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Extension of smoothed particle hydrodynamics based on Poisson brackets
Kincl, Ondřej ; Pavelka, Michal (advisor) ; Richter, Thomas (referee) ; Violeau, Damien (referee)
The thesis aims to find a generalization of smoothed particle hydrodynamics to fluid models which are compatible with Hamiltonian formulation of physics. We develop an approach based on a particle discretization of Poisson brackets. The main advantage of this approach is easy verification of conservation laws, which are related to the degree of consistency of discrete derivatives. Firstly, we demonstrate our technique on a particle approximation of symmetric hyperbolic thermodynamically compatible equations, which allow for unified description of fluids, viscoelastic materials and solids. Secondly, we develop a novel particle approximation for superfluid helium-4. 1
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Emergence of irreversible dynamics by the lack-of-fit reduction
Mladá, Kateřina ; Pavelka, Michal (advisor) ; Klika, Václav (referee)
The thesis studies theories of dimensional reduction on the example of the Kac- Zwanzig (heat bath) model. The studied methods are the Mori-Zwanzig projection for- malism and the lack-of-fit reduction, both applied for two sets of resolved variables. The methods give integro-differential and ordinary differential evolution equations re- spectively. For the Mori-Zwanzig formalism, a limit of the number of particles going to infinity is made, which leads to an exponential memory kernel and consequently to a set of stochastic differential equations. The evolution equations of the two methods are compared using numerical simulations. 1
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The Connection between Continuum Mechanics and Riemannian Geometry
Burýšek, Miroslav ; Pavelka, Michal (advisor) ; Klika, Václav (referee)
We investigate the systems of quasi-linear partial differential equations of hydrody- namic type. These equations occur mainly in hydrodynamics and continuum mechanics, but they arise in other various applications. In the study of such systems, one finds an intersection of Poisson and pseudo-Riemannian geometry. The Poisson bracket is deter- mined by functions that turn out to be metrics and Christoffel symbols. If the metric is non-degenerate, the existence of Poisson structure is equivalent to the existence of flat metric and Levi-Civita covariant derivative with zero curvature. Moreover, one can find special flat coordinates where the bracket is trivial. This result was found in the eighties by Dubrovin and Novikov for the one-dimensional case and later on extended to more dimensions. In this thesis we provide the proof of the Dubrovin-Novikov theorem, which was only sketched in the original paper. We also conducted an overview of current knowledge in the multi-dimensional case, where the theory gets much more complicated. In particular, the link between the compatible brackets and the possibility of finding flat coordinates is discussed. The Riemannian character of the Hamiltonian equations of hydrodynamic type can be used to prove their symmetric hyperbolicity, even when the equations are not in the...
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Consistent non-equilibrium thermodynamic modeling of hydrogen fuel cells
Jambrich, Jakub ; Pavelka, Michal (advisor) ; Souček, Ondřej (referee)
At first, a classical irreversible thermodynamic model of the hydrogen pump is derived in this thesis. The model is then numerically implemented by using the Finite volume method in the VoronoiFVM library in Julia. The numerical implementation is further used to explain the measured experimental data from [1]. The plateau observed in the Voltage-current figure could not be explained in the original work, as the membrane was approximated with a single point. Such a zero-dimensional model did not predict the plateau, and it was believed to originate from some Interfacial effects. This work will focus on the correct implementation of the equations inside the membrane and try to explain the observed effects using no additional assumptions.
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Thermodynamic modelling of hydrogen fuel cells
Nováček, Marek ; Pavelka, Michal (advisor) ; Němec, Tomáš (referee)
In this thesis, proton exchange membrane fuel cells are studied. At the beginning, the ideas underlying their function are exposed and some possibilities of usage are pre- sented. Thereafter, we aim to describe the processes inside the fuel cells with the aid of thermodynamics and in agreement with constitutive relations that have been obtained experimentally. Namely, we are interested in the fluxes of water and protons inside the membrane, where they are acted upon by thermodynamic forces, and the electrochemical reactions at the electrodes, which can be described by the Butler-Volmer equations. Also do we study the efficiency of the fuel cell by evaluating the production of entropy due to the diverse processes that take place in the fuel cell. It is the goal of the computational part of this thesis to propose a zero-dimensional model and compare it with the results provided in the supervisor's doctoral thesis. 1
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Thermodynamic analysis of processes in Hydrogen fuel cells.
