|
| |
|
|
Nonnewtonian fluid flow simulation using lattice Boltzmann method
Kuriščák, Pavel ; Hron, Jaroslav (advisor) ; Málek, Josef (referee)
Title: Non-newtonian fluid flow simulation using lattice Boltzmann method Author: Bc. Pavel Kuriščák Department: Mathematical Institute, Charles University Supervisor: RNDr. Ing. Jaroslav Hron Ph.D. Supervisor's e-mail address: Jaroslav.Hron@mff.cuni.cz Abstract: The aim of this thesis is to find and estabilish a modification to the Lattice Boltzmann Method, allowing it to simulate non-newtonian behaviour of fluids. In the theoretical part of thesis, there is introduced a derivation, based on the work of [22], that is capable of arriving to macroscopical Navier-Stokes equa- tions completely a priori from the Boltzmann equation, utilizing the Hermite basis expansion. This derivation is afterwards applied to the method suggested by [11], that uses the changed equilibrium distribution to fine-tune the local fluid viscosity according to the non-newtonian model. In the last part of thesis, this method is implemented in the form of lattice kinetic scheme and tested on three sample problems. Keywords: Lattice Boltzmann Method, non-newtonian fluids, Hermite expansion, lattice kinetic scheme
|
|
|
Finite Element Approximation of Problems in Non-Newtonian Fluid Mechanics
Hirn, Adrian ; Málek, Josef (advisor) ; Málek, Josef (referee) ; Rannacher, Rolf (referee)
This dissertation is devoted to the finite element (FE) approximation of equations describing the motion of a class of non-Newtonian fluids. The main focus is on incompressible fluids whose viscosity nonlinearly depends on the shear rate and pressure. The equations of motion are discretized with equal-order d-linear finite elements, which fail to satisfy the inf-sup stability condition. In this thesis a stabilization technique for the pressure-gradient is proposed that is based on the well-known local projection stabilization (LPS) method. If the viscosity solely depends on the shear rate, the well-posedness of the stabilized discrete systems is shown and a priori error estimates quantifying the convergence of the method are proven. In the shear thinning case, the derived error estimates provide optimal rates of convergence with respect to the regularity of the solution. As is well-known, the Galerkin FE method may suffer from instabilities resulting not only from lacking inf-sup stability but also from dominating convection. The proposed LPS approach is then extended in order to cope with both instability phenomena. Finally, shear-rate- and pressure-dependent viscosities are considered. The Galerkin discretization of the governing equations is analyzed and the convergence of discrete solutions is...
|
|
|
Shear and vorticity banding
Skřivan, Tomáš ; Průša, Vít (advisor) ; Málek, Josef (referee)
Some non-newtonian fluids exhibit nonmonotonous dependence of the shear stress on shear rate. This nonmonoticity leads to flow instabilities which result in formation of banded flow, namely in shear banding and vorticity banding. An important role is played here by so called stress diffusion which uniquely determines size of bands in the flow. If the classical kinetic approach is employed and the spatial inhomogeneity of the flow is taken into the account, then stress diffusion can be obtained in the fluid model, however this approach has difficulties with identifying heat transfer within the continuum. In this thesis, we present alternative approach how to introduce stress diffusion to fluid models. We employ thermodynamical framework proposed by Rajagopal and Srinivasa (2000), this approach guaranties thermodynamical consistency of resulting model and also the interplay between stress diffusion and heat transfer can be easily established. Furthermore, we extend this framework such that wider range of viscoelastic models can be obtained, in particular we derive Johnson-Segalman model. Powered by TCPDF (www.tcpdf.org)
|
|
|
Towards efficient numerical computation of flows of non-Newtonian fluids
Blechta, Jan ; Málek, Josef (advisor) ; Herzog, Roland (referee) ; Süli, Endré (referee)
In the first part of this thesis we are concerned with the constitutive the- ory for incompressible fluids characterized by a continuous monotone rela- tion between the velocity gradient and the Cauchy stress. We, in particular, investigate a class of activated fluids that behave as the Euler fluid prior activation, and as the Navier-Stokes or power-law fluid once the activation takes place. We develop a large-data existence analysis for both steady and unsteady three-dimensional flows of such fluids subject either to the no-slip boundary condition or to a range of slip-type boundary conditions, including free-slip, Navier's slip, and stick-slip. In the second part we show that the W−1,q norm is localizable provided that the functional in question vanishes on locally supported functions which constitute a partition of unity. This represents a key tool for establishing local a posteriori efficiency for partial differential equations in divergence form with residuals in W−1,q . In the third part we provide a novel analysis for the pressure convection- diffusion (PCD) preconditioner. We first develop a theory for the precon- ditioner considered as an operator in infinite-dimensional spaces. We then provide a methodology for constructing discrete PCD operators for a broad class of pressure discretizations. The...
