Steady and unsteady 2D numerical solution of generalized Newtonian fluids flow

summary:This article presents the numerical solution of laminar incompressible viscous flow in a branching channel for generalized Newtonian fluids. The governing system of equations is based on the system of balance laws for mass and momentum. The generalized Newtonian fluids differ through choice of a viscosity function. A power-law model with different values of power-law index is used. Numerical solution of the described models is based on cell-centered finite volume method using explicit Runge--Kutta time integration. The unsteady system of equations with steady boundary conditions is solved by finite volume method. Steady state solution is achieved for $t \rightarrow \infty$. In this case the artificial compressibility method can be applied. For the time integration an explicit multistage Runge--Kutta method of the second order of accuracy in the time is used. In the case of unsteady computation two numerical methods are considered, artificial compressibility method and dual-time stepping method. The flow is modelled in a bounded computational domain. Numerical results obtained by this method are presented and compared

Numerical modelling of viscous and viscoelastic fluids flow through the branching channel

summary:The aim of this paper is to describe the numerical results of numerical modelling of steady flows of laminar incompressible viscous and viscoelastic fluids. The mathematical models are Newtonian and Oldroyd-B models. Both models can be generalized by cross model in shear thinning meaning. Numerical tests are performed on three dimensional geometry, a branched channel with one entrance and two output parts. Numerical solution of the described models is based on cell-centered finite volume method using explicit Runge–Kutta time integration. Steady state solution is achieved for $t \rightarrow \infty$. In this case the artificial compressibility method can be applied

Numerical simulation of generalized Newtonian and Oldroyd-B fluids flow

summary:This work deals with the numerical solution of generalized Newtonian and Oldroyd-B fluids flow. The governing system of equations is based on the system of balance laws for mass and momentum for incompressible laminar viscous and viscoelastic fluids. Two different definition of the stress tensor are considered. For viscous case Newtonian model is used. For the viscoelastic case Oldroyd-B model is tested. Both presented models can be generalized. In this case the viscosity is defined as a shear rate dependent viscosity function $\mu (\dot{\gamma})$. One of the most frequently used shear-thinning models is a cross model. Numerical solution of the described models is based on cell-centered finite volume method using explicit Runge Kutta time integration. The numerical results of generalized Newtonian and generalized Oldroyd-B fluids flow obtained by this method are presented and compared

Validation of numerical simulations of a simple immersed boundary solver for fluid flow in branching channels

summary:This work deals with the flow of incompressible viscous fluids in a two-dimensional branching channel. Using the immersed boundary method, a new finite difference solver was developed to interpret the channel geometry. The numerical results obtained by this new solver are compared with the numerical simulations of the older finite volume method code and with the results obtained with OpenFOAM. The aim of this work is to verify whether the immersed boundary method is suitable for fluid flow in channels with more complex geometries with difficult grid generation

Numerical solution of 2D and 3D incompressible laminar flows through a branching channel

summary:In this paper, we are concerned with the numerical solution of 2D/3D flows through a branching channel where viscous incompressible laminar fluid flow is considered. The mathematical model in this case can be described by the system of the incompressible Navier-Stokes equations and the continuity equation. In order to obtain the steady state solution the artificial compressibility method is applied. The finite volume method is used for spatial discretization. The arising system of ordinary differential equations (ODE) is solved by a multistage Runge-Kutta method. Numerical results for both 2D and 3D cases are presented

Steady and unsteady 2D numerical solution of generalized Newtonian fluids flow

summary:This article presents the numerical solution of laminar incompressible viscous flow in a branching channel for generalized Newtonian fluids. The governing system of equations is based on the system of balance laws for mass and momentum. The generalized Newtonian fluids differ through choice of a viscosity function. A power-law model with different values of power-law index is used. Numerical solution of the described models is based on cell-centered finite volume method using explicit Runge--Kutta time integration. The unsteady system of equations with steady boundary conditions is solved by finite volume method. Steady state solution is achieved for $t \rightarrow \infty$. In this case the artificial compressibility method can be applied. For the time integration an explicit multistage Runge--Kutta method of the second order of accuracy in the time is used. In the case of unsteady computation two numerical methods are considered, artificial compressibility method and dual-time stepping method. The flow is modelled in a bounded computational domain. Numerical results obtained by this method are presented and compared

Numerical study of viscous and viscoelastic fluids flow

MI: Global COE Program Education-and-Research Hub for Mathematics-for-IndustryグローバルCOEプログラム「マス･フォア･インダストリ教育研究拠点」In this paper the numerical results for steady and unsteady flows of viscous and viscoelastic fluids are presented. The governing system of equations is based on the system of balance laws for mass and momentum for incompressible fluid. Two rheological models for the stress tensor are tested. The models used in this study are generalized Newtonian model with power-law viscosity model and Oldroyd-B model with constant viscosity. Numerical results for these models are presented

Numerical study of viscous and viscoelastic fluids flow

In this paper the numerical results for steady and unsteady flows of viscous and viscoelastic fluids are presented. The governing system of equations is based on the system of balance laws for mass and momentum for incompressible fluid. Two rheological models for the stress tensor are tested. The models used in this study are generalized Newtonian model with power-law viscosity model and Oldroyd-B model with constant viscosity. Numerical results for these models are presented.MI: Global COE Program Education-and-Research Hub for Mathematics-for-IndustryグローバルCOEプログラム「マス･フォア･インダストリ教育研究拠点

Numerical study of viscous and viscoelastic fluids flow

Abstract. In this paper the numerical results for steady and unsteady flows of viscous and viscoelastic fluids are presented. The governing system of equations is based on the system of balance laws for mass and momentum for incompressible fluid. Two rheological models for the stress tensor are tested. The models used in this study are generalized Newtonian model with power-law viscosity model and Oldroyd-B model with constant viscosity. Numerical results for these models are presented