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Experimental and theoretical study of ozone generation in pulsed positive dielectric barrier discharge
Vacuum 104 (2014) 61e64
Contents lists available at ScienceDirect
Vacuum journal homepage: www.elsevier.com/locate/vacuum
Experimental and theoretical study of ozone generation in pulsed positive dielectric barrier discharge L.-S. Wei*, D.-K. Yuan, Y.-F. Zhang, Z.-J. Hu, G.-P. Dong School of Environmental & Chemical Engineering, Nanchang University, Nanchang 330031, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 September 2013 Received in revised form 10 January 2014 Accepted 10 January 2014
This paper studies ozone synthesis in a dielectric barrier discharge reactor powered by a high voltage positive pulse power supply with a short duration (w400 ns). The influence of ozone concentration on the peak pulsed voltage (4.8 kVe20 kV), the pulse repetition rate (50 ppse300 pps) and gas flow rate is investigated. It is shown that ozone concentration reaches its maximum of 74.1 g/m3 at pulse repetition rate of 300 pps and applied voltage of 20 kV. A numerical model which describes the influence of both electrical and discharge configuration parameters on ozone concentration is developed. The ozone destruction factor is taken into account. The derived equation turns out to be validated by comparing the experimental results with numerical data. This investigation offers substantial insight in practical design of ozonizers and selection of an appropriate set of operating conditions. Ó 2014 Elsevier Ltd. All rights reserved.
Keywords: Dimensional analysis Dielectric barrier discharge Ozone generation Ozone concentration
1. Introduction Due to its strong oxidability and better environmental friendless, Ozone is increasing being used in lots of applications including the treatment of water and exhausted smoke, odor control, color removal, disinfection, medical therapy, agriculture and food processing and storage [1]. This directly leads to increasing demand for high ozone production efficiency. However, in terms of thermochemical theory, the theoretical ozone yield is 1226 g/kWh [2], while with respect to current commercial ozonizers, practical yields reach to 50 w 60 g/kWh and 100 w 120 g/kWh in air and oxygen, respectively. Hence, many attempts have been conducted in order to improve the ozone production efficiency [3e20]. Takamura [19] reported the maximum ozone yield in the oxygen-fed case reaches 736 g/kWh at 10 pps, 60 kV and 20.2 g/m3 using negative nano-seconds pulse discharge. Those high energy electrons generated in ultra-short pulsed dielectric barrier discharge (DBD) reactor are then involved in the dissociation of oxygen molecules to produce oxygen atoms for ozone generation via electron-impact reaction with oxygen molecules and third particles. Meanwhile during the discharge process, dielectric layer serves to reduce the electron emission from the cathode, distributes the streamers over a wide area near the dielectric layer, and further inhibits the streamer-arc transition to promote the streamer discharges. In addition, less energy are
* Corresponding author. Tel.: þ86 791 83969145. E-mail addresses: [email protected], [email protected] (L.-S. Wei). 0042-207X/$ e see front matter Ó 2014 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.vacuum.2014.01.009
transferred to ions and neutral gas utilizing short high-voltage pulses when compared with AC power supply configuration. The cooling system is also needless. Therefore cost reduction and promotion of efficiency are in sight [21]. Dimensional theory is introduced to investigate the ozone generation characteristics in pulsed streamer discharge (PSD) by Buntat [22], Wei [21] and Bo [23,24] employing a coaxial wirecylinder, a spiral wire-cylinder or a wire-plate reactor with oxygen or air feed gas. Unlike in the literature to data, the dimensional analysis is extended to the positive parallel plates in DBD with oxygen feed gas in the study. A numerical model is developed based on dimensional analysis theory and experimental results. The derived equation is validated with theoretical and experimental data. Moreover, discussion regarding the influence of the destruction factor is also included.
2. Experimental details Fig. 1 shows a schematic diagram of the experimental setup to generate ozone. Oxygen was obtained from a gas cylinder. Oxygen was fed into the reactor with gas flow rate from 0.6 to 1.6 L/min. The flow rate was measured by a flow meter. The concentration of ozone was measured by online ozone monitor (IN, USA). The reactor in which ozone was produced consisted of two parallel plates of 90 mm 120 mm in valid area and a dielectric barrier ceramic of 1 mm in thickness. In present work the following parameters were kept constant: the gaseous gap spacing (1 mm), the gas pressure (1.01 105 Pa) and temperature (26 4 C).
