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Modeling study on the circuit model of AC plasma anemometer
Accepted Manuscript Modeling Study on the Circuit Model of AC Plasma Anemometer Bing Yu, Pei Yuan, Enyu Shen PII: DOI: Reference:
S0263-2241(17)30511-0 http://dx.doi.org/10.1016/j.measurement.2017.08.012 MEASUR 4910
To appear in:
Measurement
Received Date: Revised Date: Accepted Date:
2 May 2017 10 July 2017 7 August 2017
Please cite this article as: B. Yu, P. Yuan, E. Shen, Modeling Study on the Circuit Model of AC Plasma Anemometer, Measurement (2017), doi: http://dx.doi.org/10.1016/j.measurement.2017.08.012
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Modeling Study on the Circuit Model of AC Plasma Anemometer
Bing Yu a, *, Pei Yuan a, Enyu Shen a
a
Nanjing University of Aeronautics and Astronautics, Jiangsu Province Key Laboratory of Aerospace
Power System, Key Laboratory of Aero-engine Thermal Environment and Structure, Ministry of Industry and Information Technology, Nanjing 210016, China
* Corresponding author at: Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China.
E-mail address: [email protected] (B.Yu).
Abstract A new approach to establish the circuit model of alternating current (AC) plasma anemometer is proposed. Firstly, experimental system is introduced to illustrate the experimental studies. Then all circuit models are built on basis of theoretical and experimental analysis, including the equivalent circuits of the positive column space and the sheath, the circuit models of AC plasma anemometer without airflow and under airflow, parameter matching of the equivalent circuit models without airflow and under airflow. Finally, the circuit models are verified by comparing the simulation currents with experimental currents. The final circuit model takes into account the whole framework of AC plasma anemometer containing the positive column space, the sheath and the diffusion region, which is proved feasible and reliable, and it can provide an effective tool for the future research of AC plasma anemometer.
Keywords: Plasma anemometer; Circuit model; Glow discharge; Airflow velocity
1. Introduction
Nowadays, studies on the hypersonic aircraft and near-space hypersonic vehicle (NSHV) have become research hotspots, more and more research institutes pay great attentions to this field [1,2]. In
order to promote the developments of the hypersonic flight technology, the hypersonic airflow and its aerodynamic characteristics should be investigated intensively [3,4]. Due to the hypersonic aircraft and NSHV work in the high-speed and high-temperature environments, which brings huge challenges to the experiment and validation works [5]. The traditional measurement methods have strict requirements for their working environment. The cup-type mechanical anemometer and the Pitot tube anemometer have defects of large size and poor accuracy, which limit their developments. On the other hand, the piezoelectric anemometer is susceptible to ambient temperature and cannot be applied for measuring hypersonic airflow. Therefore, new measurement technology that can meet these strict requirements is urgently desired. In the existing schemes, alternating current (AC) plasma anemometer is a very promising method for its advantages of high precision, wide range, high signal-to-noise ratio, and it will have a wide application prospect for researches on the hypersonic flight technology [6–8]. Recently, the AC plasma anemometer studied by Marshall, Matlis and Corket [7–10] has made great success, their contributions include: 1). the experimental circuit including resistance and capacitance components could simulate a dielectric-barrier to maintain the diffuse plasma; 2). hot-wire anemometer and AC plasma anemometer were comparatively studied, the performances of AC plasma anemometer were found to be better in harsh environments or at high Mach numbers, in which hot-wire anemometer may either have difficulty in surviving or lack the necessary frequency response. However, currently the AC plasma anemometer researches are still limited to experimental study [6–10], the lack of sufficient theoretical and simulation studies has greatly restricted its development. Actually, in addition to Mettler’s attempt to derive the theory of AC plasma anemometer [11], its theoretical study has not made great progress. With the rapid development of simulation technology and computer technology, the circuit model for glow discharge has been established successfully [12], which makes the simulation theoretical research for AC plasma anemometer possible. Circuit model simulation can reflect characteristics of the discharge circuit, which will be helpful for the optimal parameters selection of a plasma anemometer, and eventually promote the further developments of AC plasma anemometer in field of hypersonic flight technology. In this study, a novel modeling method for AC plasma anemometer is proposed. The experimental arrangement used for conducting experiments is introduced firstly. Then the theoretical analysis of glow discharge is presented, and the different circuit components are chosen and quantitatively determined.
Finally, comparisons between the simulation currents and the experimental currents have been carried out to validate the circuit models.
2. Experimental Set-up
The structure diagram of experiment system is shown in Fig. 1. The system includes the power-supply module, the plasma generator module, two negative feedback coupling circuit modules, the airflow supply module, the digital anemometer, data acquisition module and data processing module. The power-supply module adopts a CTP-2000K AC voltage source, its voltage and frequency output can be adjusted continuously, where the voltage range is 0-30 kV, and the frequency range is 5-20 kHz. The plasma generator adopts the structure of needle-to-needle, which is composed of two metal probes, the probe spacing can be adjusted between 0-5 mm, and the discharge end of the probe is equivalent to a small flat plate. One probe connected to the high voltage side is the anode, the other one is the cathode. The plasma will be generated between two probes when glow discharge occurs. As shown in Fig. 1, the coupling resistor ( R1 , R2 ) and the coupling capacitor ( C1 , C2 ) are connected in series to form the negative feedback coupling circuit module, it can be used for improving the stability of the system and suppressing the positive feedback process of the discharge [6,13], where C1 C2 , R1 R2 . The airflow supply module consists of three parts: air compressor, valve and air nozzle. The provided airflow velocity can be adjusted continuously in a range of 0-150 m/s. In addition, a thermal digital anemometer is adopted in the experiment; its measurement range is 0-30 m/s with accuracy ±3%. The relationship between airflow velocity and discharge current is calibrated by the thermal digital anemometer. The data acquisition module also contains three parts: the sampling resistance Rs =50 Ω, a voltage sensor and an analog-to-digital (AD) conversion circuit (sampling rate is 250 kS/s). The discharge current is measured indirectly by measuring the voltage value on Rs , and then through the AD conversion circuit to convert the analog signal into digital signal, finally, the digital signal is processed and analyzed by the data processing module [6].
