Issue 
Eur. Phys. J. Appl. Phys.
Volume 81, Number 3, March 2018



Article Number  30801  
Number of page(s)  12  
Section  Plasma, Discharges and Processes  
DOI  https://doi.org/10.1051/epjap/2018170151  
Published online  08 June 2018 
https://doi.org/10.1051/epjap/2018170151
Regular Article
Numerical model of A.C. glow discharge plasma anemometer via the coupling of gas flow and plasma model
Nanjing University of Aeronautics and Astronautics, Jiangsu Province Key Laboratory of Aerospace Power System, Key Laboratory of Aeroengine Thermal Environment and Structure, Ministry of Industry and Information Technology,
210016
Nanjing, PR China
^{*} email: yb203@nuaa.edu.cn
Received:
25
April
2017
Received in final form:
23
November
2017
Accepted:
24
March
2018
Published online: 8 June 2018
A new approach to build the numerical modeling of AC (alternating current) plasma anemometer is proposed. Firstly, the plasma model and gas flow model utilized in the proposed method are introduced. The plasma model (xpdp2) is built by PIC/MCC modeling method, while gas flow field model is the fluid model. By combining the flow field model and plasma model, the proposed anemometer model could be obtained. Then the effects of flow velocity on the ion density distribution, electron density distribution and electric potential distribution are studied from micro perspective, and the results show that charged particles move towards the direction of flow velocity. Another facts can also be observed, the movement of electron is not obvious, and flow velocity has no effect on the electronic potential. Finally, the effects of supply voltage, discharge frequency and electrode spacing on the discharge characteristics are investigated from macro perspective, and the results show that there is a nearly linear relationship between flow velocity and gap voltage, which indicate that the plasma anemometer could be applied for flow velocity measurement. The simulation result shows that linear relationships are pretty good when the frequencies are 2 MHz and 3.65 MHz. In addition, the result also shows that, within our chosen distance, small spacing is more suitable for high frequency plasma anemometer.
© EDP Sciences, 2018
1 Introduction
Due to the unique advantages of plasma anemometer, such as high signaltonoise ratio, high measurement accuracy, convenient to calibrate and so on, it has broad prospects in aviation, spaceflight, meteorology, military and other fields [1]. At the very beginning, Mettler had made a study on the DC (direct current) glow discharge plasma anemometer [2]. Then both DC and AC (alternating current) plasma anemometers were simultaneously researched by Vrebalovich in 1954, it was found that AC plasma anemometer had more advantages in the measurement range and discharge stability [3]. After that, Matlis, Corket, Marshall and their collaborators improved the AC plasma anemometer, they had achieved great success, and the measurement range and precision of flow velocity were greatly improved [4–13].
Nevertheless, almost all of the existing AC plasma anemometer researches are limited to the experimental method, which obtain the information of airflow velocity through the parameters (voltage and current) measurement of the discharge circuit. In addition, the discharge parameters are selected by trialanderror method in the experiment, this experimental method lacks sufficient theoretical basis. Nowadays, almost all researchers noticed that the theoretical and simulation studies are important for this field. However, only elementary works have been achieved. Mettler tried to conduct theoretical deductions on the DC plasma anemometers, and one argument about the motion path of the charged particles was validated in the later experimental researches, however, his other theoretical analysis have not been widely adopted. Up to now, due to few people have been involved in the theoretical research or numerical simulation of AC plasma anemometer, A deep understanding of the interaction mechanism on plasma anemometer is unavailable, and various phenomena produced in the process of airflow velocity measurement can't be explained very well. To solve these problems, it is necessary to study the modeling theory of plasma anemometer. With the rapid progress of plasma simulation technology and computing technology, the plasma simulation technology has been greatly improved [14–17], which makes the simulation of AC plasma anemometer possible. In this paper, a novel simulation method is presented, and it will have an important influence on the future study of plasma anemometer.
To carry out the study, the simulation gas needs to be determined before this simulation. In fact, most of the plasma anemometer experiments are carried out in the air environment. As it is known, the composition of air is very complex, it contains a lot of gas types, so the simulation of plasma is difficult to succeed in air [18,19]. Considering that nitrogen is the main element of air, the simulation of AC glow discharge plasma anemometer is carried out in nitrogen.
