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4. FLUID MODELLING OF CO2 DISSOCIATION 4.2. DETAILS OF THE MODEL A typical DBD is generally composed of many filaments that are distributed stochastic- ally across the surface of the dielectrics. Thus, a spatially two- or even three-dimensional model including a stochastic description of the filament generation is needed to the- oretically describe discharges in this flow reactor configuration. As a step towards such complex modelling, here a time-dependent, spatially one-dimensional approach has been used to model and analyse the spatiotemporal discharge dynamics of the active zone. The corresponding discharge geometry considering the axial component x of the plasma between the plane-parallel, dielectric covered electrodes is displayed in figure 4.1b. Such spatially one-dimensional treatment is well suited for the analysis of DBD operating in the homogeneous or glow mode [36] and has successfully been applied for the analysis of single microdischarges e.g. in [130, 172]. 4.2.1 Basic relations For the theoretical description of the symmetric DBD in CO2 under consideration, a time- dependent, spatially one-dimensional fluid model, based on the one reported in [130] was adapted. The fluid model consists of particle balance equations for the densities nj of electrons (j = e), and several neutral and charged heavy particles; the electron energy balance equation to determine the mean energy Ue of the electrons; and Poisson’s equation providing the electric potential φ and electric field E(x, t) = −∂φ(x, t)/∂x. These balances are represented by the relations ∂ nj(x,t) + ∂ Γj(x,t) = Sj(x,t), (4.4) (4.5) (4.6) ∂t ∂ ∂x (ne(x, t)Ue(x, t)) + ∂ Qe(x, t) = −e0Γe(x, t)E(x, t) + Pe(x, t) , ∂x Zjnj(x,t), ∂t −∂x2 φ(x,t) = ε ∂2 e0 ∑ 0j where e0, ε0 and Zj denote the elementary charge, vacuum permittivity and particle charge number, respectively. The particle fluxes Γj in (4.4) and the electron energy flux Qe in (4.5) in the x-direction are expressed by the drift-diffusion approximation according to Γj (x, t) = sgn(Zj )bj (x, t)nj (x, t)E(x, t) − ∂ (Dj (x, t)nj (x, t)) , (4.7) ∂ ( ∂x ) Qe(x,t)=− ̃be(x,t)ne(x,t)E(x,t)−∂x D ̃e(x,t)ne(x,t) . (4.8) Here, bj and Dj are the mobility and diffusion coefficient of species j, ̃be and D ̃e desig- nate the mobility and diffusion coefficient of electron energy transport and the function 80PDF Image | Understanding CO2 containing non-equilibrium plasmas
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