical force F_e in cylindrical coordinate system are defined as below:

F_{e_r} = eZ E_{r},

(15)

F_{e_z} = eZ E_{z} .

(16)

Where e represents the elementary charge and Z denotes the accumulated charge per particle.

The determination of the accumulated charge on particles is achieved through the application of the Lawless-Altman equations.¹²

The collection efficiency is obtained as follows:

η = \frac{N_{1} - N_{2}}{N_{1}} \times 100 % .

Where N₁ represents the number of particles at the inlet of the precipitator, and N₂ is the number of particles at the outlet of the precipitator.

Boundry conditions

At the inlet of the precipitator:

$u = u_{0}$ ,

$- n . J = 0 .$

At the oulet of the precipitator:

$P = P_{0},$

$- n . J = 0 .$

At the collective walls :

No-slip boundary condition,

$- n . J = 0,$

$V = 0 .$

At the corona electrode :

No-slip boundary condition,

$n . E = E_{0},$

$V = V_{0}$ .

In this numerical problem, Peek’s law is used to calculate E₀, ensuring that the electric field value matches real values and provides accurate physical predictions²⁷:

E_{0} = 3 \times 10^{6} δ (1 + \frac{0.03}{\sqrt{δ \frac{R_{in}}{2}}}) .

where E₀ represents the breakdown electric field and δ is the gas number density.

Numerical procedure

COMSOL Multiphysics was the CFD simulation software employed for coupling the various mentioned fields, allowing for the integrated resolution of the governing equations. We have coupled the Navier-Stokes equations for fluid dynamics, the Poisson equations for electrostatics, and the continuity equation for the transport of charged particles. The direct coupling in COMSOL allows these equations to be solved simultaneously, ensuring precise interaction between the electric field, gas flow, and movement of particles. The use of a coupled nonlinear solver guarantees the coherence and stability of the solution, thereby improving the accuracy and efficiency of the simulation. This method ensures an integrated and reliable modeling approach, taking into account all the complex physical interactions present in the system.

To ensure the reliability of the results, the generated mesh, consisting of triangular elements, was carefully refined to test the model’s convergence. This is where the advantage of using the finite element method (FEM) in COMSOL lies. Indeed, this method, widely used for solving nonlinear equations,^28,29 handling complex geometries, and accommodating varied boundary conditions, ensures that simulations are as accurate as possible while optimizing computational resources. In the specific case of an ESP with an inclination of D =−5%, R_{ex_in} = 75 mm, R_in = 0.5 mm, H = 0.5 m, Figure 2 illustrates the structured triangular mesh used for solving the equations. This mesh is composed of 29,439 domain elements and 1107 boundary elements.

Figure 2.

Description of the triangular mesh used for a truncated conical electrostatic precipitator (ESP) with D =−5%.

Results and discussion

Effect of the variation of the upper diameter of the truncated cone

Effect on local distributions

Figure 3 provides a visual representation of the local distributions of velocity magnitude, gauge pressure, potential, and charge density within the electrostatic precipitator. These distributions are presented for various values of D, representing different variations in the upper diameters of the cone trunk, namely D =−10%, −5%, 0%, 5%, and 10%. For the configuration where D = 0%, the precipitator adopts a perfect cylindrical shape. The laminar airflow entering from below maintains virtually constant stability throughout the length of the precipitator. The electric potential (V) and charge density (ρ_q) exhibit a uniform distribution at the discharge electrode, measuring 20 kV and 6 × 10⁻⁵ C/m³, respectively. These values gradually decrease as one approaches the collecting electrode. Consequently, the electrostatic force acting on particles is particularly pronounced near the corona discharge, specifically around the discharge electrode. During the transition from a cylindrical shape to a slightly truncated cone shape at the top (D =−5%), a progressive increase in pressure is observed at the precipitator’s entrance. A simultaneous increase in particle velocity is observed in the upper half of the precipitator where the pressure is lower. Additionally, thanks to the truncated conical geometry, the precipitator’s diameter gradually decreases toward the device’s outlet. Consequently, the distance between the electrodes decreases progressively. This leads to an improvement in corona discharge in the upper part of the precipitator, allowing for a higher charge density in this region of the device.

