14-moment maximum-entropy modelling of collisionless ions for Hall thruster discharges

Ions in Hall thruster devices are often characterized by a low collisionality. In the presence of acceleration fields and azimuthal electric field waves, this results in strong deviations from thermodynamic equilibrium, introducing kinetic effects. This work investigates the application of the 14-moment maximum-entropy model to this problem. This method consists in a set of 14 PDEs for the density, momentum, pressure tensor components, heat flux and fourth-order moment associated to the particle velocity distribution function. The model is applied to the study of collisionless ion dynamics in a Hall thruster-like configuration, and its accuracy is assessed against different models, including the kinetic solution. Three test cases are considered: a purely axial acceleration problem, the problem of ion-wave trapping and finally the evolution of ions in the axial-azimuthal plane. Most of this work considers ions only, and the coupling with electrons is removed by prescribing reasonable values of the electric field. This allows us to obtain a direct comparison among different ion models. However, the possibility to run self-consistent plasma simulations is also briefly discussed, considering quasi-neutral or multi-fluid models. The maximum-entropy system appears to be a robust and accurate option for the considered test cases. The accuracy is improved over the simpler pressureless gas model (cold ions) and the Euler equations for gas dynamics, while the computational cost shows to remain much lower than direct kinetic simulations

Lagrangian diffusive reactor for detailed thermochemical computations of plasma flows

The simulation of thermochemical nonequilibrium for the atomic and molecular energy level populations in plasma flows requires a comprehensive modeling of all the elementary collisional and radiative processes involved. Coupling detailed chemical mechanisms to flow solvers is computationally expensive and often limits their application to 1D simulations. We develop an efficient Lagrangian diffusive reactor moving along the streamlines of a baseline flow simulation to compute detailed thermochemical effects. In addition to its efficiency, the method allows us to model both continuum and rarefied flows, while including mass and energy diffusion. The Lagrangian solver is assessed for several testcases including strong normal shockwaves, as well as 2D axisymmetric blunt-body hypersonic rarefied flows. In all the testcases performed, the Lagrangian reactor improves drastically the baseline simulations. The computational cost of a Lagrangian recomputation is typically orders of magnitude smaller with respect to a full solution of the problem. The solver has the additional benefit of being immune from statistical noise, which strongly affects the accuracy of DSMC simulations, especially considering minor species in the mixture. The results demonstrate that the method enables applying detailed mechanisms to multidimensional solvers to study thermo-chemical nonequilibrium flows

Stagnation point heat flux characterization under numerical error and boundary conditions uncertainty

International audienceThe numerical simulation of hypersonic atmospheric entry flows is a challenging problem. Prediction of quantities of interest, such as surface heat flux and pressure, is strongly influenced by the mesh quality using conventional second-order spatial accuracy schemes, while depending on the boundary conditions, which generally suffer from uncertainty. This paper explores these two aspects, illustrating a CFD study on the forebody of the EXPERT vehicle of the European Space Agency employing the US3D solver

Influence of thermochemical modelling of CO2-N2 mixtures on the shock interaction patterns at hypersonic regimes

The effect of finite-rate internal energy transfer on shock interaction mechanisms of CO2-dominated flows is investigated. The polyatomic molecule has a relatively low characteristic vibrational temperature that causes vibrational degrees of freedom to be excited across a shock wave at hypersonic regimes. In this paper, the impact of accounting for the time associated to the relaxation of this process, as opposed to assuming instant thermal equilibrium, on the shock structures occurring in the flowfield over a double-wedge geometry is numerically studied. A Mach 9 flow over two different geometries is simulated with two different models, the two-temperature model of Park and the thermally perfect gas model. Simulations are carried out with the SU2 software that is coupled to the Mutation++ library, providing thermodynamic, chemical kinetic and transport properties of any mixture of gases for a given state of the flow. Anisotropic mesh adaption is used with the AMG library to accurately capture highly directional and high-gradient localized flow features. Results show that different ways of modelling the effect of vibrational relaxation have a major impact on the size of the compression corner separation bubble, leading to different shock wave systems in this region. As a consequence, the obtained shock interaction mechanisms differ as well. The shock patterns obtained for the thermally perfect gas model result in stronger impingement on the surface and higher aerodynamic loads of pressure and heat flux