Jan Vimmr

Non-Newtonian effects of blood flow in complete coronary and femoral bypasses

A numerical investigation of non-Newtonian steady blood flow in a complete idealized 3D bypass model with occluded native artery is presented in order to study the non-Newtonian effects for two different sets of physiological parameters (artery diameter and inlet Reynolds number), which correspond to average coronary and femoral native arteries. Considering the blood to be a generalized Newtonian fluid, the shear-dependent viscosity is evaluated using the Carreau-Yasuda model. All numerical simulations are performed by an incompressible Navier-Stokes solver developed by the authors, which is based on the pseudo-compressibility approach and the cell-centred finite volume method defined on unstructured hexahedral computational grid. For the time integration, the fourth-stage Runge-Kutta algorithm is used. The analysis of numerical results obtained for the non-Newtonian and Newtonian flows through the coronary and femoral bypasses is focused on the distribution of velocity and wall shear stress in the entire length of the computational model, which consists of the proximal and distal native artery and the connected end-to-side bypass graft.

Numerical analysis of non-Newtonian blood flow and wall shear stress in realistic single, double and triple aorto-coronary bypasses.

Considering the fact that hemodynamics plays an important role in the patency and overall performance of implanted bypass grafts, this work presents a numerical investigation of pulsatile non-Newtonian blood flow in three different patient-specific aorto-coronary bypasses. The three bypass models are distinguished from each other by the number of distal side-to-side and end-to-side anastomoses and denoted as single, double and triple bypasses. The mathematical model in the form of time-dependent nonlinear system of incompressible Navier-Stokes equations is coupled with the Carreau-Yasuda model describing the shear-thinning property of human blood and numerically solved using the principle of the SIMPLE algorithm and cell-centred finite volume method formulated for hybrid unstructured tetrahedral grids. The numerical results computed for non-Newtonian and Newtonian blood flow in the three aorto-coronary bypasses are compared and analysed with emphasis placed on the distribution of cycle-averaged wall shear stress and oscillatory shear index. As shown in this study, the non-Newtonian blood flow in all of the considered bypass models does not significantly differ from the Newtonian one. Our observations further suggest that, especially in the case of sequential grafts, the resulting flow field and shear stimulation are strongly influenced by the diameter of the vessels involved in the bypassing.

Smoothed particle hydrodynamics and finite volume modelling of incompressible fluid flow

Fundamentals of two different numerical approaches to the fluid flow modelling are presented. The smoothed particle hydrodynamics (SPH) is a meshless approach, while the finite volume (FV) method is defined on a grid. Within SPH, the computational grid is replaced by a finite set of interpolating points. The fluid flow is described by Euler equations and dissipative effects are treated by artificial viscosity terms. Within the cell-centred FV method, the computational domain is discretised with a structured grid and the fluid flow is defined by a non-linear conservative system of the Navier-Stokes equations. The artificial dissipation and the algebraic turbulence model are applied. Implemented SPH and FV codes are tested on a two-dimensional flow of Newtonian fluid through a rigid channel.

Mathematical modelling of compressible inviscid fluid flow through a sealing gap in the screw compressor

In this article, the essential steps of the numerical simulation of compressible inviscid fluid flow in a sealing gap of the screw compressor starting from the description of a mathematical model to its final numerical solution are presented. The mathematical model of compressible inviscid flow is described by the conservative system of the Euler equations. For the numerical solution of this system, the cell-centred finite volume formulation of the explicit two-step MacCormack scheme with Jamesons artificial dissipation was used.

Modelling of complex clearance flow in screw-type machines

The study is concerned about a mathematical modelling of complex clearance flow in two-dimensional models of a male rotor-housing gap and of an undesirable gap caused by the incorrect contact of rotor teeth in a screw-type machine. Both problems are solved as a non-stationary turbulent compressible Newtonian fluid flow with ideal gas properties. The turbulent flow is assumed to be statistically steady and the mathematical model is described by the non-linear conservative system of the compressible Favre-averaged Navier-Stokes (FANS) equations written in non-dimensional form. Its numerical solution is performed using the cell-centred finite volume formulation of the explicit two-step TVD MacCormack scheme which is proposed by Causon and is defined on a structured quadrilateral grid. The algebraic Baldwin-Lomax turbulence model is implemented into the presented numerical code.