62
L.-S. Wei et al. / Vacuum 104 (2014) 61e64
Fig. 1. Schematic of experimental setup.
A magnetic pulse compressor provided the voltage and the current pulses with a repetition rate of up to 300 pps. A typical duration of 400 ns, defined as the full-width half maximum of the positive pulsed voltage, was measured at 6.2 kV, pulse repetition rate of 150 pps, 0.6 L/min oxygen flow rate. The pulsed voltage and the discharge current were measured using an oscilloscope (TDS3034B) and two probes (P6015, TCP202). The former had a maximum bandwidth of 300 MHz and a maximum sample rate of 2.5 GS/s. A typical positive pulsed voltage applied to the discharge reactor is shown in Fig. 2. The peak voltage was determined at the maximum positive value of the wave including the oscillations. The tail of the voltage wave arose from reflections due to impedance mismatch between the power source and the discharge reactors.
pressure, gaseous gap spacing, reactor length, type of dielectric material used to form the barrier, thickness of dielectric material, cooling method and so on, in which the type of gas, gas temperature, reactor length, thickness of dielectric material and cooling method are invariable. Moreover, other parameters are excluded in the model. Considering the pulse repetition frequency f, the difference of the peak pulsed voltage and the corona inception voltage V V0, the gap length dg, the relative permittivity εr, the pressure P, the gas flow rate fr and the pulse duration s, we build the dimensional set
½O3 ¼ ½O3 fr ; εr ; f ; V V0 ; dg ; P; s
(R1)
The dimensional matrix is
3. Dimensional analysis Dimensional analysis treats the general forms of equations that describe natural phenomena. Applications of dimensional analysis abound in nearly all fields of engineering applications. In order to conduct dimensional analysis, it is necessary to make sense of the variables which impact the ozone generation and afterwards sort out an appropriate selection of parameters. Actually ozone concentration depends on the peak pulsed voltage, pulse repetition rate, pulse duration, type of gas, flow rate, gas temperature,
L M T A
k1 [O3]
k2 fr
k3 V V0
k4 f
k5 s
k6 εr
k7 dg
k8 P
3 1 0 0
3 0 1 0
2 1 3 1
0 0 1 0
0 0 1 0
3 1 4 2
1 0 0 0
1 1 2 0
The rank of the matrix is four. Consequently, there are four dimensionless products in a complete set. The equations corresponding to the dimensional matrix are
3 k1 þ 3 k2 þ 2k3 3 k6 þ k7 k8 ¼ 0
(R2)
k1 þ k3 k6 þ k8 ¼ 0
(R3)
k2 3k3 k4 þ k5 þ 4k6 2k8 ¼ 0
(R4)
k3 þ 2k6 ¼ 0
(R5)
The matrix of solution is.
Fig. 2. Typical waveform of the pulsed voltage (1 ms/div, 2 kV/div).
p1 p2 p3 p4
k1 [O3]
k2 fr
k3 VV0
k4 f
k5 s
k6 εr
k7 dg
k8 P
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
2 1 0 1
0 0 0.5 0
2 3 1 0
1 0 0.5 0
L.-S. Wei et al. / Vacuum 104 (2014) 61e64
63
Accordingly, a complete set of dimensionless products is
)
100pps, Exp.
3
(R6)
150pps, Exp.
80
p2 ¼
p3 ¼
fr $s d3g
(R7)
pffiffiffiffiffiffiffi Pεr ðV V0 Þ dg
(R8)
p4 ¼ f $s
(R9)
p1 ¼ Dcp2ε2 p3ε3 p4ε4
(R11)
where Dc is a dimensional constant. Introducing (R6)e(R9) into (R11) gives
½O3 ¼ Dc
d2g
!
!ε2 pffiffiffiffiffiffiffi ε Pεr ðV V0 Þ 3 fr $s ðf $sÞε4 3 dg dg
(12)
Where Dc, ε2, ε3 and ε4 are all constants yet to be determined. Experimental evidence however enables (R12) to be much simplified, since the ozone concentration [O3] has been confirmed experimentally nearly proportional to V e V0 and f and as inversely proportional to the gas flow rate fr0:8 from the experimental data. Andε2, ε3 and ε4 are 0.8, 1 and 1 respectively. (R12) therefore gives
pffiffiffiffiffiffiffi
½O3 ¼ Dc
300pps, Exp.
s2:2 $P$ Pεr ðV V0 Þ$f
! (R13)
0:8 d0:6 g fr
4. Results and discussion
150pps, Cal. 100pps, Cal.
