Modeling an Electrospray Propulsion System Using an Open-Source Smoothed Particle Hydrodynamics Method
摘要
Electrospray Thrusters are being investigated by many researchers because of their small size, which is suitable for small spacecraft. Different models have been proposed in the literature, including simple analytical models with limited accuracy and more complex weak-coupled Electromagnetic Fluid Dynamic numerical approaches. However, accurate and time efficient solutions are still unavailable. To address this problem, this paper proposes an open-source Python tool based on the Smoothed Particle Hydrodynamics (SPH) method. SPH is a Lagrangian mesh-free approach that can naturally incorporate fluid dynamics physical effects, and it has been successfully applied to many fluid dynamics problems, such as free surface flow and electrophoretic deposition. The proposed tool aims to balance efficiency, simplicity, and code reuse. The Navier-Stokes governing equations can be represented in state-space form, and they can be efficiently solved using the open-source Scientific Computing Python Library. This library provides a variety of Initial Value Problem solvers, making it well-suited for performing the SPH integration scheme. The tool is validated using the Poiseuille Flow Problem, where analytical solutions are available to check the accuracy and performance of the different SciPy solvers. Computational aspects, including the neighbor particle search and surface detection, are also investigated. The results obtained using different particle numbers showed good agreement with the analytical velocity profile, with errors ranging from 3% to 12%, depending on the particle number. The analytical solution also demonstrates that the Scientific Computing Python Library offers a variety of implicit and explicit solvers capable of addressing the problem. Due to the simplicity of the problem, implicit methods tend to outperform explicit ones. However, as shown by the results, as the complexity of the problem increases, the opposite behavior is observed. Among the methods analyzed, the RK45 solver proved to be a good and reliable solution. Finally, the tool is validated and a simplified bidimensional planar Electrospray Thrusters model is simulated. Despite the simplifications made, the problem was successfully addressed by employing various values of the electric field, confirming the theoretical stability limit between electric force and surface tension. However, instabilities were observed under conditions near equilibrium.