R1
C1
Digital anemometer
R2
RS
C2 Air compressor
Data acquisition module Data processing module
Fig. 1. Experimental arrangement The experiment can be conducted by using the above system. Fig. 2 are the enlarged pictures of experimental phenomena.
Fig. 2. Experimental phenomena without airflow (left) and under airflow (right)
3. Circuit Model of AC Plasma Anemometer
The whole circuit model is built on basis of the theoretical and experimental analysis. Due to the plasma in the experiment is produced by glow discharge, the theoretical analysis of glow discharge is introduced firstly, and the equivalent circuits of the discharge regions are proposed. Then the circuit models of AC plasma anemometer without airflow and under airflow are analyzed and established separately. Finally, circuit component parameters under different airflow velocities are matched according to theoretical and experimental analysis.
3.1. Theoretical analysis of glow discharge in the experiment
The plasma in the experiment is produced by glow discharge; therefore, the characteristics of glow discharge in air are necessary to be investigated. Glow discharge is a phenomenon of gas self-sustaining discharge, which contains five different spaces: cathode space (Aston dark space, cathode glow space, and Crookes dark space), negative glow space, Faraday dark space, positive column space, and anode space. The positive column space is the plasma region, the electron and ion densities are large and equal in this space [14]. The remaining spaces constitute the sheath, the changes of electric field are concentrated in this region [15]. Thus, the circuit model of glow discharge should be studied from two aspects: the positive column space and the sheath. The discharge end of the metal probe is the flat plate structure, and the basic model of flat plate glow discharge is shown in Fig. 3. The sinusoidal current I (t ) flows through the two discharge plates (a and c), which can be expressed in the plural form: I (t ) Re ( I i e jt ) , where I i is current amplitude, is supply frequency. Considering a glow discharge system as shown in Fig. 3, the spacing between the two electrodes is l , each plate area is S , the plate gap is filled with air, its density is g . When plasma discharge occurs, a voltage V (t ) appears between the plates, and the power injected into the plasma is
P(t ) , in the plasma area: e i , however, in the sheath: e i , where e is electron density, and the i is ion density. The instantaneous sheath thickness is d (t ) , its time average value is d t , dt l . Sheath a
e i
da(t) a
Plasma
dc(t)
e i h
c
Sheath c
e i
l
I (t )
Fig. 3. Glow discharge model of flat plate
3.2. Equivalent circuits of the positive column space and sheath 3.2.1. The positive column space When the thickness of the flat plate plasma is h and the cross-sectional area is S , its admittance
Yp can be calculated according to the following equations [16,17]:
Yp j p
p 0 [1
S h
(1)
2 pe ] ( jvn )
(2)
where p is the permittivity of plasma, 0 is the permittivity of vacuum, pe is the electron plasma frequency, it is also the fundamental characteristic frequency of plasma, vn is the collision frequency between electrons and neutral particles. When the ion density is approximately uniform,
h l 2dt constant, and the admittance of the flat plate plasma Y f could be presented as:
Y f jC p
1
(3)
j Lp Rp
where C p 0 S / h is the vacuum capacitance value, Lp fe2C p1 is the plasma inductance value, and Rp vn Lp is the plasma resistance value, in this form, the positive column space can be equivalent to a capacitor and a series circuit in parallel, and the series circuit includes a resistor and an inductor. However, when is small, according to the Eq. (3), the plasma can be equivalent to a resistor. In this experiment, the supply frequency is 10 KHz, which belongs to the low frequency discharge in the discharge field. Therefore, the positive column space can be equivalent to a resistor based on the above analysis. The equivalent circuit is shown in Fig. 4.
Rp
Low frequency
Cp
R0 Lp
Fig. 4. Equivalent circuit of the positive column space 3.2.2. The sheath In essence, when the plasma is disturbed, the Debye shielding will occur. The sheath is the space charge layer produced by Debye shielding, which is the area where the plasma interacts with the boundary. Regardless of the high frequency or low frequency, the current in the sheath is the sum of the conduction current and the displacement current. In order to investigate the proportion of displacement current I d , a parallel plate model in the vacuum state is used to estimate it.
Id
0Vv
(4)
d (t )
where Vv is power supply voltage amplitude. To study the conduction current, taking cathode sheath as an example, the current reaching the cathode is almost only the ion current, therefore, the conduction current I c can be expressed by the ion current.
Ic
2 0V0i 3d (t )
2T i pi e V0
(5)
1
4
(6)
where V0 is the voltage applied to sheath, i is the boundary of the frequency, pi is the ion plasma frequency at the sheath boundary, Te is the electronic temperature. When i , it belongs to low frequency discharge, otherwise it belongs to high frequency discharge, in this field of gas discharge,
i 5MHz . I d 3 Vv Ic 2 V0 i
(7)
For the high voltage sheaths, Vv V0 and 10KHz in this experiment ( i ), therefore,
I d I c , so the displacement current is very small and can be ignored. Under the action of conduction current, the sheath can be seen as purely resistive. In addition, due to the symmetry of the structure, it is necessary to satisfy the condition that the time-averaged conduction current flowing to the electrode should be zero in a cycle. However, the current reaching the cathode is almost only the ion current in the sheath, so it is also necessary to make the electrons in the plasma have the opportunity to reach the plate, in this case, the thickness of the sheath
d (t ) must be zero at a certain time, and at this moment, voltage drop in the sheath should be reduced to zero. This property of the sheath is like the nature of diode, so this characteristic can be equivalent by a diode, and the positive direction is the direction from the electrode to the plasma. According to the above analysis, the sheath of low frequency discharge can be equivalent to the diode and resistor in parallel. The specific form is shown in Fig. 5.