During this study, a new approach to build the numerical modeling of AC plasma anemometer is proposed, which is realized by merging the established gas flow field codes to a mature opensource plasma simulation program xpdp2 (an explicit electrostatic planar twodimensional particleincell code) [20–24]. The effects of the ion density distribution, electron density distribution and electric potential distribution by flow velocity can be researched from microscopic aspect. Meanwhile, the effects of supply voltage, discharge frequency and electrode spacing by flow velocity on the discharge characteristics can be discussed from macroscopic aspect. The simulation results will provide an important basis for the study of plasma anemometer.
2 Simulation model
The anemometer model is usually represented as a twodimensional model, so a coordinate system is defined as Figure 1. At the same time, the simulation area should be divided into a number of grids. In this approach, the grids are drawn in the twodimensional plane, and the grid density is 40Δx × 20Δy, where Δx and Δy are the grid sizes in the directions ofxandyrespectively (Δx = Δy), and both of them are equal to the Debye length.
The plasma model is built by PIC/MCC modeling method, while the gas flow field model takes idea of the fluid model, and they will be introduced separately.
Fig. 1
Twodimensional plasma anemometer model. 
2.1 PIC/MCC plasma modeling method
The plasma simulation program is an open source plasma simulation program (xpdp2), which is based on the PIC/MCC modeling method. The PIC/MCC simulation method is one of the most accurate plasma simulation methods. Compared with other modeling methods, it can illustrate the process of gas discharge dynamically and figure out the density distribution of ions and electrons separately. The basic principle of the PIC/MCC simulation method is replacing a large number of real particles with less simulated particles, the simulated particles are also called super particles, and then simulating the dynamic characteristics of the plasma by tracking the motion of these simulated particles [25].
The PIC/MCC modeling process is shown in Figure 2, which is divided into the following six steps.
Step 1: Initializing the displacement and velocity distribution of particles according to the characteristics of the discharge gas, which is used to distribute all charged particles into the space of simulation. Then giving a certain initial velocity for each charged particle. As shown in equation (1), the initial energy of the particle obeys Maxwell's velocity distribution, thus the particle's motion rate satisfies the equation (2): (1) (2) (3) where v_{t} represents the mean velocity of particles' thermal motion, T represents the temperature of particles, and k is the Boltzmann constant, m is the mass of particles, R represents random number between 0 and 1.
Step 2: As to the position of the charged particles, the electric charges of these charged particles are distributed to the grid nodes via the PIC method (First order weighting method), and then the distribution of charge density in space is obtained. The calculation equation of charge density is shown as follows: (4) where ρ_{j,k} represents charge density at the node, Q_{j,k} is the charge at the node, Δx and Δy are the grid sizes in the directions of x and y, respectively.
Step 3: Considering the distribution density of charged particles and the electrode potential caused the external circuit, the electric field and potential distribution could be obtained by solving the Poisson equation. A twodimensional plasma simulation is employed in this article, so its Poisson equation [26] is presented as equation (5): (5) where ϕ represents potential, ρ(x, y) represents the space charge density, ϵ_{0} is the permittivity of vacuum.
Step 4: Based on the grid electric field, the electric field in the position of charged particles is calculated by interpolation method, and then the forces on the charged particles can be solved out. After that, the displacements and velocities of charged particles at the next time can be calculated according to Newton's law of motion.
Step 5: The position of charged particles after a step is utilized to judge whether the particle reaches the boundary of the simulation space, and the particles arriving at the boundary will be processed by boundary conditions.
Step 6: Whether the charged particles would collide with the neutral particles is determined by the energy of charged particles. If the collision occurs, the velocity and position of various particles should be calculated after collision. If there are many kinds of collisions between the charged particles and the neutral particles, the total collision cross section parameters are the sum of all the collision cross sections, the collision probability of charged particles in the time step is presented as equation (6): (6) where p_{c} is the collision probability, N is the number density of neutral particles, σ_{t}(ϵ) is the total collision cross section parameters when the charged particle energy is _{ϵ}, v represents the motion velocity of particles.
