Multi-fidelity Analysis and Optimization of a Cold-Gas Thruster

In the study of the response of complex engineering systems, especially in the aerospace field, computer experiments play a crucial role, enabling the simulation of the behaviour of such systems through the implementation of mathematical models, that can be extremely complex. For instance, optimization problems involving aerodynamic surfaces, turbomachinery components, as well as structural and thermo-fluid dynamic assessments that arise in various phases of aerospace design, require numerical simulations that are often extremely demanding in terms of simulation time and computational costs, when a high level of accuracy is sought. In these cases, the use of High Fidelity models, which aim for the most accurate representation possible of the phenomenon, often becomes infeasible. On the other hand, transitioning to Low Fidelity models allows for significant speed-up and reduction of computational burdens, but results in lower accuracy outputs. Multi-fidelity techniques enable the combination of the Low Fidelity models’ ability to provide numerous low-cost insights with the High Fidelity models’ capacity to ensure high result accuracy, allowing for a reduction in the required simulations. Moreover, they lead to the creation of surrogate models to use in outer loop applications, such as optimization tasks. A multi-fidelity modeling technique that has gained prominence in the aeronautical field in recent years is Co-Kriging. Rooted in geostatistics, Co-Kriging is a spatial interpolation technique for predicting the behaviour of a variable or function in untested locations. This thesis implements a detailed study of the Co-Kriging technique for the development of a surrogate model to predict the thrust coefficient of a cold gas thruster, as the geometry of its exhaust nozzle varies. Cold gas thrusters are small propulsion system used for attitude control maneuvers of nanosatellites that rely on the simple expansion of pressurized gas in a nozzle, without combustion. For these systems, viscosity significantly impacts the performance in terms of achievable thrust and the boundary layer is found to occupy a significant portion of the exit area. For various geometrical configurations of the nozzle, the thrust coefficient is calculated using both a High Fidelity model, which involves solving the Navier-Stokes equations to study the flow, and a Low Fidelity one, where viscous effects are neglected, requiring only the Euler equations. Additionally, the use of a 1D ideal nozzle model is considered as a potential Low Fidelity approach. Adaptive sampling techniques for the implementation of the Co-Kriging surrogate models are explored, testing three different algorithms, namely Maximum Variance, Expected Improvement and Information Gain, on benchmark single and two-variable functions. The last two algorithms are applied to the cold gas thruster case and the Information Gain criterion is found to outperform the other one. Moreover, leveraging the 1D ideal nozzle model as Low Fidelity, led to a reduction in overall computational cost while ensuring high global accuracy, despite the potential for minor local inaccuracies depending on the sampled points’ locations. Once a Co-Kriging surrogate is obtained, a multi-objective optimization is carried on with the aim of maximizing CF while minimizing the nozzle’s mass. A Pareto front for the optimal points is obtained, allowing for the selection of the geometry that best meets the mission objectives during the cold gas thruster’s design phase.