Numerical Study Of Low Pressure Air Plasma In An Actuated .
JOURNAL OF APPLIED PHYSICS 118, 233303 (2015)Numerical study of low pressure air plasma in an actuated channelTomas Houba and Subrata Roya)Applied Physics Research Group, Department of Mechanical and Aerospace Engineering,University of Florida, Gainesville, Florida 32611, USA(Received 1 October 2015; accepted 3 December 2015; published online 18 December 2015)A model for air plasma discharge based on drift-diffusion with local mean energy approximation isdescribed. The model consists of 7 species and 18 reactions. The code is benchmarked with experimental and numerical results for low pressure glow discharge in a cylindrical tube. The code isused to simulate the discharge produced by a wire placed in a rectangular channel with groundedelectrodes at the top and bottom walls. The discharge is concentrated near the wire. The actuatoracts on the neutral gas through a body force and Joule heating. Around 80%–90% of the electricalpower is converted to Joule heating of the neutral gas and the wall. The actuator produces a bodyforce on the order of 0.1 mN/m. The effectiveness of the actuator increases from 100 to 300 V, andplateaus from 300 to 600 V. The results of the study suggest a further exploration of the channelC 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4938023]concept. VI. INTRODUCTIONThe air flow produced by a gas discharge, known as the“electric wind,” has been known since the early 1700s.1 Adevice which uses a gas discharge to add momentum andenergy to a fluid flow is known as a plasma actuator. The actuator creates a gas discharge by applying a sufficient voltagedifference between two electrodes, ionizing the fluid in thevicinity. The bulk of research carried out on plasma actuatorsin more recent years has focused on their application to flowcontrol.2 Plasma actuators have been shown to delay transition in motorized glider flight tests,3 and there is ongoingwork to implement the actuators in real world applications.A plasma pump can be created by placing plasma actuators inside a channel. The actuator can consist of plate electrodes,4 wire electrodes,5,6 or needle electrodes.7 The advantagesof producing a fluid flow in this manner include low powerconsumption, instantaneous response, and a lack of movingparts. The technology is also suitable for miniaturization. Inthis work, the plasma discharge in a channel produced by awire electrode is studied numerically under lower than atmospheric pressure condition. The simulation of the plasma is performed using the fluid model with the drift-diffusionapproximation. The most typical air plasma chemistry modelused in fluid simulations contains three charged species, whichare a positive ion, a negative ion, and an electron.8,9 Morecomplex models which include additional species have alsobeen considered.10,11 The model chosen to simulate the channel geometry in this work is first validated with experimentaldata.12 The model is then applied to the new geometry, and thecharacteristics of the plasma discharge are studied. Finally,thrust inducement is predicted for the plasma actuated channel.II. METHODOLOGYA. Air chemistry modelThe numerical model for the air plasma assumes aweakly ionized gas composed of positive ions, negative ions,a)Electronic mail: roy@ufl.edu. URL: )/233303/9/ 30.00and electrons. The air chemistry model in this work is basedon the models by Mahadevan and Raja11 and Pancheshnyiet al.13 with several simplifying assumptions. The positiveions considered in the study include the two main ions N2þand O2þ, and the cluster ions N4þ and O4þ. The O2þN2 cluster ion is not considered in the model, because the simulations by Mahadevan and Raja11 which include the ion showthat its number density is not significant at the given conditions. When the ion was included in the current model, virtually no change in computed discharge current was observed.The negative species consist of the oxygen ions O and O2 along with electrons. The model presented by Mahadevanand Raja11 also includes the solution of the neutral moleculesN2, O2, and O. It is assumed that the number densities of N2and O2 remain approximately constant due to the low degreeof ionization. The concentration of the monoatomic oxygenO is also