20
50pps, Cal.
0 4
6
8
10 12 14 16 18 20 22 24 26
Pulsed Voltage (kV) Fig. 4. Experimental and calculated ozone concentration as a function of pulsed voltage.
at a given repetition rate and increases with increasing repetition rates at a fixed pulsed voltage. Moreover, it also elucidates that at a specific pulsed voltage and pulse repetition rate in the range of 5.9 kVe18 kV and 50 ppse300 pps, ozone concentration increases linearly with increasing pulse repetition rate and pulsed voltage, respectively. The former is due to increasing number of microdischarges and high-energy electrons per unit time. The enhancement of high energy electrons amount is attributed to increasing electric field, which contributes to increase the energy input into the discharge process and produces more higher-energy electrons. Meanwhile, at a constant pulsed voltage and repetition rate above 15 kV and 150 pps, the increase extent of ozone concentration decreases with increasing repetition rate and pulsed voltage due to the fact that excess discharge energy is mainly consumed as a thermal loss in decomposing ozone. In this investigation, ozone concentration reaches the maximum of 74.1 g/m3 at 20 kV, 300 pps. And an interesting phenomenon should be noted in the experiment is that ozone production efficiency becomes higher with the enhancement of ozone concentration and more details are to be reported in the future articles. Taking the destruction factor [DF] into account, we obtain
pffiffiffiffiffiffiffi
(R14)
pffiffiffiffiffiffiffi 0:8 If the constant factor ðs2:2 $P$ Pεr ðV V0 Þ$f =d0:6 g fr Þ in (R14) is replaced by K, then
The numerical values for Dc is obtained by dividing the measured ozone concentration for the constant term K, and holding this value as a constant while the peak pulsed voltage is increased, which enables [DF] to be calculated throughout the experiment and up to the gap breakdown voltage. The pressure, pulse repetition rate, dielectric constant, flow rate, corona inception voltage, pulse duration and gap spacing are all available. Using regression techniques, (R16) is obtained as below, which is valid for values of V below the gap breakdown voltage. It takes into account the relationship of the input voltage V to the ozone generation and destruction rate, and on factorizing.
18kV
50
½DF
½O3 ¼ Dc K½DF
20
0
0:8 d0:6 g fr
!
10kV
15kV
40
½O3 ¼ Dc
s2:2 $P$ Pεr ðV V0 Þ$f
5.9kV
12kV
(
Ozone Concentration g/m
3
)
The ozone concentration as functions of pulsed voltage and pulse repetition is depicted in Figs. 3 and 4, respectively. It reveals that ozone concentration increases with increasing pulsed voltage
60
200pps, Cal.
40
(R10)
Which, by considering the monomial form [26], the relationship is described as,
s2 $P
250pps, Cal.
250pps, Exp.
60
By Buckingham’s theorem [25], (R1) must now reduce to the form,
p1 ¼ jfp2; p3; p4g
300pps, Cal.
200pps, Exp.
(
s2 $P
Ozone Concentration g/m
p1 ¼ ½O3
50pps, Exp.
100
d2g
100
150
200
250
Repetition Rate (pps) Fig. 3. Dependence of ozone concentration on repetition rate.
300
DF ¼ 3:24 V 0:64
(R15)
(R16)
Combining (R14) and (R16), gives the final equation (R17) for the ozone concentration as
64
L.-S. Wei et al. / Vacuum 104 (2014) 61e64
4) The calculated ozone concentration as a function of pulsed voltage and gas flow rate agrees well with the experimental results.
35
Ozone Concentration g/m
) 3
40
(
45 200pps, 12kV, Exp. 200pps, 15kV, Exp.
Acknowledgments 200pps, 15kV, Cal.
30
The work was supported by the National Natural Science Foundation of China (51366012, 11105067) and Jiangxi Province Young Scientists (Jinggang Star) Cul"tivation Plan (No. 20133BCB23008).
25 20 200pps, 12kV, Cal.