Da
Ra
Fig. 5. Equivalent circuit of sheath at low frequency
3.3. Circuit model of AC plasma anemometer without airflow As described in 3.1, the overall framework of the air glow discharge includes the positive column space and the sheath, therefore, the whole circuit model of glow discharge can be obtained by studying the equivalent model of each part. For the sake of proper design, the connection structure should be considered. In the experiment, the two metal probes of the plasma generator are symmetrical, indicating that the structure of the two plate electrodes is symmetrical, so the two sheaths near the two different electrode plates are also symmetrical. Actually, the glow discharge has the following regional structure: sheath - plasma region - sheath, on this basis, the connection of each region can be represented by a series circuit. In summary, the whole circuit model of glow discharge in air is shown as Fig. 6.
Ra
Da
R0
Rc
Dc
Fig. 6. Equivalent circuit of glow discharge in air The normal gas discharge is a positive feedback process, resulting in the low frequency glow discharge easily transits to the arc discharge, which is an unstable discharge state. In order to limit the transition, the negative feedback coupling circuit module ( R1 , R2 , C1 , C2 ) is introduced into the experimental system, the added R-C circuits can produce a dielectric-barrier-discharge (DBD) effect to stabilize the discharge plasma and discharge waveforms under airflow. To establish the circuit model of AC plasma anemometer here, the overall structure of the model needs to be consistent with the
experimental system. Therefore, it is necessary to add the negative feedback coupling circuit modules, and in this way, the circuit model of AC plasma anemometer without airflow can be obtained, its specific form is shown in Fig. 7. C1
R1
Ra
Da
R0
Rc
C2
Dc
R2
Fig. 7. Circuit model of AC plasma anemometer without airflow The plasma in the positive column space may be regarded as a dielectric or a conductor depending on the relationship of and vn . If vn , the plasma in the positive column space is seen as a dielectric, and its permittivity p can be calculated by
p 0 [1
2 pe ] 2
(8)
If vn , the plasma in the positive column space can be regarded as conductor, its conductivity p follows the relation:
p
2 0 pe
vn
e2 e mvn
where vn [Hz] 1.52 107 P[pa] Te[ev] 500MHz , Te 10ev
(9)
is the electronic temperature,
m 9.1095 1031 kg is the electronic mass, electron charge e 1.6 1019 C , e 1016 cm-3 is electron density. Then the resistance R0 in the positive column space can be presented as:
R0
1 l p S
(10)
where S is the cross-sectional area of plasma, here it is a circular section, S r 2 , r 0.4mm ,
l 3mm .
In the experiments, 10KHz vn , therefore, the plasma in the positive column space needs to be calculated as a conductor. Through the above calculation, the resistance R0 can be obtained, it is about
90Ω , and this resistance can be ignored compared to the sheath resistance. In case of no airflow velocity, the resistance R0 is set to 90Ω .
3.4. Circuit model of AC plasma anemometer under airflow The plasma in the plasma region will diffuse under the action of airflow, so a diffusion region will be added, and the particles in the diffusion region are dominated by the diffusion motion of charged particles. As we all know, in the sheath, the number of electrons and ions is small, and it is much smaller than the plasma region. Therefore, the discharge parameters in sheath remain almost constant under the action of airflow, and the main changes are in the plasma region. Mettler [11] had conducted a theoretical analysis of the plasma anemometer, as shown in Fig. 8, by the action of airflow in the direction of Y-axis, all particles including electrons and ions should have velocities in the direction of Y-axis. However, the mass of electron is very small and it will obtain a very large velocity in the direction of X-axis under the action of electric field, compared to the velocity in the X-axis direction, the velocity of airflow attached to electron in the Y-axis direction can be neglected, so the electrons are still moving along the X axis, but the mass of ion is much larger than electron, the velocity of airflow attached to ion can’t be neglected. Therefore, under the action of airflow, only the ions movement in the plasma region will change. Thus, through the above analysis, it can be known that the current in the diffusion region is mainly the ion conduction current. electron + ion
y
+ Anode
x
+ + - + + -
Cat hode
gas flow direction
Air Nozzle
AC
Fig. 8. The movement of particles under airflow
According to previous studies [18–21], the ion conduction current in the diffusion region can be equivalent to a series circuit，which contains a resistor and an inductor. The series circuit conforms to the characteristics of the diffusion region generated by AC plasma anemometer, the inductance L1 represents the ion conduction current, and the resistance R3 consists of two aspects: the resistance of conduction current and the resistance of ion thermal motion in the diffusion region. Therefore, the final circuit model of AC plasma anemometer under airflow can be obtained, as shown in Fig. 9. C1
R1
Ra
Da
L1 R0 R3 Rc
C2
Dc
R2
Fig. 9. Circuit model of AC plasma anemometer under airflow
3.5. Parameter Matching of the Circuit Models Firstly, the circuit model without airflow velocity is analyzed here. As shown in Fig. 10, the simulation circuit is established in the circuit simulation software OrCAD. According to the establishing rules of simulation circuit in OrCAD, the coupling capacitance can’t be connected in series with the simulation circuit directly, so a high value resistance R5 is added in parallel with the coupling capacitance, the high value resistance is equal to the broken circuit, it has no effect on the original circuit. Before matching the parameters of the model, the experimental data of voltage and current are respectively imported into two circuits, as shown in Fig. 10, the experimental voltage data is imported into the left circuit, the experimental current data is imported into the right circuit, and this is achieved by the data communication technology between OrCAD and MATLAB. In order to match the parameters of the model, the values of the circuit model components need to be adjusted so that the simulation current of the left circuit can be the same as the experimental current of the right circuit. Furthermore, in order to be
consistent with the experiment C1 C2 220pF , R1 R2 200Ω , these values are same as those in the experiment. In addition, R0 90Ω , which has been analyzed in 3.3. The diode is close to the ideal diode and its value does not need to be adjusted. Therefore, only the resistance values in the sheath need to be adjusted. The two sheaths are symmetrical so that the two resistors are also symmetrical, they should have the same value. According to the analysis in 3.3, these resistance values are much larger than the resistance in the plasma region. The comparative analysis of the experimental current and the simulation current is conducted, the final resistance values are selected as follows: Ra Rc 3.2kΩ , in this case,
C1
R1
220p
200
1
the simulation current is more consistent with the experimental current.
