|
|
Implicitly constituted fluids and their flows in complicated geometries
Janečka, Adam ; Průša, Vít (advisor) ; Grmela, Miroslav (referee) ; Neustupa, Jiří (referee)
We study behavior of incompressible non-Newtonian fluids with a relation be- tween the shear stress and the shear rate given by a non-monotone S-shaped curve. These fluids are described with a special class of implicit constitutive relations that may be derived in a thermodynamically consistent manner us- ing the entropy production maximization principle or gradient dynamics. In the latter approach, the constitutive relation is given as the derivative of a non-convex dissipation potential. The concept of dissipation potential allows us to discuss stability of the constitutive relation and explain the experimen- tally observed response discontinuities. We are also concerned with hydrody- namic stability of flows of implicitly constituted fluids. Finally, we propose a numerical scheme for simulation of transient flows of fluids with a specific non-monotone constitutive relation. We employ the numerical scheme in a simulation of two-dimensional Taylor-Couette flow and the numerical results confirm our theoretical observations concerning the admissible flow states.
|
|
|
Generace vířivosti rychlostního pole gradientem entropie
Novák, Martin ; Maršík, František (advisor) ; Grmela, Miroslav (referee)
The master thesis studies the impact of the entropy gradient on the vorticity of ve- locity field, particularly by applying the linear momentum balances. These balances are formulated for Thermo-viscous fluids (later fluids) and Thermo-viscous-elastic ma- terial (later solids) with the other balances (energy, mass, etc.). In order to derive these balances, the Classical continuum mechanics approach is used along with the respec- tive Variational principles. The thesis emphasizes the Variational principles applica- tion representing the modification of the Bateman principle [Bat29] and its comparison with the Classical approach, linked to the L. Crocco work [Cro37], particularly in the case of vorticity generation. It is pointed that by the definition of the dissipative en- tropy sdis a harmony of both approaches can be achieved and that, in the case of an appropriate limit, the direct effect of the entropy gradient on the vorticity of velocity field can be demonstrated. By applying this conclusion the relationship between the change of circulation among a closed curve and released heat on the given geometry is indicated.
|
|
|
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.
|
|
|
Thermodynamic analysis of solid oxide cells
Vágner, Petr ; Maršík, František (advisor) ; Grmela, Miroslav (referee) ; Pekař, Miloslav (referee)
Thermodynamic analysis of solid oxide cells Petr Vágner The thesis deals with continuum thermodynamic modeling and analysis of phe- nomena in solid oxide electrochemical cells. A general description of the evo- lution of charged mixtures using partial mass densities, momentum density, entropy density, electric induction, magnetic field, polarization, and magnetiza- tion based on the GENERIC framework is formulated. The formulation is used to recover the Landau-Lifshitz magnetization relaxation model, the Single Re- laxation Time model for dielectrics, and the generalized Poisson-Nernst-Planck model. The latter model is consequently linked to the second part, where a novel double layer model of an yttria-stabilized zirconia interface is formulated within non-equilibrium thermodynamics. The model is solved for numerically in the time domain, and cyclic voltammetry of the system is analyzed. The last part of the thesis demonstrates the limits of Exergy Analysis on a simple solid oxide hydrogen fuel cell model with non-isothermal boundary. It is demon- strated that the minimization of entropy production does not necessarily lead to the maximization of the electric power for certain optimization scenarios. The thesis consists of a compilation of published and unpublished results of the author.
|
|
|
Implicitly constituted fluids and their flows in complicated geometries
Janečka, Adam ; Průša, Vít (advisor) ; Grmela, Miroslav (referee) ; Neustupa, Jiří (referee)
We study behavior of incompressible non-Newtonian fluids with a relation be- tween the shear stress and the shear rate given by a non-monotone S-shaped curve. These fluids are described with a special class of implicit constitutive relations that may be derived in a thermodynamically consistent manner us- ing the entropy production maximization principle or gradient dynamics. In the latter approach, the constitutive relation is given as the derivative of a non-convex dissipation potential. The concept of dissipation potential allows us to discuss stability of the constitutive relation and explain the experimen- tally observed response discontinuities. We are also concerned with hydrody- namic stability of flows of implicitly constituted fluids. Finally, we propose a numerical scheme for simulation of transient flows of fluids with a specific non-monotone constitutive relation. We employ the numerical scheme in a simulation of two-dimensional Taylor-Couette flow and the numerical results confirm our theoretical observations concerning the admissible flow states.
|
|
|
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.
|
|
|
Generace vířivosti rychlostního pole gradientem entropie
Novák, Martin ; Maršík, František (advisor) ; Grmela, Miroslav (referee)
The master thesis studies the impact of the entropy gradient on the vorticity of ve- locity field, particularly by applying the linear momentum balances. These balances are formulated for Thermo-viscous fluids (later fluids) and Thermo-viscous-elastic ma- terial (later solids) with the other balances (energy, mass, etc.). In order to derive these balances, the Classical continuum mechanics approach is used along with the respec- tive Variational principles. The thesis emphasizes the Variational principles applica- tion representing the modification of the Bateman principle [Bat29] and its comparison with the Classical approach, linked to the L. Crocco work [Cro37], particularly in the case of vorticity generation. It is pointed that by the definition of the dissipative en- tropy sdis a harmony of both approaches can be achieved and that, in the case of an appropriate limit, the direct effect of the entropy gradient on the vorticity of velocity field can be demonstrated. By applying this conclusion the relationship between the change of circulation among a closed curve and released heat on the given geometry is indicated.
|
guest ::
