Abstract
Gas turbines require filtered air to preserve operability, availability, and efficiency. Fouling, corrosion, and erosion severely affect the performance of the axial compressor and it can be in part prevented by filtering the air intake. For this reason, several stages of filters can be used in series to catch pollutant particles gradually smaller and with a high level of capturing efficiency. Traditionally, the separation is obtained using cartridges of porous material, which provide a high level of filtration but at the same time generate a pressure drop increasing over time. Another common type of filter is the inertial one, whose operating principle is based on the inertial force acting on the solid particles to separate them from the mainstream. The capturing efficiency of the inertial filter is not comparable with the porous one and for this reason, it is used upstream as a pre-filter. In recent years, another technique has been developed to filter air flows thanks to an electrostatic field, that is induced inside the flow. The electrostatic force generated is able to attract and separate metallic particles. In the present work, numerical investigations are carried out to simulate the effect of the electrostatic force for gas turbine filtering systems. The computational fluid dynamics tool used is openfoam, whose official release can simulate inertial and porous filtering media, while for electrostatic one is not possible due to the absence of a library able to simulate the electrostatic force that acts on the discrete phase. A new library was developed in order to calculate the electric field, the electric potential, and the charge density of the continuous phase. Simulation results show how the calculation of these quantities allows us to predict the electrostatic force acting on particle flows in the presence of electrostatic fields.
1 Introduction
The intake filter is an important component for a Gas Turbine (GT) since preserves the operating life and the efficiency of the machine reducing contaminants ingestion from the environment. The first purpose of an intake filtering system is to avoid the ingestion of foreign objects that could damage the compressor blades, blocking them upstream the compressor. The other two phenomena reduced by the filter are fouling and erosion, both mechanisms affect the aerodynamic profile of the blade and therefore cause a decay in time of the gas turbine performance. Fouling is caused by the adherence of micro-sized particles in the intake air, which are present in the surrounding environment [1,2] and it can be responsible for a decrease in polytropic efficiency up to 3%, as shown in Ref. [3]. Erosion, instead, is due to the impact between contaminants transported by the air on both rotating and stationary vanes, especially in the turbine stages [4].
Different types of filtering concepts can be used to separate the contaminant from inlet airflow to a gas turbine, such as mechanical, inertial, and electrostatic. Even if the best ideal filter should have zero pressure losses and maximum filtration efficiency for all the inflow particle diameters and velocities, the most suitable filter or combination of filtration mechanisms is selected according to different parameters: filtration efficiency, inflow velocity, inflow particle diameters, pressure losses, maximum acceptable fouling, maintenance service time range, ambient and environmental conditions. The filters commonly used in gas turbine applications that have a very high capture efficiency are EPA, HEPA, and ULPA. They are mechanical filters that use fiber to trap the particles upstream of the compressor inlet. The capture efficiency is evaluated according to the standard EN 1822 [5] it defines several levels of efficiency (85%, 99.95%, and 99.9995%) for particles with a diameter greater than ( for ULPA). As a first stage of filtration inertial separators are used thanks to their capability to separate the biggest particles and droplets above [6] by leveraging on the delayed reaction of particles to follow the airflow stream. The other fundamental parameter for the characterization of a filter is its pressure drop because it influences the efficiency of the entire system. In particular, as the pressure drop due to the filter decreases, the power required by the compressor decreases and consequently the net shaft power increases with the same fuel consumption. For gas turbine applications, the typical values of filter pressure loss are between 100 Pa and 1500 Pa and it increases over its operating life because the caught particles obstruct the airflow. For this reason, to preserve the efficiency of the GT, after a certain amount of time, it is necessary to replace the clogged filter with a new one. This work aims to introduce a new hybrid typology of filter, obtained by coupling an inertial element with a direct current (DC) electric field that helps to separate the particles with lower diameters, due to the action of the electrostatic force. Pre-charged electrostatic filters can be used to catch small particles as a result of the electrostatic force. The limit of this filtering typology is the reduction of electrostatic charge over time since is neutralized by the caught particles which occupy the charged area. Differently, in the proposed new typology of filter, the electrostatic charge does not vary in time, as in the traditional electrostatic filter, due to the continuous application of the electrical potential. A numerical approach is necessary to evaluate, in a limited time, the capability of this system as the geometry and the applied electrical potential on the wire vary. For this reason, taking advantage of the open-source nature of the computational fluid dynamics code OpenFOAM a new Lagrangian solver that allows to take into account the effects of the electric field on both continuous and discrete phase is developed and applied.