Figure 3.

Local distributions of velocity magnitude, gauge pressure, potential, and charge density for different D.

When D =−10%, the apex of the precipitator becomes sharper. The flow velocity is accentuated in the upper part of the cone trunk, following regions of low pressure, and the charge density accumulates only at the upper part of the precipitator due to the pronounced reduction in electrode distance. However, with D values of 5% and 10%, the upper diameter of the precipitator becomes larger than its base. This modification induces increased pressure in the upper part and an acceleration of particle velocity at the device’s entrance (its maximum value equals the imposed entrance velocity u₀ = 1 m/s), followed by a decrease as it approaches the top. It is noteworthy that at an inclination of D = 5%, the charge density primarily extends around the lower half of the discharge electrode, where the distance between the electrodes is shorter. As the inclination increases to D = 10%, an increased concentration of charge density is observed around the lower part of the discharge electrode.

To highlight the impact of the electric force, Figure 4 presents the evolution of axial velocity, both in the absence (in red) and in the presence (in blue) of the potential, on successive planes perpendicular to the axis of the precipitator, starting from the precipitator inlet defined as z = 0. It is important to note that the abscissa 0% corresponds to the discharge electrode, while the abscissa 100% coincides with the collecting electrode.

Figure 4.

Axial velocity and pressure on different planes z = 0, z = H/4, z = H/2, and z = 3H/4.

In the absence of potential, just at the precipitator inlet, the flow velocity (air + particles) is uniform and equal to its imposed value, u₀ = 1 m/s. As the flow progresses in the inter-electrode space, the flow is governed by the air drag force. The flow velocity then takes a parabolic shape on the planes z = H/4, H/2, and 3H/4, and its value amplifies further as it moves toward the precipitator outlet due to the progressive decrease in pressure.

In the presence of an electric potential, the effect of the electric force becomes evident near the collecting electrode. Examining different planes z = 0, z = H/4, z = H/2, and z = 3H/4, it is observed that the pressure gradually increases as one approaches the collecting electrode. This is explained by the action of the electric force, which directs the charged particles toward the collecting electrode. Furthermore, a slight decrease in flow velocity is observed on the various planes examined as one approaches the collecting electrode, as the flow is diverted toward the discharge electrode where the pressure is lower.

Effect on collection efficiency

In the electrostatic precipitator developed in this study, particles enter the device from the bottom, driven by the airflow, and move toward the precipitator’s outlet under the influence of drag force. Throughout their journey through the precipitator, particles acquire an electric charge, and their trajectories are deflected by the electric force, which acts to direct them toward the collecting electrodes. Thus, particle trajectories are primarily determined by these two forces. Figure 5 highlights the impact of particle diameter on the collection percentage of the precipitator in question. It is observed that the collection percentage is maximum when the particle diameter is 0.01 and 10 μm (the two extreme cases studied), regardless of the value of the coefficient D.

Figure 5.

Effect of particles diameter on ESP collection efficiency for D =−10%, −5%, 0%, 5%, and 10%.

For particles with a diameter of 0.01 µm, electric forces dominate over drag forces. This means that all particles of this size are attracted and captured by the collecting plates, resulting in a 100% collection efficiency. At this scale, the particles are small enough to be primarily influenced by the electric field generated by the electrostatic precipitator, and the drag forces due to the airflow are negligible.

However, as the particle diameter increases to 0.1 µm, drag forces start to play a more significant role. Particles of this size are less likely to be captured by the charged electrodes due to their greater inertia and the resistance from the airflow. This leads to a decrease in collection efficiency within this size range. Between 0.1 and 1 µm, a minimum collection efficiency is observed, which does not exceed 20% regardless of the value of the coefficient D. This can be attributed to a balance between electric forces and drag forces, where particles of this size have a lower probability of being efficiently captured by the electrodes due to the relatively weak electric and drag forces. At this scale, neither the electric forces nor the drag forces are sufficiently dominant to ensure effective collection. Beyond 1 µm, drag forces become dominant again. In this larger diameter range, particles are more easily captured due to their ability to accumulate a larger charge. Larger particles, having a greater surface area, can capture more electric charges, which increases the influence of electric forces despite the increased drag force. This results in an increase in collection efficiency, reaching 100% at 10 µm. At this stage, the particles are massive enough that the drag forces do not prevent them from being captured by the electrostatic forces generated by the precipitator.

