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Behaviour of new types of material models in a squeeze flow geometry
Řehoř, Martin ; Průša, Vít (advisor) ; Hron, Jaroslav (referee)
Investigation of material behaviour in a squeeze flow geometry provides an impor- tant technique in rheology and it is relevant also from the technological point of view (some types of dampers, compression moulding). To our best knowledge, the sque- eze flow has not been solved for fluids-like materials with pressure-dependent material moduli. In the main scope of the present thesis, an incompressible fluid whose visco- sity strongly depends on the pressure is studied in both the perfect-slip and the no-slip squeeze flow. It is shown that such a material model can provide interesting departures compared to the classical model for viscous (Navier-Stokes) fluid even on the level of analytical solutions, which are obtained using some physically relevant simplificati- ons. Numerical simulation of a free boundary problem for the no-slip squeeze flow is then developed in the thesis using body-fitted curvilinear coordinates and spectral collocation method. An interesting behaviour is expected especially in the corners of the computational domain where the stress singularities are normally located. Unfor- tunately, numerical results reveal some fundamental drawbacks related to the physical model and its possible improvement is discussed at the end of the thesis.
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Solution of Poiseuille and plane Couette flow associated with the dynamic boundary conditions
Vejvoda, Martin ; Málek, Josef (advisor) ; Kaplický, Petr (referee)
In the presented work we study the effect of dynamic boundary conditions on Couette and Poisseuille flows that represent two types of flow between two parallel impervious plates. In the firts part, the Navier-Stokes equations are considered describing flows of an incompressible Newtonian fluid, and dynamic boundary conditions in general three- dimensional setting. Then we look at how our problem reduces in the simplified geome- trical setting. In the second part, we study several selected problems, some of them are supported by numerical simulations. 1
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On fluids with pressure-dependent viscosity flowing through a porous medium
Žabenský, Josef ; Pokorný, Milan (advisor)
Experimental data convincingly show that viscosity of a fluid may change significantly with pressure. This observation leads to various generalizations of well-known models, like Darcy's law, Stokes' law or the Navier-Stokes equations, among others. This thesis investigates three such models in a series of three published papers. Their unifying topic is development of existence theory and finding a weak solution to systems of partial differential equations stemming from the considered models.
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Solution of Poiseuille and plane Couette flow associated with the dynamic boundary conditions
Vejvoda, Martin ; Málek, Josef (advisor) ; Kaplický, Petr (referee)
In the presented work we study the effect of dynamic boundary conditions on Couette and Poisseuille flows that represent two types of flow between two parallel impervious plates. In the firts part, the Navier-Stokes equations are considered describing flows of an incompressible Newtonian fluid, and dynamic boundary conditions in general three- dimensional setting. Then we look at how our problem reduces in the simplified geome- trical setting. In the second part, we study several selected problems, some of them are supported by numerical simulations. 1
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Thermodynamically compatible models capable of describing flows of viscoelastic fluids
Nádeníček, Václav ; Málek, Josef (advisor) ; Průša, Vít (referee)
Title: Thermodynamically compatible models capable of describing flows of vis- coelastic fluids Author: Václav Nádeníček Department: Mathematical Institute of Charles University Supervisor: prof. RNDr. Josef Málek, CSc., DSc. Abstract: In the present thesis we develop a thermodynamic framework pro- posed by Rajagopal and Srinivasa and use it to derive several thermodynam- ically compatible rate-type models of viscoelastic fluids. We derive a general form of a model which encompasses common rate-type models some of which are later in the text developed. 1
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Bingham-Korteweg fluids - modeling, analysis and computer simulations
Los, Tomáš ; Málek, Josef (advisor) ; Bulíček, Miroslav (referee)
Flow of granular materials is usually initiated when the shear stress is large enough and exceeds certain critical value. This can result in the presence of the dead-zones in which the flow itself does not take place. Motions of such materials are frequently described by Bingham model. Flows of granular fluids are frequently connected with the presence of free surface. In the thesis Bingham model is incorporated into a more general framework of Bingham-Korteweg fluids, which is a suitable way how to transfer free- boundary problems into the problems on fixed domains. A part of the thesis concerns mathematical analysis of interesting relevant problems for incompressible fluids. 1
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On fluids with pressure-dependent viscosity flowing through a porous medium
Žabenský, Josef ; Pokorný, Milan (advisor) ; Pražák, Dalibor (referee) ; Breit, Dominic (referee)
Experimental data convincingly show that viscosity of a fluid may change significantly with pressure. This observation leads to various generalizations of well-known models, like Darcy's law, Stokes' law or the Navier-Stokes equations, among others. This thesis investigates three such models in a series of three published papers. Their unifying topic is development of existence theory and finding a weak solution to systems of partial differential equations stemming from the considered models.
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Incompressible fluids with temperature dependent viscosity - numerical analysis and computational simulations
Ulrych, Oldřich ; Málek, Josef (advisor) ; Dolejší, Vít (referee) ; Šístek, Jakub (referee)
Title: Incompressible fluids with temperature dependent visco- sity, numerical analysis and computational simulations Author: RNDr. Oldřich Ulrych Department: Mathematical Institute of Charles University Supervisor: prof. RNDr. Josef Málek, CSc., DSc. Abstract: Flows of incompressible fluids connected with significant exchange of ther- mal and mechanical energy and with material moduli varying with the temperature and the shear rate, are described by the balance equations for linear momentum and energy, complemented by suitable constitution equations for the Cauchy stress and the heat flux. Assuming sufficient smoothness of quantities involved, the energy balance equation exhibits several equivalent formulations. However, within the context of weak solution, these formulations are, in general, not equivalent. This thesis is based on the existence theory for the generalized Navier-Stokes-Fourier system describing planar flow of fluids with a shear and temperature dependent vis- cosity. We specify parameters of a generalized power-law model under which weak formulations of balance equations are meaningful and both considered formulations of the energy balance equation are equivalent. Supported by the existence theory, we propose and numerically solve several problems pursuing the aim to systematically compare the...
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Behaviour of new types of material models in a squeeze flow geometry
Řehoř, Martin ; Průša, Vít (advisor) ; Hron, Jaroslav (referee)
Investigation of material behaviour in a squeeze flow geometry provides an impor- tant technique in rheology and it is relevant also from the technological point of view (some types of dampers, compression moulding). To our best knowledge, the sque- eze flow has not been solved for fluids-like materials with pressure-dependent material moduli. In the main scope of the present thesis, an incompressible fluid whose visco- sity strongly depends on the pressure is studied in both the perfect-slip and the no-slip squeeze flow. It is shown that such a material model can provide interesting departures compared to the classical model for viscous (Navier-Stokes) fluid even on the level of analytical solutions, which are obtained using some physically relevant simplificati- ons. Numerical simulation of a free boundary problem for the no-slip squeeze flow is then developed in the thesis using body-fitted curvilinear coordinates and spectral collocation method. An interesting behaviour is expected especially in the corners of the computational domain where the stress singularities are normally located. Unfor- tunately, numerical results reveal some fundamental drawbacks related to the physical model and its possible improvement is discussed at the end of the thesis.
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On fluids with pressure-dependent viscosity flowing through a porous medium
Žabenský, Josef ; Pokorný, Milan (advisor)
Experimental data convincingly show that viscosity of a fluid may change significantly with pressure. This observation leads to various generalizations of well-known models, like Darcy's law, Stokes' law or the Navier-Stokes equations, among others. This thesis investigates three such models in a series of three published papers. Their unifying topic is development of existence theory and finding a weak solution to systems of partial differential equations stemming from the considered models.
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