Noninvasive assessment of carotid artery stenoses by the principle of multiscale modelling of non-Newtonian blood flow in patient-specific models

The concept of geometrical multiscale modelling of non-Newtonian blood flow in patient-specific models is presented with the aim to provide a methodology for the assessment of hemodynamic significance of carotid artery stenoses. The content of the paper is divided into two consequent parts. In the first one, the principle of the fractional flow reserve (FFR) as an indicator of ischemia-inducing arterial stenoses is tested on three large arterial models containing the aortic arch and both left and right carotid arteries. Using the three-element Windkessel model as an outflow boundary condition, the blood flow simulations are carried out on the basis of data taken from the literature due to unavailable information on patient-specific flow and pressure waveforms. In the second part of the paper, the incorporation of real in-vivo measurements into the multiscale simulations is addressed by presenting a sequential algorithm for the estimation of Windkessel parameters. The ability of the described estimation method, which employs a non-linear state estimator (unscented Kalman filter) on zero-dimensional flow models, is demonstrated on two different patient-specific carotid bifurcation models.

NUMERICAL ANALYSIS OF FLUTTER INSTABILITY IN SIMPLIFIED BLADE CASCADE

NUMERICAL ANALYSIS OF FLUTTER INSTABILITY IN SIMPLIFIED BLADE CASCADE Jan Vimmr, Ondřej Bublı́k, Aleš Pecka, and Luděk Pešek 1European Centre of Excellence NTIS New Technologies for the Information Society, Faculty of Applied Sciences, University of West Bohemia Univerzitnı́ 8, Pilsen, CZ-306 14, Czech Republic e-mail: jvimmr@kme.zcu.cz, {obublik, pecka}@ntis.zcu.cz 2 Institute of Thermomechanics AS CR, v.v.i., Academy of Sciences of the Czech Republic Dolejškova 1402/5, Prague, CZ-182 00, Czech Republic e-mail: pesek@it.cas.cz

ANALYSIS OF VIBRO-ACOUSTIC PROPAGATION IN A MOBILE SCREW COMPRESSOR FOR THE DETERMINATION OF EMITTED ACOUSTIC POWER RADIATED OUTSIDE ITS HOUSING

The method for a numerical solution of the vibro-acoustic problem in a mobile screw compressor is proposed and in-house 3D finite element (FE) solver is developed. In order to reduce the complexity of the problem, attention is paid to the numerical solution of the acoustic pressure field in the compressor cavity interacting with the linear elastic compressor housing. Propagation of acoustic pressure in the cavity is mathematically described by the Helmholtz equation in the amplitude form and is induced by periodically varying surface velocity of the engine and compressor assembly. In accordance with prescribed boundary conditions, numerical solution of the Helmholtz equation for the distribution of acoustic pressure amplitudes within the cavity is performed using the finite element method on tetrahedral meshes. For the FE discretisation of the elastic compressor housing, a new 6-noded thin flat shell triangular finite element with 21 DOF based on the Kirchhoff plate theory was developed and implemented. The resulting strong coupled system of linear algebraic equations describing the vibro-acoustic problem, i.e., the problem of interaction between the air inside the cavity and the screw compressor housing, is solved numerically by well-known algorithms implemented in MATLAB. By considering two different benchmark test cases, the developed 3D FE solver is successfully verified against the numerical results provided by the professional computational FE system Radioss. Finally, the vibro-acoustic problem is solved in a simplified model of a real mobile screw compressor by prescribing experimentally measured acoustic velocity on the surface of the engine and compressor assembly. The numerical solution is carried out only with the professional computational FE system Radioss as our developed solver is still unable to process large-sized problems without encountering memory limits. Thus, for the assessment of results computed by Radioss, we use results acquired during experimental measurements on a real mobile screw compressor under operating conditions.

Analytical solution of gaseous slip flow between two parallel plates described by the Oseen equation

This paper is focused on the derivation of analytical solution describing the development of gas pressure driven microflow in a gap between two parallel plates. The gas flow is assumed to be steady, laminar and incompressible. For the mathematical description of the problem, the Oseen flow model is used. The first-order velocity slip boundary conditions are considered at the walls of the gap. The analytical solution for the velocity profile development is obtained using the method of Laplace transformation. The applicability of the Oseen flow model is analysed on two test cases in this study: pressure driven microflow of argon and pressure driven airflow with Kn?0 for which the analytical solution is compared with the numerical one.

PULSATILE NON-NEWTONIAN BLOOD FLOW MODELLING IN REALISTIC AORTO-CORONARY BYPASS GRAFTS

Nowadays it is generally accepted that hemodynamics has significantly influence on the performance and patency of implanted bypass grafts. In this regard blood flow modelling in realistic geometries can provide a valuable insight into the problem of graft failures associated with restenosis and/or occlusive intimal hyperplasia [Haruguchi, 2003]. Present study tries to contribute to this investigation by modelling pulsatile non-Newtonian blood flow in three realistic aorto-coronary bypass models and by analysing the distribution of hemodynamically significant factors such as wall shear stress (WSS) and oscillatory shear index (OSI).