Paolo Scuderi
A new MagnetoFluid Dynamics model for Low Magnetic Reynolds number regime in the Hybridized Discontinuous Galerkin Framework.
Rel. Domenic D'Ambrosio, Thierry Magin, Georg May. Politecnico di Torino, Corso di laurea magistrale in Ingegneria Aerospaziale, 2021

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Abstract: 
The MagnetoFluid Dynamics has many aerospace applications when the gas is an ionized mixture. Typically, this happens when the temperature of the mixture is very high. Indeed, we need to consider new degrees of freedom of the molecules, the presence of the chemical reactions, and the possibility to have free electrons that can move from one point to another. This is the typical situation during a normal atmospheric entry problem. In this context, all the physical properties cannot be computed with the classical approximation laws. The ChapmanEnskong method gives us the possibility to perturb the Boltzman Transport Equation and to understand which are the different contributions (of electrons and heavy particles) to take into account. Hence, the modeling of the transport properties can be conducted. The latter, which are functions of pressure and temperature, can also change their values with the presence of external magnetic and electric fields. The physical models that try to describe all these peculiar characteristics and the macroscopic properties of electrically conducting flows are, from a numerical point of view, highly stiff. In the last years, a simplified version of the full MagnetoFluid Dynamics system was proposed. Two limiting cases are present based on the dimensionless parameter Magnetic Reynolds number. When it is very small, the externally applied magnetic field is called rigid. Hence, the induced magnetic field can be considered null. Therefore, the classical NavierStokes equations with additional external electromagnetic source terms make up the simplified MagnetoFluid Dynamics system. The source term is composed of the Lorentz force for the momentum equation and the Joule heating for the energy equation. No source terms for the continuity equations must be taken into account under the assumption of frozen flow, which is generally adopted in many hypersonic applications. The system cannot be solved analytically, except where we are considering parallel flow, where the nonlinear convective terms drop down, i.e. Hartmann flow. As a consequence, we need to introduce numerical discretization. One of the most innovative methods to solve nonlinear PDEs is called Hybridizable Discontinuous Galerkin. It can be considered as a mix between FE and FV methods. The hybridization concept introduces the possibility to parallelize efficient the code and to reduce the high computational cost associated with the highorder methods, e.g. Discontinuous Galerkin. In the past years, many MagnetoFluid Dynamics physical models were developed into FV solvers. From the literature review, only one researcher Group from the Massachusetts Institute of Technology and Imperial College London, in 2019, has developed an MHD model for compressible flow in their HDG solver. The HighOrder Unifying Framework, developed by May et al. at RWTH Aachen and currently at The VKI, was empty of the MagnetoFluid Dynamics model for low Magnetic Reynolds number. The implementation from a physical, mathematical, and computer science point of view, is explained in this work. Finally, the model has been tested with simple test cases. Comparison with analytical data, i.e. Hartmann flow, has been conducted to validate the model. 

Relators:  Domenic D'Ambrosio, Thierry Magin, Georg May 
Academic year:  2020/21 
Publication type:  Electronic 
Number of Pages:  175 
Subjects:  
Corso di laurea:  Corso di laurea magistrale in Ingegneria Aerospaziale 
Classe di laurea:  New organization > Master science > LM20  AEROSPATIAL AND ASTRONAUTIC ENGINEERING 
Ente in cotutela:  The von Karman Institute for Fluid Dynamics (BELGIO) 
Aziende collaboratrici:  Von Karman Institute for Fluid Dynamics 
URI:  http://webthesis.biblio.polito.it/id/eprint/18929 
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