Ra 3.2k
2
Da
R5
100000000000000
l1
V1
S
-
S
R0 90
Implementation = Vin
-
Implementation = lin
R4 1
100000000000000 0 2
R5
R2
220p
200
Rc 3.2k
Dc 1
C2
0
Fig. 10. Simulation diagram of the circuit model without airflow For the circuit model under airflow, the number of parameters required to be adjusted will increase. For example, when the airflow velocity is 3.02m/s, its simulation diagram is shown in Fig. 11, as analyzed in 3.4, the parameters of the sheath remain unchanged, while the parameters R0 , L1 , R3 will change. Since the experiments belong to the low-frequency discharge, i , resulting in the change of inductance in the diffusion region cannot significantly change the current waveform of the discharge circuit, therefore, the inductance value is set to 300 H here. Under the action of airflow, the remaining two parameters ( R0 , R3 ) will change obviously, some ions will escape from the discharge region, which
causes the increase of R0 . The number of ions in the diffusion region is small, so the resistance R3 is larger than R0 . However, with the increase of the airflow velocity, the number of ions in the discharge region will decrease, so the resistance R0 will increase, and the number of ions in the diffusion region will increase, so the resistance R3 will decrease. The parameters of R0 and R3 need to be adjusted based on the above rules, and according to the comparative analysis of the experimental and simulation current, when the airflow velocity is 3.02 m/s, it can be found that the simulation current is more consistent with experimental current in the case of R0 98Ω , R3 420Ω . In addition, when the airflow velocity is 6.52m/s, a similar analysis is conducted, and the final matching parameters are R0 117Ω and
C1
R1
220p
200
1
R3 406Ω .
Ra 3.2k
Da 2
L1 300H
R5 V1
S
-
100000000000000
l1
S
R0 98
Implementation = Vin
-
Implementation = lin
R4 1
R3 420
100000000000000
0 2
R5
R2
220p
200
Rc 3.2k
Dc 1
C2
0
Fig. 11. Simulation diagram of the circuit model under airflow
4. Verification of the Circuit Models
As described in 3.5, the simulation currents are compared with the experimental currents in case of different airflow velocities. The simulation voltage data is derived from the experimental voltage data, so the simulation voltage is same as the experimental voltage in the same group. As shown in Figs. 12-14, by
comparing the simulation current and the experimental current, it can be seen that the obtained simulation results are in good agreement with the experimental results, and the largest current relative error of the three groups is not more than 0.8%, which indicate that the circuit model is feasible and reliable.
0.08
6000
0.8%
Current/A Current/A Voltage/V
0.06
Current error 0.6%
4000 0.04
0.4%
0
-0.02 -2000
Voltage (V)
Current (A)
0.00
Current error
2000 0.02
-0.04
0.2%
0.0%
-0.2% -4000
-0.06 -0.4% -0.08
-6000 0.10
0.15
0.20
0.25
0.30
0.10
0.35
0.15
0.20
0.25
0.30
0.35
Time (ms))
Time (ms)
Fig. 12. Experimental and simulation results (left), current error (right), Vg 0m/s , V 5000V and 10KHz . Vg : airflow velocity, V : supply voltage, : supply frequency
6000 Current/A Current/A Voltage/V
0.06
Current error 0.4% 4000
0.04
0
-0.02
-2000
Current error
0.00
Voltage (V)
Current (A)
0.2%
2000
0.02
0.0%
-0.2%
-0.04 -4000 -0.4%
-0.06 -6000 0.10
0.15
0.20
0.25
Time (ms)
0.30
0.35
0.10
0.15
0.20
0.25
0.30
0.35
Time (ms)
Fig. 13. Experimental and simulation results (left), current error (right), Vg 3.02m/s , V 5000V and 10KHz . Vg : airflow velocity, V : supply voltage, : supply frequency
0.06
6000
Current error 0.6% 4000
0.02
2000
0.00
0
-0.02
-2000
-0.04
-4000
-0.06
-6000
0.4% Current error
0.04
Voltage (V)
Current (A)
Current/A Current/A Voltage/V
0.2%
0.0%
-0.2%
0.10
0.15
0.20
0.25
0.30
0.35
Time (ms)
0.10
0.15
0.20
0.25
0.30
0.35
Time (ms)
Fig. 14. Experimental and simulation results (left), current error (right), Vg 6.52m/s , V 5000V and 10KHz . Vg : airflow velocity, V : supply voltage, : supply frequency
5. Conclusion
The circuit model of AC plasma anemometer based on the theoretical and experimental analysis is obtained in this article. Its equivalent circuit structure is studied from three aspects: the positive column space, the sheath and the diffusion region. The positive column space is equivalent to a resistor. The sheath is composed of a diode and a resistor in parallel. The diffusion region is equivalent to a series circuit， which contains a resistor and an inductor. After the whole circuit model is established, its feasibility and reliability are verified by the OrCAD simulation. According to the simulation results, it is known that the discharge current decreases with the increase of airflow velocity, which is consistent with the experimental results of plasma anemometer conducted by previous researchers [7–11]. The circuit characteristics of AC plasma anemometer are considered by the established circuit model, so it can in turn be used as a tool to study and improve the plasma anemometer.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (No. 51406083); the Natural Science Foundation of Jiangsu Province (BK20140820); the Fundamental Research Funds for
the Central Universities (No. NJ20160037); and the Funding of Jiangsu Innovation Program for Graduate Education (No. SJZZ16_0055).
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Highlights 1. The plasma anemometer experiments based on R-C coupling negative feedback AC glow discharge are conducted. 2. A novel circuit model of AC plasma anemometer is proposed by analyzing the whole discharge structure. 3. Circuit models of AC plasma anemometer without airflow and under airflow are established separately. 4. Circuit component parameters under different airflow velocities are matched according to theoretical and experimental analysis. 5. Simulation results are in good agreement with the experimental results shows that the obtained circuit model is feasible and reliable.
