Fluid model for a partially packed dielectric barrier discharge plasma reactor

In this work, a two-dimensional numerical fluid model is developed for a partially packed dielectric barrier discharge (DBD) in pure helium. Influence of packing on the discharge characteristics is studied by comparing the results of DBD with partial packing with those obtained for DBD with no packing. In the axial partial packing configuration studied in this work, the electric field strength was shown to be enhanced at the top surface of the spherical packing material and at the contact points between the packing and the dielectric layer. For each value of applied potential, DBD with partial packing showed an increase in the number of pulses in the current profile in the positive half cycle of the applied voltage, as compared to DBD with no packing. Addition of partial packing to the plasma-alone DBD also led to an increase in the electron and ion number densities at the moment of breakdown. The time averaged electron energy profiles showed that a much higher range of electron energy can be achieved with the use of partial packing as compared to no packing in a DBD, at the same applied power. The spatially and time averaged values over one voltage cycle also showed an increase in power density and electron energy on inclusion of partial packing in the DBD. For the applied voltage parameters studied in this work, the discharge was found to be consistently homogeneous and showed the characteristics of atmospheric pressure glow discharge.


I. INTRODUCTION
2][3] The non-equilibrium nature of DBD provides major advantage, by allowing operation at atmospheric pressure and ambient conditions.This helps to overcome the thermodynamic barriers in chemical reactions and provides high reactivity at room temperatures. 4,5In cases, when the packing material is a catalyst, the so called "plasma-catalysis" provides a synergistic effect and also helps to improve the selectivity towards desirable products. 2,6Additional features such as easy operation, moderate capital cost, and simple scalability have led to extensive research on packed bed DBDs. 74][15] This unfavorable response has been shown to be related to packing configuration and the void fraction of the discharge in the packed bed DBD. 16It has been observed that in a fully packed DBD, which provides a very low void fraction, the packing leads to a significant change in discharge behaviour.7][18] Suppression of the filamentary discharges in a fully packed DBD was suggested to be responsible for the negative performance. 16An alternative packing configuration, in which the packing material (catalyst particles or dielectric pellets) are placed along the bottom of the dielectric barrier layer over the entire length of the discharge (partial packing), was evaluated. 16,19,20It was found that such a packing configuration provided a large void fraction and exhibited strong filamentary microdischarges in the discharge gap without causing any significant change to the discharge mode.Partially packed DBD thus induces effective plasma-catalyst interactions, which may generate a synergistic effect and hence promote plasmacatalytic chemical reactions. 16,19,20mprovement of performance in either partial or fully packed bed DBD is typically attributed to the effective polarization and enhanced electric field strength at the contact points and in some cases to the synergistic effect of plasmacatalysis; however, the exact fundamental mechanisms are still not fully understood. 16,21,223][24] However, experimental studies have their limitations in terms of parameters that can be accurately measured during plasma operation, and the packing itself adds an extra impediment in visibility for optical/laser analysis.While such experimental diagnostic studies are indispensable, we believe computational modeling can be used as a complementary tool to optimize the system in a directed way, providing more quantitative process-parameter relationships. 2530][31][32][33] Takaki et al. 31 developed a one-dimensional physical model for ferroelectric packed bed barrier discharge reactor in a pure nitrogen environment and found that all the plasma parameters increase linearly with applied ac voltage and pellet dielectric constant.Kang et al. 26 carried out a numerical study of ferroelectric packed discharge (FPD) using a 2 D finite-element method (FEM) model considering single and double pellet cases.Their model however did not include any plasma chemistry and was limited to nano-second time-scale.Russ et al. 30 developed a 2D fluid model for a packed bed DBD filled with synthetic, dry exhaust gas (80% N, 20% O, and 500 ppm NO) at atmospheric pressure for simulation of transient microdischarges based on the so-called "donor cell" method.While this study included comprehensive plasma chemistry, it presented very short one-directional discharge (of a few 10s of nanoseconds) with limited results of spatial electric field and electron density distributions. 30Van Laer and Bogaerts 21 developed a fluid model for a packed bed dielectric barrier discharge plasma reactor using two complementary axisymmetric 2D geometries and pure helium gas plasma chemistry.Their results showed enhancement in electric field and electron energy due to effective polarization of the beads in the packed bed.They also observed a change in discharge mode (from Townsend to glow mode) on increasing the applied potential.In a later study, Van Laer and Bogaerts 32 studied the influence of the dielectric constant of the packing on the plasma characteristics, for two different gap sizes using a 2D axisymmetric fluid model.They observed that a stronger discharge is obtained in a microgap reactor and that increasing dielectric constant of the beads enhances the electric field strength but only up to a certain extent.In addition to fluid models, some other modelling strategies have also been used to study the propagation of microdischarges in packed bed DBD, such as 2D particlein-cell/Monte Carlo technique, multi-fluid simulator nonPDPSIM code, etc. 27,33 Although fully packed DBD systems have been well investigated both experimentally and numerically, the same cannot be said about partially packed DBDs.Therefore in this work, for the first time, we have developed a 2D fluid model to understand the discharge characteristics in a partially packed DBD and compared the discharge parameters with that of a plasma-alone DBD reactor with no packing.
