Mathematical and Experimental Simulation of Operating Modes of Capillary Emitter of Electrostatic Colloidal Microthruster

Abstract

This work experimentally and theoretically analyzes the dynamics of the process of ion emission from a capillary emitter filled with an ionic liquid as a working fluid. Such emitters can be used in the energy system of low-mass satellites as a source of jet propulsion. The dependence of the thrust of a micromotor on the electrical power supplied to it was experimentally studied, which made it possible to determine the most efficient operating modes of the microthruster. This is of interest from the point of view of increasing the energy efficiency of the latter in conditions of limited power availability of low-mass satellites. It was found that the characteristic “electric field voltage – emitter thrust” is non-monotonic with a pronounced maximum, which imposes restrictions on the magnitude of the electric field in the emitter. To explain the limit of emission intensity, a diffusion-convective model of ion movement inside the capillary was constructed. The main idea of the proposed model is the assumption that the intensity of ion emission is determined by their concentration at the outlet of the capillary, and the velocity of the emitted ions is higher than the velocity of flow of the ionic liquid in the capillary as a continuous medium. Moreover, the acceleration of ions at the outlet of the emitter increases nonlinearly with increasing external forces. The decrease in the concentration of ions as they are emitted must be compensated by their diffusion inside the capillary and convective flows, the velocity of which is limited. The constructed system of equations is analyzed numerically. For the system of Navier – Stokes equations, the projection method proposed by Chorin is applied. Based on the known velocity field, density, and concentration distribution, a time step is taken for the equations of motion. Then, taking into account the found velocity, a time step is taken for the convective diffusion equations and the density field is recalculated. The created code made it possible to confirm the possibility of the existence of a maximum mass flow rate of ions, i.e., micromotor thrust, which is in qualitative agreement with the experimental data. The main factor on which the magnitude of the maximum and its position depend is the degree of nonlinearity of the coefficient responsible for the acceleration of ions at the outlet of the capillary.