A two-fluid model for pulsatile flow in catheterized blood vessels

The pulsatile flow of blood through a catheterized artery is analyzed, assuming the blood as a two-fluid model with the suspension of all the erythrocytes in the core region as a Casson fluid and the peripheral region of plasma as a Newtonian fluid. The resulting non-linear implicit system of partial differential equations is solved using perturbation method. The expressions for shear stress, velocity, flow rate, wall shear stress and longitudinal impedance are obtained. The variations of these flow quantities with yield stress, catheter radius ratio, amplitude, pulsatile Reynolds number ratio and peripheral layer thickness are discussed. It is observed that the velocity distribution and flow rate decrease, while, the wall shear, width of the plug flow region and longitudinal impedance increase when the yield stress increases. It is also found that the velocity increases, but, the longitudinal impedance decreases when the thickness of the peripheral layer increases. The wall shear stress decreases non-linearly, while, the longitudinal impedance increases non-linearly when the catheter radius ratio increases. The estimates of the increase in the longitudinal impedance are considerably lower for the present two-fluid model than those of the single-fluid model.     

Two-phase non-linear model for blood flow in asymmetric and axisymmetric stenosed arteries

The pulsatile flow of a two-phase model for blood flow through axisymmetric and asymmetric stenosed narrow arteries is analyzed, treating blood as a two-phase model with the suspension of all the erythrocytes in the core region as the Herschel-Bulkley material and plasma in the peripheral layer as the Newtonian fluid. The perturbation method is applied to solve the resulting non-linear implicit system of partial differential equations. The expressions for various flow quantities are obtained. It is found that the pressure drop, plug core radius, wall shear stress increase as the yield stress or stenosis height increases. It is noted that the velocity increases, longitudinal impedance decreases as the amplitude increases. For asymmetric stenosis, the wall shear stress increases non-linearly with the increase of the axial distance. The estimates of the increase in longitudinal impedance to flow of the two-phase Herschel-Bulkley material are significantly lower than those of the single-phase Herschel-Bulkley material. The results show the advantages of two-phase flow over single-phase flow in small diameter arteries with stenosis.     

Two-fluid model for transient analysis of slug flow in oil wells

In this work it is presented a transient, one-dimensional, adiabatic model for slug flow simulation, which appears when liquid (mixture of oil and water) and gas flow simultaneously through pipes. The model is formed by space and time averaged conservation equations for mass, momentum and energy for each phase, the numerical solution is based on the finite difference technique in the implicit scheme. Velocity, pressure, volumetric fraction and temperature profiles for both phases were predicted for inclination angles from the horizontal to the vertical position (unified model) and ascendant flow. Predictions from the model were validated using field data and ten correlations commonly used in the oil industry. The effects of gas heating or cooling, due to compression and expansion processes, on the predictions and numerical stability, were studied. It was found that when these effects are taken into account, a good behavior of temperature predictions and numerical stability are obtained. The model presents deviations lower than 14% regarding field data and it presents better predictions than most of the correlations.     

Numerical simulation of pulsatile non-Newtonian flow in the carotid artery bifurcation

Both clinical and post mortem studies indicate that, in humans, the carotid sinus of the carotid artery bifurcation is one of the favored sites for the genesis and development of atherosclerotic lesions. Hemodynamic factors have been suggested to be important in atherogenesis. To understand the correlation between atherogenesis and fluid dynamics in the carotid sinus, the blood flow in artery was simulated numerically. In those studies, the property of blood was treated as an incompressible, Newtonian fluid. In fact, however, the blood is a complicated non-Newtonian fluid with shear thinning and viscoelastic properties, especially when the shear rate is low. A variety of non-Newtonian models have been applied in the numerical studies. Among them, the Casson equation was widely used. However, the Casson equation agrees well only when the shear rate is less than 10 s-1. The flow field of the carotid bifurcation usually covers a wide range of shear rate. We therefore believe that it may not be sufficient to describe the property of blood only using the Casson equation in the whole flow field of the carotid bifurcation. In the present study, three different blood constitutive models, namely, the Newtonian, the Casson and the hybrid fluid constitutive models were used in the flow simulation of the human carotid bifurcation. The results were compared among the three models. The results showed that the Newtonian model and the hybrid model had verysimilar distributions of the axial velocity, secondary flow and wall shear stress, but the Casson model resulted in significant differences in these distributions from the other two models. This study suggests that it is not appropriate to only use the Casson equation to simulate the whole flow field of the carotid bifurcation, and on the other hand, Newtonian fluid is a good approximation to blood for flow simulations in the carotid artery bifurcation.     