The paper is structured as follows: geometry and mathematical model used in the analysis including the respective governing equations and boundary conditions are described in Sec.II.Results obtained from the analysis, including the discharge current profiles, spatial distribution profiles of electric field strength, electron and ion density, and time averaged electron energy plots are presented and discussed in Sec.III.Section IV summarizes the final conclusion of this study.

A. Geometry
In this work, the co-axial DBD plasma reactor is modeled using a 2-D fluid model in COMSOL Multiphysics. 29he model is applied to a cylindrical DBD reactor with two co-axial metal cylinders as electrodes.The inner electrode is connected to a high voltage AC power supply and the outer electrode is grounded.The diameters of the internal and external cylinders of the DBD reactor are 16 mm and 23 mm, respectively.The outer electrode is covered (on the inside) with a 1.5 mm dielectric barrier layer of alumina (relative permittivity, r ¼ 9).The discharge is sustained in the 2 mm co-axial gap between the inner electrode and the alumina layer.The length of the electrodes is 100 mm.These dimensions represent a generic geometry, based on the wide range of DBD reactors with different discharge gaps, dielectric layer thickness, and electrode lengths that have been used as chemical reactors in several experimental studies. 20,34,35he partial packing approach 16,19,20 has been adopted in the work and a layer of catalyst particles is packed along the bottom of the discharge tube (on top of the dielectric layer).Ni-Al 2 O 3 ( r ¼ 50) is used as a representative packing particle in the model. 14,16,36Particles are assumed to be perfectly spherical for simplicity, and unless mentioned otherwise, the particle diameter is 1 mm.Also as the particles are fixed on the top of the dielectric layer using quartz wool, it is assumed that the particles are not touching the surface with a point edge.While the fixing material (such as quartz wool) may have an effect on the plasma discharge, such an effect is neglected in this analysis.A 3D representation of a section of the partially packed co-axial DBD reactor is shown in Fig. 1.
A full 3D simulation of the DBD will be able to replicate the real system and provide a thorough understanding of the effect of packing on the discharge behaviour.However, due to complexity of the equations involved and considering the current computational constraints, it will be impractical to run a 3D simulation. 21Thus, in this study, we have used a representative 2D model by considering a small section of the DBD reactor, which includes the inner and outer electrode boundaries, the discharge gap, dielectric barrier, and two packing particles.The final 2D geometries of the DBD FIG. 1. 3D representation of the partially packed co-axial DBD.

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Gadkari, Tu, and Gu Phys.Plasmas 24, 093510 (2017) (both with and without catalyst packing) used in the model are shown in Fig. 2. Symmetry of catalyst particles aligned axially is used, and only half section of the each catalyst is represented [Fig.2(a)].The selected geometry helps in reducing the computational size of the model while also allowing to analyze the discharge in the region between two particles.
The typical target molecules in gas cleaning applications in co-axial DBD reactors are NOx, SOx, CH 4 , CO 2 , Toluene, Naphthalene, etc.However, the plasma chemistries of these molecular gases frequently involves tens of species and hundreds or even thousands of reactions including the electron impact, electron-ion recombination, neutral-neutral, ion-neutral, and ion-ion reactions. 24,37Solving fluid models with such complex chemistries is computationally very expensive, particularly on a 2D geometry.Thus, in this study, we have decided to use pure helium as the discharge gas.Helium has a relatively simpler plasma chemistry, low breakdown voltage, and ionizes easily to form a stable homogeneous glow discharge, which is easier to simulate using a fluid model, as opposed to the filamentary discharge typically observed with molecular gases. 4,38,39These factors further help in reducing the model size and the computational cost, thereby providing more leverage in performing a longer study over more periods of applied potential such that stable behaviour can be studied.It should be noted that the difference in discharge performance between helium and molecular gases also limits the applicability of the current model.However, using helium is a good starting point and helps in expanding our understanding of the partially packed DBDs, which will be useful in future investigations of the same.

B. Governing equations and boundary conditions
Governing equations describing the fluid theory originate by solving a set of moments of the Boltzmann equation. 4ypically, for most applications, the first three moments are considered, which describe the particle, momentum, and energy conservation.By taking these moments, the Boltzmann equation is reduced to a 3-dimensional, time dependent problem and describes the plasma in terms of averaged quantities such as density, momentum, and mean energy. 4,40he zeroth moment of the Boltzmann equation gives the continuity equation describing the rate of change of particles (electrons, ions, or neutral species) The subscript p refers to different species such as electrons, ions, or neutral species.n represents the density of species, C represents the flux vector, and R p represents either the source/ sink term and accounts for the production or loss of a particular species p in chemical reactions, ionization events, etc. Losses at the walls are accounted in the boundary conditions and are not explicitly considered in the particle continuity equation.
In the fluid model, the first moment of the Boltzmann equation is not solved explicitly but is replaced by another simplification known as the drift diffusion approximation, 4,40 which is used to derive the flux term in Eq. (1).
Flux term for the particles (based on drift-diffusion approximation) consists of a diffusion term and a drift term, given as where E refers to the electric field, l and D refer to the mobility and diffusion coefficient of the species, respectively, and their values have been taken from Ref. 21.The first term of Eq. ( 2) is zero for the neutral species.Source/sink term, R p , is calculated as where c p represents the stoichiometric coefficient and r p represents the reaction rate of the target species for reaction j.