Graphical abstract
S0263-2241(17)30511-0 http://dx.doi.org/10.1016/j.measurement.2017.08.012 MEASUR 4910
To appear in:
Measurement
Received Date: Revised Date: Accepted Date:
2 May 2017 10 July 2017 7 August 2017
Please cite this article as: B. Yu, P. Yuan, E. Shen, Modeling Study on the Circuit Model of AC Plasma Anemometer, Measurement (2017), doi: http://dx.doi.org/10.1016/j.measurement.2017.08.012
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Modeling Study on the Circuit Model of AC Plasma Anemometer
Bing Yu a, *, Pei Yuan a, Enyu Shen a
a
Nanjing University of Aeronautics and Astronautics, Jiangsu Province Key Laboratory of Aerospace
Power System, Key Laboratory of Aero-engine Thermal Environment and Structure, Ministry of Industry and Information Technology, Nanjing 210016, China
* Corresponding author at: Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China.
E-mail address: [email protected] (B.Yu).
Abstract A new approach to establish the circuit model of alternating current (AC) plasma anemometer is proposed. Firstly, experimental system is introduced to illustrate the experimental studies. Then all circuit models are built on basis of theoretical and experimental analysis, including the equivalent circuits of the positive column space and the sheath, the circuit models of AC plasma anemometer without airflow and under airflow, parameter matching of the equivalent circuit models without airflow and under airflow. Finally, the circuit models are verified by comparing the simulation currents with experimental currents. The final circuit model takes into account the whole framework of AC plasma anemometer containing the positive column space, the sheath and the diffusion region, which is proved feasible and reliable, and it can provide an effective tool for the future research of AC plasma anemometer.
Keywords: Plasma anemometer; Circuit model; Glow discharge; Airflow velocity
1. Introduction
Nowadays, studies on the hypersonic aircraft and near-space hypersonic vehicle (NSHV) have become research hotspots, more and more research institutes pay great attentions to this field [1,2]. In
order to promote the developments of the hypersonic flight technology, the hypersonic airflow and its aerodynamic characteristics should be investigated intensively [3,4]. Due to the hypersonic aircraft and NSHV work in the high-speed and high-temperature environments, which brings huge challenges to the experiment and validation works [5]. The traditional measurement methods have strict requirements for their working environment. The cup-type mechanical anemometer and the Pitot tube anemometer have defects of large size and poor accuracy, which limit their developments. On the other hand, the piezoelectric anemometer is susceptible to ambient temperature and cannot be applied for measuring hypersonic airflow. Therefore, new measurement technology that can meet these strict requirements is urgently desired. In the existing schemes, alternating current (AC) plasma anemometer is a very promising method for its advantages of high precision, wide range, high signal-to-noise ratio, and it will have a wide application prospect for researches on the hypersonic flight technology [6–8]. Recently, the AC plasma anemometer studied by Marshall, Matlis and Corket [7–10] has made great success, their contributions include: 1). the experimental circuit including resistance and capacitance components could simulate a dielectric-barrier to maintain the diffuse plasma; 2). hot-wire anemometer and AC plasma anemometer were comparatively studied, the performances of AC plasma anemometer were found to be better in harsh environments or at high Mach numbers, in which hot-wire anemometer may either have difficulty in surviving or lack the necessary frequency response. However, currently the AC plasma anemometer researches are still limited to experimental study [6–10], the lack of sufficient theoretical and simulation studies has greatly restricted its development. Actually, in addition to Mettler’s attempt to derive the theory of AC plasma anemometer [11], its theoretical study has not made great progress. With the rapid development of simulation technology and computer technology, the circuit model for glow discharge has been established successfully [12], which makes the simulation theoretical research for AC plasma anemometer possible. Circuit model simulation can reflect characteristics of the discharge circuit, which will be helpful for the optimal parameters selection of a plasma anemometer, and eventually promote the further developments of AC plasma anemometer in field of hypersonic flight technology. In this study, a novel modeling method for AC plasma anemometer is proposed. The experimental arrangement used for conducting experiments is introduced firstly. Then the theoretical analysis of glow discharge is presented, and the different circuit components are chosen and quantitatively determined.
Finally, comparisons between the simulation currents and the experimental currents have been carried out to validate the circuit models.
2. Experimental Set-up
The structure diagram of experiment system is shown in Fig. 1. The system includes the power-supply module, the plasma generator module, two negative feedback coupling circuit modules, the airflow supply module, the digital anemometer, data acquisition module and data processing module. The power-supply module adopts a CTP-2000K AC voltage source, its voltage and frequency output can be adjusted continuously, where the voltage range is 0-30 kV, and the frequency range is 5-20 kHz. The plasma generator adopts the structure of needle-to-needle, which is composed of two metal probes, the probe spacing can be adjusted between 0-5 mm, and the discharge end of the probe is equivalent to a small flat plate. One probe connected to the high voltage side is the anode, the other one is the cathode. The plasma will be generated between two probes when glow discharge occurs. As shown in Fig. 1, the coupling resistor ( R1 , R2 ) and the coupling capacitor ( C1 , C2 ) are connected in series to form the negative feedback coupling circuit module, it can be used for improving the stability of the system and suppressing the positive feedback process of the discharge [6,13], where C1 C2 , R1 R2 . The airflow supply module consists of three parts: air compressor, valve and air nozzle. The provided airflow velocity can be adjusted continuously in a range of 0-150 m/s. In addition, a thermal digital anemometer is adopted in the experiment; its measurement range is 0-30 m/s with accuracy ±3%. The relationship between airflow velocity and discharge current is calibrated by the thermal digital anemometer. The data acquisition module also contains three parts: the sampling resistance Rs =50 Ω, a voltage sensor and an analog-to-digital (AD) conversion circuit (sampling rate is 250 kS/s). The discharge current is measured indirectly by measuring the voltage value on Rs , and then through the AD conversion circuit to convert the analog signal into digital signal, finally, the digital signal is processed and analyzed by the data processing module [6].
