Graduate Thesis Or Dissertation


Optimization under Uncertainty of a Magnetohydrodynamics Generator Public Deposited

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  • Within this dissertation, we develop tools and techniques to demonstrate the feasibility of real-time optimization of a magnetohydrodynamics generator. To ease computational complexity, we work on the kinematic magnetohydrodynamic system, prescribing the fluid-flow and model the material response of the system through an updated Generalized Ohm’s law. We focus on two optimization difficulties specific for this application: model accuracy and feasibility. These both are crucial in the determination of optimal operating conditions, and thus optimal power. To address these concerns, several concepts are introduced to the model. First, we introduce the ion-slip parameter, a term which characterizes the material interac-tions between the fluid and electromagnetic fields. It is shown that this mechanism does not disrupt the well-posedness of the system. We then develop a function space parameter estimation convergent deterministic parameter estimation scheme, imply-ing that recovery of a more realistic functional parameter set is possible. We also discuss the inclusion of uncertainty within the theoretical MHD frame-work. This uncertainty is introduced through the parameters, viewing them as random processes rather than deterministic functions. We extend the well-posedness of the de-terministic system to the stochastic system, demonstrating that the uncertain forward problem is well-posed, and that the finite-dimensional approximation to the inverse problem method stable. We validate the theoretical results using simulations for both the deterministic and stochastic magnetohydrodynamic systems. For the numerical implementation of the deterministic system, we make use of COMSOL, a finite-element based differential equation solver. We investigate two distinct Faraday geometries, the continuous and the segmented. To verify the numerical model, we develop new ideal power equations for each geometry, again introducing the concept of the ion-slip mechanism into pre-vious theory. Under the deterministic scheme, we also implement a numerical method for recovering parameters from fabricated ‘true’ data. Furthermore, the results from these numerical tests again confirmed the need for uncertainty to be included, as re-covery was not only sensitive to noise, but also asymmetric with respect to expected error. To verify the stochastic theory developed for the forward and inverse problem, we utilize the cross-platform compatibility of Matlab and COMSOL. We use the native optimization techniques and data manipulation capabilities of Matlab, paired with the deterministic forward solver in COMSOL. We apply an existing numerical method, stochastic collocation, under the new context of the kinematic MHD system, for the numerical treatment of the propagation of uncertainty within the forward problem. This method effectively capitalizes on assumed orthogonality of a finite number of random variables describing the system. We perform an error analysis of stochastic collocation, and then demonstrate that the inclusion of uncertainty does not propagate linearly through the magnetohydrodynamics system, i.e. the expected value of the so-lutions is not the deterministic solution of the expected value of the parameter set. We then confirm the numerical theory as well, discussing the necessary assumptions and implementation steps to apply the stochastic collocation in the uncertain parameter estimation problem. Finally, we turn to a numerical demonstration of the feasibility of a two stage optimization of an MHD generator. We use fabricated data to recover the parameters’ distributions on the domain. Using these recovered distributions, we then optimize the performance of the generator, using a single optimization variable.
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