Effect on particle trajectory

Trajectory of 1 µm diameter particles

It is crucial to note that the particle diameter has a significant influence on the balance between drag force and electric force. This impact is clearly evident in particle trajectories and, consequently, affects the collection percentage of the precipitator. Figure 6 illustrates the trajectories of particles with a diameter of 1 μm, providing (according to Figure 5) the lowest collection percentage for different values of D. According to the figure, to ensure a maximum collection percentage, it is preferable to opt for a truncated precipitator at the top with D =−10%. Indeed, by examining the trajectories of particles for D =−10%, it is observed that the particle velocity is low over a large part of the precipitator. This results in a slowing down of the drag force, allowing the electric force to prevail over the particles and direct them toward the collecting electrode over the majority of the precipitator volume. By increasing the value of D, the flow velocity becomes quite high over a large part of the precipitator, leading to a predominance of drag force and a decrease in the collection percentage. For D values equal to 5% and 10%, particle trajectories are practically parallel to the discharge electrode, resulting in a minimal collection percentage.

Figure 6.

Particle trajectories with a diameter of 1 μm for different inclinations D.

Trajectory of particles with diameters of 0.01, 0.1, 1, 5, and 10 µm for the case D = 0%

Figure 7 presents the trajectories of particles with different diameters (d_p = 0.01, 0.1, 1, 5, and 10 μm) for a cylindrical-shaped precipitator (D = 0%). It is noteworthy that particles with a diameter of d_p = 0.01 μm are the most collected on the collecting electrode, given that the drag force weakens with smaller diameter particles. Their collection percentage is approximately 90%, as indicated by the previous curve. As the particle diameter increases up to 1 μm, they capture very little charge (due to their small diameter), and the majority of them escape without being collected on the collecting electrode. However, when the diameter increases to 5 and 10 μm, the particle size becomes sufficiently large to capture more charge. The electric force then prevails, deflecting their trajectories toward the collecting electrode, improving the collection percentage to 40% with d_p = 10 μm. This observation highlights the importance of the targeted particle diameter in the collection process, where smaller diameter particles (d_p = 0.01 μm) are more effectively captured due to a lower drag force. Additionally, the cylindrical precipitator is capable of capturing about 40% of larger particles with diameters d_p = 10 μm.

Figure 7.

Trajectory of particles with diameters of 0.01, 0.1, 1, 5, and 10 µm for the case of cylindrical ESP.

Trajectory of particles with diameters of 0.1, 0.5, 1, 5, and 10 µm for the case D = 0%

Figure 8 illustrates significantly the trajectories of particles with different diameters (0.1, 0.5, 1, 5, and 10 μm), along with the number of adhered charges, within the context of a cylindrical electrostatic precipitator (D = 0%). The predominant observation concerns particles with a diameter of d_p = 0.1 μm, for which the surface limitation considerably hampers their ability to capture a substantial number of particles. Indeed, the number of adhered charges remains notably low, resulting in a collection percentage that does not exceed 20%, as shown in the previous Figure 5.

Figure 8.

Trajectory of particles with diameters of 0.1, 0.5, 1, 5, and 10 µm for the case of cylindrical ESP.

A remarkable phenomenon occurs as the particle diameter increases. The electric force becomes predominant, promoting a gradual deviation of trajectories and the migration of an increasing number of charged particles toward the collecting electrode. This progressive increase in the number of adhered charges contributes to a significant rise in the collection percentage. It is particularly noteworthy that with a particle diameter of d_p = 10 μm, the electric force attains such dominance that the collection percentage peaks at 100%, signaling maximum efficiency in the capture process.

