coronaChargingFoam: An OpenFOAM based solver for multi-physical simulations of direct unipolar diffusion charging of aerosol particles☆,☆☆
Introduction
The need to electrically charge aerosol particles has increased dramatically over the last few decades in various fields including pollution control [1], [2], material preparation [3], separation technology [4], [5], and aerosol measurements [6], [7], [8]. Aerosol particles may acquire charges through flame charging, static electrification, diffusion charging, and field charging, among which the diffusion charging is the most common mechanism for charging ultrafine particles (with diameter less than 0.2 μm) [9]. This method requires a continuous production of high enough concentration of unipolar ions, usually achieved by corona discharges, which generally takes place around a thin wire or a sharp-needle electrode. A common corona charger comprises a needle-plate configuration into which the aerosol particles enter and in direct contact with the discharge electrodes, formally called “direct corona charger” [10]. Great effort has been made to increase the charging efficiency of this kind of chargers all the time [11], [12], [13], [14], [15], [16], [17]. Understanding their charging mechanism affected by various physical fields, as a part of aerosol dynamics [18], [19], is extremely important for the optimization of chargers and prediction of particle evolution in particulate systems.
Fluid flow, aerosol charging, gas discharge, and heat transfer are highly coupled in a direct unipolar diffusion charger employing corona discharge because of nonlinear dependence of charging process on the distribution of flow velocity, ion density, and temperature [20]. Fig. 1 schematically illustrates the phenomena of charging process occurring in a direct unipolar diffusion charger. Corona discharge takes place in the thin layer (ionization zone) around the surface of the needle anode due to the sufficiently high field strength in this region, where electrons are accelerated to sufficiently high velocities and their collisions with air molecules lead to the creation of more positive ions. The corona may be operated with the needle electrode held at a high positive potential or at a negative potential. The positive corona is frequently used to charge aerosol particles because it produces less O3 than negative corona [9]. In this type of chargers, the positive ions will stream away from the needle to the plate in high concentrations owing to the electric field built between the positive needle and the grounded plate. During the migration process, they will collide with aerosol particles, introduced by aerosol flow between the needle and the plate, attach to them and form charged particles. Meanwhile, heat transfer arises as a result of current flows and heat exchange in the space. Due to the complex coupling among so many phenomena associated with corona discharge and particle charging, the numerical methods capable of accurately characterizing the working mechanism of direct chargers are still far from perfect.
Research has been conducted on the modelling of indirect unipolar diffusion chargers [21], [22], [23], where the unipolar diffusion charging and gas discharge take place in different regions. While in a direct charger, heat transfer and electromigration of charged particles may couple with gas discharge and particle charging processes since they occur in the same place. This may induce a more complicated model. Some parts of the coupling fields in the direct unipolar diffusion charger have been presented in previous studies. For instances, Go et al. [24] and Cagnoni et al. [25] conducted multi-physical simulations of corona discharge and flow to describe the heat transfer enhancement induced by ionic wind employing a staggered solution algorithm. Zhao and Adamiak [26] solved the coupled electric field and gas flow for a corona discharge between a needle and a plate using a hybrid numerical algorithm based on boundary-element method and Finite-element method. Zakari et al. [27] developed a Finite-volume method based on unstructured triangular meshes to numerically model gas discharge and verified its feasibility in a point-to-plane geometry. Yang et al. [20] used the commercial software Comsol to solve the coupled equations of fluid model of gas discharge and Poisson equation. Their method and results were helpful for improving the charging efficiency of aerosol particles in a narrow channel of corona discharge. Verma and Venkattraman [28] developed an OpenFOAM solver, SOMAFOAM, to simulate low-temperature plasmas in the continuum regime.
In this work, we introduce a solver called coronaChargingFoam based on the framework of OpenFOAM in order to simulate the various fully-coupled phenomena in a direct unipolar diffusion charger. OpenFOAM is a widespread open source library toolbox organized by C++ syntax by which models of several physical fields, such as fluid flow, heat transfer, and magnetic field are provided [29], [30]. It has already been employed to carry out multi-physical simulations in a variety of areas including corona discharge [25], detonation [31], polyurethane foams [32], combustion [33], nuclear reactor [34], direct ultraviolet photoionization[35], indirect unipolar diffusion charging [22], [23], and aerosol nucleation [18]. Similar to the purpose of these solvers, coronaChargingFoam aims to provide an open-source platform on which researchers may analyze the complex interplay among the phenomena in direct diffusion chargers, predict the particle evolution, and find the method of improving charging efficiency. The symbols of physical quantities, parameters and their values, subscripts and superscripts used in this paper are summarized in Table 1, Table 2 and Table 3, respectively.
Section snippets
Corona discharge
The problem depicted in Fig. 1 is three-dimensional in a strict sense, but here we simplified it into a 2D model in order to compromise between accuracy and efficiency following a previous study [25]. For the corona discharge and particle charging process given in Fig. 1, the thickness of the ionization layer around the anode is much smaller than the scale of the migration region according to Townsend model of gas discharge, and therefore this region is replaced by a portion of the anode
Finite-volume discretization of the governing equations
In this paper, we concentrate on the small direct chargers. The diameter of the needle is 40 μm and the gap distance between the anode and the cathode is several hundreds of microns. Following the finite-volume discretization, we decompose the computational domain in Fig. 2 into hexahedral elements. Fig. 3 presents a cross-section of the entire decomposed domain. The next step of the Finite-volume method (FVM) is discretizing the governing equations over each control volume. The one within the
Solver validation
A complete file structure of the OpenFOAM cases to implement the solver coronaChargingFoam is shown in Fig. 7. The file “physicalProperties” provides the values of the concerned isotropic coefficients and constant parameters used in the case study. The files stored inside the directory “0” are used to specify the initial and boundary conditions for all the variables defined at the beginning of the simulation. The “system” directory contains four files in which: “controlDict” sets the values of
Conclusion
This study focuses on the development of an open-source solver for simulations of direct unipolar diffusion charging of aerosol particles. The governing equations of the multi-physical processes in this type of chargers are modelled by incorporating the phenomena of corona discharge and aerosol diffusion charging in the continuum regimes. Based on the finite volume schemes, the governing equations are discretized and transformed into a system of linear algebraic equations. A solver named
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
The authors would like to acknowledge the useful discussions about the charging mechanism with Dr. Robert T. Nishida and Dr. Adam M. Boies from University of Cambridge.
Funding. This work was supported by Beijing Natural Science Foundation under Grant 3214048 and the National Natural Science Foundation of China under Grant 52005033.
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The review of this paper was arranged by Prof. Hazel Andrew.
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