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The streamer propagation and electric field distribution in a two-dimensional fluid model of a packed bed reactor (PBR) filled with carbon dioxide are comprehensively studied by utilizing the PASSKEy simulation platform in this work. The spatiotemporal evolution of electron density, electric fields and key plasma species in the discharge process are studied in depth. The PBR with layered dielectric spheres is simulated by using the model, indicating that the inner sides of the first layer and the second layer of dielectric spheres are not the main regions for reactions such as CO2 dissociation; instead, the main regions are along the streamer propagation path and the outer side of the first layer of dielectric sphere. In this work, the propagation of streamers in an electric field is investigated, highlighting the influence of anode voltage rise and dielectric polarization on local electric field enhancement. This enhancement leads the electron density and temperature to increase, which facilitats streamer propagation and the formation of filamentary microdischarges and surface ionization waves. This work provides a detailed analysis of the local electric field evolution at specific points within the PBR, and a further investigation of the spatiotemporal dynamics of spatial and surface charges, revealing that negative charges concentrate in the streamer and on the dielectric surface, with density being significantly higher than that of positive charges. The positive charge distribution is closely related to the streamer path, and with time going by, the charge distribution becomes dominated in the discharge space. This work also explores the surface charge deposition on the dielectric spheres, and discusses the evolution trend of the distribution. Additionally, this work discusses the temporal and spatial evolution of key plasma species, including ions and radicals, and their contributions to the overall discharge characteristics. The production mechanisms of carbon monoxide particles, carbon dioxide ions, and oxygen ions are analyzed, with a focus on their spatial distribution and correlation with electron density. Finally, the energy deposition within the PBR is examined by integrating the spatial energy deposition of electrons and major positive ions. The results indicate a total energy deposition value of approximately 1.428 mJ/m, with carbon dioxide ions accounting for 8.8% of this value.
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Keywords:
- packed-bed dielectric barrier discharge /
- dissociation of carbon dioxide /
- numerical simulation of plasma /
- reaction mechanism.
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图 1 三项亥姆霍兹方程拟合图
Figure 1. Fitted plot of the three terms Helmholtz equation.
图 2 模型结构图 (a)几何结构; (b)电压波形; (c)网格剖分示意图
Figure 2. Model structure: (a) Geometry; (b) voltage; (c) mesh.
图 3 电子密度的时空演化
Figure 3. Time evolution of electron density
图 4 约化电场的时空演化
Figure 4. Time evolution of the reduced electric field.
图 5 局部电场的时间演化 (a) 6个节点的空间位置, 背景图为5 ns时的约化电场; (b) 6个节点处的约化电场强度随时间的变化
Figure 5. Time evolution of the local electric field: (a) The location of the six points, with the reduced electric field at 5 ns in the background image; (b) the variation of the reduced electric field amplitude with time at the six points.
图 6 空间电荷数密度的时空演化
Figure 6. Time evolution of the number density of space charge.
图 7 介质表面电荷的时空演化 (a), (f) D2; (b) (e) D1; (c) (d) D0
Figure 7. Time evolution of the dielectric surface charge (a), (f) D2; (b) (e) D1; (c) (d) D0.
图 8 二氧化碳离子的时空演化
Figure 8. Time evolution of carbon dioxide ions.
图 10 一氧化碳的时空演化
Figure 10. Time evolution of carbon monoxide.
图 9 氧气分子离子的时空演化
Figure 9. Time evolution of oxygen molecular ions.
图 11 电子温度的时空演化
Figure 11. Time evolution of the electron temperature.
图 12 电子和二氧化碳离子的空间能量沉积
Figure 12. Total energy deposition of electrons and carbon dioxide ions.
表 1 三项亥姆霍兹方程系数An与λn
Table 1. Coefficients of the three terms Helmholtz equation An and λn.
n An/(cm–2·torr–1) λn /(cm–1·torr–1) 1 3.74×10–5 2.31 2 4.35×10–6 0.837 3 1.55×10–4 7.79 
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表 2 模型中包含的粒子概述
Table 2. Overview of particles included in the model.
分子 CO2, CO, O2 离子 ${\mathrm{CO}}_2^+ $, CO+, C+, O+, ${\mathrm{O}}_2^+ $, O–, ${\mathrm{O}}_2^- $ 自由基 O, C
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表 3 模型中包含的电子碰撞反应
Table 3. Electron collision reactions included in the model.