The second moment of the Boltzmann equation is used to derive the energy conservation equation.The final expression for rate of change of electron energy density including the drift diffusion approximation is described as where n is the electron energy density, and R is the energy loss/gain due to inelastic collisions.The flux vector for electron energy C is given as A self-consistent electric field distribution is calculated by solving the Poisson's equation [Eq.( 6)] in the plasma region and the Laplace's equation [Eq.(7)] in the dielectric material.
À r Á 0 r rV ¼ q; (6) where 0 is the permittivity of free space, r the relative permittivity, q the space charge density (C/m 3 ), and V the applied potential.Surface charge accumulation on the dielectric layer due to difference in fluxes between the electrons and ions is taken into account using the following boundary conditions: where n is the unit normal, q s is the surface charge density, D1 and D2 are the electric displacement fields on both sides of the boundary, and Ji and Je are the total ion and electron current densities at the wall.
A set of 23 reactions involving helium atoms (He), ions (He þ and He þ 2 ), metastables (He Ã and He Ã 2 ), and electrons is used in the model. 21At the walls, helium metastables quench and change back to neutral helium atoms.Helium ions also change back to neutral helium atoms while emitting secondary electrons with emission coefficient of 0.05 and mean energy 5 eV. 21Gas temperature is assumed to be constant at 300 K. Discharge is driven by applying a sinusoidal electric potential to the inner cylinder with different values of applied voltage amplitude at a fixed frequency of 20 kHz.Initial densities of electrons and ions are assumed as spatially uniform and set as 10 14 m -3 .
A sinusoidal electric potential (V) is applied to the top boundary (inner electrode) where V 0 is the applied peak voltage and x is the angular frequency.The RF frequency value is kept constant at 20 kHz.
The electric potential at the exterior boundary of the dielectric barrier (bottom boundary) is 0 V.

III. RESULTS AND DISCUSSION
The model developed in this study is first validated with an experimental result published in a previous study by Tu et al. 41 for a helium DBD. Figure 3 shows the comparison of discharge current profiles obtained from an experimental study 41 with that predicted by the model developed in this study for a helium DBD with no packing with the same set of operating parameters and reactor geometry.Since the 2D simulation is being performed on a small section of the coaxial DBD reactor, it should be noted that the predicted value of current obtained from the simulation needs to be multiplied by a factor to account for the total height and circumference of the reactor.Also, the model was run until stable predictions could be obtained, and in this particular case, the simulation predictions had stabilized by the 3rd period of applied voltage.The predicted discharge current profile shown in Fig. 3(b) is that obtained for the 4th period of applied voltage.As can be seen from Fig. 3, the predicted discharge current profile may not exactly overlap the one observed in the experimental study, and still reasonable agreement is obtained between the two.Also, the magnitude of current and the position of the major current peaks in the positive and negative half cycles of applied potential predicted by the numerical analysis are in fairly good agreement with that obtained from the experimental study.This is particularly encouraging, as real systems typically have at least some fraction of impurities in the helium gas, whereas in the model we have assumed a pure helium discharge gas.For DBD with partial packing, the numerical results cannot be directly compared with experimental studies at this point, as all the reported studies on partially (axial) packed DBDs have used molecular gases 16,19,20 and not helium.However, we have attempted to draw qualitative comparisons of discharge characteristics with relevant experimental studies, as the results are discussed ahead.
Results obtained from the numerical analysis, comparing the plasma-alone DBD with a DBD with partial packing, are presented next.Figure 4 shows the discharge current profiles in helium DBD without any packing and with partial packing during one cycle of the applied potential of 3 kV peak-to-peak at a frequency of 20 kHz.As can be seen from Fig. 4(a), for helium DBD with no packing, the current profile exhibits a single distinct pulse in both the positive and negative half cycle of the applied voltage.Such a current profile is characteristic of helium DBD operating under homogeneous mode and is referred to as the atmospheric pressure glow discharge (APGD). 42This will be further confirmed ahead, as we discuss the typical electron and ion densities observed in APGD.It should also be noted that the current profiles for DBD with no packing, for frequencies 20 kHz [Fig.4(a)] and 60 kHz [Fig.3(b)], are quite different.At a higher frequency, 60 kHz, the current profile exhibits a sinusoidal shape, much different from the standard pulse-like waveform observed for atmospheric DBDs. 38Such a distinct difference in current profiles at higher frequencies has been observed before 43,44 and has been attributed to the constant production of charged particles due to continuous existence of excited species at higher frequencies. 44n inclusion of partial packing, discharge current profile [Fig.4(b)] changes in the positive half cycle, showing two current peaks (of successively decreasing amplitude).These current peaks are marked 1 and 2 in the Fig. 4(b).Helium DBD exhibiting multiple pulses in the discharge current profiles is said to be operating as pseudo-glow discharge. 45Such an increase in current peaks on inclusion of catalyst packing in helium DBD has been previously observed by Tu et al. 41 for a DBD with radial partial packing of Al 2 O 3 compared to DBD with no packing.Tu and Whitehead 16 also observed an increase in current pulses with radial and axial partial packing of Ni/c-Al 2 O 3 in co-axial DBD reactor during dry reforming of CH 4 .The increase in current pulses is typically attributed to the increase in charge density due to additional charge deposition on the surface of the catalyst packing material. 16,41The discharge ignites once the gap voltage reaches the breakdown voltage and extinguishes once the gap voltage falls below the breakdown voltage.This is expressed in the current signal in the form of a peak.Multiple peaks occur due to multiple breakdown in a single voltage cycle, 38,45 which can happen if the gap voltage crosses the breakdown voltage more than once in one cycle.Large accumulation of charges increases the external voltage significantly, making multiple breakdowns feasible. 46n addition to undergoing this transition from single peak to multi-peak behaviour in the positive half cycle of applied voltage, the amplitude of the current pulses for DBD with partial packing also increases in comparison to DBD without any packing.This signifies a stronger discharge and is in accordance with previously reported studies, 16,41 where a slight increase in current amplitude is observed on use of catalyst packing.
