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Diffuse discharges generated under fast nanosecond-pulse rising edges possess a larger discharge radius compared to classic streamer discharges. However, existing simulation studies often employ boundary ranges similar to those used for simulating streamer discharges, thereby neglecting the influence of the boundary range on their characteristics. This study investigates the characteristics of diffuse discharges in atmospheric-pressure air using a fluid model. The research focuses on the influence of plasma and Poisson equation boundary ranges on discharge evolution, particularly the top and right boundaries of the rectangular computational domain. Numerical simulations and experimental comparisons reveal several key findings: When both plasma and Poisson equation boundaries are set to 5 cm×5 cm (exceeding six times the maximum discharge radius), the simulated discharge width and propagation velocity agree well with experimental measurements. However, a consistent delay is observed in the simulated arrival time at the plate electrode, highlighting inherent limitations of current fluid models in accurately simulating temporal scales. Reducing the plasma boundaries results in negligible fluctuations in electric field intensity and electron density at the discharge head, indicating a minimal impact on macroscopic discharge characteristics. Narrowing the Poisson equation’s right boundary significantly reduces the discharge width while simultaneously increasing the discharge width relative to the domain size. Asymmetric propagation patterns emerge between the upper and lower halves of the discharge gap. Nevertheless, appropriate reduction of the right boundary improves morphological consistency with experimental observations, suggesting practical optimization strategies. Conversely, reducing the top boundary weakens the electric field “focusing effect” at the discharge head, homogenizes the spatial field distribution, and delays acceleration, thereby exacerbating deviations from experimental data. These results demonstrate that Poisson boundary conditions critically govern spatiotemporal discharge dynamics. Top boundary truncation severely compromises simulation accuracy, whereas adjusting the right boundary allows for a balanced optimization between computational efficiency and result reliability. This work provides theoretical guidance for selecting boundary conditions in the numerical modeling of diffuse discharges.
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Keywords:
- nanosecond pulsed diffuse discharge /
- fluid model /
- streamer discharge /
- boundary conditions
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图 1 仿真中采用的电极结构和计算域示意图, 图中边界范围大小的数值仅作为结构示意, 在下文中针对其进行修改以研究仿真结果变化规律
Figure 1. Schematic diagram of the electrode structure and computational domain used in the simulation, the numerical values for the boundary extent shown in the figure are purely for schematic illustration. These values will be systematically modified in the subsequent sections to investigate the trends in simulation results.
图 2 仿真中所采用的外施电压
Figure 2. Applied voltage waveform in the simulation.
图 3 ICCD拍摄到的放电发展过程, 拍摄门宽为200 ps
Figure 3. Discharge development captured by ICCD, gate used is 200 ps.
图 4 仿真计算得到的电子密度分布随时间演化分布
Figure 4. Simulated electron density evolution with time.
图 5 放电发展过程中传播距离和宽度的实验和仿真值对比 (a)放电传播距离; (b)放电最大宽度
Figure 5. Simulated and experimental discharge length and width comparison: (a) Discharge length; (b) discharge width.
图 6 放电发展过程中电子密度和约化电场强度(单位: Td)在轴线上的分布 (a)电子密度; (b)约化电场强度
Figure 6. Electron density and reduced electric field (in Td) distribution on the axis during the discharge development: (a) Electron density; (b) reduced electric field.
图 7 放电发展过程中约化电场强度(单位: Td)在轴线上的演化
Figure 7. Reduced electric field (in Td) evolution on the axis during the discharge development.
图 8 两种不同计算策略下放电发展过程中传播距离和宽度的实验和仿真值对比 (a)放电传播距离; (b)放电最大宽度
Figure 8. Simulated and experimental discharge length and width comparison in two different calculation strategies: (a) Discharge length; (b) discharge width.
图 9 不同等离子体边界范围条件影响下放电传播距离和宽度变化规律 (a)放电传播距离; (b) 放电最大宽度
Figure 9. Discharge length and width influenced by different plasma boundaries: (a) Discharge length; (b) discharge width.
图 10 不同等离子体边界范围条件影响下t = 0.6 ns时刻下电子密度和电场强度在轴线上的分布 (a)电子密度; (b)约化电场强度
Figure 10. Electron density distribution on the axis at t = 0.6 ns under the influence of different plasma boundaries: (a) Electron density; (b) reduced electric field.
图 11 将等离子体边界范围缩减至0.5 cm时对放电计算结果造成的影响
Figure 11. Impact of plasma boundary reduction to 0.5 cm on discharge simulation results.
图 12 不同泊松方程边界范围条件下的放电电子密度演化过程
Figure 12. Electron density evolution process under different boundary range of Possion’s equation.
图 13 不同泊松方程边界范围下放电特性的变化规律 (a)放电传播距离; (b)放电最大宽度
Figure 13. Discharge characteristics under different boundary range of Possion’s equation: (a) Discharge length; (b) discharge width.
图 14 不同泊松边界范围下放电通道附近的拉普拉斯场电场线分布示意图
Figure 14. Schematic diagram of the distribution of Laplace electric field lines near the discharge channel under different boundary ranges of Possion’s equation.