Pavelka, Michal ; Maršík, František (advisor) ; Grmela, Miroslav (referee) ; Sciacovelli, Adriano (referee)
Non-equilibrium thermodynamics, which serves as a framework for formulating evolution equations of macroscopic and mesoscopic systems, is briefly reviewed and further developed in this work. For example, the relation between the General Equation for the Nonequilibrium Reversible- Irreversible Coupling (GENERIC) and (ir)reversibility is elucidated, and Onsager-Casimir reciprocal relations are shown to be an implication of GENERIC. Non-equilibrium thermodynamics is then applied to describe fuel cells and related devices, and theoretical conclusions are compared to experimental data. Moreover, a generalization of standard exergy analysis is developed bringing a new method for revealing a map of useful work losses in electricity producing devices. This method requires a non-equilibrium thermodynamic model, and so the general theory of non- equilibrium thermodynamics and optimization of real power generating devices stand side by side.
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Modelling of heterogeneous catalytic reactions in chemical reactors
Orava, Vít ; Hron, Jaroslav (advisor) ; Pavelka, Michal (referee) ; Růžička, Marek (referee)
This thesis consists of two parts discussing modelling of heterogeneous catalytic reactors. In the first one, an industrial prototype of a fluidized bed reactor serving as a hydrogen generator based on endothermic decomposition of formic acid is studied. After initial determination of the main reactor characteristics a system of nine con- stituents is derived and, consequently, reduced to a three phase flow. The solid and bubble particles immersed in a liquid are modelled by the Basset-Boussinesq- Ossen equation. Furthermore, an averaging technique is used to derive a three phase Euler-Euler model. Finally, numerical computations with a verification towards the measurements and a CFD analysis are proceeded. The second part discusses interfacial transport phenomena between a bulk and catalytic surfaces of a reactor mediated via the boundary conditions. The constitu- tive relations, that by construction comply with the second law of thermodynamics, follow from the specification of suitable thermodynamic potentials together with an identification of the bulk and surface entropy productions. The derived model is suitable for further analysis providing clear guidelines for the incorporation of the Langmuir-type adsorption model as well as other sorption models. Keywords: Heterogeneous catalysis, multi-phase...
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Termodynamická analýza procesů v polymerní elektrolytické membráně palivového článku
Pavelka, Michal ; Maršík, František (advisor) ; Málek, Josef (referee)
Thermodynamic analysis of processes in electrolytic fuel cell membrane Michal Pavelka April 12, 2012 Abstract Hydrogen fuel cells1 may become a key technology of 21st century, and it is important to be able to describe their behavior, therefore. In this work we focus on hydrogen fuel cells with a polymer-electrolyte membrane. For the membrane we adopt an existing model2 . We for- mulate the model in the framework of the mixture theory which we develop similarly as has been done in the classical textbook of Mazur and de Groot3 . However, refining the concept of potential energy of a material point, we introduce new terms called internal potential ener- gies which enable us to describe macroscopic consequences of internal forces between water and polymer in the membrane and to describe the influence of gradient of surface tension of water in the membrane. We solve the model in 1D approximation. Consequently, we calculate the influence processes in the membrane have on efficiency of the fuel cell. 1 see for example Larminie, J. and A. Dicks. Fuel Cell Systems Explained. 2nd edition. John Wiley & Sons Ltd., 2003. ISBN 0-470-84857-X. 2 Weber, A. Z. and J. Newman. Transport in Polymer-Electrolyte Membranes I, II, III. J. Electrochem. Soc., 150 (7), A1008-A1015, 2003; 151 (2), A1311-A1325, 2004.; 151 (2), A1326-A1339,...
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Geometric integrators
Mladá, Kateřina ; Pavelka, Michal (advisor) ; Hron, Jaroslav (referee)
This thesis gives a brief introduction to the Hamiltonian formalism and symplectic geometry. The Hamilton theory is applied on three systems - the pendulum, a parti- cle in a central potential field and rigid body rotation.The main focus of this thesis is to derive several symplectic integrators: the symplectic Euler schemes, Verlet schemes, implicit mid-point rule method and a parametric symplectic integrator. The symplectic integrators will be compared with each other and with two non-symplectic integrators - the explicit Euler scheme and the Ehrenfest integrator. For the comparison we will use harmonic oscillator, a particle in a central gravitational field and rigid body rotation. 1
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Thermodynamic analysis of processes in Hydrogen fuel cells.
Pavelka, Michal
Non-equilibrium thermodynamics, which serves as a framework for formulating evolution equations of macroscopic and mesoscopic systems, is briefly reviewed and further developed in this work. For example, the relation between the General Equation for the Nonequilibrium Reversible- Irreversible Coupling (GENERIC) and (ir)reversibility is elucidated, and Onsager-Casimir reciprocal relations are shown to be an implication of GENERIC. Non-equilibrium thermodynamics is then applied to describe fuel cells and related devices, and theoretical conclusions are compared to experimental data. Moreover, a generalization of standard exergy analysis is developed bringing a new method for revealing a map of useful work losses in electricity producing devices. This method requires a non-equilibrium thermodynamic model, and so the general theory of non- equilibrium thermodynamics and optimization of real power generating devices stand side by side.
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