Effect of the velocity

Figure 9 highlights the significant impact of flow velocity on the trajectories of 3 µm diameter particles in two different types of precipitators: a cylindrical precipitator (D = 0%) and a truncated cone-shaped precipitator inclined at D =−5%. Three flow velocities were explored, namely u₀ = 1, 1.5, and 2 m/s. For the cylindrical precipitator (D = 0%), a noteworthy observation is that increasing the flow velocity induces progressively deviating trajectories of particles toward the discharge electrode, aligning them more and more parallel to the collecting electrode. This trend is explained by the simultaneous improvement of the drag force with the increasing flow velocity. However, it is important to note that this improvement leads to a reduction in the collection percentage and, consequently, a decrease in the efficiency of the precipitator. Indeed, according to the results in Figure 10, at a velocity of 2 m/s, the collection percentage of a 3 µm diameter particles does not exceed 5%. This finding emphasizes that velocity plays a decisive role in the efficiency of the precipitator and its collecting capacity. Excessive increase in velocity can lead to a significant decrease in the device’s effectiveness. Regarding the truncated cone-shaped precipitator (D =−5%), an interesting observation emerges when increasing the velocity at the inlet of the device. The flow accelerates more pronouncedly toward the outlet due to the narrowing of the exit section of the precipitator. Similar to the case of the cylindrical precipitator, particle trajectories deviate increasingly toward the discharge electrode as the flow velocity increases. The effect of this velocity increase is equally significant on the collection percentage, as indicated in Figure 10, where it reaches 10% for a fluid inlet velocity u₀ equal to 2 m/s. This observation underscores the direct impact of flow velocity on the efficiency of the truncated cone-shaped precipitator.

Figure 9.

Particle trajectories with a diameter of 3 μm for different velocities (u₀) for both cases D = 0% and D =−5%.

Figure 10.

Collection efficiency of the ESP for different velocity u₀ for both cases D = 0% and D =−5%.

Regarding the evolution of the collection efficiency as a function of particle diameter, similarly to the trend observed in Figure 5, it is noted that this evolution follows a parabolic curve with increasing particle diameter, regardless of the velocity. A minimum is observed for particles with diameters ranging between 0.1 and 1 µm. This is due to the balance between drag forces and electric forces. At this scale, both electric and drag forces are relatively weak and insufficient to ensure effective collection of particles of this size.

Voltage effect

Figure 11 illustrates the influence of applied voltage on the trajectories and velocities of particles with a diameter of d_p = 5 μm, examining two different inclinations of the truncated cone precipitator: D = 0% (cylindrical precipitator) and D =−5%. The elevation of the applied voltage to the active electrode results in an increase in the potential difference between the two electrodes. This increase further accentuates the electric force, allowing it to dominate the movement of particles. Significantly, the trajectories of particles bend more toward the collecting electrode as the voltage is increased. This observation clearly emphasizes that the voltage increase enhances the ability of the electric force to direct particles toward the collecting electrode. This dynamic evolution of trajectories undoubtedly contributes to an improvement in the collection percentage and overall efficiency of the device. Indeed, according to the results in Figure 12, the collection percentage of particles with a diameter d_p = 5 μm increases from 23% with a voltage of 20 kV to 70% with a voltage of 25 kV for the case of cylindrical ESP (D = 0%). This significant improvement convincingly confirms the crucial role of the applied voltage in optimizing the device’s performance. Strikingly, this trend becomes more pronounced with larger diameter particles (d_p = 10 μm), where the collection percentage evolves from 40% with a voltage of 20 kV to a maximum efficiency of 100% with a voltage of 25 kV for a cylindrical precipitator. These results clearly demonstrate that adjusting the applied voltage can have a considerable impact on the precipitator’s ability to effectively collect particles of different sizes. The impact of voltage is particularly notable in the case of a truncated cone-shaped precipitator with an inclination D =−5%. Not only does the increase in potential difference contribute to dominance by the electric force, but also the narrowing of the upper part of the collecting electrode contributes to a perfect domination. This configuration leads to a maximal deviation of particle trajectories toward the collecting electrode. It is interesting to note that the collection percentage of this truncated cone precipitator is higher than that of a cylindrical precipitator, regardless of the applied voltage. This observation suggests that the specific geometry of the truncated cone, combined with the increased effect of voltage, offers superior collection efficiency compared to the cylindrical precipitator, as illustrated in the Figure 12. Indeed, the collection percentage of particles with a diameter of 5 μm increases significantly, going from 31% with a voltage of 20 kV to 86% with a voltage of 25 kV.