not computed, because the species does not appearas a reactant in the set of reactions considered. These simplifications help reduce the computational effort necessary toobtain results.The reactions used in the present work are given inTable I. The reactions which involve electrons as reactantsare calculated as a function of the mean electron energy. Thefree software BOLSIGþ14 is used to obtain the rates of a majority of the electron-driven reactions. A dry air mixture of80% nitrogen and 20% oxygen is assumed. The excitationreactions include the effects of multiple excited N2 and O2species, and the expressions for these reaction rates are provided by Mahadevan and Raja.11 The remaining reactionrates are obtained from Ref. 15. A majority of the reactionrates involving only heavy species are a function of the gastemperature. The ions are assumed to be in thermal equilibrium with the neutrals, so the ion temperature is identical tothe gas temperature.B. Governing equationsThe continuity equation that is solved for each plasmaspecies is given as118, 233303-1C 2015 AIP Publishing LLCV
233303-2T. Houba and S. RoyJ. Appl. Phys. 118, 233303 (2015)TABLE I. Air chemistry model.Formula123456789101112131415161718 ðe /Þ ¼ eReaction type@nkþ Ck ¼ Sk :@t(1)Zk nk :(4)kReferenceN2 þ e ! N2 þ þ 2e Impact ionizationBOLSIGþ14þ O2 þ e ! O2 þ 2eImpact ionizationBOLSIGþ14þþN2 þ N2 þ M ! N4 þ MIon-neutral association Kossyi et al.15þþO2 þ O2 þ M ! O4 þ MIon-neutral association Kossyi et al.15O2 þ e ! O þ OElectron attachmentBOLSIGþ14 2O2 þ e ! O2 þ O2Electron attachmentKossyi et al.15þþN2 þ O2 ! O2 þ N2Charge exchangeKossyi et al.15þþN4 þ O2 ! O2 þ 2N2Charge exchangeKossyi et al.15O2 þ þ O ! O2 þ OIon-ion recombination Kossyi et al.15O2 þ þ O2 þ M ! 2O2 þ M Ion-ion recombination Kossyi et al.15O4 þ þ O2 þ M ! 3O2 þ M Ion-ion recombination Kossyi et al.15O4 þ þ O2 ! 3O2Ion-ion recombination Kossyi et al.15O2 þ þ e ! 2OIon-electron recombination Kossyi et al.15O4 þ þ e ! 2O2Ion-electron recombination Kossyi et al.15 O2 þ e ! 2ODissociationBOLSIGþ14 O2 þ e ! O þ ODissociationBOLSIGþ14N2 þ e ! N2 þ e ExcitationMahadevan11O2 þ e ! O2 þ e ExcitationMahadevan11XThe governing equations are written in a non-dimensionalform using a reference number density of 1015 m 3, electricpotential of 1 V, length scale of 1 m, and timescale of 10 6 s.The ionization source rates obtained from the solutionof the governing equations are used to obtain the photoionization source terms. Photoionization has been studied previously at atmospheric pressure in literature,20 and it wasincorporated in the present model in an effort to bring inadditional physics. The photoionization model used in thiswork was proposed by Bourdon et al.21 and has been previously used in dielectric barrier discharge (DBD) plasma actuator simulations.22 The photoionization source term iswritten using the third order approximationSph ¼ pO2 c3XAk W0;k ;(5)k¼1where PO2 is the partial pressure of O2 in air and c is thespeed of light. The photon distribution function W0;k is acombination of two functions /1;k and /2;kc2 /1;k c1 /2;k:c2 c1The right-hand side of Eq. (1) contains the source and sinkterms which represent the air chemistry. The mean electronenergy used in the reaction rate coefficient calculations isobtained using the electron energy equation, which is writtenin the form recommended by Hagelaar and Pitchford16The functions are calculated using a solution of Helmholtzequations of the form@neþ Ce ¼ Ce E þ Se :@tr2 /1;k C11;k /1;k ¼ C12;k Sizr2 /2;k C21;k /2;k ¼ C22;k Siz :(2)The first term on the right-hand side of Eq. (2) is the Jouleheating, which is responsible for adding energy to the electrons. The second term contains electron energy losses dueto the inelastic and elastic collisional processes. The collisional term has a standard form which is given by Rafatovet al.,17 for example.The flux terms in Eqs. (1) and (2) are approximatedusing the drift-diffusion model, which separates the flux intoa drift part proportional to the electric field, and a diffusivepart. The flux is written in the formCk ¼ Zk nk lk E Dk nk :(3)For the electron energy flux, Ze ¼ Ze ¼ 1. The electronmobility and diffusion coefficients are calculated as a function of the mean electron energy using BOLSIGþ.14 