Modelling Of Electric Field Distribution In A Non-thermal .
Modelling of Electric Field Distribution in A Non-thermal Plasma Reactor UsingCOMSOL MultiphysicsM. Mortazavi1, L. Amato1, N. Manivannan2, Maysam Abbod1, W. Balachandran11. Electronic and Electrical Engineering Department, Brunel University London, Uxbridge, London, United Kingdom2. School of Design, Brunel University London, Uxbridge, London, United KingdomAbstractThe importance of the electric field and charged particles dynamics in various applications including plasma reactors hasbeen recognized more than ever. Furthermore, the role of the multiphysics modelling and simulation in the process ofinvestigation, design and product prototyping is also becoming more popular due to increased speed of computers andadvanced software techniques. In this work, electric field distribution in a non-thermal plasma (NTP) reactor has beenstudied using COMSOL multiphysics for the application of NOx reduction in the emission control. NTP was created indielectric barrier discharge (DBD) cylindrical reactor with high voltage- ground electrodes. This study investigates theelectric field distribution in non-thermal plasma under different reactor configurations. We investigated electric fielddistribution with and without applying space charge density; reactor design with multi ground electrodes, reactor designwith a 1.2 m ground electrode and variable HV electrode dimensions. This study has provided an overall insight on theelectric field distribution in non-thermal plasma and can be used as a guide for the electric field behaviour within anitrogen gas non-thermal plasma.Keywords: COMSOL modelling, NON-Thermal Plasma, Electric field in Plasma, DBD Plasma1. IntroductionThe state-of-the-art technology is moving towards morecomplex and multidisciplinary processes and systems.There is a growing interest in using multi-physicssimulations to have a better understanding of theunderpinning science of the processes as well asproviding cost-effective solutions leading to practicallyachievable systems and products. The importance of theelectric field and charged particles dynamics in variousapplications including but not limited to batteries,plasma reactors, healthcare, manufacturing, foodindustries and climate studies has been recognized morethan ever and it has highlighted the need for an in-depthunderstanding of the electrodynamics in such processesusing computer modelling and simulations. In this work,electric field distribution in a non-thermal plasma reactorhas been studied using COMSOL Multiphysics.Plasma science has been of specific interest during lastthree decades and its applications have been expandedinto different industrial fields. Plasma can be generatedby applying sufficient energy such as electric fieldenergy, thermal energy, radiations, to a neutral gas, andis characterized by the existence of a mixture of freeelectrons, excited species, radicals, and ions.Non-thermal plasma (NTP) process occurs underextremely non-equilibrium conditions for all species. Itdistinguishes from the thermal plasma as the species arein their excited state, but their kinetic energy is muchlower than the electrons. In fact, even if the electrontemperature is high (1-10 eV mean electron energy) thegas temperature can be maintained low [1]. The highconcentration of species in their excited state allows thechemical reactions that require high activation energy tooccur. The reduction in the activation energy barriermakes NTP an alternative technology to catalystsprocess to produce species that are not favoured at theroom temperature.Plasma can be created from most gaseous mixturesamong them are oxygen, nitrogen, and dry air. Collisionsbetween energetic electrons and gas molecules generatea blend of reactive species. The basic fact of NTP is thatelectron temperature (𝑻𝒆 ) is much lower than gastemperature (𝑻𝒈 ), where 𝑻𝒆 𝑻𝒈 ) [2].NTP is generated by high intensity electric field exciteddischarges in different approaches including dielectricbarrier discharge (DBD), corona discharges (CD), localTownsend discharge (LTD), constricted glows (CG) andelectron avalanches (EA).