Figure 11.

Particle trajectories with a diameter of 5 μm for different voltage for both cases D = 0% and D =−5%.

Figure 12.

Collection efficiency of the ESP for different voltages for both cases D = 0% and D =−5%.

The study of the influence of applied voltage and particle diameter on the performance of electrostatic precipitators reveals complex yet crucial interactions for optimizing particle collection efficiency. While increasing the voltage significantly improves the collection percentage, the effect of particle diameter remains a critical factor that cannot be ignored. The evolution of the collection percentage as a function of particle diameter follows a parabolic curve, with a minimum located between 0.1 and 1 µm. At these diameters, both drag forces and electric forces are relatively weak, making particle collection less efficient. This effect is observed regardless of the applied voltage and the outer radius of the precipitator. Thus, adjusting the voltage can enhance collection efficiency, but to maximize this efficiency, it is also essential to consider the effect of particle diameter. An appropriate precipitator design, taking these factors into account, allows for the development of more efficient and reliable particle collection devices.

Effect of the conduit diameter

The impact of the outer conduit radius (R_ex-in) on particle trajectories (d_p = 4 µm) and collection efficiency is examined for two precipitator shapes: cylindrical and truncated cone with an inclination of D =−5%, as illustrated in Figures 13 and 14, respectively. What is particularly noteworthy for both studied precipitator shapes is that an increase in R_ex-in results in a deviation of particle trajectories toward the active electrode. Indeed, the enlargement of R_ex-in weakens the corona discharge, requiring a higher breakdown voltage. The electric force weakens compared to drag, causing the particles to deviate toward the discharge electrode. This trend is also observed in the decrease of the collection efficiency, as shown in Figure 14. For a cylindrical precipitator, the collection efficiency of particles with diameters d_p = 0.01 μm decreases from 90% with R_ex-in = 75 mm to 10% with R_ex-in = 125 mm. Similarly, for a truncated cone-shaped precipitator (D =−5%), the collection efficiency of particles with diameters d_p = 0.01 μm decreases from 100% with R_ex-in = 75 mm to 15% with R_ex-in = 125 mm. The influence of R_ex-in is also significant for particles with diameters d_p = 10 μm, where no particle with a diameter greater than 0.1 μm is captured in a cylindrical precipitator when R_ex-in = 125 mm. The evolution of the collection efficiency is still parabolic with the increase in particle diameters, having a minimum for particles with diameters ranging between 0.1 and 1 µm, regardless of the outer radius R_ex-in. At this level, the drag forces and electric forces are weak and incapable of effectively collecting the strongly deviated particles. The degradation of collection efficiency with the increase in R_ex-in highlights the need for specific design considerations for electric precipitators to ensure their optimal performance.

Figure 13.

Particle trajectories with a diameter of 4 μm for different R_ex-in for both cases D = 0% and D =−5%.

Figure 14.

Collection efficiency of the ESP for different R_ex-in for both cases D = 0% and D =−5%.

Effect of the conduit length

The impact of conduit length on the trajectories of 6 μm diameter particles in a cylindrical precipitator is illustrated in the Figure 15. Three lengths are tested: H = 0.5 m, H = 1 m, and H = 1.5 m. Increasing the conduit length results in an enhancement of the capture surface of the precipitator. This improvement leads to an increase in the collection efficiency and effectiveness of the precipitator.

Figure 15.

Particle trajectories with a diameter of 6 μm for different conduit length (H) for case D = 0%.

With H = 0.5 m, the electric force deflects particle trajectories toward the collecting electrode, but only 27% (according to Figure 17) of particles are captured by the collecting electrode. The remaining particles are carried with the airflow toward the precipitator exit following specific trajectories.

