Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 418493, 8 pages

http://dx.doi.org/10.1155/2015/418493

## Numerical Simulation of Interaction between Hall Thruster CEX Ions and SMART-1 Spacecraft

^{1}Department of Mechanical Engineering and Automation, Harbin Institute of Technology Shenzhen Graduate School, Shenzhen, Guangdong 518055, China^{2}Department of Natural Sciences and Humanities (Mathematics/Mechanics/Humanities), Harbin Institute of Technology Shenzhen Graduate School, Shenzhen, Guangdong 518055, China

Received 11 June 2014; Accepted 13 September 2014

Academic Editor: Junuthula N. Reddy

Copyright © 2015 Kang Shan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The interaction between the plume of Hall thruster and the surface of the SMART-1 spacecraft is investigated by developing a three-dimensional IFE-PIC-MCC code, with the emphasis on the effect of the disturbance force and thermal loading caused by charge exchange ions (CEX) impingement on the surface of the spacecraft. The parameters such as heat flux and forces of CEX ions which impinge on SMART-1 and solar arrays are obtained. The disturbance force of CEX ions to the spacecraft is calculated for different divergence angles and different solar array rotation cases. The simulation results show that the disturbance force and heat flux on spacecraft change very little as the divergence angle changes. The effect of maximum disturbance force can be neglected since it is so small comparing with the nominal value of the main thrust. Solar arrays receive the least thermal heating from the CEX ions when the beam ions flow is perpendicular to the solar array plane.

#### 1. Introduction

The motion of the satellite is usually controlled by the ejection of the plume from the thruster into the space. Then, the interaction between the plume and the spacecraft surface may cause undesirable effects such as causing the disturbance force and thermal loads and contaminating sensitive equipment and sensors. The disturbance force can be a fraction of the total thrust, while thermal loads on the surface of spacecraft body result in the heating of the surface and affect the working status of electronic components which can only function properly in a range of temperatures. So the accurate modeling and predictions of these effects are very crucial to the design of a satellite [1–3].

The interaction between the exhausted plume of thrusters and the satellite components has been studied by some researchers for both chemical thrusters and electric propulsions thrusters [2, 4]. Park et al. [2] used three-dimensional discrete simulation Monte Carlo (DSMC) to investigate the interaction of the chemical thruster (a 4.45N MRE-1 monopropellant hydrazine liquid rocket engine) plume with satellite components in KOMPSAT-II. The results showed a negligible disturbance force/torque and thermal loading compared with its nominal thrust/torque and solar heating. Xiao et al. [5] analyzed molecules adsorption and transmission on the surface of satellite by using numerical simulation and ground experiment method. Also, the motion of plume pollutants which leads to performance degradation of satellite key functional surfaces (optical systems, solar panels, thermal control object surface, etc.) is calculated. Different from the plume of the chemical thrusters, the plume of electric propulsion is plasma which consists of a large number of ions and electrons except neutral atoms. In addition, charge exchange collisions will occur between the high-speed ions and neutral atoms which result in the generation of low-speed CEX ions that have significant impact on the plume characteristics. These charged particles are affected heavily by their self-consistent electric fields. Therefore, compared with the plume of the chemical thrusters, the plume of the electric propulsion thruster is different in not only the ingredients of the plume but also the flow characteristics of the plume. A number of simulation models or numerical methods have been developed for the plume in the electric propulsion thruster to investigate the interaction with the spacecraft surface and the results from these numerical models were verified through the comparison with the experiment data in recent years [6–13]. Yan et al. [10] used particle in cell (PIC) code with DSMC techniques to model Hall thruster plume and sputtering erosion on SPT-70. Kafafy and Cao [11] investigated plume effects from indirect plume impingement on formation flying satellites using ion propulsion by developing an immersed-finite-element PIC (IFE-PIC) algorithm on parallel computers. Tajmar et al. [12] developed a hybrid PIC code with Monte Carlo collision (MCC) to study spacecraft-environment interaction. Boyd [13] studied the ion current density profile and ion energy distribution by using a detailed particle-fluid PIC-DSMC model, which was compared with the experimental measurements taken in space. However, most of them were concerned about CEX ions sputtering erosion or the accuracy of simulation model, but few of them were concerned about the disturbance force and thermal loading on the spacecraft which are caused by the impinging of the backflow CEX ions on the surface of the spacecraft.

Therefore, in this paper, the study of the force and thermal loads on the spacecraft caused by backflow CEX ions is performed by using a three-dimensional IFE-PIC-MCC code. The PIC-MCC [12] code is used to simulate the generation and movement of CEX ions. The DSMC method [14] is applied to model neutral atoms. Electric field in the plume is obtained by solving Poisson’s equation which is calculated by IFE-PIC [15, 16] method which is designed to handle complex boundary conditions accurately while maintaining the computational speed of the standard PIC code. The code is then applied to the numerical simulations of the SMART-1 spacecraft which had traveled to the moon using a PPS-1350 Hall thruster with the maximum thrust of 70 mN [17].

Section 2 describes the interaction model between the plume of Hall thruster and the surface of the spacecraft. The numerical method is presented in Section 3. The simulation results are then shown in Section 4 and some discussions on these results are carried out. Finally, the summary and conclusions are presented at the end of this paper.

#### 2. SMART-1 Spacecraft-Plume Interactions Model

The geometry and dimensions of SMART-1 spacecraft model are illustrated in Figure 1. The main body of SMART-1 can be considered as the cubic shape with the dimensions of . In this model, the Hall thruster is simplified as a cylinder with the diameter of 100 mm and the height of 50 mm; two thin rectangles with 5400 mm length and 1000 mm width are utilized to represent the solar arrays which can rotate around the satellite.