R1
C1
Digital anemometer
R2
RS
C2 Air compressor
Data acquisition module Data processing module
Fig. 1. Experimental arrangement The experiment can be conducted by using the above system. Fig. 2 are the enlarged pictures of experimental phenomena.
Fig. 2. Experimental phenomena without airflow (left) and under airflow (right)
3. Circuit Model of AC Plasma Anemometer
The whole circuit model is built on basis of the theoretical and experimental analysis. Due to the plasma in the experiment is produced by glow discharge, the theoretical analysis of glow discharge is introduced firstly, and the equivalent circuits of the discharge regions are proposed. Then the circuit models of AC plasma anemometer without airflow and under airflow are analyzed and established separately. Finally, circuit component parameters under different airflow velocities are matched according to theoretical and experimental analysis.
3.1. Theoretical analysis of glow discharge in the experiment
The plasma in the experiment is produced by glow discharge; therefore, the characteristics of glow discharge in air are necessary to be investigated. Glow discharge is a phenomenon of gas self-sustaining discharge, which contains five different spaces: cathode space (Aston dark space, cathode glow space, and Crookes dark space), negative glow space, Faraday dark space, positive column space, and anode space. The positive column space is the plasma region, the electron and ion densities are large and equal in this space [14]. The remaining spaces constitute the sheath, the changes of electric field are concentrated in this region [15]. Thus, the circuit model of glow discharge should be studied from two aspects: the positive column space and the sheath. The discharge end of the metal probe is the flat plate structure, and the basic model of flat plate glow discharge is shown in Fig. 3. The sinusoidal current I (t ) flows through the two discharge plates (a and c), which can be expressed in the plural form: I (t ) Re ( I i e jt ) , where I i is current amplitude, is supply frequency. Considering a glow discharge system as shown in Fig. 3, the spacing between the two electrodes is l , each plate area is S , the plate gap is filled with air, its density is g . When plasma discharge occurs, a voltage V (t ) appears between the plates, and the power injected into the plasma is
P(t ) , in the plasma area: e i , however, in the sheath: e i , where e is electron density, and the i is ion density. The instantaneous sheath thickness is d (t ) , its time average value is d t , dt l . Sheath a
e i
da(t) a
Plasma
dc(t)
e i h
c
Sheath c
e i
l
I (t )
Fig. 3. Glow discharge model of flat plate
3.2. Equivalent circuits of the positive column space and sheath 3.2.1. The positive column space When the thickness of the flat plate plasma is h and the cross-sectional area is S , its admittance
Yp can be calculated according to the following equations [16,17]:
Yp j p
p 0 [1
S h
(1)
2 pe ] ( jvn )
(2)
where p is the permittivity of plasma, 0 is the permittivity of vacuum, pe is the electron plasma frequency, it is also the fundamental characteristic frequency of plasma, vn is the collision frequency between electrons and neutral particles. When the ion density is approximately uniform,
h l 2dt constant, and the admittance of the flat plate plasma Y f could be presented as:
Y f jC p
1
(3)
j Lp Rp
where C p 0 S / h is the vacuum capacitance value, Lp fe2C p1 is the plasma inductance value, and Rp vn Lp is the plasma resistance value, in this form, the positive column space can be equivalent to a capacitor and a series circuit in parallel, and the series circuit includes a resistor and an inductor. However, when is small, according to the Eq. (3), the plasma can be equivalent to a resistor. In this experiment, the supply frequency is 10 KHz, which belongs to the low frequency discharge in the discharge field. Therefore, the positive column space can be equivalent to a resistor based on the above analysis. The equivalent circuit is shown in Fig. 4.
Rp
Low frequency
Cp
R0 Lp
Fig. 4. Equivalent circuit of the positive column space 3.2.2. The sheath In essence, when the plasma is disturbed, the Debye shielding will occur. The sheath is the space charge layer produced by Debye shielding, which is the area where the plasma interacts with the boundary. Regardless of the high frequency or low frequency, the current in the sheath is the sum of the conduction current and the displacement current. In order to investigate the proportion of displacement current I d , a parallel plate model in the vacuum state is used to estimate it.
Id
0Vv
(4)
d (t )
where Vv is power supply voltage amplitude. To study the conduction current, taking cathode sheath as an example, the current reaching the cathode is almost only the ion current, therefore, the conduction current I c can be expressed by the ion current.
Ic
2 0V0i 3d (t )
2T i pi e V0
(5)
1
4
(6)
where V0 is the voltage applied to sheath, i is the boundary of the frequency, pi is the ion plasma frequency at the sheath boundary, Te is the electronic temperature. When i , it belongs to low frequency discharge, otherwise it belongs to high frequency discharge, in this field of gas discharge,
i 5MHz . I d 3 Vv Ic 2 V0 i
(7)
For the high voltage sheaths, Vv V0 and 10KHz in this experiment ( i ), therefore,
I d I c , so the displacement current is very small and can be ignored. Under the action of conduction current, the sheath can be seen as purely resistive. In addition, due to the symmetry of the structure, it is necessary to satisfy the condition that the time-averaged conduction current flowing to the electrode should be zero in a cycle. However, the current reaching the cathode is almost only the ion current in the sheath, so it is also necessary to make the electrons in the plasma have the opportunity to reach the plate, in this case, the thickness of the sheath
d (t ) must be zero at a certain time, and at this moment, voltage drop in the sheath should be reduced to zero. This property of the sheath is like the nature of diode, so this characteristic can be equivalent by a diode, and the positive direction is the direction from the electrode to the plasma. According to the above analysis, the sheath of low frequency discharge can be equivalent to the diode and resistor in parallel. The specific form is shown in Fig. 5.