Theelectron energy mobility and diffusion are directly related tothe electron properties through the relations le ¼ ð5 3Þleand De ¼ ð5 3ÞDe . All of the ion transport properties arecomputed as a function of the reduced electric field. The mobility for the N2þ, O2þ, and O ions are obtained from Ref.18. The N4þ mobility is taken from Ref. 19, and the O4þ mobility is assumed to be identical. The ion diffusion coefficients are assumed to behave according to the Einsteinrelation.The system of equations is closed by the solution of theelectrostatic Poisson equationW0;k ¼(6)(7)The right-hand side of Eq. (7) contains the source termrelated to the rate of ionization. The parameters in Eqs.(5)–(7) and the boundary conditions for Eq. (7) are takenfrom Ref. 21. In total, three coupled pairs of Helmholtzequations are solved to obtain the photoionization sourceterm defined by Eq. (5).C. Boundary conditionsThe boundary conditions for the plasma conservationlaws are specified through the definition of the flux normal tothe boundary. The wall normal vector is labeled nw . At thecathode boundary, the electron flux is calculated asX1cs Cs nw :Ce nw ¼ ne vth;e 4s(8)The first term on the right hand side of Eq. (8) is the thermal flux, and the second term is the secondary electron emission, which is calculated only for the N2þ and O2þ ion fluxes.For the anode boundary, the secondary emission term is zero.For the ions, the boundary flux at the anode and the cathode is1Ck nw ¼ nk vth;k þ aZk nk lk E nw ;4(9)where a is equal to one if the second term points toward thewall, and zero otherwise. Finally, the electron energy flux is
233303-3T. Houba and S. RoyJ. Appl. Phys. 118, 233303 (2015)kB T eCe nw :eThe surface charge contributes to the right-hand side sourceterm of the Poisson equation for cells neighboring the dielectric surface.a channel with a height of 5 cm. The grounded electrodes areplaced at the top and the bottom of the channel. These electrodes have a length of 5 cm each, and the distance in the xdirection between the center of the wire and the leading edgeof the grounded electrode is 10 cm. The simulation domainextends an additional 2 cm behind the wire in the xdirection. It is only necessary to solve one half of the domainnumerically due to symmetry.The computational grid consists of 221 181 rectangular cells with variable sizes. The smallest cell size in eitherdirection is 10 lm, located in the proximity of the wire toresolve the large electric field in this region. The modelapproximates the wire cross-section as a square with sides of80 lm, similar to a 40 AWG wire. All cells with centerslocated inside the wire are modeled as solid cells.D. Numerical methodologyIII. RESULTS AND DISCUSSIONThe system of governing equations is solved using thefinite volume module of the Multiscale Ionized Gas (MIG)code. The face fluxes are approximated using the first orderaccurate Scharfetter-Gummel scheme.23 The steady Poissonequation is coupled to the unsteady charged species conservation laws. This coupling poses a computational challengein time marching the solution due to the frequent necessityto update the electric potential. The electric potential isupdated based on Maxwell time, given byA. Code benchmarkingCe nw ¼ 2(10)The normal component of the electric field, species flux, andelectron energy flux is taken to be zero at the outer domainboundaries that are not solid. At a dielectric boundary, thespecies impacting the surface are assumed to recombineinstantly with the dielectric material. The surface charge atthe dielectric is then computed based on the relationXdr¼ Zk Ck nw :(11)dtke0:sM ¼ Xenk lk(12)kThe ion and electron equations are integrated in time using asecond order explicit Runge-Kutta method in between successive updates of the electric potential. The value of the stepsize changes based on the stability condition of the simulation.The time step restrictions imposed by the electrons and the airchemistry are much more strict than those required by theheavy species transport. The time integration of the heavyspecies fluxes is therefore carried out separately based on themost restrictive Courant-Friedrichs-Lewy (CFL) conditionamong the ions. The electrons and the chemical source termsare integrated based on the CFL condition imposed