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Motion of a body in a fluid with pressure dependent viscosity
Sláčík, Stanislav ; Průša, Vít (advisor) ; Süli, Endré (referee)
A lot of technologically relevant incompressible fluids exhibit a substantial variaton of viscosity with the pressure;a falling cylinder viscometer is frequently used for the measurements, determining the viscosity indirectly from the time it takes the sinker to fall a given distance. The relation between the sinker fall velocity and the fluid viscosity is, however, derived under the constant viscosity assumption. The objective of the present thesis is to perform a numerical simulation of the viscometric experiment, assuming an explicit form of the pressure-viscosity dependence and realistic parameter values and to quantitatively assess the difference in body motion to the Navier- Stokes model. The computational method proposed, handling both the nonlinear constitutive relation and the body motion, was tested on simple problems with analytical solutions. The semianalytical relation for the Navier-Stokes model, also re-derived here, is compared to the computational results.The validity of the assumptions used in the theoretical derivation, based on the results of the numerical simulation, is discussed regarding the geometry of the viscometer. Powered by TCPDF (www.tcpdf.org)
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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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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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Motion of a body in a fluid with pressure dependent viscosity
Sláčík, Stanislav ; Průša, Vít (advisor) ; Süli, Endré (referee)
A lot of technologically relevant incompressible fluids exhibit a substantial variaton of viscosity with the pressure;a falling cylinder viscometer is frequently used for the measurements, determining the viscosity indirectly from the time it takes the sinker to fall a given distance. The relation between the sinker fall velocity and the fluid viscosity is, however, derived under the constant viscosity assumption. The objective of the present thesis is to perform a numerical simulation of the viscometric experiment, assuming an explicit form of the pressure-viscosity dependence and realistic parameter values and to quantitatively assess the difference in body motion to the Navier- Stokes model. The computational method proposed, handling both the nonlinear constitutive relation and the body motion, was tested on simple problems with analytical solutions. The semianalytical relation for the Navier-Stokes model, also re-derived here, is compared to the computational results.The validity of the assumptions used in the theoretical derivation, based on the results of the numerical simulation, is discussed regarding the geometry of the viscometer. Powered by TCPDF (www.tcpdf.org)
|
|
|
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.
|
|
|
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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