Figures 5-8 show the electric field strength, space charge density, electron number density, and ion number density distributions at the moment of breakdown during the positive half cycle of the voltage period, corresponding to times shown in Fig. 4. Accordingly, in these three figures, we obtain one distribution profile (a) for the DBD with no packing and two distribution profiles [b(i) and (ii)] for DBD with partial packing.As can be seen in Figs.8][49] As expected three distinct regions are observed between cathode to anode, namely, cathode fall, negative glow space, and positive column region.In Fig. 5(a), at the point of breakdown, the electric field is maximum at the instantaneous cathode, and linearly decreases in the cathode fall region.Following this, it decreases to its lowest point in the negative glow region, then rises subsequently to an intermediate value and remains uniform in the positive column region.Electron density profile, as seen in Fig. 7(a), shows a distinct cathode fall region near cathode at the moment of breakdown, where a low intensity electron density region is observed.Accordingly, ion density is maximum near the cathode and is higher than the maximum electron density at the moment of breakdown, as can be seen in Fig. 8(a).The intensification is maximum when the electric field is perpendicular to the surface of the solid object. 50,51In the given configuration of the DBD and spherical packing particles, this enhancement in electric field occurs at the vertical poles, which is the top surface of the particles and a region of low electric field strength can be observed in the area between the two particles where the distance between them is minimum (this is the equatorial plane in the given configuration).
On the other hand, at the moment of second breakdown, the electric field strength is maximum at the contact points between the packing particles and dielectric barrier, as can be seen from Fig. 5(b-ii).This enhancement is typically attributed to increased charge deposition due to more effective polarization at the packing and dielectric barrier surfaces.Similar enhancement in electric field strength at the poles of packing material and at the contact points between packing and dielectric layer has been reported in previous studies on packed bed DBDs. 21,26,27,32,50,52igure 6 shows the spatial distribution of space charge density (cm -3 ) at the moment of breakdown during the positive half cycle of the voltage period, for DBD with no packing and with partial packing, corresponding to the breakdown moments during the positive half cycle of the applied voltage as shown in Fig. 4. As can be seen from Fig. 6, the space charge density corresponding to the two current peaks for DBD with partial packing is consistently higher than that obtained for DBD with no packing, which also suggests an improvement in ionization by the addition of partial packing at the same applied potential.The main contribution to the space charge comes from positive ions, and at the moment of breakdown for DBD with no packing, high density of space charge is located near the dielectric layer.For DBD with partial packing, however, at the moment of first peak, the maximum space charge is located at the top surface of the packing beads [Fig.6(b-i)], corresponding to the high electric field strength at this point.The accumulated charge then moves away from the top surface towards the space between the beads near the dielectric layer, and a second maxima of charge density is obtained at moment of second breakdown [Fig.6(b-ii)].Here, the space charge density decreases slightly but manages to induce an electric field such that the gap voltage reaches the breakdown voltage again, within the same voltage period causing a second breakdown.
Figures 7(b-i) and 7(b-ii) correspond to the electron density distributions at the two breakdown moments during the positive half cycle of the applied voltage as seen in Fig. 4(b).At the moment of first breakdown for DBD with partial packing, a distinct low electron density region extends from the dielectric barrier surface up to the top surfaces of the packing particles, in a shape reminiscent of the electric field distribution as seen in Fig. 5(b-i).This area exhibits characteristics of the cathode fall region and the distinct pointy knob shape of this region is probably obtained due to electric field distortion caused by the curvatures of the adjacent spherical packing particles.After this cathode fall region, the maximum electron density is obtained at the top surface of the two particles [Fig.7(b-i roughly about one order of magnitude higher than that observed at the breakdown for DBD with no packing [Fig.7(a)].It should also be noted that the maximum electron density at the moment of first breakdown ($3 Â 10 12 cm -3 ) is slightly higher compared to that at the second breakdown ($2.5 Â 10 12 cm -3 ) for DBD with partial packing.Comparatively, the maximum electron density for DBD with no packing ($5 Â 10 11 cm -3 ) is lower than the maximum electron density at both the breakdown moments for DBD with partial packing.
