Numerical study of viscosity and heat flux role in heavy species dynamics in Hall thruster discharge

A two-and three-dimensional velocity space axisymmetric hybrid-PIC model of Hall thruster discharge called Hybrid2D has been developed.The particle-in-cell(PIC) method was used for neutrals and ions(heavy species),and fluid dynamics on a magnetic field-aligned(MFA) mesh was used for electrons.A time-saving method for heavy species moment interpolation on a MFA mesh was developed.The method comprises using regular rectangle and irregular triangle meshes,connected to each other on a pre-processing stage.The electron fluid model takes into account neither inertia terms nor viscous terms and includes an electron temperature equation with a heat flux term.The developed model was used to calculate all heavy species moments up to the third one in a stationary case.The analysis of the viscosity and the heat flux impact on the force and energy balance has shown that for the calculated geometry of the Hall thruster,the viscosity and the heat flux terms have the same magnitude as the other terms and could not be omitted.Also,it was shown that the heat flux is not proportional to the temperature gradient and,consequently,the highest moments should be calculated to close the neutral fluid equation system.At the same time,ions can only be modeled as a cold non-viscous fluid when the sole aim of modeling is the calculation of the operating parameters or distribution of the local parameters along the centerline of the discharge channel.This is because the magnitude of the viscosity and the temperature gradient terms are negligible at the centerline.However,when a simulation’s focus is either on the radial divergence of the plume or on magnetic pole erosion,three components of the ion temperature should be taken into consideration.The non-diagonal terms of ion pressure tensor have a lower impact than the diagonal terms.According to the study,a zero heat flux condition could be used to close the ion equation system in calculated geometry.

Inverse design of mesoscopic models for compressible flow using the Chapman-Enskog analysis

In this paper,based on simplified Boltzmann equation,we explore the inverse-design of mesoscopic models for compressible flow using the Chapman-Enskog analysis.Starting from the single-relaxation-time Boltzmann equation with an additional source term,two model Boltzmann equations for two reduced distribution functions are obtained,each then also having an additional undetermined source term.Under this general framework and using Navier-Stokes-Fourier(NSF)equations as constraints,the structures of the distribution functions are obtained by the leading-order Chapman-Enskog analysis.Next,five basic constraints for the design of the two source terms are obtained in order to recover the NSF system in the continuum limit.These constraints allow for adjustable bulk-to-shear viscosity ratio,Prandtl number as well as a thermal energy source.The specific forms of the two source terms can be determined through proper physical considerations and numerical implementation requirements.By employing the truncated Hermite expansion,one design for the two source terms is proposed.Moreover,three well-known mesoscopic models in the literature are shown to be compatible with these five constraints.In addition,the consistent implementation of boundary conditions is also explored by using the Chapman-Enskog expansion at the NSF order.Finally,based on the higher-order Chapman-Enskog expansion of the distribution functions,we derive the complete analytical expressions for the viscous stress tensor and the heat flux.Some underlying physics can be further explored using the DNS simulation data based on the proposed model.