The whole process performs multiple cycles until the convergence of simulation results.
Fig. 2
PIC/MCC simulation flow chart, including model initialization, charge division, solving Poisson equation, particle collective motion, boundary condition, MCC model for dealing with particle collisions. 
2.2 The gas flow field model between the electrodes
The flow field model between electrodes is a twodimensional gas flow field model, as shown in Figure 3, and it is established according to the characteristics of electrode gap. In order to simplify the simulation process, and based on the characteristics of twodimensional gas flow, it can be set that the gas flow between electrodes is stable, incompressible, and isothermal, which is the viscous laminar flow. The overall modelling work on gas flow field model are as followings.
Step 1: Establishing mathematical model:
The flow field can be described by the following basic equations:
Momentum equation of x direction: (8)
Momentum equation of y direction: (9) where u is the velocity of gas flow in the x direction and v is the velocity of gas flow in the y direction, ρ is the gas flow density, p is the gas pressure, υ is the kinematic viscosity coefficient of gas particle. The flow function ϕ and vorticity ω are defined as follows: (10)
After the introduction of the flow function ϕ and vorticity ω, dependent variables of the basic equations are transformed from u, v, p to ϕ and ω, so the dependent variable is reduced.
Each variable is replaced with its corresponding dimensionless quantity in the equations (10) and (11), and then the two equations can be transformed into dimensionless form as follows (the original symbols are used for the sake of simplicity) (13) (14)
Equations (12)–(14) are the basic equations for the numerical simulation of twodimensional flow field.
Step 2: Discretization
The above equations are discretized by using the finite difference method. The loopiterationcalculation relaxation coefficientsf_{1}and f_{2} are introduced during the process of discretization. Finally, the discrete calculation equations of flow function and vorticity are obtained as follows: (16) (17)
In the above equations, P could represents any point in the computation domain, and E, W, N, S are its adjacent points. Superscripts in the above equations represent loopiteration times.
Step 3: Boundary condition
Taking the electrode boundary as an example to illustrate the boundary conditions, on the condition that there isn't gas flow sliding on the fixed wall surface, the flow function: ϕ(i, j) = q (q is gas flow supply volume), vorticity: , velocity: u(i, j) = v(i, j) = 0.
Step 4: Designing the program:
Based on the analysis of the above gas flow field model, the simulation program is written by C/C++ language, and the program block diagram is shown in Figure 4.
In the calculation program, Δ = 0.0001 is the convergence criterion, and nmg = 1000 is the maximum number of cycles. This flow field model adopts the idea of fluid model, the velocity, density and pressure distribution of different time and space can be calculated by fluid equation.
Fig. 3
The typical flow field between electrodes. 
Fig. 4
Simulation program block diagram of gas flow field, it contains multiple loop processes until the output is stable. Program codes are written based on this program block diagram. 
2.3 Discharge circuit model
The discharge circuit model used in this simulation is shown in Figure 5, which could be divided into three parts: AC voltage source, external coupling capacitance and discharge electrode. AC voltage source provides energy for discharge, and C is the external coupling capacitance, which is used to limit the current growth and to avoid the glow discharge transition to arc discharge [27]. The discharge electrodes are two metal electrodes which are parallel arranged, and the electrode gap is filled with nitrogen. The discharge process is as follows: when the supply voltage is greater than the gas breakdown voltage, the electrons get enough energy from the electric field, so they will collide with the neutral particles, then producing new charged particles and gradually forming the plasma, finally gas is breakdown, and the discharge status is gradually transition to the AC glow discharge.
The equation for calculating the discharge gap voltage is: (18) where V_{d} represents the discharge gap voltage, V represents the supply voltage, ϵ_{0} is the permittivity of vacuum, s is electrode area, E is the electric field strength, I_{i} is the conduction current of ion, I_{e} is the conduction current of electron, the magnitude of I_{i} and I_{e} is determined by the number of electrons and ions produced by the gas discharge.
Fig. 5
Discharge circuit model containing a sinusoidal AC voltage source, an external coupling capacitance and the discharge electrode. 
2.4 Simulation program