Figures 8(b-i) and 8(b-ii) show the ion density distributions at the two breakdown moments during the positive half cycle of the applied voltage as seen in Fig. 4(b) for DBD with partial packing.By comparing the plots, it can be seen that the maximum ion density at both the breakdown moments for DBD with partial packing is higher in magnitude than that observed at the breakdown for DBD with no packing [Fig.8(a)].Similar to the electron density distribution profiles for DBD with partial packing, ion density distribution at the moment of first breakdown shows maximum ion density at the top surface of the packing particles [Fig.8(b-i)], and at the second breakdown, the maximum is observed in the region between the two particles [Fig.8(b-ii)].
Comparing Figs. 7 and 8, it can be seen that the ion density is always higher compared to the corresponding electron density for both DBD with packing and with no packing.This is another characteristic feature of the APGD, which is found valid for both the configurations.Typical electron and ion densities for APGD are in the range of 10 10 -10 11 cm -3 and 10 11 -10 12 cm -3 , respectively. 53,54The electron and ion densities for both the DBD configurations studied in this work, fall within the typical range observed for APGD, further confirming the occurrence of homogeneous discharge.
As the major difference in discharge current profiles for the DBDs with and without packing is seen in the positive half cycle of the applied voltage (3 kV peak-to-peak), we wanted to see how this difference is reflected in terms of average electron energy, which is an important factor in determining the decomposition efficiency of the DBD reactor.Figure 9 shows the time averaged electron energy distribution during the positive half cycle of applied potential of 3.0 kV peak-to-peak for both DBD without any packing and DBD with partial packing.
As can be seen from the Fig. 9(a), for DBD with no packing, the maximum electron energy during the half voltage cycle is just below 5 eV and is observed near the instantaneous cathode close to the dielectric surface.On the other hand, for DBD with partial packing [Fig.9(b)], the maximum electron energy during the half voltage cycle is close to 10 eV, which is twice of that obtained for DBD when no packing is used.The maximum electron energy ($10 eV) is observed at the contact points between the packing material and the dielectric barrier.The electron energy is also significantly higher ($5 eV) on the surface of the packing material except in the small region where the distance between the packing beads is minimum.The enhancement in electric field strength at the top surface of the packing particle and at the contact points between the barrier layer and the packing induces higher electron energy in these regions, and thus the half-period time averaged electron energy distribution in Fig. 9 shows enhanced electron energy in these areas.
On application of a higher applied potential, 6 kV peakto-peak, the discharge behaviour changes to a certain extent, more in the case of partially packed DBD. Figure 10 shows the discharge current profiles in helium DBD without any packing and with partial packing, during one cycle of the applied potential of 6 kV peak-to-peak at a frequency of 20 kHz.
As can be seen from Fig. 10(a), for helium DBD with no packing, the current profile exhibits a single distinct pulse in the positive half cycle of the applied voltage.In the negative half cycle, discharge current shows multiple peaks, with the first peak being of higher amplitude followed by six peaks of much smaller amplitudes.As opposed to DBD with no packing, the discharge current profile for DBD with partial packing [Fig.10(b)] shows multiple peaks in both the positive and negative half cycles of applied voltage, showing characteristics of a pseudoglow discharge.In addition, the amplitude of the peaks are also higher in both positive and negative voltage cycle, signifying a stronger discharge.The discharge current profile shows five peaks of varying amplitude, marked 1-5 in the Fig. 10(b), with peaks 1, 2, and 4 of much higher amplitude than peaks 3 and 5. Similar increase in number of peaks on inclusion of packing materials has been observed before in various experimental studies. 16,41igher applied potential induces higher electric field strength in the discharge gap, increasing the chances of multiple gas breakdown.Such an irregular multipeak behaviour occurs due to independent discharges occurring in different parts of FIG. 9. Time averaged electron energy (eV) distribution during the positive half cycle at an applied potential of 3.0 kV peak-to-peak as shown in Fig. 4 for (a) DBD with no packing and (b) DBD with partial packing.

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Gadkari, Tu, and Gu Phys.Plasmas 24, 093510 (2017)     the reactor progressively depending on the electric field strength in a given region at a given time.Similar behaviour was also observed in the numerical study of fully packed DBDs by Van Laer and Bogaerts 21 at an applied potential of 7.5 kV peak-to-peak.The current profile in the negative half cycle of the applied voltage is similar for both DBD configurations, except for the fact that the amplitude of the first major peak for DBD with partial packing is almost double of that obtained for DBD with no packing.Figures 11-13 show the electric field, electron number density, and ion number density distributions at the particular moments of breakdown during the positive half cycle of the voltage period, corresponding to times shown in Fig. 10 for both DBD configurations.In all the three figures, for DBD with no packing, we have plotted the distribution profiles for the first major peak corresponding to the breakdown moment observed in discharge current profile in Fig. 10(a), which are represented as plot A in Figs.11-13.For DBD with partial packing, however, we have plotted the distribution profiles for the three major peaks (1, 2, and 4) corresponding to breakdown moments observed in discharge current profile in Fig. 10(b), which are represented as plots B (i, ii, and iii) in Figs.11-13.