by theelectron energy transport. The simulation is performed fromuniform initial conditions for the species number densitiesand marched in time until the steady state is reached.E. Geometry and gridThe governing equations are solved for the geometryshown in Fig. 1. A copper wire is placed at the centerline ofThe code was benchmarked for the test problem of DCglow discharge in a cylindrical tube. Lisovskiy andYakovin12 carried out experiments in which they studied theglow discharge inside a large diameter tube for a range ofpressures and several discharge tube lengths. The cylindricaltube chosen for the benchmark case had a length of 32 mm.The computational grid for the test case was varied from 100to 400 computational cells stretched with the hyperbolic tangent function. The pressure was set to 0.6 Torr, and the neutral gas temperature was kept at 300 K. The geometryconsists of a cathode at x ¼ 0 and an anode at x ¼ 32 mm.The particular length and pressure were chosen because theaxial structure of the discharge is described for this case.12This experimental geometry was also simulated numericallyin 2-D by Mahadevan and Raja.11Due to the large diameter of the tube (100 mm) relativeto the length, the discharge along the centerline of the tubewas simulated in 1-D along the axial direction. To obtain thenet current, the 1-D current density is multiplied by the cylindrical area normal to the discharge axis. Since the channelcase is not in cylindrical coordinates, the choice of 1-D geometry avoids the necessity of discretizing the governingequations in the cylindrical coordinates for the radial direction. The 2-D spatial discretization is a direct extension ofthe 1-D case.Fig. 2 shows a plot of the voltage drop between the electrodes versus the discharge current. The computed currentshows a linear variation with voltage. The voltage-currentline shows a slope that is similar to the other numericalresult, with the difference that the current is higher for aFIG. 1. The schematic of the actuatorinside the channel.
233303-4T. Houba and S. RoyJ. Appl. Phys. 118, 233303 (2015)Fig. 4 compares the electron temperature distribution inthe axial direction. The experimental data for the three testvoltages show a larger variation than the numerical results.The numerical data predict an electron temperature of about1 eV in the bulk plasma region away from the electrodes.The electron temperature toward the electrodes rises at aslope comparable to the experimental measurements at350 V. The profile of the electron temperature shows goodqualitative agreement with the experiment.The 1-D results were also compared with the results ofMahadevan and Raja11 along the centerline of tube. Fig. 5shows the charge and number density graph for a voltage of408 V. The computed net charge shows a very good agreement with the published result. The primary differenceoccurs in the negatively charged species. In the MIG results,a larger number of electrons are predicted to attach to neutralatoms and form negative ions. This is reflected in adecreased electron number density and an increased negativeFIG. 2. Comparison of the current versus voltage for the DC glow dischargein a tube.given voltage drop. This is to be expected, because the 1-Dsimulation will not lose any particles to the side walls. Theslight differences between the slopes can be attributed tosmall differences between the models.Fig. 3 shows a comparison of the positive ion numberdensity distribution in the axial direction. The numerical profile of the positive ion density exhibits a double layer nearthe cathode region which is not observed in the experimentaldata, but has been computed by the simulation ofMahadevan and Raja.11 The experimental number densityprofiles for the lower voltages experience a sharper drop-offthan predicted by the numerical result, which can be partiallyattributed to the larger error of the drift-diffusion model inthe sheath region. Despite these discrepancies, the numberdensities predicted by the numerical model fall in a similarrange to the experimentally measured values.FIG. 4. Electron temperature along the axial direction of the tube.FIG. 3. Positive ion number density along the axial direction of the tube.**FIG. 5. Comparison of number density and charge at 408 V.