This simulation of plasma anemometer is carried out by coupling the gas flow field model and the plasma model, which is arranged as follow:
2.5 Setting up the plasma simulation program
During this period, the simulation work has been carried out without gas flow. The plasma simulation program uses an open source plasma simulation program (xpdp2) which is based on the PIC/MCC modeling method as described in 2.1, and the working gas is set to nitrogen. Programming language is the C/C++ language, and the operating environment is the Linux operating system. The discharge circuit model in this program is as described in 2.3.
2.6 Achieving the coupling of gas flow field model and plasma model
In this simulation, it is necessary to realize the coupling of the gas flow field model and plasma model. The specific coupling process is as follows. The main program (xpdp2) is based on particle model, and the gas flow field program takes the idea of the fluid model. The velocity, density and pressure distribution of different time and space are calculated by the fluid equations as described in 2.2. Then through the code programming, the interpolation method is used to calculate the velocity and the force on each particle, interpolation is achieved by the program. The coupling between the gas flow field and the plasma model is realized by interpolating the parameters calculated by fluid equations to the particles in the grids. The flow chart of the coupling process is shown in Figure 6.
During this simulation, it is necessary to ignore the velocity of electrons in the y direction while interpolating the particles, otherwise, it is equivalent to the yaxis flow velocity is added manually to the electron, and the simulation result will be wrong. The reason is: as shown in Figure 7, when the gas flow velocity is parallel to the direction of y axis, the mass of the electron is very small and it will obtain a very large velocity in the direction of x axis under the action of the electric field, so the velocity of the gas flow field attached to the electrons in the yaxis direction can be neglected compared to the velocity in the xaxis direction, and the electrons are still moving along the xaxis. But the mass of the ion is much larger than the electron, the velocity of the gas flow field attached to the ions in the yaxis direction can't be neglected [2].
The simulation program is realized by interpolation, and the adding of the gas flow field can lead to the overflow of some ions from the discharge space, which will cause the change of the discharge voltage and current.
Fig. 6
Coupling process of gas flow field and plasma model. 
Fig. 7
Motion path of the charged particles under the action of gas flow field. 
2.7 Completing the preparation of the simulation program
After the whole simulation program is encapsulated, the modeling of the plasma anemometer is basically completed. The running interface of the simulation program includes a control interface and a diagnostic interface. The control interface is used to control the running process of the simulation. The diagnostic interface is mainly used to observe the dynamic responses of parameters, including electric potential, voltage, current, electron density, ion density and other parameters. It will take about 227 min to calculate 40 cycles when the simulation program occupies two 3.3 GHz CPUs.
2.8 Simulation parameters setting
For the proposed simulation program, corresponding simulation parameters need to be set before running a simulation, and the simulation parameters can be modified directly in the program. The main parameters, such as the supply voltage, the discharge frequency and the electrode spacing, are required to be set differently depending on the research needs, however, it is necessary to ensure that the discharge belongs to glow discharge and the simulation can be run stably. In this study, the value of the gas pressure is set to 760 Torr, the capacitance is 5e–10F.
3 Microscopic simulation results and discussion
The particle model is mainly used in this simulation, so the electron density and ion density distributions can be discussed separately. In order to facilitate the statistics and records, a velocity value is selected in every 50 m/s velocity range, and the simulation analysis is conducted when the flow velocity is 0 m/s, 50 m/s, 100 m/s, 150 m/s, 200 m/s and 250 m/s, respectively, the velocity can be adjusted by changing the code of the simulation program. Then the simulation results are introduced into MATLAB to achieve the twodimensional projections of ion density, electron density and electric potential distribution. Through these twodimensional projections, we can observe the changes of ion density, electron density and electric potential distribution under the action of gas flow field. According to these changes, we can analyze the changing mechanism of the plasma under different flow velocities from microscopic aspect.
3.1 Effect of flow velocity on the distribution of ion density