As can be seen in Figs.11( observed for lower applied potential of 3 kV, with an expected increase in magnitude due to higher input power.These profiles also show characteristics of APGD with three distinct regions, cathode fall, negative glow space, and positive column region. For DBD with partial packing, electric field distribution at first major peak [Fig.11(b-i)] shows a higher electric field strength at the top surface of the packing particles, and for peaks 2 [Fig.11(b-ii)] and 4 [Fig.11(b-iii)], the maximum electric field strength is observed at the two contact points between packing and dielectric layer, and in the region of discharge between the contact points touching the dielectric layer.Also, for DBD with partial packing, the electric field strength at the three major peaks is slightly higher than that observed at the major peak for DBD with no packing.As can be seen in Fig. 10, the current pulses spread over more than half of the discharge current profile, providing regions of high electric field strength (as seen in Fig. 11) for a larger section and longer time of discharge in the positive half cycle of the applied voltage.
Figures 12(b-i), 12(b-ii), and 12(b-iii) show the electron density distributions at the three breakdown moments (peak 1, 2, and 4) during the positive half cycle of the applied voltage as seen in Fig. 10(b) for DBD with partial packing.For higher applied potential 6 kV peak-to-peak, the maximum electron density distributions corresponding to the three peaks of discharge current profile for DBD with partial packing [Figs.12(b-i), 12(b-ii) and 12(b-iii)] are roughly about one magnitude higher than that obtained for DBD with no packing [Fig.12(a)].The maximum electron density for the peak 2 [Fig.12(b-ii)] is slightly higher ($6.5 Â 10 12 cm -3 ) compared to that obtained for peak 1 ($1.7 Â 10 12 cm -3 ) and peak 4 ($2.5 Â 10 12 cm -3 ), for DBD with partial packing.Comparatively, the maximum electron density for DBD with no packing ($5 Â 10 11 cm -3 ) obtained at the moment of breakdown is lower than the maximum electron density observed for peaks 1, 2, and 4 for DBD with partial packing.For peak 1 [Fig.12(b-i)], the maximum electron density is observed near the top surface of two particles, just after a low electron density region in the shape of a pointy knob upwards from the dielectric barrier layer, signifying a cathode fall region at the moment of breakdown.The electron density distributions corresponding to peaks 2 and 4 [Figs.12(b-ii) and 12(b-iii)] exhibit cylindrical regions of high electron density in the regions between the two particles.It should be pointed out that the higher applied potential of 6 kV peak-to-peak indeed extends the region of high intensity electron density distributions compared to that observed with applied potential of 3 kV.This is a result of the higher number of breakdowns in the current profile obtained at the applied voltage of 6 kV peak-to-peak.Figures 13(b-i), 13(b-ii), and 13(b-iii) show the ion density distributions at the three breakdown moments (peaks 1, 2, and 4) during the positive half cycle of the applied voltage as seen in Fig. 10(b) for DBD with partial packing.The ion density distributions reproduce similar profiles as obtained for electron density distribution (Fig. 12) at the three peaks, except for the low intensity region of cathode fall.The maximum ion density at the three peaks for DBD with partial packing is about one magnitude higher than that obtained for DBD with no packing, suggesting a much stronger ionization on inclusion of packing.Also, similar to what was observed for applied potential of 3 kV, even at the higher applied potential of 6 kV, the ion densities (Fig. 13) at the breakdown moments are always higher compared to the electron densities (Fig. 12) for both DBD configurations with and without packing.As mentioned earlier, this is an important feature of APGD.Also, the electron and ion densities, though higher at applied potential of 6 kV, are still within the range of typical values observed for APGD.
The space charge density profiles for applied potential of 6 kV peak-to-peak (not shown here) follow the same pattern as the ion density distributions (Fig. 13), suggesting the movement of charges from the top surface of packing beads to the region between the beads close to the dielectric layer, leading to the multiple breakdowns in discharge current, manifested as various peaks in Fig. 10(b).
Figure 14 shows the time averaged electron energy distribution during the positive half cycle of applied potential FIG. 13.Ion density (cm -3 ) at the moment of gas breakdown in (a) DBD with no packing, corresponding to time at a major current peak from Fig. 10 6.0 kV peak-to-peak for both DBD configurations.Compared with Fig. 9, the average electron energy at an applied potential of 6 kV is higher than that obtained for an applied potential of 3 kV, for both the DBD configurations with and without packing.For DBD with no packing [Fig.14(a)], the maximum electron energy during the half voltage cycle is about 6 eV and is observed near the instantaneous cathode close to the dielectric surface.On the other hand, for DBD with partial packing [Fig.14(b)], the maximum electron energy during the half voltage cycle is close to 18 eV, which is three times of that obtained for DBD with no packing.In the average plot [Fig.14(b)], the highest intensity of electron energy is observed at the contact points between the packing material and the dielectric barrier.The average electron energy in the vicinity of the packing surface is about 5-10 eV.This local enhancement in electron energy at the contact points and near the surface of the packing is obtained due to the augmentation of the electric field strength in these regions.It should be noted that compared to the applied potential of 3 kV peak-to-peak, where the maximum of the average electron energy for DBD with partial packing increased twice that of DBD with no packing, at a higher electron potential of 6 kV, the increase in the average electron energy is much more pronounced for DBD with partial packing.The multiple breakdowns in the discharge at a higher applied potential (6 kV), lead to a much longer and wider distribution of the high intensity discharge compared to that obtained at a lower applied potential (3 kV), which can lead to the substantially higher electron energy distribution at an applied potential of 6 kV.
