Simulation of the Three-Dimensional Flow of Blood Using a Shear-Thinning Viscoelastic Fluid Model

This paper is concerned with the numerical simulation of a thermodynamically compatible viscoelastic shear-thinning fluid model, particularly well suited to describe the rheological response of blood, under physiological conditions. Numerical simulations are performed in two idealized three-dimensional geometries, a stenosis and a curved vessel, to investigate the combined effects of flow inertia, viscosity and viscoelasticity in these geometries. The aim of this work is to provide new insights into the modeling and simulation of homogeneous rheological models for blood and a basis for further developments in modeling and prediction

Unsteady two-layered blood flow through a w-shape stenosed artery using the generalized oldroyd-b fluid model

A theoretical study of unsteady two-layered blood flow through a stenosed artery is presented in this article. The geometry of rigid stenosed artery is assumed to be w-shaped. The flow regime is assumed to be laminar, unsteady and uni-directional. The characteristics of blood are modeled by the generalized Oldroyd-B non-Newtonian fluid model in the core region and a Newtonian fluid in the periphery region. The governing partial differential are derived for each region by using mass and momentum conservation equations. In order to facilitate numerical solutions, the derived differential equations are non-dimensionalized. A well-tested explicit finite difference scheme (FDM) which is forward in time and central in space is employed for the solution of nonlinear initial-boundary value problem corresponding to each region. Validation of the FDM computations is achieved with a variational finite element method (FEM) algorithm. The influence of the emerging geometric and rheological parameters on axial velocity, resistance impedance and wall shear stress are displayed graphically. The instantaneous patterns of streamlines are also presented to illustrate the global behavior of blood flow. The simulations are relevant to hemodynamics of small blood vessels and capillary transport wherein rheological effects are dominant

One-dimensional modelling of mixing, dispersion and segregation of multiphase fluids flowing in pipelines

The flow of immiscible liquids in pipelines has been studied in this work in order to formulate a one-dimensional model for the computer analysis of two-phase liquid-liquid flow in horizontal pipes. The model simplifies the number of flow patterns commonly encountered in liquid-liquid flow to stratified flow, fully dispersed flow and partial dispersion with the formation of one or two different emulsions. The model is based on the solution of continuity equations for dispersed and continuous phase; correlations available in the literature are used for the calculation of the maximum and mean dispersed phase drop diameter, the emulsion viscosity, the phase inversion point, the liquid-wall friction factors, liquid-liquid friction factors at interface and the slip velocity between the phases. In absence of validated models for entrainment and deposition in liquid-liquid flow, two entrainment rate correlations and two deposition models originally developed for gas-liquid flow have been adapted to liquid-liquid flow. The model was applied to the flow of oil and water; the predicted flow regimes have been presented as a function of the input water fraction and mixture velocity and compared with experimental results, showing an overall good agreement between calculation and experiments. Calculated values of oil-in-water and water-in-oil dispersed fractions were compared against experimental data for different oil and water superficial velocities, input water fractions and mixture velocities. Pressure losses calculated in the full developed flow region of the pipe, a crucial quantity in industrial applications, are reasonably close to measured values. Discrepancies and possible improvements of the model are also discussed. The model for two-phase flow was extended to three-phase liquid-liquid-gas flow within the framework of the two-fluid model. The two liquid phases were treated as a unique liquid phase with properly averaged properties. The model for three-phase flow thus developed was implemented in an existing research code for the simulation of three-phase slug flow with the formation of emulsions in the liquid phase and phase inversion phenomena. Comparisons with experimental data are presented