|
|
|
Homogenization of flows of non-Newtonian fluids and strongly nonlinear elliptic systems
Kalousek, Martin ; Kaplický, Petr (advisor)
The theory of homogenization allows to find for a given system of partial differential equations governing a model with a very complicated internal struc- ture a system governing a model without this structure, whose solution is in a certain sense an approximation of the solution of the original problem. In this thesis, methods of the theory of homogenization are applied to three sys- tems of partial differential equations. The first one governs a flow of a class of non-Newtonian fluid through a porous medium. The second system is utilized for modeling of a flow of a fluid through an electric field wherein the viscosity depends significantly on the intensity of the electric field. For the third system is considered an elliptic operator having growth and coercivity indicated by a general anisotropic inhomogeneous N-function. 1
|
|
|
Towards efficient numerical computation of flows of non-Newtonian fluids
Blechta, Jan ; Málek, Josef (advisor) ; Herzog, Roland (referee) ; Süli, Endré (referee)
In the first part of this thesis we are concerned with the constitutive the- ory for incompressible fluids characterized by a continuous monotone rela- tion between the velocity gradient and the Cauchy stress. We, in particular, investigate a class of activated fluids that behave as the Euler fluid prior activation, and as the Navier-Stokes or power-law fluid once the activation takes place. We develop a large-data existence analysis for both steady and unsteady three-dimensional flows of such fluids subject either to the no-slip boundary condition or to a range of slip-type boundary conditions, including free-slip, Navier's slip, and stick-slip. In the second part we show that the W−1,q norm is localizable provided that the functional in question vanishes on locally supported functions which constitute a partition of unity. This represents a key tool for establishing local a posteriori efficiency for partial differential equations in divergence form with residuals in W−1,q . In the third part we provide a novel analysis for the pressure convection- diffusion (PCD) preconditioner. We first develop a theory for the precon- ditioner considered as an operator in infinite-dimensional spaces. We then provide a methodology for constructing discrete PCD operators for a broad class of pressure discretizations. The...
|
|
|
Homogenization of flows of non-Newtonian fluids and strongly nonlinear elliptic systems
Kalousek, Martin ; Kaplický, Petr (advisor)
The theory of homogenization allows to find for a given system of partial differential equations governing a model with a very complicated internal struc- ture a system governing a model without this structure, whose solution is in a certain sense an approximation of the solution of the original problem. In this thesis, methods of the theory of homogenization are applied to three sys- tems of partial differential equations. The first one governs a flow of a class of non-Newtonian fluid through a porous medium. The second system is utilized for modeling of a flow of a fluid through an electric field wherein the viscosity depends significantly on the intensity of the electric field. For the third system is considered an elliptic operator having growth and coercivity indicated by a general anisotropic inhomogeneous N-function. 1
|
|
|
Homogenization of flows of non-Newtonian fluids and strongly nonlinear elliptic systems
Kalousek, Martin ; Kaplický, Petr (advisor) ; Diening, Lars (referee) ; Schwarzacher, Sebastian (referee)
The theory of homogenization allows to find for a given system of partial differential equations governing a model with a very complicated internal struc- ture a system governing a model without this structure, whose solution is in a certain sense an approximation of the solution of the original problem. In this thesis, methods of the theory of homogenization are applied to three sys- tems of partial differential equations. The first one governs a flow of a class of non-Newtonian fluid through a porous medium. The second system is utilized for modeling of a flow of a fluid through an electric field wherein the viscosity depends significantly on the intensity of the electric field. For the third system is considered an elliptic operator having growth and coercivity indicated by a general anisotropic inhomogeneous N-function. 1
|
|
|
Shear and vorticity banding
Skřivan, Tomáš ; Průša, Vít (advisor) ; Málek, Josef (referee)
Some non-newtonian fluids exhibit nonmonotonous dependence of the shear stress on shear rate. This nonmonoticity leads to flow instabilities which result in formation of banded flow, namely in shear banding and vorticity banding. An important role is played here by so called stress diffusion which uniquely determines size of bands in the flow. If the classical kinetic approach is employed and the spatial inhomogeneity of the flow is taken into the account, then stress diffusion can be obtained in the fluid model, however this approach has difficulties with identifying heat transfer within the continuum. In this thesis, we present alternative approach how to introduce stress diffusion to fluid models. We employ thermodynamical framework proposed by Rajagopal and Srinivasa (2000), this approach guaranties thermodynamical consistency of resulting model and also the interplay between stress diffusion and heat transfer can be easily established. Furthermore, we extend this framework such that wider range of viscoelastic models can be obtained, in particular we derive Johnson-Segalman model. Powered by TCPDF (www.tcpdf.org)
|
guest ::