DBD plasma is one of the prominent technologies ingenerating NTP under the atmospheric pressure andambient temperature [3]. Atmospheric pressure DBD hasbeen used for different applications such as sterilizationbiological decontamination, ozone production, surfacemodification, decontamination of environmentalpollutant and water treatment [4, 5]. DBD dischargeoften forms with streamer breakdown procedure in anon-uniform electric field. The streamers are the resultsof an avalanche of electrons produced by high intensityelectric field. The collisions of the electrons with neutralgas molecules generate a cloud of positive and negativecharges in the gas phase that represents the plasma.When the breakdown field is achieved, the NTP isproduced while attachment of electrons to other heavyparticles and recombining of products reduces the NTPconductivity and as a result, it is terminated. If theelectric field strength is lower than the breakdown fieldstrength, this discharge and consequently NTP isaffected. The effective parameters in generation andmaintaining the NTP in the reactor, in addition to thechemistry of the plasma, are dielectric properties andthickness, geometry of the electrodes and the size of thedischarge gap (distance between electrodes).A better understanding of the underpinning physics andprecise analysis of the DBD reactor can increase theefficiency of the NTP process and improve the outcomeof the intended activity. DBD can be designed indifferent configurations based on the application. Themultiphysics simulation would facilitate the reactordesign optimization considering electrodes’ size andshape, dielectric materials, applied voltages andfrequency.In this work, electric field distribution of a designedreactor is investigated under different scenarios. Firstly,the electric field distribution within the reactor wasinvestigated when a potential of 20kV was applied to theactive electrode with and without the presence of freespace charge. Second, scenario is to assess the effect ofground electrode design on the electric field distributionand thirdly, the effect of the HV electrode diameter onthe electric field distribution was investigated. In thesecond and third cases space charge density was notincluded.The plasma chemistry including excitation, deexcitation, ionization, and recombination processes arein the range of micro-seconds time scale and needs highvolume of computational tasks. Therefore, most plasmamodels available in literature are 1D to consume lesscomputing time and cost.However, having the benefit of electrostatics interface inthe AC/DC module in COMSOL and eliminating thechemical reactions calculations, this investigation wasdone in 3D. The simulation is a stationary study when 20kV is applied on the HV electrode surfaceThe model considered a cylindrical Dielectric BarrierDischarge plasma reactor with an axial high voltage(HV) electrode surrounded by a cylindrical glass tube asdielectric with a ground electrode on the outercircumference of the dielectric. Non-thermal plasma isgenerated using nitrogen gas that occupies the spacebetween the axial HV electrode and the inner surface ofthe dielectric.Figure 1 Schematic diagram of the reactorFigure 1 presents the schematic diagram of the reactorand Figure 2 demonstrates the designed 3D geometry ofthe reactor in COMSOL.2. Theory / Experimental Set-upComplex nature of the plasma chemistry consisting ofvarious reactions and different products and their widerange timescale characteristics, are a challenge when itcomes to modelling and simulation and it createscomputational difficulties and costly simulations.Figure 2 COMSOL model- Reactor 3D-geometryThe 3D model geometry features are as follows:
vertical axis (z) indicates the length of the tube which is1.2 m; HV electrode is a stainless steel cylinder of 2.5mm radius and 1.18 m length, the outer radius of thedielectric (quartz) tube is 25mm and it has a thicknessof 2.5 mm, the ground electrode is made of copper andcovers 30 cm of the length of the tube in the middle andat its outer circumference. The relative permittivity ofnitrogen and quartz are 1 and 4.2, respectively.By applying high voltage to the inner electrode, a strongelectric field is generated in the gap between twoelectrodes. The electric field flux moves from HVelectrode towards the ground electrode. Obviously, incase of applying AC voltage, the direction of electricfiled follows the alternating voltage.In realistic application, the plasma is generated when theelectric field is much high to promote the dielectricbreakdown of the gas. In the presence of a strong electricfield, free electrons gain enough energy to initiate theionization reactions. Created electrons move toward theboundary surfaces in the opposite direction to theelectric field. An equal number of ions (electrons andions are generated in equal pairs) moves in the samedirection of the electric field. Therefore, surface chargewith opposite sign accumulates on both boundarysurfaces.