However, with a precipitator of length H = 1 m, the collection efficiency improves to 55%, and with a longer precipitator (H = 1.5 m), all trajectories converge toward the collecting electrode, capturing all charged particles and achieving a collection efficiency of 100% as depicted in Figure 17. This observation underscores the significant effect of conduit length on the precipitator’s ability to efficiently collect particles.

To highlight the impact of conduit length on the truncated cone precipitator illustrated in Figure 16, the same outer radii (R_ex-in and R_ex-out) of the truncated cone have been retained, and three different lengths have been tested (H = 0.5, 1, 1.5 m). The improvement in the efficiency of the precipitator is noticeable when transitioning to the case of truncated cone precipitators. In addition to benefiting from the enhanced discharge using a truncated conical collecting electrode instead of a cylindrical one, increasing the length of the electrode also allows for the majority of trajectories to converge toward it. According to Figure 17, with a length H = 1 m, the collection efficiency reaches 87%, and with a length H = 1.5 m, all trajectories converge, thus enabling the capture of all charged particles.

Figure 16.

Particle trajectories with a diameter of 6 μm for different conduit length (H).

Figure 17.

Collection efficiency of the ESP for different conduit lengths H.

Effect of relative permeability on collection efficiency

Figure 18 illustrates the impact of relative permeability on the collection efficiency of two types of precipitators, one cylindrical and the other truncated cone with an inclination of D = −5%. A significant observation emerges from this analysis: the effect of relative permeability is negligible for particles with a diameter less than or equal to 2 µm. Beyond this diameter, a slight improvement in the collection efficiency is observed with an increase in permeability, ranging from 5 to 100. This maximum improvement is achieved with particles of 10 µm in diameter. For a cylindrical precipitator, the collection efficiency increases from 40% to 54%, while for a truncated cone precipitator, it increases from 54% to 77%. Thus, the effect of relative permeability is more significant for capturing larger particles. The specific geometry of the precipitator also appears to influence this response, with the truncated cone precipitator showing a more pronounced improvement compared to the cylindrical precipitator.

Figure 18.

Collection efficiency of the ESP for different relative permeability (Er) for both cases D = 0% and D = −5%.

Conclusion

This numerical study was developed in order to enhance the overall efficiency of truncated cone electrostatic precipitator by systematically analyzing the impact of key parameters on particle trajectories and collection efficiency. Our results highlight that, regardless of the inclination value (D), the precipitator exhibits optimal efficiency in capturing particles at extreme diameters (0.01 and 10 μm), under the predominant influence of the electric force. Significantly, a sharper apex at the precipitator’s summit enhances its efficiency substantially.

In addition, the study revealed that increased flow velocities induce higher drag forces, thereby diminishing the precipitator’s efficiency. Conversely, elevated voltages contribute to a more dominant electric force, thus improving collection efficiency. Optimal choices for radii amplify corona discharge, reinforcing the electric force and enhancing collection efficiency. Furthermore, increased precipitator height proves crucial for more effectively guiding particle trajectories toward the collecting electrode. These in-depth insights provide valuable guidance for strategically optimizing electrostatic precipitators in various applications.

To improve the efficiency of electrostatic precipitators, optimization of the geometric configuration of the precipitator can also be targeted, including the shape, orientation, and arrangement of the electrodes. In fact, optimization of the precipitator’s geometry could maximize the interaction between charged particles and the electric field, thereby increasing particle capture efficiency. For example, by altering the shape of the electrodes to create more uniform electric fields or adjusting the spacing between electrodes to optimize airflow, significant improvements in precipitator performance can be achieved. Additionally, optimizing the arrangement of electrodes based on specific flow conditions can reduce dead zones and increase the likelihood of particle capture. These geometric optimization approaches can play a crucial role in enhancing the efficiency of electrostatic precipitators, providing more effective solutions for atmospheric emission control.

Footnotes

Handling Editor: Aarthy Esakkiappan

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Khaoula Ben Abdelmlek

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