233303-5T. Houba and S. RoyFIG. 6. Comparison of the electric potential at 408 V.ion number density. Fig. 6 shows the electric potential forthe two cases. Here, the comparison shows excellent agreement, which is to be expected based on the good matchobtained for the net charge density.The benchmark case produces reasonable values for thecomputed current, positive ion number density, and electrontemperature compared with the experiment. In order to maintain a practical fidelity of the model, it should be applied atconditions similar to the experiment. Substantial deviationsfrom the conditions of the experiment could cause largererrors and hinder the predictive capability of the model.J. Appl. Phys. 118, 233303 (2015)densities show that the discharge is concentrated in the vicinity of the wire, which is the region of the highest electricfield. The electron density at 600 V peaks at around 6 1016m 3, while the 100 V case reaches peak values of about 9 1015 m 3. The positive ions in Fig. 8 show a similar spatialdensity profile, with the exception of the immediate neighborhood of the anode wire. In this region, the positive ionnumber density shows a large drop-off. The negative ionnumber density is plotted in Fig. 9. The results indicate thatthe number densities of the negative ions are on averageabout an order of magnitude below those of the electrons andpositive ions. A detailed breakdown of the positive and negative ion species for 600 V is provided in Figs. 10 and 11.Fig. 12 shows the comparison of the electron temperature for the two cases. As expected, the region near the wirecontains hotter electrons. At 100 V, the electron temperaturein the majority of the domain does not exceed 1 eV. At600 V, the region of high electron temperature extends farther from the wire, and the electron temperature near thewire is above 2 eV.The photoionization source term over the simulation domain is presented in Fig. 13. The photoionization occurs primarily in the cathode region of the discharge. Thephotoionization rate at 600 V is over two orders of magnitude higher than the rate computed at 100 V, which shows anincreasing role of photoionization with increasing voltage.Despite the large increase, the photoionization does notappear to have a significant impact for the given conditionsand voltage range. Even at the highest voltages considered,the photoionization rate is still just a small fraction of theionization rate.B. Plasma discharge in the channelC. Discharge characteristicsThe model was applied to the wire and channel geometry described in Section II E. The wire is powered by a continuous DC voltage signal. The applied voltage was variedfrom 100 to 600 V. The pressure and temperature were set to0
The numerical model for the air plasma assumes a weakly ionized gas composed of positive ions, negative ions, and electrons. The air chemistry model in this work is based on the models by Mahadevan and Raja11 and Pancheshnyi et al.13 with several simplifying assumptions. The positive ions considered in the study include the two main ions N 2 þ .
Acceptance Factor is calculated using the pressure tank precharge pressure (2 psig below the pump cut-in pressure). The pressure tank will oper ate between the pressures set by the pressure switch. The tank precharge pressure should be set at 2 psig below the low pressure cut -in to prevent a noticeable drop in pressure at the fixture.
1301 -x- - Low pressure fault (63L operation) low pressure sensor sensing less than 1 bar immediately before starting 1302 xx- - High pressure fault - check pressure in system for more than 29 bar (R407c) 38 bar (R410A). Check high pressure sensor against gauge pressure 1368 xx- - Pressure sensor fault (PS1) at BC - compare pressure reading on .
Earth Pressure (P) 8 Earth pressure is the pressure exerted by the retaining material on the retaining wall. This pressure tends to deflect the wall outward. Types of earth pressure: Active earth pressure or earth pressure (Pa) and Passive earth pressure (P p). Active earth pressure tends to deflect the wall away from the backfill.File Size: 1MBPage Count: 55
Bosch Rexroth AG, RE 92650/06.2016 6 A1VO Series 10 Axial piston variable pump Working pressure range Working pressure range Pressure at service line port B Definition Nominal pressure p nom 250 bar The nominal pressure corresponds to the maximum design pressure. Maximum pressure p max 280 bar The maximum pressure corresponds the maximum working pressure within the
Supply port for pressure to be regulated VOLUME CONTROLLER For fine adjustment of pressure OUTPUT PORTS For regulated pressure output . PCS-01 Pressure Controlling System. PGS-01 Pressure Generating System 0-2000 PSI PRESSURE REGULATOR For pressure control to target pressure FILL PORT Input port for filling internal single cylinder INTERNAL .
Pressure support Pressure control ventilation Pressure-controlled inverse-ratio ventilation Airway pressure release ventilation Volume-assured pressure modes (1-5 below) 1. Pressure augmentation (Bear 1000) 2. Volume Support (Siemens) 3. Pressure Regulated Control (Siemens) Main Parameters Pressure support level, sensitivity, FIO 2, and PEEP
“numerical analysis” title in a later edition [171]. The origins of the part of mathematics we now call analysis were all numerical, so for millennia the name “numerical analysis” would have been redundant. But analysis later developed conceptual (non-numerical) paradigms, and it became useful to specify the different areas by names.
the numerical solution of second-order optimization methods. Next step development of Numerical Multilinear Algebra for the statistical analysis of multi-way data, the numerical solution of partial di erential equations arising from tensor elds, the numerical solution of higher-order optimization methods.
