3D simulations of negative streamers in CO$_2$ with admixtures of C$_4$F$_7$N

TL;DR

The paper tackles the challenge of modeling negative streamer discharges in CO$_2$–CFN mixtures as eco-friendly insulators, where rapid attachment and uncertain photoionisation complicate propagation. It systematically compares electron transport data from multiple cross-section databases and Boltzmann solvers, selecting Hayashi CO$_2$ data with Flynn CFN data for fluid simulations, and then evaluates LFA, LEA, and PIC models in 3D. The results show that 3D fluid models can reasonably reproduce PIC results, with LEA often producing faster propagation and particle simulations exhibiting more stochastic branching. The work highlights the importance of solver choice, cross-section datasets, boundary conditions, and stochastic effects for accurate 3D streamer simulations and points toward experimental validation and model extensions to include additional ionisation and detachment mechanisms.

Abstract

CO$_2$ with an admixture of C$_4$F$_7$N could serve as an eco-friendly alternative to the extreme greenhouse gas SF$_6$ in high-voltage insulation. Streamer discharges in such gases are different from those in air due to the rapid conductivity decay in the streamer channels. Furthermore, since no effective photoionisation mechanism is known, we expect discharge growth to be more stochastic than in air. In this paper we investigate whether conventional fluid models can be used to simulate streamers in CO$_2$ with admixtures of C$_4$F$_7$N of 1 or 10%. We focus on 3D simulations of negative streamers. First we review cross section databases for C$_4$F$_7$N and CO$_2$. Then we compare a two-term Boltzmann solver with a Monte Carlo method to compute reaction and transport coefficients from the cross sections. Afterwards we compare 3D fluid simulations with the local field (LFA) or local energy approximation (LEA) against particle simulations. In general, we find that the results of particle and fluid models are quite similar. One difference we observe is that particle simulations are intrinsically stochastic, leading to more branching. Furthermore, the LEA model does not show better agreement with the particle simulations than the LFA model. We also discuss the effect and choice of different boundary conditions on the negative rod electrode.

Figures (14)

• Figure 1: Comparison of the reduced flux transport and reaction coefficients calculated with BOLSIG+ (solid lines) and particle_swarm code (dotted lines). The coefficients are flux coefficients and were calculated for CO$_2$ with admixtures of $1\%,10\%,20\%$ and $50\%$ CFN as a function of $E/N$. Cross section data of Hayashi for CO$_2$ and Flynn for CFN were used. $\mu N$, $\alpha/N$, and $\eta/N$ agree well, while $DN$ differs as discussed in the main text.
• Figure 2: Comparison of the Flynn and Zhang reduced transport and reaction coefficients in pure CFN as functions of $E/N$. The coefficients are flux coefficients and were calculated with BOLSIG+. Differences of up to $40\%$ for all coefficients are observed.
• Figure 3: Comparison of reduced transport and reaction coefficients of different CO$_2$ databases with an admixture of 1% (left) or 10% (right) CFN as functions of $E/N$. The coefficients are bulk coefficients, and were calculated with the particle_swarm code. The black crosses indicate experimental swarm data from chachereau2018electricalvemulapalli2023pulsed at 296 K and 100 Pa. The CFN cross sections here have a minor influence, so for the Zhang database only the combination with the Hayashi CO$_2$ cross section is shown. The Flynn cross sections are used to calculate the input data for the fluid simulations. Experimental data agree well with the Flynn/Hayashi and Zhang/Hayashi results.
• Figure 4: A view of the plate-to-plate computational domain of $5\;\mathrm{mm}\times5\;\mathrm{mm}\times10\;\mathrm{mm}$ with protruding top electrode of $2\;\mathrm{mm}$. The dashed box zooms into the location of the stochastic initial condition after the first time step of $0.2\;\mathrm{ns}$.
• Figure 5: Evolution of the electron density of the LFA, LEA and PIC models for CO$_2$ with an admixture of $1\%$ CFN in a background field of $E_{\mathrm{bg}} = 36.1\;\mathrm{kV/cm}$. The simulations show the same initial stochastic growth, with some disagreement in later phases due to branching. Figures are generated using ray-traced 3D volume rendering in Visit VISIT.