2 Methodology
This section describes the method developed for the design of the filter. The CFD study has been performed thanks to OpenFOAM 10, which has been modified by adding some of the required physics modeling to simulate the new filter functioning. The changes include both transported particles and carried fluid to take into account the effect of the electric field on them. In addition, the implementation of a new boundary condition for the ionic charge density has been required. In the following, a detailed description of this modeling is shown.
2.1 Electrostatic Solver.
To capture the physics of the electrostatic filter precipitator (ESP), it is necessary to modify OpenFOAM source code in two different parts. First of all, the flow solver needs to consider the additional effect due to the electrostatic field. This can be considered as a quantity that does not interact with the flow field or, conversely, includes its effect in the source term of the momentum equation. The flow perturbation due to the presence of a strong electrostatic potential will be considered here. The second point regards particle motion since the effect of the ESP is to charge particles and collect them on the grounded electrode. This is driven by the electrostatic force due to the charges that are transferred to the particles.
The electrostatic field is governed by the Maxwell equations. At this stage, the assumption of steady-state condition is employed. According to this condition, the system of equations is reduced to
- Gauss lawwhere the electric field E is measured in , is the ionic charge density (), and is the permittivity of free space.(1)
- The gas ions are attracted to the grounded electrodes due to the Coulomb force, resulting in an electric current defined bywhere represents the ionic mobility in air, is the gas speed, and represents the ion diffusion coefficient. Typically, the diffusion term is neglected due to a lower impact on the charge transfer, but in this case, all the terms are included.(4)
The flow solver is validated on a test case proposed by Penney and Matick [7], and the used numerical setup is reported in Fig. 1, which was freely inspired by Feldkamp et al. [8]. The details of the results are reported in Sec. 3.1. The boundary conditions for the case are taken from Ref. [9], and it is of particular interest the condition imposed on the wire. Indeed, in order to have a boundary condition for the ion charge density it is necessary to respect the Peek condition, Eq. (5), which provides a value for at the onset of the corona effect, which remains constant increasing the potential. A new condition has been developed specifically for this case, that calculates in a way the gradient of the electrical potential is consistent with the Peek condition. On the other hand, this relation is valid only for cylindrical electrodes therefore for another shape the experimental tension-current characteristic of the apparatus must be implemented to retrieve the ion density.
2.2 Particle Charging.
2.3 Parcel Collision.
The collision models are implemented for the Spray cloud model of OpenFOAM, which derives from momentum, thermal, and reaction clouds. Two different state-of-the-art stochastic collision models are available in the traditional release: the O’Rourke [12] and Nordin [13] collision models.
The approach proposed by O’Rourke [12] is stochastic in its essence. Specifically, O’Rourke’s algorithms begin evaluating the probability that a single particle from one parcel will impact any particles from another parcel within a given control volume (i.e., finite volume cell). As the particles are assumed to spread homogeneously within the parcel, the collision probability of the parcel i colliding with parcel j is equal to the probability of presence within the collision cylinder, which is the volume ratio of the collision cylinder and the control volume. A Metropolis–Hastings algorithm is therefore employed to determine if a collision occurs or not based on its probability.
The collision model by Nordin [13] belongs to the hybrid approaches category. These algorithms generally are composed of two steps
Deterministic step: Potential collision partners are chosen based on their relative trajectory. In other words, to have a collision between two particles, they must be moving toward each other. Moreover, the parcels’ relative displacement must be larger than the distance between them. This constraint is intended to ensure that parcels are close enough that their motion could bring them together.
Stochastic step: The collision probability is determined by particle distance and displacement.
The deterministic collision model proposed in OpenFOAM is based on the work of Ref. [14]. In this case, particle collision occurs only if the parcels they belong to intersect their trajectory. The intersection is evaluated among cylindrical-shaped volumes whose base area is user-defined. In particular, the area can be equal to the particle or greater. This latter case is useful when more than one particle per parcel is considered, and a certain degree of packing is to be taken into account. Concerning the stochastic models, this approach is much more time-consuming when dense granular flows are to be kept into account. However, a detailed description of the impact can be obtained, and given the relatively low concentration of our application the resulting computational effort is acceptable. The outcome of the collision is evaluated on the particles’ characteristics and kinetics upon impact.