As shown in Figure 8, when the flow velocity is 0 m/s, the maximum value of ion density is distributed in the center area of discharge space. With the increase of the flow velocity, the ion density distribution region is advancing towards the direction of flow velocity (yaxis). From the perspective of the distribution region size of ion density, the introduction of flow velocity can lead to the change of the distribution area of ion density, the peak declines and the occupied space is gradually shrinking. When the flow velocity is 250 m/s, compared with 0 m/s, the space occupied by the ion is reduced to about 5/6. The change of the ion density distribution under the action of different flow velocities can be interpreted as: the mass of the ion is much larger than that of the electron, the velocity of gas flow field attached to the ion in the yaxis direction can't be neglected, and the ion has the velocity of y direction under the action of flow velocity, resulting in flow velocity affects the peak position of the ion density, after a period of time, some moving ions will reach the simulation boundary and escape from the discharge space, resulting in the decrease of the ion density and the shrinking of their occupied space.
Fig. 8
Distributions of ion density under different flow velocities. 
3.2 Effect of flow velocity on the distribution of electron density
As illustrated in Figure 9, when the flow velocity is 0 m/s, the maximum value of electron density is basically distributed in the center area of discharge space. However, when the flow velocity is 250 m/s, compared with 0 m/s, the center position of the electron density moves toward the yaxis, but the movement is not obvious. This phenomenon can be explained by the following principles: as described in 2.4, the mass of the electron is very small and it will obtain a very large velocity in the direction of x axis under the action of the electric field, so the velocity of the gas flow field attached to the electrons in the yaxis direction can be neglected compared to the velocity in the xaxis direction, and the electrons are still moving along the x axis, however, electrons and ions are interacting (via collisions and Coulomb forces to achieve the coupling of electrons and ions), and the ions move toward the y axis, which leads to the tendency of the electrons to move toward the y axis.
Fig. 9
Distributions of electron density under different flow velocities. 
3.3 Effect of flow velocity on the distribution of electric potential
The electric potential distributions under different flow velocities are shown in Figure 10. It can be seen from the figures, in most areas, the electric potential is a certain value. The change of electric potential is mainly concentrated in the vicinity of the electrodes, and this potential distribution is consistent with the electric potential distribution of glow discharge, so it can be determined that this discharge belongs to the glow discharge mode. The changing area of potential is called the plasma sheath, the charged particles obtain energy from the sheath and maintain the gas discharge process [28,29]. The region that the potential remains unchanged is the plasma region (positive column region), in this region, the charges of electrons and ions are equal, and from a macro perspective, it is electrically neutral [30]. It can also be seen from the Figure 10: the change of the electric potential is very small under the action of different flow velocities, this is because in the plasma region (positive column region), the effect of flow velocity will make some ions escape from the discharge space, but electronic velocity is very fast in this area, on the macro perspective, the area is still electrically neutral, so the change of the potential in this area is very small. In the plasma sheath, the number of electrons and ions is much less than the plasma region, even if the action of flow velocity causes some ions to escape from the discharge space, the electric potential can't be changed obviously.
Fig. 10
Distributions of electric potential under different flow velocities. 
4 Macroscopic simulation results and discussion
Voltage is one of the most common macro signals, so the effective value of discharge gap voltage is adopted in this simulation. In addition, some representative velocity values are chosen to observe the relationship between the gap voltage and flow velocity. Flow velocity values are 10 m/s, 50 m/s, 100 m/s, 150 m/s, 200 m/s, 250 m/s and 300 m/s, respectively.
When the supply voltage is 600 V, discharge frequency is 2 MHz, electrode spacing is 3 mm and flow velocity is 100 m/s, the simulation waveforms of the supply voltage and the gap voltage are shown in Figure 11.
As shown in Figure 11, the gap voltage waveform is close to the sine wave when the discharge gas is a single gas.
Fig. 11
Simulation waveforms of the supply voltage and the gap voltage. 
4.1 The effect of supply voltage