Effect of couple stresses on the flow in a constricted annulus

The flow of an incompressible couple stress fluid in an annulus with local constriction at the outer wall is considered. This configuration is intended as a simple model for studying blood flow in a stenosed artery when a catheter is inserted into it. The effects couple stress fluid parameters α and σ, height of the constriction (ε), and ratio of radii (k) on the impedance and wall shear stresses are studied graphically. Graphical results show that the resistance to the flow as well as the wall shear stress increases as the ratio of the radii increases and decreases as the couple stress fluid parameters increases.     

A two-fluid model of non-Newtonian blood flow induced by peristaltic waves

The problem of blood flow induced by peristaltic waves in a uniform small diameter tube has been investigated. Blood has been represented by a two-fluid model consisting of a core region of suspension of all the erythrocytes, assumed to be a Casson fluid, and a peripheral layer of plasma as a Newtonian fluid. The expressions for dimensionless pressure drop and friction force have been obtained. The results obtained in the analysis have been evaluated numerically and discussed briefly. The significance of the present model over the existing models has been pointed out by comparing the results with other theories both analytically and numerically.     

The micropolar fluid model for blood flow through a tapered artery with a stenosis

A micropolar model for axisymmetric blood flow through an axially nonsymmetreic but radially symmetric mild stenosis tapered artery is presented. To estimate the effect of the stenosis shape, a suitable geometry has been considered such that the axial shape of the stenosis can be changed easily just by varying a parameter （referred to as the shape parameter）. The model is also used to study the effect of the taper angle Ф. Flow parameters such as the velocity, the resistance to flow （the resistance impedance）, the wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis （stenosis throat） have been computed for different values of the shape parameter n, the taper angle Ф, the coupling number N and the micropolar parameter m. It is shown that the resistance to flow decreases with increasing the shape parameter n and the micropolar parameter m while it increases with increasing the coupling number N. So, the magnitude of the resistance impedance is higher for a micropolar fluid than that for a Newtonian fluid model. Finally, the velocity profile, the wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis are discussed for different values of the parameters involved on the problem.     

The steady/pulsatile flow and macromolecular transport in T-bifurcation blood vessels

IntroductionThefluiddynamicsofbloodcyclesystemplayanimportantroleinthepathogenesisofatherosclerosis.ThephysiologicalanatomyfoundthattheatherosclerosisappearsoftenatthebifurcationorcurvedflowareatoallkindsofRefs.[1 ,2 ] .Theshearstressvariesgreatlyinthoseareaandinfluencesthemacromoleculartransportacrossthebloodwall[3,4].Thus ,theinvestigationoftheflowandmacromoleculartransportinthesecomplexbloodvesselaandthecorrelationbetweenthemareinterestingtoresearchers.Intheseaspect,Liepschstudiedtheflowi…     

BLOOD FLOW AND MACROMOLECULAR TRANSPORT IN CURVED BLOOD VESSELS

A numerical analysis of the steady/pulsatile flow and macromolecular (such as LDL and Albumin) transport in curved blood vessels was carried out. The computational results predict that the vortex of the secondary flow is time-dependent in the aortic arch. The concentration of macromolecule concentrates at the region of sharp curve, and the wall concentration at the outer part is higher than that at the inner part. Atherosclerosis and thrombosis are prone to develop in such regions with sharp flow.     