Energetic and excited metastable helium atoms (He Ã and He Ã 2 ) produced in the plasma discharge can interact with impurities in the helium gas (nitrogen or oxygen).Since most impurities have an ionization potential lower than the threshold of metastable states, they can be easily ionized via the so-called penning effect. 44,45Even though this study considers a pure helium gas, it is interesting to see if the addition of partial packing leads to any change in the density of metastable helium atoms or its distribution.This information will provide a rough estimate of the potential penning ionization contribution towards increasing the ionization coefficient of the reactor given the percentage of impurities is equal in the two DBD configurations.
Figure 15 shows the time averaged helium metastable atoms density distribution during the positive half cycle of applied potential 6.0 kV peak-to-peak for both DBD configurations.As can be seen from the figure, the time averaged distribution of helium metastable atoms density is quite different in the two configurations.For DBD with no packing, high density of metastable helium atoms is observed near the two boundaries of the discharge space.On the other hand, for DBD with partial packing, the metastable helium atoms are seen to be concentrated in the gap between the two packing beads and at the center point directly opposite this gap, close to the boundary of the inner cylinder.Regions close to the top surface of the packing beads also have a relatively high density of metastable atoms compared to the remaining of the discharge space.It should however be noted that although the distribution of metastable atoms density changes considerably on addition of partial packing, the magnitude of the time averaged density is roughly the same in both DBD configurations.Time averaged metastable atoms' density for a lower applied potential of 3 kV peak-topeak (not shown here) has a similar distribution for both DBD with no packing and DBD with partial packing.
In addition to electron density and electron energy, power consumption of the discharge is also an important indicator of the performance and energy efficiency of the DBD reactor.The average power density over a period T is obtained by integrating the instantaneous power dissipated in the system, as follows: where V gap and I cond represent the gap voltage and conduction current, respectively.Table I shows the spatially and time averaged dissipated power density, electron density, and electron energy for one voltage cycle, at different applied voltage amplitudes for both the DBD configurations (without packing and with partial packing).
As can be seen from Table I, when the applied voltage potential is increased from 3 kV to 6 kV, the spatially and time averaged power density over one voltage cycle also increases ($150%) for both DBD configurations.The power density is also found to be increasing when a partial packing is added to the DBD, for applied potential of both 3 kV and 6 kV.The percentage increase in power density on addition of packing is approximately the same ($50%) at both values of the applied potential.The spatially and time averaged electron density over one voltage cycle is seen to be of roughly similar magnitude (of the order 1 Â 10 10 ) at different applied potentials (3 kV or 6 kV) and DBD configurations (no packing/partial packing).This is in accordance with the previously reported work by Tu et al., 41 who calculated the average electron density from electrical parameters for helium DBD and found that partial radial packing of Al 2 O 3 had little effect on the average electron density.However, it should be noted that in this work, we have used the axial partial packing and addition of partial packing is seen to slightly reduce (although no change in order of magnitude) the average electron density values for applied voltage of both 3 kV and 6 kV.
In addition to the electron density, the DBD reactor performance is also influenced by the total number of electrons present in the reactor.This factor may become more significant in the current study, as the volume of the reactor is reduced due to the addition of partial packing.To obtain the total electron count, the volume of DBD reactor with no packing and for DBD with partial packing is calculated based on the dimensions of the DBD reactor and packing beads, and multiplied to the spatially and time averaged electron density over one voltage cycle as described in Table I.Note that the volume of DBD with partial packing is calculated by subtracting the total volume occupied by the beads from the volume of the discharge space of DBD with no packing.Based on the calculations, the total electron number count for DBD with no packing and DBD with partial packing is 2.70 Â 10 11 and 2.44 Â 10 11 , respectively, for an applied potential of 3 kV peak-to-peak.The same at a higher potential of 6 kV is 2.70 Â 10 11 and 2.51 Â 10 11 , respectively.As can be seen, similar to electron density even the total electron count for the two DBD configurations are of the similar magnitude for both values of applied potential.This is mainly because the volume displaced by the addition of partial packing is a very small fraction compared of the total volume of the DBD reactor.In the case of a fully packed DBD reactor, however, the volume displaced by the packing is significantly higher, and this is known to change the discharge characteristics. 16t can also be seen from Table I that spatially and time averaged electron energy over one voltage cycle increases on inclusion of partial packing ($45%-50%) at both applied potential values.The spatially and time averaged electron energy also shows a small increase as the applied potential is raised from 3 kV to 6 kV (peak-to-peak) for both DBD configurations.