In order to study the influence of the supply voltage on the discharge characteristics of plasma anemometer, the discharge frequency is set to 2 MHz, the electrode spacing is 3 mm. The peak values of supply voltage are 600 V, 800 V, 1000 V and 1200 V, respectively. The relationship diagram between gap voltage and flow velocity under different supply voltages is presented in Figure 12.
As presented in Figure 12, supply voltage has a great influence on the discharge characteristics, with the increase of the supply voltage, the effective value of discharge gap voltage increases. Furthermore, as the flow velocity increases, the gap voltage increases, and it can be found that the flow velocity has a good linear relationship with the gap voltage in an allowable error range, and this is consistent with the experimental results of plasma anemometer conducted by previous researchers [3–13]. The linear relationship is the basis for flow velocity measurement by plasma anemometer, which can be used to calibrate the flow velocity.
Fig. 12
Relationship between gap voltage and flow velocity under different supply voltages. 
4.2 The effect of discharge frequency
The frequency of power source will affect the stability of discharge, and it is an important parameter which affects the measuring range of plasma anemometer. The effect of discharge frequency is researched here, the peak value of supply voltage is set to 600 V, and the electrode spacing is 3 mm. The discharge frequencies are 700 KHz, 2 MHz, 3.65 MHz and 13.56 MHz, respectively. Figure 13 is the relationship diagram between gap voltage and flow velocity under different discharge frequencies.
As shown in Figure 13, the increase of frequency will cause the increase of the gap voltage under the same flow velocity, this is because the increase of frequency will reduce the capacitive reactance, so the voltage on the capacitor will be reduced, and the gap voltage will increase when the supply voltage remains constant. From the simulation results, it can be found the linear relationships are better when the frequencies are 2MHz and 3.65MHz, the linear relationship will become worse if the frequency becomes larger or smaller. Good linear relationship is more suitable for plasma anemometer, therefore, it is important to choose a reasonable discharge frequency for the plasma anemometer.
Fig. 13
Relationship between gap voltage and flow velocity under different discharge frequencies. 
4.3 The effect of electrode spacing
The electrode spacing is one of the important parameters which affect the gas discharge. In order to research the effect of electrode spacing, the peak value of supply voltage is set to 600 V, and the discharge frequency is 2 MHz. The electrode spacing are 1 mm, 2 mm, 3 mm and 4 mm, respectively. The relationship diagram between gap voltage and flow velocity under different electrode spacing is shown in Figure 14.
As shown in Figure 14, with the increase of the electrode spacing, the effective value of discharge gap voltage increases, this is because the greater the electrode spacing, the greater the impedance of discharge region, the greater the voltage between electrodes. In addition, the following simulation result can be obtained by comparing the data of different electrode spacing: the smaller the electrode spacing, the better the linear relationship. It can be found that the plasma anemometer should be developed in the direction that the electrode spacing is smaller and smaller, this conclusion is also confirmed by previous experiments [3–13]. Within our chose distance, small spacing is more suitable for high frequency plasma anemometer.
Fig. 14
Relationship between gap voltage and flow velocity under different electrode spacing. 
5 Conclusion
In this research, the coupling of gas flow field model and plasma model (xpdp2) is realized, and then the modeling of the AC glow discharge plasma anemometer in nitrogen is completed. The microscopic simulation results show charged particles in the discharge space move towards the direction of flow velocity, the movement of electron is not obvious, and these movements cause the change of the distributions of ion density and electron density, however, the change of electric potential is small under different flow velocities. The macroscopic simulation results show that there is a linear relationship between flow velocity and gap voltage in an allowable error range, which can be applied for flow velocity measurement. The discharge frequency has a great effect on the performance of plasma anemometer, so it is important to choose a reasonable discharge frequency for the plasma anemometer. In terms of high frequency plasma anemometer, the smaller the electrode spacing, the better the linear relationship, and the wider the measurement range, therefore, among the selectable electrode spacings, small spacing is more appropriate.
Author(s) contribution statement
Bing Yu proposed the idea of this research and studied the method of plasma modeling. Bing Yu and Pei Yuan established the gas flow field model. Bing Yu, Pei Yuan, Enyu Shen, and Huaxu Shen realized the coupling of gas flow field model and plasma model. Pei Yuan, Enyu Shen, and Huaxu Shen carried out the simulation analysis. Bing Yu and Pei Yuan finished the manuscript writing.