Numerical modeling of slug flow initiation in a horizontal channels using a two-fluid model

This paper presents a methodology for modeling slug initiation and growth in horizontal ducts. Transient two-fluid equations are solved numerically using a class of high-resolution shock capturing methods. The advantage of this method is that slug formation and growth in a stratified regime can be calculated directly from the solutions to the flow field differential equations. In addition, by using high-resolution shock capturing methods that do not contain numerical diffusion, the discontinuity generated by slugging in the flow field can be modeled with good accuracy. The two-fluid model is shown to be well-posed mathematically only under certain conditions. Under these circumstances, the two-fluid model is capable of correctly predicting and modeling the flow physics. When ill-posed, an unbounded instability occurs in the flow field solution, and the instability amplitude increases exponentially with decreasing mesh sizes. This work shows that there are three zones associated with slug formation. In addition, long wavelength slugs are shown to initiate from short wavelength waves. These short waves are generated at the interface of the two phases by the Kelvin-Helmholtz hydrodynamic instability. The results obtained through numerical modeling show good agreement with experimental results.     

An improved semi-empirical friction model for gas-liquid two-phase flow in horizontal and near horizontal pipes

Pressure drop and liquid hold-up are two very important fluid flow parameters in design and control of multiphase flow pipelines. Friction factors play an important role in the accurate calculation of pressure drop. Various empirical and semi-empirical closure relations exist in the literature to calculate the liquid-wall, gas-wall and interfacial friction in two-phase pipe flow.However most of them are empirical correlations found under special experimental conditions. In this paper by modification of a friction model available in the literature, an improved semiempirical model is proposed. The proposed model is incorporated in the two-fluid correlations under equilibrium conditions and solved. Pressure gradient and velocity profiles are validated against experimental data. Using the improved model, the pressure gradient deviation from experiments diminishes by about 3%; the no-slip condition at the interface is satisfied and the velocity profile is predicted in better agreement with the experimental data.     

Simulation of the two-fluid model on incompressible flow with Fractional Step method for both resolved and unresolved scale interfaces

In the present paper, the Fractional Step method usually used in single fluid flow is here extended and applied for the two-fluid model resolution using the finite volume discretization. The use of a projection method resolution instead of the usual pressure-correction method for multi-fluid flow, successfully avoids iteration processes. On the other hand, the main weakness of the two fluid model used for simulations of free surface flows, which is the numerical diffusion of the interface, is also solved by means of the conservative Level Set method (interface sharpening) (Strubelj et al., 2009). Moreover, the use of the algorithm proposed has allowed presenting different free-surface cases with or without Level Set implementation even under coarse meshes under a wide range of density ratios. Thus, the numerical results presented, numerically verified, experimentally validated and converged under high density ratios, shows the capability and reliability of this resolution method for both mixed and unmixed flows.     

Scaling laws for gas-solid riser flow through two-fluid model simulation

Scale up of gas-solid circulating fluidized bed (CFB) risers poses many challenges to researchers.In this paper,CFD investigation of hydrodynamic scaling laws for gas-solid riser flow was attempted on the basis of two-fluid model simulations,in particular,the recently developed empirical scaling law of Qi,Zhu,and Huang (2008).A 3D computational model with periodic boundaries was used to perform numerical experiments and to study the effect of various system and operating parameters in hydrodynamic scaling o...     

A LGA model for fluid flow in heterogeneous porous media

A lattice gas automaton (LGA) model is proposed to simulate fluid flow in heterogeneous porous media. Permeability fields are created by distributing scatterers (solids, grains) within the fluid flow field. These scatterers act as obstacles to flow. The loss in momentum of the fluid is directly related to the permeability of the lattice gas model. It is shown that by varying the probability of occurrence of solid nodes, the permeability of the porous medium can be changed over several orders of magnitude. To simulate fluid flow in heterogeneous permeability fields, isotropic, anisotropic, random, and correlated permeability fields are generated. The lattice gas model developed here is then used to obtain the effective permeability as well as the local fluid flow field. The method presented here can be used to simulate fluid flow in arbitrarily complex heterogeneous porous media.     

A computer model of the two-roll mill for generalised Newtonian flow

We investigate the flow of a generalised Newtonian liquid between two contra-rotating cylinders of equal size — the so called two-roll mill problem. A finite element method is used to obtain solutions for the case of a Carreau model and for a power law model. Consideration is given to the influence of shearthinning on the flow pattern around the cylinders. Results are presented for different speeds of rotation of the cylinders and for various values of fluid parameters. A comparison is made with the analytical solution of Jeffrey.     