Da
Ra
Fig. 5. Equivalent circuit of sheath at low frequency
3.3. Circuit model of AC plasma anemometer without airflow As described in 3.1, the overall framework of the air glow discharge includes the positive column space and the sheath, therefore, the whole circuit model of glow discharge can be obtained by studying the equivalent model of each part. For the sake of proper design, the connection structure should be considered. In the experiment, the two metal probes of the plasma generator are symmetrical, indicating that the structure of the two plate electrodes is symmetrical, so the two sheaths near the two different electrode plates are also symmetrical. Actually, the glow discharge has the following regional structure: sheath - plasma region - sheath, on this basis, the connection of each region can be represented by a series circuit. In summary, the whole circuit model of glow discharge in air is shown as Fig. 6.
Ra
Da
R0
Rc
Dc
Fig. 6. Equivalent circuit of glow discharge in air The normal gas discharge is a positive feedback process, resulting in the low frequency glow discharge easily transits to the arc discharge, which is an unstable discharge state. In order to limit the transition, the negative feedback coupling circuit module ( R1 , R2 , C1 , C2 ) is introduced into the experimental system, the added R-C circuits can produce a dielectric-barrier-discharge (DBD) effect to stabilize the discharge plasma and discharge waveforms under airflow. To establish the circuit model of AC plasma anemometer here, the overall structure of the model needs to be consistent with the
experimental system. Therefore, it is necessary to add the negative feedback coupling circuit modules, and in this way, the circuit model of AC plasma anemometer without airflow can be obtained, its specific form is shown in Fig. 7. C1
R1
Ra
Da
R0
Rc
C2
Dc
R2
Fig. 7. Circuit model of AC plasma anemometer without airflow The plasma in the positive column space may be regarded as a dielectric or a conductor depending on the relationship of and vn . If vn , the plasma in the positive column space is seen as a dielectric, and its permittivity p can be calculated by
p 0 [1
2 pe ] 2
(8)
If vn , the plasma in the positive column space can be regarded as conductor, its conductivity p follows the relation:
p
2 0 pe
vn
e2 e mvn
where vn [Hz] 1.52 107 P[pa] Te[ev] 500MHz , Te 10ev
(9)
is the electronic temperature,
m 9.1095 1031 kg is the electronic mass, electron charge e 1.6 1019 C , e 1016 cm-3 is electron density. Then the resistance R0 in the positive column space can be presented as:
R0
1 l p S
(10)
where S is the cross-sectional area of plasma, here it is a circular section, S r 2 , r 0.4mm ,
l 3mm .
In the experiments, 10KHz vn , therefore, the plasma in the positive column space needs to be calculated as a conductor. Through the above calculation, the resistance R0 can be obtained, it is about
90Ω , and this resistance can be ignored compared to the sheath resistance. In case of no airflow velocity, the resistance R0 is set to 90Ω .
3.4. Circuit model of AC plasma anemometer under airflow The plasma in the plasma region will diffuse under the action of airflow, so a diffusion region will be added, and the particles in the diffusion region are dominated by the diffusion motion of charged particles. As we all know, in the sheath, the number of electrons and ions is small, and it is much smaller than the plasma region. Therefore, the discharge parameters in sheath remain almost constant under the action of airflow, and the main changes are in the plasma region. Mettler [11] had conducted a theoretical analysis of the plasma anemometer, as shown in Fig. 8, by the action of airflow in the direction of Y-axis, all particles including electrons and ions should have velocities in the direction of Y-axis. However, the mass of electron is very small and it will obtain a very large velocity in the direction of X-axis under the action of electric field, compared to the velocity in the X-axis direction, the velocity of airflow attached to electron in the Y-axis direction can be neglected, so the electrons are still moving along the X axis, but the mass of ion is much larger than electron, the velocity of airflow attached to ion can’t be neglected. Therefore, under the action of airflow, only the ions movement in the plasma region will change. Thus, through the above analysis, it can be known that the current in the diffusion region is mainly the ion conduction current. electron + ion
y
+ Anode
x
+ + - + + -
Cat hode
gas flow direction
Air Nozzle
AC
Fig. 8. The movement of particles under airflow
According to previous studies [18–21], the ion conduction current in the diffusion region can be equivalent to a series circuit，which contains a resistor and an inductor. The series circuit conforms to the characteristics of the diffusion region generated by AC plasma anemometer, the inductance L1 represents the ion conduction current, and the resistance R3 consists of two aspects: the resistance of conduction current and the resistance of ion thermal motion in the diffusion region. Therefore, the final circuit model of AC plasma anemometer under airflow can be obtained, as shown in Fig. 9. C1
R1
Ra
Da
L1 R0 R3 Rc
C2
Dc
R2
Fig. 9. Circuit model of AC plasma anemometer under airflow
3.5. Parameter Matching of the Circuit Models Firstly, the circuit model without airflow velocity is analyzed here. As shown in Fig. 10, the simulation circuit is established in the circuit simulation software OrCAD. According to the establishing rules of simulation circuit in OrCAD, the coupling capacitance can’t be connected in series with the simulation circuit directly, so a high value resistance R5 is added in parallel with the coupling capacitance, the high value resistance is equal to the broken circuit, it has no effect on the original circuit. Before matching the parameters of the model, the experimental data of voltage and current are respectively imported into two circuits, as shown in Fig. 10, the experimental voltage data is imported into the left circuit, the experimental current data is imported into the right circuit, and this is achieved by the data communication technology between OrCAD and MATLAB. In order to match the parameters of the model, the values of the circuit model components need to be adjusted so that the simulation current of the left circuit can be the same as the experimental current of the right circuit. Furthermore, in order to be
consistent with the experiment C1 C2 220pF , R1 R2 200Ω , these values are same as those in the experiment. In addition, R0 90Ω , which has been analyzed in 3.3. The diode is close to the ideal diode and its value does not need to be adjusted. Therefore, only the resistance values in the sheath need to be adjusted. The two sheaths are symmetrical so that the two resistors are also symmetrical, they should have the same value. According to the analysis in 3.3, these resistance values are much larger than the resistance in the plasma region. The comparative analysis of the experimental current and the simulation current is conducted, the final resistance values are selected as follows: Ra Rc 3.2kΩ , in this case,
C1
R1
220p
200
1
the simulation current is more consistent with the experimental current.