15
10
References
0.6
0.8
1.0
1.2
1.4
1.6
Gas Flow Rate (L/min) Fig. 5. Experimental and calculated ozone concentration as a function of gas flow rate.
pffiffiffiffiffiffiffi
½O3 ¼ 3:24Dc
s2:2 $P$ Pεr ðV V0 Þ$f 0:8 d0:6 g fr
! $V 0:64
(R17)
It means that in addition to the dependencies noted earlier, the 1.5 2.2 ozone concentration [O3] is directly related to ε0:5 and is r , P , s inversely proportional to d0:6 . g Fig. 5 illustrates the ozone concentration increases with decreasing gas flow rate. The calculated results show good agreement with the measured data. It’s known that ozone formation is a two-step process, where the rate coefficient of three body reaction is much smaller than that of electron-impact reaction. As the gas residence time decreases with increasing gas flow rate, the ozone production is gradually suppressed because O atoms produced by (R18) are exhausted quickly to external space, without evoking ozone formation via (R19) [15].
e þ O2 /2O þ e
(R18)
O þ O2 þ O2 /O3 þ O2
(R19)
The validity of theoretical analysis is therefore confirmed by comparing results obtained employing (R17) with the comprehensive experimental results. The comparisons of theoretical and experimental results in Figs. 4 and 5 have seen to be in good agreement. 5. Conclusions For pulsed positive dielectric barrier discharge in oxygen we study the ozone generation by employing both experimental and numerical method. By taking destruction factor into account, the formula of ozone concentration is obtained on the basis of dimensional theory. Experimental data regarding the dependences of ozone concentration power characteristics are studied. Moreover, numerical results are also plotted for the sake of comparison. Our findings can be summarized as follows: 1) Pulsed discharge clearly offers considerable potential for efficient ozone generation. The highest ozone concentration of 74.1 g/m3 is obtained at 20 kV and 300 pps positive pulsed voltage. 2) The value for Dc is 0.086, and the destruction factor [DF] calculated utilizing regression techniques is 3.24 V0.64. 3) The formula can be useful for the prediction for ozone concentration and selection of suitable parameters.
[1] Wei LS, Zhou JH, Wang ZH, Cen KF. Kinetic modeling of homogeneous lowtemperature multi-pollutant oxidation by ozone. Ozone Sci Eng 2007;29: 207e14. [2] Chang JS, Lawless PA, Yamamoto T. Corona discharge processes. IEEE Trans Plasma Sci 1991;19:1152e66. [3] Samaranayake WJM, Miyahara Y, Namihira T, Katsuki S, Hackam R, Akiyama H. Ozone production using pulsed dielectric barrier discharge in oxygen. IEEE Trans Dielectr Electr Insul 2000;7:849e54. [4] Samaranayake WJM, Namihira T, Katsuki S, Miyahara Y, Sakugawa T, Hackam R, et al. Pulsed power production of ozone using nonthermal gas discharges. IEEE Electr Insul Mag 2001;17:17e25. [5] Samaranayake WJM, Miyahara Y, Namihira T, Katsuki S, Sakugawa T, Hackam R, et al. Pulsed streamer discharge characteristics of ozone production in dry air. IEEE Trans Dielectr Electr Insul 2000;7:254e60. [6] Samaranayake WJM, Miyahara Y, Namihira T, Katsuki S, Hackam R, Akiyama H. Ozone generation in dry air using pulsed discharges with and without a solid dielectric layer. IEEE Trans Dielectr Electr Insul 2001;8:687e97. [7] Song H-J, Chun B-J, Lee K-S. Improvement of ozone yield by a multi-discharge type ozonizer using superposition of silent discharge plasma. J Korean Phys Soc 2004;44:1182e8. [8] Ahn H-S, Hayashi N, Ihara S, Yamabe C. Ozone generation characteristics by superimposed discharge in oxygen-fed ozonizer. Jpn J Appl Phys 2003;42: 6578. [9] Kaneda S, Hayashi N, Ihara S, Satoh S, Yamabe C. Application of dielectric material to double-discharge-type ozonizer. Vacuum 2004;73:567e71. [10] Shimosaki M, Hayashi N, Ihara S, Satoh S, Yamabe C. Effect of trigger electrodes configuration of a double discharge ozonizer on ozone generation characteristics. Vacuum 2004;73:573e7. [11] Ono