𝐷𝑟 is the remnant displacement and it is thedisplacement in the absence of the electric field.In order to find a distinctive solution, it is necessary toconsider the boundary conditions as well. The boundaryconditions would represent the interface betweendifferent media and follows the following equations:𝑛2 . (𝐷1 𝐷2 ) 𝜌𝑠where 𝑛2 is the outward normal from medium two,which in this case is dielectric.Different medium behaves differently when it comes toelectric charges. In dielectric materials, charges candisplace within atoms or molecules, this displacement isfar from migration of charges in conductors. Byapplying an external electric field to a dielectric material,the positive charges of its molecule are displaced alongthe field and negative charges are displaced in theopposite direction of the field.4. Simulation Results and DiscussionThis section presents the simulation results and a briefdiscussion about all different studied scenarios.Case 1Reactor design shown in Figure 23. Governing EquationsIn this section, the governing equations of electrostaticsphysics that were used in the COMSOL simulation isbriefly discussed.The numerical study of the model and identifyingequations involved, bring the fundamental interactionbetween electric field, and charged particles, alsobetween charged particles and neutral gas molecules.The equations in this study are based on Gauss’s lawIn this study, the electric filed distribution wasinvestigated at different sections in the radial direction ofthe reactor when a 20kV dc voltage was applied to theHV electrode.Figure 3 shows the surface electric potential in the scaleof 0-20kV.𝜌𝜀0where E is electric field, 𝜌 is the total volume chargedensity and 𝜀0 is the permittivity of free space. . 𝐸 The electric displacement (D) is an important parameterand it involves free charge: . 𝐷 𝜌In case of linear materials, E is directly proportional to Dwhich is presented as:𝐷 𝜀𝐸 𝜀0 𝜀𝑟 𝐸where 𝜀𝑟 is the relative permittivity of the gas.For nonlinear materials, this relationship is presented as:𝐷 𝜀0 𝜀𝑟 𝐸 𝐷𝑟Figure 3 Surface electric potential
The potential decreases from 20 to 0 kV moving fromthe HV electrode surface toward the ground in themiddle of the reactor, where the ground electrode islocated. The rest of the tube surface shows that thevoltage would not reach to zero and is in the range of 12to 15 kV. That is due to the length of the groundelectrode which only covers part of the reactor.Electric field norm is one of the important parameters inmodelling and simulation of the plasma. If the electricfield norm exceeds the onset condition about mega voltper meter, the plasma occurs.Figure 4 demonstrates the changes of electric filed normat different cross sections of the reactor. z 0 shows themiddle of the tube (vertical length), z 0.15 shows thecross section at the edge of the ground electrode andz 0.60 shows the cross section at the top of the reactor.(for more details please check Appendix A). The x-axisin this graph shows the reactor radius from HV electrodecentre (0) to the ground electrode surface at 0.026 m andy-axis presents the electric field norm magnitude.Electric field norm is decreasing exponentially bymoving toward the inner surface of the tube. Then thevalue decreases suddenly at the boundary between thedischarge gap and glass wall, then increase again in thecorresponding to the outer surface of the glass due to thepresence of the ground.electric filed norm which is due to the electric field fluxtend to create a close path.In the parts of the tube above the ground electrode (between z 0.3 and z 0.58) the peak value for electricfield norm is about 1MV/m and finally at the z 0.6 thelowest level of the electric field norm is observed.Figure 5 shows the electric field at longitudinal side ofthe reactor, at different distances from HV electrode. Inthis graph, x-axis shows the length of the reactor whichis 1.2 m and y-axis shows the electric filed normmagnitude. The interval between 0.45 m and 0.75 m isthe region in which ground electrode has covered outersurface of the reactor.Figure 5. Electric field norm along vertical length of the reactorAs Figure 5 presents electric field increases as oneapproach the first edge of the ground electrode positionand remains constant within the well-defined groundelectrode region. As you pass the other edge of theground electrode, the field values drop significantly asexpected.Figure 4. Electric field norm at different cross sectionsRegardless of the cross-section plane, maximum valuefor the electric filed norm happens at the gap near theHV electrode (at a radius of 2.5 mm around the HVelectrode) and it decreases towards the surface of thedielectric tube ; although the magnitude is still in therange of 106 V/m, the changes are significant. The peaklevel of electric field is observed in the parts of the tubewhich has been covered by ground electrode. At edge ofthe ground electrode there is a sharp increase in theWhen the plasma is formed there will be radicals, ions,and electrons in the gas gap which in this model has notbeen considered; but to understand the behaviour ofthese species, the effect of the additional free spacecharges on the electric field norm was assessed byincreasing the space charge density from 1.6 10 6 to 1.6 10 2 𝐶/𝑚3 . Hence, in addition to theapplied field, the space charge field plays a part, in thatat the inner surface of the dielectric more charge specieswill get accumulated and this results in increasedamplitude of the electric field.It was observed that a space charge density of 1.6 10 2 𝐶/𝑚3 , significantly changes the electric field normlevel in the region of the tube which is not covered byground electrode . As shown in figure 6, the peak valueof electric field in the cross sections up to the groundelectrode edge is similar to the results obtained with no
