Abstract :
[en] Plasma have an important role in the field of aerospace, more specifically in atmospheric reentry of spacecraft. Indeed, when an object (re)enters an atmosphere at supersonic speed, a shock forms in front of it. This shock converts the kinetic energy of the reentering object by ionizing the gas composing the atmosphere (air on earth), creating a plasma. The latter interacts thermally and chemically with the material. Understanding plasma behaviour is thus of capital importance in the design of spacecraft material. For instance, space shuttles are protected during reentry by thermal protection systems. The latter must be sufficiently resistant for the spacecraft to survive the reentry. On the other hand, when a satellite is decommissioned, it should fall back on earth and completely disintegrate in order to keep a clean spatial environment. Inductively coupled plasma facilities have been created in order to study these interactions. They reproduce the atmospheric reentry by heating a plasma using electric induction. There has been an increasing interest in those facilities in the past decades due to the high purity of the flow they produce and the possibility to run long experimental campaigns. Over the years, the complexity of the experiments performed has also increased. For instance, nozzles are now placed at the exit of the ICP torch in order to study supersonic plasma. More complex geometries are investigated, such as semi-elliptical nozzles for the study of shear flows. Unsteady and turbulent behavior are also studied. New thermal protection systems involving electron transpiration cooling, i.e. the spontaneous emission of electrons from a surface carrying the heat away, are tested. Another example is the study of communication black-out during reentry, and the possible ways to mitigate this phenomenon. Due to the wide variety of configurations encountered in ICP facilities and the possibility to perform measurements in specific locations only, it is difficult to predict the flow features beforehand. Flow prediction is very important before planning an ICP experimental campaign, as the plasma modes could damage the facility. Moreover, predicting the flow correctly saves not only preparation time, but also funds. In this context, numerical solvers have been developed to simulate the ICP flows. The legacy numerical solvers are based upon the finite volume method, demanding a high mesh quality, making this approach very cumbersome for complex geometries. Moreover, these solvers are only axisymmetric, most of them performing computations at local thermodynamic equilibrium and steady state, missing many important physical features of ICP flows. Moreover, they are not robust, as they are based on a staggered solution strategy, converging in thousands of iterations and sometimes requiring to be carefully monitored. In order to address all these issues, we develop in this work the first monolithic multi-domain high order solver for inductively coupled plasma using the hybridized discontinuous Galerkin method. The high-order aspect of the method brings accuracy and mesh flexibility, while the monolithic solution strategy brings robustness to the code.
In this thesis, we first discuss the various plasma models stemming from the kinetic theory of gas, each one representing a different degree of thermal and/or chemical non-equilibrium. Unfortunately, we are not able to explore all of them in this work, as the task is far too ambitious. The goal is to give an overview of the possible improvements to the relatively simple thermochemical model used in this thesis, which is the local thermodynamic equilibrium (LTE). Then, we particularize the LTE plasma equations to the axisymmetric approximation of inductively coupled plasma flows. In particular, we discuss hypotheses made on the electromagnetic field. We also present the boundary conditions, explicitly stating that, in steady numerical simulations, a coflow is introduced in the chamber in order to stabilize the flow. Then, we present the multi-domain hybridized discontinuous Galerkin solver, which is the first solver of its kind. We prove that the correct orders of convergence of the method are retrieved on a manufactured solution. We also study the impact of the coflow on the steady state result, and conclude that it does not have a significant influence on the flow features in the jet. We also show that the HDG code is able to produce the same result as a legacy FV solver, COOLFluiD, and that it is robust and converges in only a few Newton iterations. Finally, we study a realistic case and assess the impact of various experimental parameters on the flow features.
To summarize, we developed a robust and easy-to-use high order solver for inductively coupled plasma which easily adapts to complex geometries. This thesis marks a turning point in the field of ICP simulation, as it proves that high-order methods are well suited for this applications. Thanks to its robustness, precision, ease of use and flexibility, it opens the door to future developments in this field: supersonic flow simulations, instability and turbulence studies, or more complex thermochemical models.
