Numerical investigation of MPD thrusters using a density-based method with semi-discrete central-upwind schemes for MHD equations

The magnetohydrodynamic (MHD) equations which combines the Navier-Stokes equations with the Maxwell equations are essential for the investigations of many research areas as earth's core modelling, metal casting, fusion devices and electrical and aerospace devices. In the present work, the central-upwind schemes proposed by Kurganov, Noelle and Petrova for hydrodynamics are extended and combined with the divergence cleaning method of Dedner in order to investigate the performance of the self-field and applied magneto-plasma dynamic thrusters which still involving some outstanding problems. This new algorithm is developed for the single temperature, ideal and resistive MHD equations in a finite volume discretization framework with Gaussian integration. The electrical conductivity is predicted according to the Spitzer-Härm formulation and the real gas ratio of specific heats proposed by Sankaran is implemented for higher discharge current. To improve the quality of the solution, the limiter function of first and second order interpolation scheme is used. The accuracy and the robustness of the obtained solver are demonstrated through numerical simulations of ideal MHD benchmark problems. first, the ability of the developed code to handle shocks, rarefactions and contact discontinuities is tested with the Brio-Wu shock-tube problem. The Minmod and the Van Albada limiter functions has been found to perform better than the other limiter used and the obtained results agree well with both the analytic and the simulations results of previous work. Secondly, the complex and multiple shock interactions and the transition from smooth to turbulent flow involved in the Orszag-Tang vortex problem is well described by the present code and the comparison with the WENO-5 scheme of Shen shows good agreement. Lastly, The ability to described the interaction of an denser cloud with a MHD shock is tested by simulating the 2D cloud-shock interaction problem. The main phases of the interaction are well captured by the solver and the temporal progression of the density contour is in accordance with those obtained by Xisto. The ability of the developed resistive solver to deal with plasma flow acceleration is tested by simulating the well experimental investigated thrusters: The full scale benchmark thruster and the extended anode thruster of Princeton. The results show good agreement with the experimental and simulations results of previous work for discharge current less than the critical current just before the beginning of the onset phenomenon. Simulations are also conducted on the Villani-H thruster to determine the effect of geometric changes over the thruster performance and a first designing attempts is proposed according to the stability analysis. Confident with the results obtained with ideal and resistive MHD problems, the present code is extended to applied-field MPD thrusters. The purpose is to achieve a high thrust level required for space missions with less input power than with self-field MPD thrusters and thus avoid the onset instabilities. For the verification of the code, the NASA Lewis Research Center's (NASALeRC) MPD thruster is chosen because of its wide range of experimental data bank. The method presented reproduce the theory of thrust production and plasma acceleration. Some difficulties as the limitation of the maximum rotational speed and the depletion of the plasma density on the anode surface have been captured. Moreover, the present density-based method compares very well with experimental data of Myers and simulations of Mikellides