类型 反应 焓变/eV 反应速率 电离 e+CO2$ \Rightarrow$${\mathrm{CO}}_2^+ $+e+e –13.80 BOLSIG+ 电离 e+CO2$ \Rightarrow$CO+O++e+e –19.1 BOLSIG+ 电离 e+CO2$ \Rightarrow$O+CO++e+e –19.5 BOLSIG+ 电离 e+CO2$ \Rightarrow$O2+C++e+e –27.8 BOLSIG+ 电离 e+CO$ \Rightarrow$CO++e+e –14.01 BOLSIG+ 电离 e+CO$ \Rightarrow$C++O+e+e –22.0 BOLSIG+ 电离 e+CO$ \Rightarrow$C+O++e+e –25.0 BOLSIG+ 电离 e+O2$ \Rightarrow$${\mathrm{O}}_2^+ $+e+e –12.06 BOLSIG+ 解离 e+O2$ \Rightarrow$e+O+O 0.8 BOLSIG+ 解离 e+CO2$ \Rightarrow$e+CO+O –7.0 BOLSIG+ 吸附 e+O2+O2$ \Rightarrow$${\mathrm{O}}_2^- $+O2 0 6.0×10–39$ T_{\text{e}}^{{{ - 1}}} $b* 吸附 e+O2+CO2$ \Rightarrow$CO2+${\mathrm{O}}_2^- $ 1.60 3.0×10–42b* 吸附 e+O+CO2$ \Rightarrow$CO2+O– 1.60 1.0×10–43b* 解离+吸附 e+CO2$ \Rightarrow$CO+O– 0 BOLSIG+ 解离+吸附 e+CO$ \Rightarrow$C+O– 0 BOLSIG+ 解离+吸附 e+O2$ \Rightarrow$O–+O 0 BOLSIG+ e-i复合 e+${\mathrm{CO}}_2^+ $$ \Rightarrow$CO+O 1.60 2.0×10–11$ T_{\text{e}}^{{{ - 0}}{.5}} \cdot T_{\text{g}}^{ - 1} $a* e-i复合 e+${\mathrm{CO}}_2^+ $$ \Rightarrow$C+O 1.60 3.68×10–14$ T_{\text{e}}^{{{ - 0}}{.55}} $a* e-i复合 e+${\mathrm{CO}}_2^+ $$ \Rightarrow$C+O2 1.60 3.94×10–13$ T_{\text{e}}^{{{ - 0}}{.4}} $a* e-i复合 e+${\mathrm{O}}_2^+ $$ \Rightarrow$O+O 1.60 6.0×10–13$ T_{\text{e}}^{{{ - 0}}{.5}} \cdot T_{\text{g}}^{ - 0.5} $a* e-i复合 e+O2++CO2$ \Rightarrow$O2+CO2 1.60 1.0×10–38b* e-i复合 e+O++CO2$ \Rightarrow$O+CO2 1.60 1.0×10–38b* 注: a*代表单位为m3/(mol·s), b*代表单位为m6/(mol2·s).
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表 4 模型中包含的重粒子反应
Table 4. Heavy particle reactions included in the model.
类型 反应 焓变/eV 反应速率 电子分离 O–+O$ \Rightarrow$O2+e 0 1.4×10–16a* 电子分离 ${\mathrm{O}}_2^- $+O$ \Rightarrow$O2+O+e 0 1.5×10–16a* i-i复合 ${\mathrm{O}}_2^- $+${\mathrm{O}}_2^+ $+O2$ \Rightarrow$O2+O2+O2 7.0 2.0×10–37b* 电荷转移 O++CO2$ \Rightarrow$${\mathrm{O}}_2^+ $+CO 0 9.4×10–16a* 电荷转移 O++CO2$ \Rightarrow$${\mathrm{CO}}_2^+ $+O 0 4.5×10–16a* 电荷转移 CO++CO2$ \Rightarrow$${\mathrm{CO}}_2^+ $+CO 0 1.0×10–15a* 电荷转移 C++CO$ \Rightarrow$CO++C 0 5.0×10–19a* 电荷转移 ${\mathrm{O}}_2^+ $+C$ \Rightarrow$CO++O 0 5.2×10–17a* 电荷转移 ${\mathrm{CO}}_2^+ $+O2$ \Rightarrow$CO2+${\mathrm{O}}_2^+ $ 0 5.3×10–17a* 电荷转移 ${\mathrm{CO}}_2^+ $+O$ \Rightarrow$CO+${\mathrm{O}}_2^+ $ 0 1.64×10–16a* 电荷转移 ${\mathrm{CO}}_2^+ $+O$ \Rightarrow$CO2+O+ 0 9.62×10–17a* 电荷转移 CO++O$ \Rightarrow$CO+O+ 0 1.4×10–16a* 电荷转移 CO++O2$ \Rightarrow$CO+${\mathrm{O}}_2^+ $ 0 1.2×10–16a* 中性反应 CO2+CO2$ \Rightarrow$CO+O+CO2 0.60 3.91×10–16e–(49430/Tg) a* 中性反应 CO2+O$ \Rightarrow$CO+O2 0 2.8×10–17e–(26500/Tg) a* 中性反应 CO2+C$ \Rightarrow$CO+CO 0 1.0×10–21a* 中性反应 CO+O+CO2$ \Rightarrow$CO2+CO2 0 8.2×10–46e–(1510/Tg) b* 中性反应 O2+CO$ \Rightarrow$CO2+O 0 4.2×10–18e–(24000/Tg) a* 中性反应 O2+C$ \Rightarrow$CO+O 0 3.0×10–17a* 中性反应 O+C+CO2$ \Rightarrow$CO+CO2 0 9.12×10–34 Tg–3.08 e–(2114/Tg) b* 中性反应 O+O+CO2$ \Rightarrow$O2+CO2 0 3.81×10–42 Tg–1e–(170/Tg) b* 注: a*代表单位为m3/(mol·s), b*代表单位为m6/(mol2·s).
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