All the above mentioned results suggest that the addition of partial packing enhances the electric field strength and creates a stronger discharge without making any significant change to the discharge mode of the DBD.Together the cumulative effect of higher surface area, enhanced electric field strength, higher electron and ion densities, and a broader range of electron energy will result in an increased production of excited species for the partially packed DBD as compared to DBD without any packing, for the same input power.This is in accordance with the experimental results observed by Tu and Whitehead. 16When implemented in applications for gas cleaning or chemical synthesis, production of higher density of excited species and free radicals in a partially packed DBD can result in better performance as compared to a DBD with no packing.For the helium DBD studied in this work, the discharge at a lower applied potential of 3 kV peak-to-peak is found to be localized.However, increasing the applied potential to 6 kV peak-to-peak resulted in higher charge deposition and multiple breakdowns, particularly in partially packed DBD, which thereby lead to a more spread-out distribution of the high intensity discharge.
It should be noted that in the given configuration of the partially packed DBD, the packing particles are placed only on one side of the co-axial discharge gap.This creates asymmetry in the geometry and prevents one from using a 2Daxi-symmetrical model, which can give a more accurate representation of the 3D co-axial discharge gap.The 2D geometry used in the model is only an approximation of the co-axial discharge space and neglects a substantial section of the co-axial gap which does not interact with any packing.This is a limitation of the 2D model used in this work.Thus, the results obtained in this study have to be viewed with caution, and it should be presumed that the actual change in overall discharge characteristics of the DBD may be less dramatic than what is observed here.It should also be noted that there can be many different configurations in which partial packing can be introduced in a DBD, such as radial partial packing, axial partial packing, more than one column (line) of packing at the bottom of the dielectric tube, etc.The results of this study are limited to the axial packing method as described in Fig. 1.However, the understanding developed through this study will certainly be helpful in improving our insight of the ways in which packing materials interact and influence the plasma discharge in DBDs.More extensive investigations, comparing different packing configurations in a DBD (including fully packed DBD) and specific experimental studies for more quantitative comparison of discharge parameters, needs to be carried out to explore the full capabilities of DBD reactors.A comprehensive study comparing the discharge characteristics of a fully packed DBD with a partially packed DBD, along with focused experimental studies are planned for the near future.

IV. CONCLUSION
In this work, a numerical analysis of co-axial DBD in pure helium has been carried out using 2-D fluid model.This model has been used to understand the influence of partial packing on the discharge characteristics of the DBD, and the changes are assessed by comparing the results with those

FIG. 3 .
FIG. 3. Comparison of discharge current profile (blue lines) obtained from (a) experimental study by Tu et al. 41 with (b) simulation predictions from the model developed in this study, for one voltage cycle (black lines) at a frequency of 60 kHz in a helium DBD without any packing.[Experimental result (a) has been reprinted with permission from Phys.Plasmas 18(8), 080702 (2011).Copyright 2011 AIP Publishing LLC. 41]

FIG. 4 .
FIG. 4. Discharge current profiles (red solid lines) in an atmospheric DBD in helium (A) without packing and (B) with partial packing, during once cycle of the applied potential of 3 kV peakto-peak (black dashed lines) at a frequency of 20 kHz.

Figures 5 (
FIG. 6. Space charge density (cm -3 ) at the moment of gas breakdown in (a) DBD with no packing, corresponding to time at current peak (474.2 ls) of Fig. 4(a) and (b) DBD with partial packing corresponding to time at peaks 1 and 2 as seen in Fig. 4(b).
, and Gu Phys.Plasmas 24, 093510 (2017)      field strength is slightly higher for DBD with partial packing.At the first breakdown point, the electric field strength is maximum at the top surface of the packing particles [Fig.5(b-i)].Spherical dielectric objects in an electric field produce an intensification of the electric field in the gas at the poles of the solid object and a local minima at the equatorial plane.
FIG. 8. Ion density (cm -3 ) at the moment of gas breakdown in (a) DBD with no packing, corresponding to time at current peak (474.2 ls) of Fig. 4(a) and (b) DBD with partial packing corresponding to time at peaks 1 and 2 as seen in Fig. 4(b).
FIG. 10.Discharge current profiles (red solid lines) in an atmospheric DBD in helium (a) without packing and (b) with partial packing, during once cycle of the applied potential of 6 kV peak-to-peak (black dashed lines) at a frequency of 20 kHz.

FIG. 12 .
FIG.12.Electron Density (cm -3 ) at the moment of gas breakdown in (a) DBD with no packing, corresponding to time at a major current peak from Fig.10(a) and (b) DBD with partial packing corresponding to times at the three current peaks at (Bi) peak 1, (Bii) peak 2, and (Biii) peak 4 from Fig. 10(b).
FIG.13.Ion density (cm -3 ) at the moment of gas breakdown in (a) DBD with no packing, corresponding to time at a major current peak from Fig.10(a) and (b) DBD with partial packing corresponding to times at the three current peaks at (Bi) peak 1, (Bii) peak 2, and (Biii) peak 4 from Fig. 10(b).

FIG. 15 .
FIG.15.Time averaged helium metastable atoms (He Ã and He Ã2 ) density distribution during the positive half cycle at an applied potential of 6.0 kV peak-topeak as shown in Fig.10for (a) DBD with no packing and (b) DBD with partial packing.

TABLE I .
Spatially and time averaged dissipated power density (W m -3 ) and electron density (cm -3 ) and electron energy (eV) for one voltage cycle at different applied voltage amplitudes and DBD configurations at an applied frequency of 20 kHz.