R, Oda T. Formation and structure of primary and secondary streamers in positive pulsed corona discharge e effect of oxygen concentration and applied voltage. J Phys D 2003;36:1952e8. [12] Simek M, Clupek M. Efficiency of ozone production by pulsed positive corona discharge in synthetic air. J Phys D 2002;35:1171e5. [13] Ma H, Qiu Y. A study of ozone synthesis in coaxial cylinder pulse streamer corona discharge reactors. Ozone Sci Eng 2003;25:127e35. [14] Ono R, Oda T. Ozone production process in pulsed positive dielectric barrier discharge. J Phys D 2007;40:176e82. [15] Sung TL, Teii S, Liu CM, Hsiao RC, Chen PC, Wu YH, et al. Effect of pulse power characteristics and gas flow rate on ozone production in a cylindrical dielectric barrier discharge ozonizer. Vacuum 2013;90:65e9. [16] Wei LS, Hu ZJ, Zhang YF. Dimensional analysis to ozone generation by pulsed streamer discharge in dry air. Adv Mater Res 2011;204e210:828e33. [17] Buntat Z, Smith IR, Razali NA. Ozone generation by pulsed streamer discharge in air. Appl Phys Res 2009;1:2. [18] Takaki K, Yagi I, Mukaigawa S, Fujiwara T, Go T. Ozone synthesis using streamer discharge produced by nanoseconds pulse voltage under atmospheric pressure. In: 2009 IEEE pulsed power conference, vols. 1 and 2; 2009. pp. 986e90. [19] Takamura N, Matsumoto T, Wang D, Namihira T, Akiyama H. Ozone generation using positive-and negative-nano-seconds pulsed discharges. In: IEEE pulsed power conference (PPC) 2011. pp. 1300e3. [20] Sung TL, Teii S, Liu CM, Hsiao RC, Chen PC, Wu YH, et al. Surface catalytic effect of electrode materials on ozone dissociation in a cylindrical dielectric barrier discharge ozonizer. IEEE Trans Plasma Sci 2012;40:2751e5. [21] Wei LS, Zhou JH, Wang ZH, Cen KF. Theoretical analysis of ozone generation by pulsed dielectric barrier discharge in oxygen. J Plasma Phys 2007;73:427e32. [22] Buntat Z, Harry JE, Smith IR. Application of dimensional analysis to ozone production by pulsed streamer discharge in oxygen. J Phys D 2003;36:1553e7. [23] Bo Z, Lu GH, Wang PX, Chen JH. Dimensional analysis of detrimental ozone generation by negative wire-to-plate corona discharge in both dry and humid air. Ozone-Sci Eng 2013;35:31e7. [24] Bo Z, Chen JH. Dimensional analysis of detrimental ozone generation by positive wire-to-plate corona discharge in air. J Phys D 2010:43. [25] Langhaar HL. Dimensional analysis and theory of models. New York: Wiley; 1951. [26] Szirtes T. Applied dimensional analysis and modeling. Amsterdam: Heinemann; 2007.
Contents lists available at ScienceDirect
Vacuum journal homepage: www.elsevier.com/locate/vacuum
Experimental and theoretical study of ozone generation in pulsed positive dielectric barrier discharge L.-S. Wei*, D.-K. Yuan, Y.-F. Zhang, Z.-J. Hu, G.-P. Dong School of Environmental & Chemical Engineering, Nanchang University, Nanchang 330031, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 September 2013 Received in revised form 10 January 2014 Accepted 10 January 2014
This paper studies ozone synthesis in a dielectric barrier discharge reactor powered by a high voltage positive pulse power supply with a short duration (w400 ns). The influence of ozone concentration on the peak pulsed voltage (4.8 kVe20 kV), the pulse repetition rate (50 ppse300 pps) and gas flow rate is investigated. It is shown that ozone concentration reaches its maximum of 74.1 g/m3 at pulse repetition rate of 300 pps and applied voltage of 20 kV. A numerical model which describes the influence of both electrical and discharge configuration parameters on ozone concentration is developed. The ozone destruction factor is taken into account. The derived equation turns out to be validated by comparing the experimental results with numerical data. This investigation offers substantial insight in practical design of ozonizers and selection of an appropriate set of operating conditions. Ó 2014 Elsevier Ltd. All rights reserved.