The deterministic model proposed by Tsuji et al. [14] is implemented for the momentum cloud library, and therefore all the other cloud types can benefit from this. The electrostatic properties have been added to the same cloud type and therefore we can easily add the electrostatic contribution to the force balance to be solved upon collision.
2.4 Force Balance Upon Impact.
- The elastic force, according to the Hertzian contact theory, is defined bywhere is the stiffness, is the deformation, and the exponent is user-selectable depending on the Hertzian theory (3/2) or linear (1). The stiffness is dependent on several material properties [14] for the proper definition.(14)
- The dissipative force is related to the coefficient of restitution of the particle viawhere m is the particle mass.(15)
- The Van Der Waals force stems from the instantaneous dipole-induced dipole interactions among adjacent apolar atoms and molecules, and it is an attractive force defined aswhere A is the Hamaker constant in J, is the effective radius in m, is the separation distance in m, and is the unit vector directed as the relative position of the particles.(16)
- The electrostatic force derives from the repulsion particles of equal charge exert. Upon impact, its value can be evaluated aswhere and are the charge of the particle and respectively.(17)
3 Results
In the first part of this section, the validity of the flow solver is evaluated using the test case supplied by Penny and Matick [7]. After that, the same test case is used to introduce the particles for the capability evaluation to induce the electrostatic force on them. Subsequently, the effect of humidity, number of wires, geometry, and power supply on the system capability is evaluated. At this point taking into account all the mentioned effects the final geometry of the filter is developed and numerically tested. At the end of the section, the performances of the optimal geometry in terms of capture efficiency, pressure drop, and flow pattern are discussed.
3.1 Validation of the Flow Solver.
Penney and Matick [7] have realized an experimental setup in which four cylindrical electrodes positively charged having a radius of 0.1524 mm are inserted in the midline of a channel. The geometrical information and the characteristics of the test case are reported in Table 1. Different simulations changing the DC power supply have been performed using a voltage between 25.5 kV and 43.5 kV.
Parameters for the numerical modeling of the experiment from Penney and Matick [7]
Parameter | Value |
---|---|
Wire radius (mm) | 0.1524 |
Wire-to-plate spacing (mm) | 114.3 |
Wire-to-wire spacing (mm) | 152.4 |
Voltage (kV) | 25.5–43.5 |
Number of wires | 4 |
Peek |
Parameter | Value |
---|---|
Wire radius (mm) | 0.1524 |
Wire-to-plate spacing (mm) | 114.3 |
Wire-to-wire spacing (mm) | 152.4 |
Voltage (kV) | 25.5–43.5 |
Number of wires | 4 |
Peek |
The test case is modeled with a two-dimensional and symmetrical geometry as shown in Fig. 1 a grid sensitivity analysis is performed, showing that convergence is reached also with a number of elements around 25,000. The mesh is generated with the open-source CFD suite cfMesh, supplied with the OpenFOAM-v2206 package. The validation proof is reported in Fig. 2, where it is shown the comparison between the experimental and numerical results of the electric potential at half length of the test case at various distances from the midline. All tested potentials and all measurement plans show very similar behavior and are not reported here for brevity. Experimental data and numerical ones are in excellent agreement for all the tested potential, therefore the flow solver can be considered as validated.