图 15 不同泊松方程边界范围下于t = 1 ns时的空间约化电场分布
Figure 15. Reduced electric field distribution at t = 1 ns under different boundary ranges of Poisson’s equation.
图 16 缩短泊松方程的上边界后放电发展过程中放电特性变化 (a)放电传播距离; (b)放电最大宽度
Figure 16. Changes in discharge characteristics during discharge development after shortening the upper boundary of the Poisson’s equation: (a) Discharge length; (b) discharge width.
图 17 缩短泊松方程的上边界后于t = 1 ns时刻下的空间约化电场分布
Figure 17. Reduced electric field distribution at t = 1 ns after shortening the upper boundary of the Poisson’s equation.
图 18 最大放电半径和泊松边界范围的比值
Figure 18. Ratio of maximum discharge radius to Poisson’s equation boundary.
图 19 调转针电极电压极性后5 cm泊松边界和2 cm泊松边界计算结果对比
Figure 19. Comparison of simulation results for 5 cm and 2 cm Poisson’s equation boundary after reversing the needle electrode voltage polarity.
表 1 仿真中所采用的等离子体边界条件
Table 1. Plasma boundary conditions used in the simulation.
通量方向 电子 正离子 负离子 电子能量 阳极向外 0 $ \nabla n = 0 $ 0 0 阳极向内 $ \nabla n = 0 $ 0 $ \nabla n = 0 $ $ \varGamma = {\varGamma _{\text{e}}}{n_{{\varepsilon }}} $ 阴极向外 $ \nabla n = 0 $ 0 $ \nabla n = 0 $ $ \varGamma = {\varGamma _{\text{e}}}{n_{{\varepsilon }}} $ 阴极向内 0 $ \nabla n = 0 $ 0 0 
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表 2 仿真中所采用的反应体系
Table 2. Reaction system used in simulation.
反应 反应速率 参考文献 R1 e+N2$ \to {\text{N}}_{2}^{+} $+e+e f(σ, ε) [16] R2 e+O2$ \to {\text{O}}_{2}^{+} $+e+e f(σ, ε) [17] R3 e+O2+O2$ \to {\text{O}}_{2}^{-} $+O2 f(ε) [17] R4 e+O2$ \to $O–+O f(ε) [17] R5 $ {\text{O}}_{2}^{-} $+M $ \to $e+ O2+M f(ε) [18] R6 O–+ N2$ \to $e+N2O f(ε) [18] R7 O–+ O2$ \to {\text{O}}_{2}^{-} $+O2 f(ε) [18] R8 O–+ O2+M $ \to {\text{O}}_{3}^{-} $+M f(ε) [18] R9 $ {\text{N}}_{2}^{+} $+N2+M $ \to {\text{N}}_{4}^{+} $+M 5×10–29×
(300/Tgas)2[19] R10 $ {\text{O}}_{2}^{+} $+ O2+M $ \to {\text{O}}_{4}^{+} $+ M 2.4×10–30×
(300/Tgas)3[19] R11 $ {\text{N}}_{4}^{+} $+ O2$ \to {\text{O}}_{2}^{+} $+N2+N2 2.5×10–10 [19] R12 e+$ {\text{O}}_{4}^{+}\to $O2+ O2 1.4×10–6×
(300/Tgas)0.5[19] R13 e+$ {\text{N}}_{4}^{+}\to $N2+N2 2×10–6×
(300/Tgas)0.5[19] R14 e+N2$ \to $e+ N2(C3Πu) f(ε) [16] R15 N2(C3Πu) $ \to $N2+hv 2.38×107 [20] R16 $ {\text{N}}_{2}^{+} $+ O–$ \to $N+N+O 10–7 [19] R17 $ {\text{N}}_{2}^{+} $+$ {\text{O}}_{2}^{-}\to $N+N+ O2 10–7 [19] R18 $ {\text{N}}_{2}^{+} $+$ {\text{O}}_{3}^{-}\to $N+N+ O3 10–7 [19] R19 $ {\text{O}}_{2}^{+} $+ O–$ \to $O+O+O 10–7 [19] R20 $ {\text{O}}_{2}^{+} $+$ {\text{O}}_{2}^{-}\to $O+O+ O2 10–7 [19] R21 $ {\text{O}}_{2}^{+} $+$ {\text{O}}_{3}^{-}\to $O+O+ O3 10–7 [19] R22 $ {\text{O}}_{4}^{+} $+ O–$ \to $O2+ O2+O 10–7 [19] R23 $ {\text{O}}_{4}^{+} $+$ {\text{O}}_{2}^{-}\to $O2+ O2+ O2 10–7 [19] R24 $ {\text{O}}_{4}^{+} $+$ {\text{O}}_{3}^{-}\to $O2+ O2+ O3 10–7 [19] R25 $ {\text{N}}_{4}^{+} $+ O–$ \to $N2+N2+O 10–7 [19] R26 $ {\text{N}}_{4}^{+} $+$ {\text{O}}_{2}^{-}\to $N2+N2+ O2 10–7 [19] R27 $ {\text{N}}_{4}^{+} $+$ {\text{O}}_{3}^{-}\to $N2+N2+ O3 10–7 [19]
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