Modelação analítica e numérica de efeitos transitórios

O rotor cicloidal é também denominado de ciclorotor, ou propulsor cicloidal, e é uma turbomáquina que permite converter energia, quer em modo propulsivo quer como gerador. À medida que as pás do rotor se movimentam, elas oscilam periodicamente ao longo de um ciclo de rotação. O controlo do ângulo de inclinação de cada pá possibilita ao rotor cicloidal alterar de um modo quase instantâneo a direção e a magnitude da força gerada. Devido a esta importante habilidade, o rotor cicloidal pode melhorar o comportamento de veículos aéreos para uma vasta gama de aplicações, nomeadamente a descolagem e aterragem vertical, o alcance do voo em estado pairado (hover), etc. Embora a abordagem baseada em CFD (Computational Fluid Dynamics) seja o meio adequado para analisar o comportamento do escoamento em torno das pás, os modelos analíticos são úteis para fornecer informações relevantes numa fase preliminar do projeto dos rotores cicloidais. No presente trabalho fez-se a proposta de um modelo analítico composto de uma subcomponente cinemática e de uma subcomponente dinânmica. O modelo visa estudar minuciosamente a operação física dos rotores cicloidais e fornecer aproximações para a força gerada e para a potência consumida pelo rotor cicloidal. Tendo em conta as limitações deste modelo analítico, o presente trabalho incluiu ainda a modelação numérica 2D e 3D que permitiu estudar com mais precisão o desempenho e as características do escoamento em rotores cicloidais. Através da modelação numérica, realizaram-se estudos sobre o desempenho dos rotores cicloidais. Também se averiguou a existência de vantagens concernentes à operação de rotores cicloidais em modo inverso, isto é, o caso em que o rotor cicloidal funciona como uma Turbina de Vento de Eixo Vertical. A força gerada por uma pá depende do escoamento em torno dela. E o escoamento em torno de uma pá pode ser alterado através do movimento da própria pá. No presente trabalho propôs-se a alteração do movimento das pás através da imposição de uma vibração harmónica, isto é, as pás do rotor vibram à medida que descrevem o caminho cicloidal convencional. Assim, com a finalidade de melhorar o desempenho do rotor cicloidal, estudaram-se vários casos em que o perfil alar vibra à medida que descreve o movimento de picada oscilante com resultados promissores.A cycloidal rotor, also known as a cyclorotor, or cycloidal propeller, is a turbomachine that allows to convert energy in propulsive mode and in generator mode. The blades of a cycloidal rotor describe a periodic change on their pitch angle over a cycle of rotation. The control of the pitch angle provides to the cycloidal rotor the ability to vary the direction and magnitude of the thrust vector almost instantly. This important characteristic features the cycloidal rotor with an attractive vector thrust capability which may enhance the behavior of a aircraft for a wide range of applications; e.g. VTOL (Vertical Take-Off and Landing), STOL (Short Take-Off and Landing), hover, etc. Although in recent years the CFD based approaches have been able to provide adequate means to analyze the flow behavior around blades, analytical models are useful to provide immediate guidelines in the preliminary stages of the cycloidal rotor design. In the present work it was proposed a novel analytical model composed of a kinematic sub-component and a dynamic sub-component. The model aims to study the physical operation of the cycloidal rotors and to provide approximate estimations of the overall generated thrust and the power required by the operation of the cycloidal rotor. Considering the limitations of the analytical model, the present work includes also the 2D and 3D CFD models that allowed to study with more accuracy the performance and characteristics of the cycloidal rotors. Through numerical modeling, studies were conducted on the performance of the cycloidal rotors. It was also investigated the potential of cycloidal rotors operating in reverse mode, i.e., the case where the cycloidal rotor operates as a Vertical Axis Wind Turbine. The force generated by a blade depends on the flowfield around it. The flowfield around a blade can be changed by changing the motion of the blade. In the present work, it was proposed to change the movement of the blades by imposing an harmonic vibration, that is, the blades vibrate as they describe the conventional cycloidal path. Thus, in order to improve the performance of the cycloidal rotor, several cases in which an airfoil vibrates, while it describes an oscillating motion, were studied with promissing results

Ideal GLM-MHD - a new mathematical model for simulating astrophysical plasmas

Magnetic fields are ubiquitous in space. As there is strong evidence that magnetic fields play an important role in a variety of astrophysical processes, they should not be neglected recklessly. However, analytic models in astrophysical either do often not take magnetic fields into account or can do this after limiting simplifications reducing their overall predictive power. Therefore, computational astrophysics has evolved as a modern field of research using sophisticated computer simulations to gain insight into physical processes. The ideal MHD equations, which are the most often used basis for simulating magnetized plasmas, have two critical drawbacks: Firstly, they do not limit the growth of numerically caused magnetic monopoles, and, secondly, most numerical schemes built from the ideal MHD equations are not conformable with thermodynamics. In my work, at the interplay of math and physics, I developed and presented the first thermodynamically consistent model with effective inbuilt divergence cleaning. My new Galilean-invariant model is suitable for simulating magnetized plasmas under extreme conditions as those typically encountered in astrophysical scenarios. The new model is called the "ideal GLM-MHD" equations and supports nine wave solutions. The accuracy and robustness of my numerical implementation are demonstrated with a number of tests, including comparisons to other schemes available within in the multi-physics, multi-scale adaptive mesh refinement (AMR) simulation code FLASH. A possible astrophysical application scenario is discussed in detail