![Experimental (squares) [7] and computational (continuous line) results from this work for the 43.5 kV case measured at half of the length of the test section](https://asmedc.silverchair-cdn.com/asmedc/content_public/journal/turbomachinery/147/2/10.1115_1.4066817/1/m_turbo_147_2_021012_f002.png?Expires=1742301727&Signature=04~t3XVWXhU4jG4obQys3eDr9GWgFSxr0MtEwaLesfKykl2pgJCa-54X2snThG2wbJfT2rjLRP08F4VJMqCLyxAlBfUK5~9rfPtHz5~weJZKaMPLP5DIRmD~uZuLUKFP1-ov-DrHLjMkBt-JvCegump~OOYWjLZ9uowangxKDU3TjYekYougR0gEuTAfLr3o36tEACQHRiUKa53QBAoFgWaXeSyhJkRvNWXuuW1-TdhVthah3NGB5JrNc5nTG-d~zv4uytoep3~4ir2mGn5BjJYxoLYvoePFPVe8bk0eAIHY~X~rhJXnRSQy889ogicZZe0V2-ttOw70GXnWK3Xe8g__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Experimental (squares) [7] and computational (continuous line) results from this work for the 43.5 kV case measured at half of the length of the test section
![Experimental (squares) [7] and computational (continuous line) results from this work for the 43.5 kV case measured at half of the length of the test section](https://asmedc.silverchair-cdn.com/asmedc/content_public/journal/turbomachinery/147/2/10.1115_1.4066817/1/m_turbo_147_2_021012_f002.png?Expires=1742301727&Signature=04~t3XVWXhU4jG4obQys3eDr9GWgFSxr0MtEwaLesfKykl2pgJCa-54X2snThG2wbJfT2rjLRP08F4VJMqCLyxAlBfUK5~9rfPtHz5~weJZKaMPLP5DIRmD~uZuLUKFP1-ov-DrHLjMkBt-JvCegump~OOYWjLZ9uowangxKDU3TjYekYougR0gEuTAfLr3o36tEACQHRiUKa53QBAoFgWaXeSyhJkRvNWXuuW1-TdhVthah3NGB5JrNc5nTG-d~zv4uytoep3~4ir2mGn5BjJYxoLYvoePFPVe8bk0eAIHY~X~rhJXnRSQy889ogicZZe0V2-ttOw70GXnWK3Xe8g__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Experimental (squares) [7] and computational (continuous line) results from this work for the 43.5 kV case measured at half of the length of the test section
The lagrangian phase was validated against the experimental data of Parasram [15]. The experimental setup consisted of three electrodes with a diameter of with an applied electrical potential of 15 kV placed, as shown in Fig. 3. The inlet air velocity was . Figure 4 constitutes the proof of validation of the discrete part of the solver. In particular, it shows the transverse particle velocities along the flow direction at a distance of 5 mm from the collection plate. Near the wires, the transverse velocity of the particles reached its maximum values, while the minimum values were recorded between the wires, where the electric field was less intense. The obtained numerical trend was in satisfactory accordance with Parasram’s experimental data [15], as well as previous CFD works [16,17] reported in the same figure.
To assess the capture capability of the Penny and Matick system, the discrete phase is added within the domain after the flow field has converged. To perform the particle injection different parameters must be set. In the current work, the lagrangian feature reported in Table 2 is used. The diameter distribution under consideration was chosen based on Ref. [18]. The number of particles per second is selected to have a reasonable operation point of the test bench. This means a particle concentration of , therefore having a flowrates of , the resulting concentration is . Referring to the mean diameter of the normal distribution, each particle has a mass of . The final number of particles per second is equal to . Moreover, it is necessary to set the restitution factor on the boundary of the domain, in particular, a complete elastic rebound of the particles is set for all the surfaces (restitution coefficients were set to one), except the grounded one, in which a stick condition is imposed. Reasonably, the total amount of particles that remain trapped on the electrode will be higher than the amount of the rebounded ones, due to the effects of the electrostatic force, for this reason, the stick condition is applied to the grounded elements.
Details of the particulate employed in the current study
Parameter | Value |
---|---|
Particle density () | 2700 |
Particle per second | |
Type of distribution | Normal |
Mean diameter () | 1 |
Variance () | 0.5 |
Max. diameter () | 3 |
Min. diameter () | 0.5 |
Parameter | Value |
---|---|
Particle density () | 2700 |
Particle per second | |
Type of distribution | Normal |
Mean diameter () | 1 |
Variance () | 0.5 |
Max. diameter () | 3 |
Min. diameter () | 0.5 |
A comprehensive view of the situation in the channel is reported in Fig. 5. The flow field is only marginally affected by the presence of the electrostatic field, due to the relatively high velocity of the flow. On the other hand, the particles are sensitive to the electrostatic field. Two main phenomena occur: on the one hand, particles are accelerated toward the grounded plate, and this is testified by the presence of the y-component of U velocity in Fig. 5. In particular, as the distance from the wire increases, the acceleration in the y direction increases. On the other hand, the “strip” of particles injected was stretched in the flow direction. This fact is mainly due to the electrical field shape, which is reported in Fig. 6. The radial lines in proximity to the wire push the particles toward the grounded plate. However, they are also responsible for the streamwise acceleration and deceleration of particles. The variation of the electrical field direction and intensity moving from the wire toward the plate is responsible for the two effects previously mentioned.