Keywords: Dimensional analysis Dielectric barrier discharge Ozone generation Ozone concentration
1. Introduction Due to its strong oxidability and better environmental friendless, Ozone is increasing being used in lots of applications including the treatment of water and exhausted smoke, odor control, color removal, disinfection, medical therapy, agriculture and food processing and storage [1]. This directly leads to increasing demand for high ozone production efficiency. However, in terms of thermochemical theory, the theoretical ozone yield is 1226 g/kWh [2], while with respect to current commercial ozonizers, practical yields reach to 50 w 60 g/kWh and 100 w 120 g/kWh in air and oxygen, respectively. Hence, many attempts have been conducted in order to improve the ozone production efficiency [3e20]. Takamura [19] reported the maximum ozone yield in the oxygen-fed case reaches 736 g/kWh at 10 pps, 60 kV and 20.2 g/m3 using negative nano-seconds pulse discharge. Those high energy electrons generated in ultra-short pulsed dielectric barrier discharge (DBD) reactor are then involved in the dissociation of oxygen molecules to produce oxygen atoms for ozone generation via electron-impact reaction with oxygen molecules and third particles. Meanwhile during the discharge process, dielectric layer serves to reduce the electron emission from the cathode, distributes the streamers over a wide area near the dielectric layer, and further inhibits the streamer-arc transition to promote the streamer discharges. In addition, less energy are
* Corresponding author. Tel.: þ86 791 83969145. E-mail addresses: [email protected], [email protected] (L.-S. Wei). 0042-207X/$ e see front matter Ó 2014 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.vacuum.2014.01.009
transferred to ions and neutral gas utilizing short high-voltage pulses when compared with AC power supply configuration. The cooling system is also needless. Therefore cost reduction and promotion of efficiency are in sight [21]. Dimensional theory is introduced to investigate the ozone generation characteristics in pulsed streamer discharge (PSD) by Buntat [22], Wei [21] and Bo [23,24] employing a coaxial wirecylinder, a spiral wire-cylinder or a wire-plate reactor with oxygen or air feed gas. Unlike in the literature to data, the dimensional analysis is extended to the positive parallel plates in DBD with oxygen feed gas in the study. A numerical model is developed based on dimensional analysis theory and experimental results. The derived equation is validated with theoretical and experimental data. Moreover, discussion regarding the influence of the destruction factor is also included.
2. Experimental details Fig. 1 shows a schematic diagram of the experimental setup to generate ozone. Oxygen was obtained from a gas cylinder. Oxygen was fed into the reactor with gas flow rate from 0.6 to 1.6 L/min. The flow rate was measured by a flow meter. The concentration of ozone was measured by online ozone monitor (IN, USA). The reactor in which ozone was produced consisted of two parallel plates of 90 mm 120 mm in valid area and a dielectric barrier ceramic of 1 mm in thickness. In present work the following parameters were kept constant: the gaseous gap spacing (1 mm), the gas pressure (1.01 105 Pa) and temperature (26 4 C).
62
L.-S. Wei et al. / Vacuum 104 (2014) 61e64
Fig. 1. Schematic of experimental setup.
A magnetic pulse compressor provided the voltage and the current pulses with a repetition rate of up to 300 pps. A typical duration of 400 ns, defined as the full-width half maximum of the positive pulsed voltage, was measured at 6.2 kV, pulse repetition rate of 150 pps, 0.6 L/min oxygen flow rate. The pulsed voltage and the discharge current were measured using an oscilloscope (TDS3034B) and two probes (P6015, TCP202). The former had a maximum bandwidth of 300 MHz and a maximum sample rate of 2.5 GS/s. A typical positive pulsed voltage applied to the discharge reactor is shown in Fig. 2. The peak voltage was determined at the maximum positive value of the wave including the oscillations. The tail of the voltage wave arose from reflections due to impedance mismatch between the power source and the discharge reactors.
