Karel Kozel

Numerical simulations of flow through channels with T-junction

The paper deals with numerical solution of laminar and turbulent flows of Newtonian and non-Newtonian fluids in branched channels with two outlets. Mathematical model of the flow is based on the Reynolds averaged Navier-Stokes equations for the incompressible fluid. In the turbulent case, the closure of the system of equations is achieved by the explicit algebraic Reynolds stress (EARSM) turbulence model. Generalized non-Newtonian fluids are described by the power-law model. The governing equations are solved by cell-centered finite volume schemes with the artificial compressibility method; dual time scheme is applied for unsteady simulations. Channels considered in presented calculations are of constant square or circular cross-sections. Numerical results for laminar flow of non-Newtonian fluid are presented. Further, turbulent flow through channels with perpendicular branch is simulated. Possible methods for setting the flow rate are discussed and numerical results presented for two flow rates in the branch.

Numerical modelling of incompressible flows for Newtonian and non-Newtonian fluids

This paper deals with numerical solution of two-dimensional and three-dimensional steady and unsteady laminar incompressible flows for Newtonian and non-Newtonian shear thickening fluids flow through a branching channel. The mathematical model used in this work is the generalized system of Navier-Stokes equations. The right hand side of this system is defined by the power-law model. The finite volume method combined with artificial compressibility method is used for numerical simulations of generalized Newtonian fluids flow. Numerical solution is divided into two parts, steady state and unsteady. Steady state solution is achieved for t->~ using steady boundary conditions and followed by steady residual behaviour. For unsteady solution high artificial compressibility coefficient @b^2 is considered. An artificial compressibility method with a pulsation of the pressure in the outlet boundary is used.

Application of Second Order TVD and WENO Schemes in Internal Aerodynamics

We deal with the comparison of several finite volume TVD schemes and finite difference ENO schemes and we describe a second order finite volume WENO scheme which was developed for the case of general unstructured meshes. The proposed second order WENO reconstruction is much simpler than the original ENO scheme introduced in [Harten and Chakravarthy 1991]. Moreover, the proposed WENO method is very easily extendible for unstructured meshes in 3D. All above mentioned schemes are applied for the solution of 2D and 3D transonic flows in the turbines and channels and the numerical solution is compared to experimental results or to the results obtained by other authors.

Numerical modeling of unsteady flow in steam turbine stage

This work deals with numerical solution of unsteady flow in turbine stage. We use models of compressible single-phase flow of air and two-phase flow of wet steam. Presented numerical methods are based on different stator-rotor matching algorithms, as well as different numerical schemes. Numerical results achieved by both methods and flow models are discussed.

Numerical Solution of Flow in Backward Facing Step

The work deals with numerical testing of two different numerical methods based on finite volumes (FV) and finite elements (FE) for different Reynolds numbers. The finite volume method is based on upwind scheme (third order) for convective terms and central second order for dissipative terms. Finite element method consists of stabilization of weak formulation for higher Reynolds numbers with the help of streamline-upwind (Petrov-Galerkin) modification.

Numerical Modelling of Pollution Dispersion in 3D Atmospheric Boundary Layer

The main goal of this work is to present the applicable models and numerical methods for solution of flow and pollution dispersion in 3D Atmospheric Boundary Layer (ABL). Mathematical models are based on the system of Reynolds averaged Navier-Stokes equations and its simplifications. The sets of governing equations are completed by the transport equations for passive impurities and potential temperature. A simple algebraic turbulent closure model is used. The thermal stability phenomenon is taken into account. For each mathematical model a numerical scheme based on finite-difference or finite-volume discretization is proposed and discussed. Some results of numerical tests are presented for pollution dispersion from point sources and flows over simple geometries.

Application of compact finite-difference schemes to simulations of stably stratified fluid flows

Abstract This paper presents a comparison of the results of numerical simulations obtained by two different numerical methods for one specific case of stably stratified incompressible flow. The focus in this paper is on the numerical results obtained using some of the compact finite-difference discretizations introduced in the paper [1] . The numerical scheme itself follows the principle of semi-discretisation, with high order compact discretisation in space, while the time integration is carried out by the Strong Stability Preserving Runge–Kutta scheme. Results are compared against the reference solution obtained by the AUSM finite volume method. The test case used to demonstrate the capabilities of selected numerical methods represents the flow of stably stratified fluid over low, smooth, hill-like wall mounted obstacle.

Numerical solution of laminar incompressible generalized Newtonian fluids flow

This paper deals with the numerical solution of laminar viscous incompressible flows for generalized Newtonian fluids in the branching channel. The generalized Newtonian fluids contain Newtonian fluids, shear thickening and shear thinning non-Newtonian fluids. The mathematical model is the generalized system of Navier-Stokes equations. The finite volume method combined with an artificial compressibility method is used for spatial discretization. For time discretization the explicit multistage Runge-Kutta numerical scheme is considered. Steady state solution is achieved for t?∞ using steady boundary conditions and followed by steady residual behavior. For unsteady solution a dual-time stepping method is considered. Numerical results for flows in two dimensional and three dimensional branching channel are presented.

Numerical simulation of Newtonian and non-Newtonian flows in bypass

This paper deals with the numerical solution of Newtonian and non-Newtonian flows with biomedical applications. The flows are supposed to be laminar, viscous, incompressible and steady or unsteady with prescribed pressure variation at the outlet. The model used for non-Newtonian fluids is a variant of power law. Governing equations in this model are incompressible Navier-Stokes equations. For numerical solution we use artificial compressibility method with three stage Runge-Kutta method and finite volume method in cell centered formulation for discretization of space derivatives. The following cases of flows are solved: steady Newtonian and non-Newtonian flow through a bypass connected to main channel in 2D, steady Newtonian flow in angular bypass in 3D and unsteady non-Newtonian flow through bypass in 2D. Some 2D and 3D results that could have application in the area of biomedicine are presented.

Numerical solution of compressible and incompressible unsteady flows in channel inspired by vocal tract

Abstract This study deals with the numerical solution of a 2D unsteady flow of a viscous fluid in a channel for low inlet airflow velocity. The unsteadiness of the flow is caused by a prescribed periodic motion of a part of the channel wall with large amplitudes, nearly closing the channel during oscillations. The channel is a simplified model of the glottal space in the human vocal tract. Four governing systems are considered to describe the unsteady laminar flow of a viscous fluid in the channel. The numerical solution is implemented using the finite volume method (FVM) and the predictor–corrector MacCormack scheme with artificial viscosity using a grid of quadrilateral cells. The unsteady grid of quadrilateral cells is considered in the form of conservation laws using the Arbitrary Lagrangian–Eulerian method. The numerical simulations of flow fields in the channel, acquired from a developed program, are presented for inlet velocity u ˆ ∞ = 4.12 m s − 1 and Reynolds number Re ∞ = 4481 and the wall motion frequency 100 Hz.