Modellering en deeltjesmethoden voor plasmasimulatie toegepast op Air-Breathing Electric Propulsion

Recently, researchers suggested that flying satellites at lower altitude in Earth's orbit with respect to traditional satellites could provide advantages from the operational and economic point of view. However, the tenuous atmospheric gas generates a drag force which needs to be compensated if the orbit is to be maintained. Electric propulsion represents the most natural solution to compensate a rather low but constant force, in virtue of its highly efficient use of the available propellant thanks to the high exhaust velocity. Even then, however, the mass of propellant required becomes a limiting factor. The concept of air-breathing electric propulsion (ABEP) seeks to solve this problem by collecting atmospheric particles and using them as the propellant in the electric thruster. Although promising, the ABEP technology has never been tested in space, and presents many challenges for a successful operation. First, the atmospheric gas (mainly nitrogen and atomic oxygen) is different from the traditional propellants used in electric thrusters (typically noble gases like argon, krypton, and xenon). The atmospheric mixture is more difficult to ionize and it may react with surfaces by oxidizing them, which means that thrusters need to be adapted. Furthermore, the collection of the atmospheric gas is a novel effort which requires the design of an intake with appropriate shape and materials. This represents one of the critical aspect of the concept, however the nature of the gas-surface interaction at orbital speeds is still not well understood and often modeled using very crude models. Ground testing is a fundamental step to advance the concept towards in-orbit operation. A vacuum facility named DRAG-ON has been commissioned at the von Karman Institute for Fluid Dynamics with the specific objective of studying intake-collectors for ABEP and measuring their performance using a representative flow. Such flow is produced in the facility by a particle flow generator (PFG), a plasma source which accelerates ionized argon or oxygen in an electrostatic field. Simulation is necessary for calibration and interpretation of the experiments, since the plasma flow produced by the PFG is not a perfect analog of the orbital flow, and measuring the performance of the intake is done indirectly by measuring the stagnation pressure in the two chambers of the facility, which involves a complex calibration procedure. Simulation can also potentially be used to extrapolate the behavior of the ABEP system to orbital conditions, overcoming the limitations of experimental ground testing. The present work aims at developing the models and numerical tools necessary to support ABEP ground testing and aid in the design of the flight model. In general, the neutral and plasma flows that we need to deal with are in the rarefied regime, where collisions are not frequent enough to maintain thermal equilibrium, but still important, for example in sustaining the plasma discharge. In this work, we decided to focus on particle-based methods, namely on Particle-in-Cell (PIC) and stochastic collision methods of Monte Carlo collisions (MCC) and Direct Simulation Monte Carlo (DSMC). Such methods are considered accurate for rarefied plasma flows, since they can capture the nonequilibrium distribution function and the effect of charge separation. However, they become computationally expensive as the plasma density and therefore the level of collisionality are increased. In this work, we take advantage of implicit time discretization methods to extend the numerical stability range of explicit PIC, and therefore reduce the computational cost. We develop semi-implicit and fully-implicit schemes for unstructured finite element discretizations that conserve energy exactly, an important property for the stability and long-term accuracy of the simulations. The advantage of the semi-implicit version is its low computational cost, comparable to that of the explicit scheme. The fully-implicit scheme has the advantage of conserving charge, and leaving greater flexibility in algorithmic choices, at a higher computational cost per time step. For this scheme, we explore a few options to solve the nonlinear system, finding that a simple Jacobian, which is similar to the linearization done for the semi-implicit scheme, represents the most practical and efficient solution. The methods are implemented in the open source code Pantera. We compare the different schemes using simple but representative test cases of the expansion of a plasma slab into vacuum and the effusion of plasma in a box. We also perform code-to-code verification for a 2D test case designed to test incrementally the various parts of the implementation. In this process, we also include a procedure for numerical error quantification based on the grid convergence index method, adapted for the output of a stochastic code. This allows for a more robust comparison, and could be used for robust validation of the models in the future. We use these tools to reproduce numerically the experiments performed in the DRAG-ON facility. We simulate the plasma expansion from the outlet of the plasma source and its interaction with the ABEP intake. We apply different surface scattering models and compare the obtained intake transmission probabilities to the experimental measurements. The results show that diffuse reflections reproduce well the transmission probability for flows in the thermal velocity range, while for hyperthermal flows the physics-based washboard model provides a better agreement with the experimental value, indicating that shallow, high velocity surface impacts are not fully accommodated. Finally, we present the simulation of an ABEP system in orbital conditions. We use a one-way coupled approach where the neutral flow is first solved in the full domain of intake and thruster, and then the ionized flow is solved in the smaller and more refined domain of the electric thruster. We show how the simulation can be converged to a certain value of absorbed plasma power, and performance parameters of the propulsion system can be extracted. Although a proof-of-concept, we demonstrate how the methods we developed can be used to aid in the design of ABEP systems and predict their performance taking advantage of the results of ground test experiments.