Electric discharge fluid modelling with the contribution of convective and drift energy effects

Abstract

A fluid model has been used in this work to analyze the electric and energetic behavior of a low-pressure DC glow discharge in Ar chosen as a gas test. The governing equations are the first three moments of the Boltzmann transport equations under their complete form without using the classical-drift-diffusion approximation for the momentum transfer equation while the energy conservation equation involves both thermal and drift energies. In the framework of the local energy approximation, the basic data needed more particularly in the collision source terms for both momentum transfer and energy equations are determined from a multi term solution of Boltzmann equation. Due to the strong coupling with electric field obtained from Poisson equation and the high sheath gradients, the transport equations are numerically solved using a powerful Galerkin finite elements method. This model, after a validation from comparison with literature results, is then used to analyze the convective and drift energy effects on the electric discharge characteristics. Present results show a large influence of the convective term in comparison to the drift-diffusion approximation, mainly on the electric field and charged density profiles due to the antagonist effect induced by this term on the electron and ion motion which reinforces the charge space. Present results show also the discharge characteristic changes mainly in the sheath due to the drift energy consideration.