Electrical field and particles: constant voltage isolines; ionic charge density contour; lagrangian particles
To evaluate the performance of the system two parameters are used for all the configurations:
Capture efficiency : this is the ratio between the number of particles that stick to the grounded electrode and the number of incoming particles. Even though this number is very useful, it should be kept in mind that the main objective of the ESP is particle agglomeration. Therefore, the capturing of particles is a desired outcome, which allows a fast evaluation of the performances.
Concentration number : it represents the number of particles per cell. This index is intended to substitute the collision evaluation, which requires an extremely high computational time. is introduced with the underlying idea that “Higher concentration will lead to higher collision and agglomeration.” The evaluation of this parameter required low computational resources, and therefore it can be considered as a performance index.
In the case of DC 43.5 kV applied on the electrodes, considering the non-bounce of the particle on the ground surfaces this configuration supplies a capture efficiency of 76.1% and a concentration number of . In the following, different configurations will be assessed, keeping in mind the final application within the filter house.
3.2 System Parameters’ Effects on the Electrical Breakdown.
In this section, the mechanism causing the electrical breakdown is discussed, moreover, the system parameters’ effects on this threshold are assessed. In particular, the effects on the electrical breakdown threshold due to the presence of not pure air, i.e., air with humidity or moisture, inside the system is evaluated. All these effects are taken into account to develop the best geometry and “electrical” configuration which gives the highest capture efficiency to pressure drop ratio and avoids the electrical breakdown.
The ESP works by applying a voltage across a dielectric (air), which separates the wire from the grounded plate. If such voltage becomes too high, the dielectric does not behave as an insulator any longer, but it rather becomes an electrical conductor, and a current flows through it. When this happens, the ESP is not active any longer, and the filtration mechanism is no longer effective. Moreover, this translates into the formation of a spark, which is highly unwanted in a classified environment.
An electrical breakdown occurs if the applied voltage is such that the electric field induced in the dielectric is greater than the dielectric strength. For dry air, this value is equal to . To numerically predict the onset of the spark, the authors identified a criterion based on this threshold: there should not be any connecting path between the positive wire and the grounded plate where the electrical field is entirely above the dielectric strength.
The dielectric inside the filter is not pure air, but it could be air with humidity or a flammable mixture. From a literature survey, it is reported that the effect of humidity is to increase the breakdown voltage [19]. This is essentially related to three different mechanisms
Attachment of water molecules to negative ions reduces the probability of finding a free electron at the right time to start the streamer discharge.
High absorption of UV radiation by water molecules which reduces the length of the electron avalanches in front of the streamer head. A higher field is therefore necessary for the propagation of the stream.
The relaxation time of nitrogen vibrations (excited by slow electrons) is reduced by increasing water vapor contents. So makes it more efficient to transfer energy from the electrical field to vibration and a faster heating of the streamer channel.
This is testified by the experimental data reported in Ref. [19] and shown in Fig. 7, where the breakdown voltage has been evaluated in a rod-plate configuration, increasing the humidity.
![Exp. DC breakdown voltage of a rod-plane air gap as a function of absolute humidity (a=50cm, θ=40∘C) [19]](https://asmedc.silverchair-cdn.com/asmedc/content_public/journal/turbomachinery/147/2/10.1115_1.4066817/1/m_turbo_147_2_021012_f007.png?Expires=1742301727&Signature=nJtutPLzAt5AMns20-OR~x7vLiHdPIgzOonI5eXM1ighXz2UEFDHaG8tNZqAMUX4QuK8a6ylUdN~I1wXZ3uRDTgACyzQa~Lfgtcx2ky5Lna2YNt9RO7oiyGxM4EpHAVe2NMgOJ81Ev1KK6cYvCsbLcMGbIrnxiYY9YHAYU05xaRIprAkPWtmMNQ5R3yio9283jSCOyKieKiL5WSjGf53H2VPbFjV8LdzKIu7aBi~Y8uh86UC1eB8yiLn02IeQJzb5LBS069YdBTbJc2hdIAsXKaf7mRPJXYrgMgdFksCwTEi4Q4yqXq4RwbUKtGXClQZMCH02qRJ-QoEONQC7V6Xtg__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Exp. DC breakdown voltage of a rod-plane air gap as a function of absolute humidity (, ) [19]