Simulation of three-dimensional unsteady viscous free surface flow around a ship model

We present here a numerical method for solving the free surface flow around a ship at forward speed in calm water. The fluid is assumed to be Newtonian and the Reynolds-averaged Navier-Stokes equations are solved by a finite difference method. Modelization of turbulence is achieved by the algebraic model proposed by Baldwin and Lomax. Fully non-linear free surface conditions are satisfied in the model and a method to avoid the incompatibility between free surface conditions and no-slip conditions at the waterline is proposed. Numerical results obtained for a Wigley hull are compared with experimental results.     

Computational technique for flow in blood vessels with porous effects

IntroductionThehemodynamicsofflowsthroughbloodvesselsisofgreatinterest,becausethesevesselspresentasubstantialhealthriskandareamajorcauseofmortalityandmorbidityintheindustrializedworld .Researchpapersonthebloodflowhaveappearedbutmostofthemhaveneglectedtheporosityeffectsduetovesselwalls.Inthisstudyweareinterestedintheflowthroughabloodvesseltakingintoaccounttheporosityeffectsofthevessels.Fluidflowthroughaporousmediumisoffundamentalimportancetowiderangeofdisciplinesinthevariousbranchesofnaturalsci…     

磁场和Hall电流对狭窄动脉中血液流动的影响

A micropolar model for blood simulating magnetohydrodynamic flow through a horizontally nonsymmetric but vertically symmetric artery with a mild stenosis is presented. To estimate the effect of the stenosis shape, a suitable geometry has been considered such that the horizontal shape of the stenosis can easily be changed just by varying a parameter referred to as the shape parameter. Flow parameters, such as velocity, the resistance to flow （the resistance impedance）, the wall shear stress distribution in the stenotic region, and its magnitude at the maximum height of the stenosis （stenosis throat）, have been computed for different shape parameters, the Hartmann number and the Hall parameter. This shows that the resistance to flow decreases with the increasing values of the parameter determining the stenosis shape and the Hail parameter, while it increases with the increasing Hartmann number. The wall shear stress and the shearing stress on the wall at the maximum height of the stenosis possess an inverse characteristic to the resistance to flow with respect to any given value of the Hartmann number and the Hall parameter. Finally, the effect of the Hartmann number and the Hall parameter on the horizontal velocity is examined.     

Mathematical modelling of couple stresses on fluid flow in constricted tapered artery in presence of slip velocity-effects of catheter

This paper explores the mathematical model for couple stress fluid flow through an annular region. The above model is used for studying the blood flow be-tween the clogged （stenotic） artery and the catheter. The asymmetric nature of the stenosis is considered. The closed form expressions for the physiological parameters such as impedance and shear stress at the wall are obtained. The effects of various geomet-ric parameters and the parameters arising out of the fluid considered are discussed by considering the slip velocity and tapering angle. The study of the above model is very significant as it has direct applications in the treatment of cardiovascular diseases.     

A comparative study of poiseuille flow of a polar fluid under various boundary conditions with applications to blood flow

In this paper, Poiseuille flow of a polar fluid (model of a red blood cell suspension) under various boundary conditions at the wall, viz., slip or no-slip in the axial velocity and couple stresses zero or non-zero at the boundary, is considered from the point of view of its applications to blood flow. Analytic expressions for axial and rotational velocities, flow rate, effective viscosity and stresses are obtained. The magnitudes of the length ratioL and the coupling number N are determined in accordance with concentration and tube radius (in the existing literature, values ofL andN are chosen arbitrarily). Velocity profiles (both axial and rotational) and the variation of the effective viscosity with concentration, tube radius and for various values of the boundary condition parameters are shown graphically. The analytic results obtained are compared with experimental results (for blood flow). It is found that they are in a reasonably good agreement. The effective viscosity exhibits the Inverse Fahraeus-Lindquist Effect in all the cases (including the slip or no-slip in the velocity fields). A method is given for determining the non-zero couple stress boundary condition for a given concentration. Applications of this theory to blood flow are briefly discussed.