Acknowledgments
This work is supported by Natural Science Foundation of China (No. 51406083), Natural Science Foundation of Jiangsu Province (BK20140820), Fundamental Research Funds for the Central Universities (No. NJ20160037), Funding of Jiangsu Innovation Program for Graduate Education (No. SJZZ16_0055).
References
 Z. Zhou et al., Flow Meas. Instrum. 45, 118 (2015) [CrossRef] [Google Scholar]
 R.F. Mettler, The anemometric application of an electrical glow discharge in transverse air streams, Ph.D. thesis, California Institute of Technology, USA, 1949. [Google Scholar]
 T. Vrebalovich, The development of direct and alternating current glow discharge anemometers for the study of turbulence phenomena in supersonic flow, Ph.D. thesis, California Institute of Technology, USA, 1954 [Google Scholar]
 E. Matlis, T. Corket, S. Gogineni, A.C. Plasma anemometer for hypersonic mach number experiments, in International Congress on Instrumentation in Aerospace Simulation Facilities, IEEE, San Diego, California, USA, 2006, pp. 245–256 [Google Scholar]
 E. Matlis, T. Corket, S. Gogineni, Plasma anemometer and method for using same, U.S. Patent 7,275,013[P], 2007 [Google Scholar]
 E. Matlis, T. Corket, S. Gogineni, Current control of an AC plasma anemometer for hypersonic flow measurements, in Proceedings of the 59th Annual Meeting of the APS Division of Fluid Dynamics, Tampa Bay, Florida, USA, 2006 [Google Scholar]
 E. Matlis, J. Cameron, S. Morris, T. Corket, A.C. plasma anemometer for axial compressor stall warning, in Proceedings of the 60th Annual Meeting of the APS Division of Fluid Dynamics on American Physical Society, Salt Lake City, Utah, USA, 2007 [Google Scholar]
 E. Matlis, P. Bowles, T. Corket, Plasma sensor suite, in Proceedings of the 61st Annual Meeting of the APS Division of Fluid Dynamics on American Physical Society, San Antonio, Texas, USA, 2008 [Google Scholar]
 E. Matlis, T. Corket, J. Cameron, S. Morris, P. Fay, HighBandwidth plasma sensor suite for highspeed highenthalpy measurements, in Proceedings of the 46th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, USA, 2008 [Google Scholar]
 C. Marshall, E. Matlis, T. Corket, Constant current plasma anemometer, in Proceedings of the 64th Annual Meeting of the APS Division of Fluid Dynamics on American Physical Society, Baltimore, Maryland, USA, 2011 [Google Scholar]
 C. Marshall, E. Matlis, T. Corke et al., Plasma anemometer measurements and optimization, In Proceedings of the 66th Annual Meeting of the APS Division of Fluid Dynamics, Pittsburgh, Pennsylvania, USA, 2013 [Google Scholar]
 C. Marshall et al., Meas. Sci. Technol. 26, 8 (2015) [CrossRef] [Google Scholar]
 C. Marshall, Plasma anemometer and pressure sensor design and characteristics, Ph.D. thesis, University of Notre Dame, USA, 2016 [Google Scholar]
 C.K. Birdsall, A.B. Langdon, Plasma Physics Via Computer Simulation [M] (CRC Press, Florida, USA, 2004) [Google Scholar]
 D.B. Graves, M.J. Kushner, J. Vac. Sci. Technol. A Vac. Surf. Film. 21, S152 (2003) [CrossRef] [Google Scholar]
 P. Gibbon et al., IEEE Trans. Plasma Sci. 38, 2367 (2010) [CrossRef] [Google Scholar]
 R. Sentis, Mathematical Models and Methods for Plasma Physics, Vol. 1[M] (Birkhäuser, Massachusetts, USA, 2014) [CrossRef] [Google Scholar]
 G. Kirsanov et al., Simulation of cold atmospheric plasma component composition and particle densities in air, in Proceedings of the 57th Annual Meeting of the APS Division of Plasma Physics, Savannah, Georgia, USA, 2015 [Google Scholar]
 M. Shigeta, Eur. Phys. J. Appl. Phys. 18, 125 (2002) [CrossRef] [EDP Sciences] [Google Scholar]
 C.K. Birdsall, Plasma theory and simulation group, Proceedings of the California Univ Berkeley Report, California Univ., Berkeley, USA, 1991 [Google Scholar]
 V. Vahedi et al., Phys. Fluids B 5, 2719 (1993) [CrossRef] [Google Scholar]
 V. Vahedi, G. DiPeso, J. Comput. Phys. 131, 149 (1997) [CrossRef] [Google Scholar]
 Y. Ikeda et al., J. Appl. Phys. 88, 6216 (2001) [CrossRef] [Google Scholar]
 E. Eylenceoǧlu, I. Rafatov, J. Phys. Conf. Ser. 572, 012060 (2014) [CrossRef] [Google Scholar]
 F. Cheng, PIC/MCC simulation of glow discharge characteristics, Master thesis, Northwest University, China, 2014 [Google Scholar]
 F.D. Cunden, A. Maltsev, F. Mezzadri, Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 91, 318 (2015) [Google Scholar]
 Y.T. Zhang et al., Plasma Sci. Technol. 8, 438 (2006) [Google Scholar]
 D. Spasojević et al., J. Appl. Phys. 119, 241501 (2016) [Google Scholar]
 I. Enache et al., Eur. Phys. J. Appl. Phys. 33, 15 (2006) [CrossRef] [EDP Sciences] [Google Scholar]
 A.P. Golovitskii, L.D. Tsendin, Tech. Phys. 59, 353 (2014) [CrossRef] [Google Scholar]
Cite this article as: Bing Yu, Pei Yuan, Enyu Shen, Huaxu Shen, Numerical model of A.C. glow discharge plasma anemometer via the coupling of gas flow and plasma model, Eur. Phys. J. Appl. Phys. 81, 30801 (2018)
All Figures
Fig. 1
Twodimensional plasma anemometer model. 