![Exp. DC breakdown voltage of a rod-plane air gap as a function of absolute humidity (a=50cm, θ=40∘C) [19]](https://asmedc.silverchair-cdn.com/asmedc/content_public/journal/turbomachinery/147/2/10.1115_1.4066817/1/m_turbo_147_2_021012_f007.png?Expires=1742301727&Signature=nJtutPLzAt5AMns20-OR~x7vLiHdPIgzOonI5eXM1ighXz2UEFDHaG8tNZqAMUX4QuK8a6ylUdN~I1wXZ3uRDTgACyzQa~Lfgtcx2ky5Lna2YNt9RO7oiyGxM4EpHAVe2NMgOJ81Ev1KK6cYvCsbLcMGbIrnxiYY9YHAYU05xaRIprAkPWtmMNQ5R3yio9283jSCOyKieKiL5WSjGf53H2VPbFjV8LdzKIu7aBi~Y8uh86UC1eB8yiLn02IeQJzb5LBS069YdBTbJc2hdIAsXKaf7mRPJXYrgMgdFksCwTEi4Q4yqXq4RwbUKtGXClQZMCH02qRJ-QoEONQC7V6Xtg__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Exp. DC breakdown voltage of a rod-plane air gap as a function of absolute humidity (, ) [19]
Regarding the effects of explosive mixture, from a literature survey, no clear values have been found for electrical breakdown voltage, especially for a flammable mixture. However, some considerations can be required if methane is used as an insulator in electrical components since the breakdown voltage is not reduced by the presence of methane itself. Based on all these considerations, it is reasonable to assess that the breakdown voltage of dry air (i.e., ) is a value in the advantage of safety, and therefore this threshold is considered for the application.
3.3 Development of the Final Configuration.
A parametric study is carried out on the filter geometry in order to understand the best layout that maximizes the capture efficiency, minimizes the pressure losses, and keeps the ESP far from the electrical breakdown. Several different layouts are tested to assess the best solution. Also, the voltage is changed to evaluate the impact on the separation efficiency and the breakdown voltage. The starting geometry is reported in Fig. 8, where only a single wire is applied on the head of the circular element highlighted with a line in the figure.
The device is tested in the inertial-only configuration with an inlet velocity of and a relative pressure outlet equal to 0 Pa. Under these conditions, the pressure losses due to the presence of the filter are about 35 Pa. However, when the particle distribution, reported in Table 2 is injected at the inlet of the domain, a capture efficiency of 0% is detected. After that the device is tested in the combined inertial-electrostatic configuration, using a supply voltage of 45 kV on the electrodes, and an imposed zero potential on the grounded surfaces. Moreover, the same wire diameter of the Penney and Matick test case [7] is used (i.e., 0.154 mm) for the positive electrodes. Within this configuration, the capture efficiency is approximately 90% while the pressure drop is partially recovered by means of the electrostatic force on the continuous phase.

Initial geometry of the ESP: velocity magnitude contour and streamline plot, dot represents the position of the positive wire
The effect of a different geometry is investigated by acting on the spacing between the filter elements, reducing the channel width, and increasing its curvature. Having a constant inlet velocity of , the modification of the geometry translates into an increase in the meridional velocity and into a small recirculation. The inertial effects are increased by the mean velocity inside the channel and by the particles’ diameters but the smaller recirculation reduces the residence time of particles inside the filter, thus reducing the agglomeration probability and the consequent efficiency of the inertial separator. Regarding the inertial effects, a smaller residence time inside the filter means a lower deflection of the particles (and of the air) if the electrical field does not change.
The two effects highlighted are predominant with respect to the gain in inertial separation, and therefore, all the solutions that aim to accelerate the flow generate a lower separation efficiency. Based on these considerations, the initial geometry of the ESP was modified as reported in Fig. 10, with this new configuration the capture efficiency increased to 97% while the pressure drop remained practically unchanged. Figure 11 reports the electrical field trend over the shortest path between wire and plate obtained with a voltage equal to 45 kV. From this picture, it is clear how the electrical field is much greater than the threshold (dashed line in the figure) in the proximity to the wire. However, starting from it, the field decreased sharply and remained well below the threshold for roughly 90% of the channel width. This is expected, as the voltage is remarkably high at the wire surface, and then decreases quickly in the bulk of the domain. Being the electrical field the gradient of the scalar field voltage, its behavior follows the variation of such scalar field.