pressure, gaseous gap spacing, reactor length, type of dielectric material used to form the barrier, thickness of dielectric material, cooling method and so on, in which the type of gas, gas temperature, reactor length, thickness of dielectric material and cooling method are invariable. Moreover, other parameters are excluded in the model. Considering the pulse repetition frequency f, the difference of the peak pulsed voltage and the corona inception voltage V V0, the gap length dg, the relative permittivity εr, the pressure P, the gas flow rate fr and the pulse duration s, we build the dimensional set
½O3 ¼ ½O3 fr ; εr ; f ; V V0 ; dg ; P; s
(R1)
The dimensional matrix is
3. Dimensional analysis Dimensional analysis treats the general forms of equations that describe natural phenomena. Applications of dimensional analysis abound in nearly all fields of engineering applications. In order to conduct dimensional analysis, it is necessary to make sense of the variables which impact the ozone generation and afterwards sort out an appropriate selection of parameters. Actually ozone concentration depends on the peak pulsed voltage, pulse repetition rate, pulse duration, type of gas, flow rate, gas temperature,
L M T A
k1 [O3]
k2 fr
k3 V V0
k4 f
k5 s
k6 εr
k7 dg
k8 P
3 1 0 0
3 0 1 0
2 1 3 1
0 0 1 0
0 0 1 0
3 1 4 2
1 0 0 0
1 1 2 0
The rank of the matrix is four. Consequently, there are four dimensionless products in a complete set. The equations corresponding to the dimensional matrix are
3 k1 þ 3 k2 þ 2k3 3 k6 þ k7 k8 ¼ 0
(R2)
k1 þ k3 k6 þ k8 ¼ 0
(R3)
k2 3k3 k4 þ k5 þ 4k6 2k8 ¼ 0
(R4)
k3 þ 2k6 ¼ 0
(R5)
The matrix of solution is.
Fig. 2. Typical waveform of the pulsed voltage (1 ms/div, 2 kV/div).
p1 p2 p3 p4
k1 [O3]
k2 fr
k3 VV0
k4 f
k5 s
k6 εr
k7 dg
k8 P
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
2 1 0 1
0 0 0.5 0
2 3 1 0
1 0 0.5 0
L.-S. Wei et al. / Vacuum 104 (2014) 61e64
63
Accordingly, a complete set of dimensionless products is
)
100pps, Exp.
3
(R6)
150pps, Exp.
80
p2 ¼
p3 ¼
fr $s d3g
(R7)
pffiffiffiffiffiffiffi Pεr ðV V0 Þ dg
(R8)
p4 ¼ f $s
(R9)
p1 ¼ Dcp2ε2 p3ε3 p4ε4
(R11)
where Dc is a dimensional constant. Introducing (R6)e(R9) into (R11) gives
½O3 ¼ Dc
d2g
!
!ε2 pffiffiffiffiffiffiffi ε Pεr ðV V0 Þ 3 fr $s ðf $sÞε4 3 dg dg
(12)
Where Dc, ε2, ε3 and ε4 are all constants yet to be determined. Experimental evidence however enables (R12) to be much simplified, since the ozone concentration [O3] has been confirmed experimentally nearly proportional to V e V0 and f and as inversely proportional to the gas flow rate fr0:8 from the experimental data. Andε2, ε3 and ε4 are 0.8, 1 and 1 respectively. (R12) therefore gives
pffiffiffiffiffiffiffi
½O3 ¼ Dc
300pps, Exp.
s2:2 $P$ Pεr ðV V0 Þ$f
! (R13)
0:8 d0:6 g fr
4. Results and discussion
150pps, Cal. 100pps, Cal.
20
50pps, Cal.
0 4
6
8
10 12 14 16 18 20 22 24 26
Pulsed Voltage (kV) Fig. 4. Experimental and calculated ozone concentration as a function of pulsed voltage.
at a given repetition rate and increases with increasing repetition rates at a fixed pulsed voltage. Moreover, it also elucidates that at a specific pulsed voltage and pulse repetition rate in the range of 5.9 kVe18 kV and 50 ppse300 pps, ozone concentration increases linearly with increasing pulse repetition rate and pulsed voltage, respectively. The former is due to increasing number of microdischarges and high-energy electrons per unit time. The enhancement of high energy electrons amount is attributed to increasing electric field, which contributes to increase the energy input into the discharge process and produces more higher-energy electrons. Meanwhile, at a constant pulsed voltage and repetition rate above 15 kV and 150 pps, the increase extent of ozone concentration decreases with increasing repetition rate and pulsed voltage due to the fact that excess discharge energy is mainly consumed as a thermal loss in decomposing ozone. In this investigation, ozone concentration reaches the maximum of 74.1 g/m3 at 20 kV, 300 pps. And an interesting phenomenon should be noted in the experiment is that ozone production efficiency becomes higher with the enhancement of ozone concentration and more details are to be reported in the future articles. Taking the destruction factor [DF] into account, we obtain
pffiffiffiffiffiffiffi
(R14)
pffiffiffiffiffiffiffi 0:8 If the constant factor ðs2:2 $P$ Pεr ðV V0 Þ$f =d0:6 g fr Þ in (R14) is replaced by K, then
The numerical values for Dc is obtained by dividing the measured ozone concentration for the constant term K, and holding this value as a constant while the peak pulsed voltage is increased, which enables [DF] to be calculated throughout the experiment and up to the gap breakdown voltage. The pressure, pulse repetition rate, dielectric constant, flow rate, corona inception voltage, pulse duration and gap spacing are all available. Using regression techniques, (R16) is obtained as below, which is valid for values of V below the gap breakdown voltage. It takes into account the relationship of the input voltage V to the ozone generation and destruction rate, and on factorizing.