space charge (Figure 4) but from cross section at z 0.15up to the top of the reactor at z 0.58, the electric fieldpeak is much higher in comparison with Figure 4 and thepeak values reaches a value of 107 V/m.Figure 6 Electric filed norm at different cross section when the spacecharge is 1.6 10 2 𝐶/𝑚3Figure 7 shows the electric field at different radius alongthe tube length in the presence of 1.6 10 2 𝐶/𝑚3 spacecharge. Contrary to the figure 5, the field values increaseoutside the well-defined ground electrode region(x 0.45m & x 0.75m) and decrease in the region whereground electrode covers the outer surface of the tube(0.45 x 0.75m). However, for all radii the electric fieldis much higher than the values at the same radiuspresented in Figure 4.Figure 7 Electric filed norm along the length of the reactor when thespace charge is 1.6 10 2 𝐶/𝑚3The above results suggest that the ground electrodeconfiguration could have significant effect on thedistribution of electric field and consequently nonthermal plasma characteristics. Therefore, the nextsection is to study two different locations and dimensionfor the ground electrode and compare the outcomesbetween these models and the main design.Case21.2 m Ground electrode reactorIn the first attempt, the 30 cm length electrode wasreplaced by a 1.2 m length electrode to cover the fulllength of the tube. No other changes were applied to thegeometry.Figure 8 presents the electric field norm for differentcross-sections when ground electrode is 1.2 m long.As the graph shows, the electric filed distributionbehaves similar at different cross sections and wouldpossibly provide same discharge along the gap. Incontrast to Figure 4, the electric field reaches the peakvalue for all different cross sections. This may providesimilar electric field intensity at the discharge gap for thefull length of the tube which could be advantageous ininitializing the plasma in full length of the tube. One ofthe disadvantages of this configuration is the eliminationof visibility of the reactor which could not be used forvisual investigation and measurement purposes of theplasma inside the tube.Therefore, a third reactor design was considered basedon multi ground electrode approach in which two endsof the outer surface of the dielectric tube was cover with30 cm long ground electrodes (3D geometry image isavailable in the Appendix). All other features were keptunchanged.Figure 8. Electric field norm at different cross sections with 1.2 mlength ground electrode
Figure 9 illustrate the simulation results at different crosssections; in this case, the cross sections at z 0.3 up toz 0.6 m, are the tube regions under the cover of groundelectrode and the electric field norm reached its peak. Atthe edge of the ground electrode, there is a sharpincrease (z 0.3 and x 0.026 m) which is much highercompared to what is shown in Figure 4 (cross section atz 0.15 at the edge of ground electrode).Figure 9 Electric field norm at different cross sections with 30 cmlength ground electrodes at both ends of the reactorFigure 10 demonstrate the changes of electric field atdifferent radius along the full length of the tube. Incomparison with Figure 5, the electric field shows higherlevel in the region of the well-grounded tube, but themaximum value is slightly lower as shown in Figure 10.On the other hand, the maximum level of electric field inthe region of tube, which is not covered by groundelectrode, is slightly higher.One of the advantages of this configuration is thepossibility of visual monitoring and measurement of theplasma features through the interval between two groundelectrodes.Case 3Parametric investigation of HV electrode radiusThe next consideration is to assess the effect of the HVelectrode radius on the electric field norm. Usingparametric study, the HV electrode radius was changedfrom 1 mm to 16 mm in steps of 1.5 mm.Electric field has invers relation with conductor crosssection area, therefore as the HV electrode diameterdecreases, the electric field should increase. But in caseof the reactor, electric field is not only under the effectof the HV electrode diameter but the gas gap area(distance between two electrodes) which would affectthe distribution of the electric field. As the gap betweenelectrodes increases, the electric field decreases.Therefore, it is necessary to find a compromise betweenHV electrode diameter and the gap size betweenelectrodes.Figure 11 shows the electric field at z 0; the maximumlevel for electric field is recorded for 1 mm radius HVelectrode. And it decreases as HV electrode radiusincreases to 8 mm; this is the bending point by which asHV electrode radius continuous to increase, the electricfield is increasing too. The reason is that the gapbetween two electrodes decreases which in turn increasethe electric field.Figure 11 Electric field norm at z 0 for different HV electroderadius, 30 cm length ground electrodeFigure 10 Electric field norm along vertical
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