Optimal geometry of the ESP: velocity magnitude contour and streamline plot, the dot represents the position of the positive wire
The behavior reported in Fig. 11 should ensure a safe operation of the filter, with a separation efficiency equal to 97%. The idea is to reduce as much as possible the voltage keeping a high separation efficiency. To this end, two simulations with 30 kV and 20 kV applied to the positive electrode are performed. However, the performances of both cases are not satisfactory, showing a separation efficiency of 57.3% and 27.7% respectively. Interestingly, a linear dependence is found between the separation efficiency and the voltage applied within this configuration.
3.4 Effect of the Number of Wire.
The opportunity of having a higher number of wires is tested. There are two possible locations on the device where the wires can be installed, the external surfaces of the terminal cylinders. Placing the wire in this spot will maximize the electrostatic field as it encounters minimal obstruction and can spread in the radial direction. Consistently, it is required to choose which surfaces to ground and which ones to keep insulated. The chosen layout is reported in Fig. 12, where the wires are highlighted with thick lines.
A careful look will also show the presence of the wires on the insulated surface of the cylinders. The insulation in proximity of the wires is required to avoid “short circuits” of the electrical field. The resulting flow and electrical pattern inside the filter are reported in Fig. 13. It can be clearly seen that both the electrodes contribute to enforcing the inertial effect by pushing flow and particles toward the grounded plates and therefore promoting separation. The proposed configuration increases only slightly the separation efficiency up to 98% with 50 Pa of pressure losses. The redundancy offered by the second wire in case of failure is the reason why this solution is considered the optimal one.

Optimal geometry of the ESP with two electrodes: surface convolution lines representing the electrical field, velocity magnitude contour, and dots represent the position of the positive wires
4 Conclusions
The developed Lagrangian solver takes into account the effects of the electrostatic field on both continuous and discrete phases. It is validated by means of literature works. After the tool validation, the possibility of using an electrostatic separator to separate solid contaminants transported by airflow is tested by adding a particle injection to the validation case. The injected particles are selected in order to replicate the real condition present at the inlet of a gas turbine. The test case shows a capture efficiency that increases as the applied voltage increases. With a DC potential of 43.5 kV, which represents the maximum value that does not create an electrical breakdown, a capture efficiency of 76.1% is reached. The obtained value is not satisfactory, taking into account the usual filtrating performances for the filtration systems used inside a gas turbine (). For this reason, a coupling between an inertial configuration and an electrostatic one is evaluated. Different geometries with different electrical configurations are tested to find the best setup that gives the highest capture efficiency with the lowest pressure drop and avoids electrical breakdown. Finally, the optimal developed configuration has two wires on which an electrical DC potential of 45 kV was applied. With this setup, only a pressure drop of 50 Pa is predicted, which is very low compared to the traditional pressure drop for a high-efficiency filter (between 100 Pa and 1500 Pa). In conclusion, the new electrostatic solver developed in OpenFOAM for simulating ESP in gas turbine intake applications is validated against a simplified experimental setup. Further experimental investigations would be useful to validate its capabilities in predicting capture efficiency also for full-scale filter elements used in real applications.
Conflict of Interest
There are no conflicts of interest.
Data Availability Statement
The authors attest that all data for this study are included in the paper.
Nomenclature
- e =
electron charge
- m =
particle mass
- s =
separation distance for the calculation of
- A =
Hamaker constant
- E =
electric field
- J =
electric current
- K =
ionic mobility in air
- T =
temperature
- V =
electric potential field
- =
particle diameter
- =
cylindrical electrode radius
- =
particle i diameter
- =
distance between particles i and j
- =
ion diffusion coefficient
- =
electric field using the Peek condition
- =
Van der Waals force
- =
dissipative force
- =
electrostatic force
- =
resulting force exchanged between the i and j particle
- =
elastic force
- =
Boltzmann’s coefficient
- =
particle stiffness
- =
number of particles injected per second
- =
collision probability between particle i and j
- =
particle electric charge of the particle i
- =
electric saturation charge
- =
gas speed
- =
unit vector directed as the relative position of the particles i and j
- =
effective radius for the calculation of
- =
particles concentration
- DC =
direct current
- EPA =
efficiency particulate air filter
- ESP =
electro static precipitator
- GT =
gas turbine
- HEPA =
high efficiency particulate air filter
- UPLA =
ultra low penetration air filter
- =
particle deformation
- =
dielectric permittivity of free space
- =
particles relative magnetic permittivity
- =
capture efficiency
- =
concentration number
- =
ionic charge density
- =
charging time constant