18kV
50
½DF
½O3 ¼ Dc K½DF
20
0
0:8 d0:6 g fr
!
10kV
15kV
40
½O3 ¼ Dc
s2:2 $P$ Pεr ðV V0 Þ$f
5.9kV
12kV
(
Ozone Concentration g/m
3
)
The ozone concentration as functions of pulsed voltage and pulse repetition is depicted in Figs. 3 and 4, respectively. It reveals that ozone concentration increases with increasing pulsed voltage
60
200pps, Cal.
40
(R10)
Which, by considering the monomial form [26], the relationship is described as,
s2 $P
250pps, Cal.
250pps, Exp.
60
By Buckingham’s theorem [25], (R1) must now reduce to the form,
p1 ¼ jfp2; p3; p4g
300pps, Cal.
200pps, Exp.
(
s2 $P
Ozone Concentration g/m
p1 ¼ ½O3
50pps, Exp.
100
d2g
100
150
200
250
Repetition Rate (pps) Fig. 3. Dependence of ozone concentration on repetition rate.
300
DF ¼ 3:24 V 0:64
(R15)
(R16)
Combining (R14) and (R16), gives the final equation (R17) for the ozone concentration as
64
L.-S. Wei et al. / Vacuum 104 (2014) 61e64
4) The calculated ozone concentration as a function of pulsed voltage and gas flow rate agrees well with the experimental results.
35
Ozone Concentration g/m
) 3
40
(
45 200pps, 12kV, Exp. 200pps, 15kV, Exp.
Acknowledgments 200pps, 15kV, Cal.
30
The work was supported by the National Natural Science Foundation of China (51366012, 11105067) and Jiangxi Province Young Scientists (Jinggang Star) Cul"tivation Plan (No. 20133BCB23008).
25 20 200pps, 12kV, Cal.
15
10
References
0.6
0.8
1.0
1.2
1.4
1.6
Gas Flow Rate (L/min) Fig. 5. Experimental and calculated ozone concentration as a function of gas flow rate.
pffiffiffiffiffiffiffi
½O3 ¼ 3:24Dc
s2:2 $P$ Pεr ðV V0 Þ$f 0:8 d0:6 g fr
! $V 0:64
(R17)
It means that in addition to the dependencies noted earlier, the 1.5 2.2 ozone concentration [O3] is directly related to ε0:5 and is r , P , s inversely proportional to d0:6 . g Fig. 5 illustrates the ozone concentration increases with decreasing gas flow rate. The calculated results show good agreement with the measured data. It’s known that ozone formation is a two-step process, where the rate coefficient of three body reaction is much smaller than that of electron-impact reaction. As the gas residence time decreases with increasing gas flow rate, the ozone production is gradually suppressed because O atoms produced by (R18) are exhausted quickly to external space, without evoking ozone formation via (R19) [15].
e þ O2 /2O þ e
(R18)
O þ O2 þ O2 /O3 þ O2
(R19)
The validity of theoretical analysis is therefore confirmed by comparing results obtained employing (R17) with the comprehensive experimental results. The comparisons of theoretical and experimental results in Figs. 4 and 5 have seen to be in good agreement. 5. Conclusions For pulsed positive dielectric barrier discharge in oxygen we study the ozone generation by employing both experimental and numerical method. By taking destruction factor into account, the formula of ozone concentration is obtained on the basis of dimensional theory. Experimental data regarding the dependences of ozone concentration power characteristics are studied. Moreover, numerical results are also plotted for the sake of comparison. Our findings can be summarized as follows: 1) Pulsed discharge clearly offers considerable potential for efficient ozone generation. The highest ozone concentration of 74.1 g/m3 is obtained at 20 kV and 300 pps positive pulsed voltage. 2) The value for Dc is 0.086, and the destruction factor [DF] calculated utilizing regression techniques is 3.24 V0.64. 3) The formula can be useful for the prediction for ozone concentration and selection of suitable parameters.
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