In the text 
Fig. 2
PIC/MCC simulation flow chart, including model initialization, charge division, solving Poisson equation, particle collective motion, boundary condition, MCC model for dealing with particle collisions. 

In the text 
Fig. 3
The typical flow field between electrodes. 

In the text 
Fig. 4
Simulation program block diagram of gas flow field, it contains multiple loop processes until the output is stable. Program codes are written based on this program block diagram. 

In the text 
Fig. 5
Discharge circuit model containing a sinusoidal AC voltage source, an external coupling capacitance and the discharge electrode. 

In the text 
Fig. 6
Coupling process of gas flow field and plasma model. 

In the text 
Fig. 7
Motion path of the charged particles under the action of gas flow field. 

In the text 
Fig. 8
Distributions of ion density under different flow velocities. 

In the text 
Fig. 9
Distributions of electron density under different flow velocities. 

In the text 
Fig. 10
Distributions of electric potential under different flow velocities. 

In the text 
Fig. 11
Simulation waveforms of the supply voltage and the gap voltage. 

In the text 
Fig. 12
Relationship between gap voltage and flow velocity under different supply voltages. 

In the text 
Fig. 13
Relationship between gap voltage and flow velocity under different discharge frequencies. 

In the text 
Fig. 14
Relationship between gap voltage and flow velocity under different electrode spacing. 

In the text 
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