Ra 3.2k
2
Da
R5
100000000000000
l1
V1
S
-
S
R0 90
Implementation = Vin
-
Implementation = lin
R4 1
100000000000000 0 2
R5
R2
220p
200
Rc 3.2k
Dc 1
C2
0
Fig. 10. Simulation diagram of the circuit model without airflow For the circuit model under airflow, the number of parameters required to be adjusted will increase. For example, when the airflow velocity is 3.02m/s, its simulation diagram is shown in Fig. 11, as analyzed in 3.4, the parameters of the sheath remain unchanged, while the parameters R0 , L1 , R3 will change. Since the experiments belong to the low-frequency discharge, i , resulting in the change of inductance in the diffusion region cannot significantly change the current waveform of the discharge circuit, therefore, the inductance value is set to 300 H here. Under the action of airflow, the remaining two parameters ( R0 , R3 ) will change obviously, some ions will escape from the discharge region, which
causes the increase of R0 . The number of ions in the diffusion region is small, so the resistance R3 is larger than R0 . However, with the increase of the airflow velocity, the number of ions in the discharge region will decrease, so the resistance R0 will increase, and the number of ions in the diffusion region will increase, so the resistance R3 will decrease. The parameters of R0 and R3 need to be adjusted based on the above rules, and according to the comparative analysis of the experimental and simulation current, when the airflow velocity is 3.02 m/s, it can be found that the simulation current is more consistent with experimental current in the case of R0 98Ω , R3 420Ω . In addition, when the airflow velocity is 6.52m/s, a similar analysis is conducted, and the final matching parameters are R0 117Ω and
C1
R1
220p
200
1
R3 406Ω .
Ra 3.2k
Da 2
L1 300H
R5 V1
S
-
100000000000000
l1
S
R0 98
Implementation = Vin
-
Implementation = lin
R4 1
R3 420
100000000000000
0 2
R5
R2
220p
200
Rc 3.2k
Dc 1
C2
0
Fig. 11. Simulation diagram of the circuit model under airflow
4. Verification of the Circuit Models
As described in 3.5, the simulation currents are compared with the experimental currents in case of different airflow velocities. The simulation voltage data is derived from the experimental voltage data, so the simulation voltage is same as the experimental voltage in the same group. As shown in Figs. 12-14, by
comparing the simulation current and the experimental current, it can be seen that the obtained simulation results are in good agreement with the experimental results, and the largest current relative error of the three groups is not more than 0.8%, which indicate that the circuit model is feasible and reliable.
0.08
6000
0.8%
Current/A Current/A Voltage/V
0.06
Current error 0.6%
4000 0.04
0.4%
0
-0.02 -2000
Voltage (V)
Current (A)
0.00
Current error
2000 0.02
-0.04
0.2%
0.0%
-0.2% -4000
-0.06 -0.4% -0.08
-6000 0.10
0.15
0.20
0.25
0.30
0.10
0.35
0.15
0.20
0.25
0.30
0.35
Time (ms))
Time (ms)
Fig. 12. Experimental and simulation results (left), current error (right), Vg 0m/s , V 5000V and 10KHz . Vg : airflow velocity, V : supply voltage, : supply frequency
6000 Current/A Current/A Voltage/V
0.06
Current error 0.4% 4000
0.04
0
-0.02
-2000
Current error
0.00
Voltage (V)
Current (A)
0.2%
2000
0.02
0.0%
-0.2%
-0.04 -4000 -0.4%
-0.06 -6000 0.10
0.15
0.20
0.25
Time (ms)
0.30
0.35
0.10
0.15
0.20
0.25
0.30
0.35
Time (ms)
Fig. 13. Experimental and simulation results (left), current error (right), Vg 3.02m/s , V 5000V and 10KHz . Vg : airflow velocity, V : supply voltage, : supply frequency
0.06
6000
Current error 0.6% 4000
0.02
2000
0.00
0
-0.02
-2000
-0.04
-4000
-0.06
-6000
0.4% Current error
0.04
Voltage (V)
Current (A)
Current/A Current/A Voltage/V
0.2%
0.0%
-0.2%
0.10
0.15
0.20
0.25
0.30
0.35
Time (ms)
0.10
0.15
0.20
0.25
0.30
0.35
Time (ms)
Fig. 14. Experimental and simulation results (left), current error (right), Vg 6.52m/s , V 5000V and 10KHz . Vg : airflow velocity, V : supply voltage, : supply frequency
5. Conclusion
The circuit model of AC plasma anemometer based on the theoretical and experimental analysis is obtained in this article. Its equivalent circuit structure is studied from three aspects: the positive column space, the sheath and the diffusion region. The positive column space is equivalent to a resistor. The sheath is composed of a diode and a resistor in parallel. The diffusion region is equivalent to a series circuit， which contains a resistor and an inductor. After the whole circuit model is established, its feasibility and reliability are verified by the OrCAD simulation. According to the simulation results, it is known that the discharge current decreases with the increase of airflow velocity, which is consistent with the experimental results of plasma anemometer conducted by previous researchers [7–11]. The circuit characteristics of AC plasma anemometer are considered by the established circuit model, so it can in turn be used as a tool to study and improve the plasma anemometer.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (No. 51406083); the Natural Science Foundation of Jiangsu Province (BK20140820); the Fundamental Research Funds for
the Central Universities (No. NJ20160037); and the Funding of Jiangsu Innovation Program for Graduate Education (No. SJZZ16_0055).
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Highlights 1. The plasma anemometer experiments based on R-C coupling negative feedback AC glow discharge are conducted. 2. A novel circuit model of AC plasma anemometer is proposed by analyzing the whole discharge structure. 3. Circuit models of AC plasma anemometer without airflow and under airflow are established separately. 4. Circuit component parameters under different airflow velocities are matched according to theoretical and experimental analysis. 5. Simulation results are in good agreement with the experimental results shows that the obtained circuit model is feasible and reliable.
Graphical abstract