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.     

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.     

Two-fluid non-linear model for flow in catheterized blood vessels

Blood flow through a catheterized artery is analyzed, assuming the flow is steady and blood is treated as a two-fluid model with the suspension of all the erythrocytes in the core region as a Casson fluid and the plasma in the peripheral region as a Newtonian fluid. The expressions for velocity, flow rate, wall shear stress and frictional resistance are obtained. The variations of these flow quantities with yield stress, catheter radius ratio and peripheral layer thickness are discussed. It is noticed that the velocity and flow rate decrease while the wall shear stress and resistance to flow increase when the yield stress or the catheter radius ratio increases while all the other parameters were held fixed. It is found that the velocity and flow rate increase while the wall shear stress and frictional resistance decrease with the increase of the peripheral layer thickness. The estimates of the increase in the frictional resistance are significantly very small for the present two-fluid model than those of the single-fluid Casson model.     

Multidimensional modeling of the stenosed carotid artery: A novel CAD approach accompanied by an extensive lumped model

This study describes a multidimensional 3D/lumped parameter(LP) model which contains appropriate inflow/outflow boundary conditions in order to model the entire human arterial trees. A new extensive LP model of the entire arterial network(48 arteries) was developed including the effect of vessel diameter tapering and the parameterization of resistance, conductor and inductor variables. A computer aided-design(CAD) algorithm was proposed to effciently handle the coupling of two or more 3D models with the LP model, and substantially lessen the coupling processing time. Realistic boundary conditions and Navier–Stokes equations in healthy and stenosed models of carotid artery bifurcation(CAB) were used to investigate the unsteady Newtonian blood flow velocity distribution in the internal carotid artery(ICA). The present simulation results agree well with previous experimental and numerical studies. The outcomes of a pure LP model and those of the coupled 3D healthy model were found to be nearly the same in both cases. Concerning the various analyzed 3D zones, the stenosis growth in the ICA was not found as a crucial factor in determining the absorbing boundary conditions.This paper demonstrates the advantages of coupling local and systemic models to comprehend physiological diseases of the cardiovascular system.     

Unified analysis of liquefaction and the ground flow phenomenon

Loose saturated sand behaves as a solid before liquefaction but as a fluid when the excess pore water pressure equals the initial confining stress, after which it recovers its strength. A simple constitutive equation for loose saturated sand was developed to express the phase transformation between a solid and fluid during liquefaction and the ground flow phenomenon. This constitutive equation was used for a shaking table test, and its applicability was investigated by comparing numerical and experimental results Published in Prikladnaya Mekhanika, Vol. 43, No. 8, pp. 129–144, August 2007. An erratum to this article is available at .     

Numerical simulation of the non-Newtonian blood flow through a mechanical aortic valve

This work focuses on the comparison between Newtonian and non-Newtonian blood flows through a bileaflet mechanical heart valve in the aortic root. The blood, in fact, is a concentrated suspension of cells, mainly red blood cells, in a Newtonian matrix, the plasma, and consequently its overall behavior is that of a non-Newtonian fluid owing to the action of the cells’ membrane on the fluid part. The common practice, however, assumes the blood in large vessels as a Newtonian fluid since the shear rate is generally high and the effective viscosity becomes independent of the former. In this paper, we show that this is not always the case even in the aorta, the largest artery of the systemic circulation, owing to the pulsatile and transitional nature of the flow. Unexpectedly, for most of the pulsating cycle and in a large part of the fluid volume, the shear rate is smaller than the threshold level for the blood to display a constant effective viscosity and its shear thinning character might affect the system dynamics. A direct inspection of the various flow features has shown that the valve dynamics, the transvalvular pressure drop and the large-scale features of the flow are very similar for the Newtonian and non-Newtonian fluid models. On the other hand, the mechanical damage of the red blood cells (hemolysis), induced by the altered stress values in the flow, is larger for the non-Newtonian fluid model than for the Newtonian one.     

峰后岩石非Darcy渗流的分岔行为研究

煤矿采动围岩大多处于峰后应力状态或破碎状态,其渗流一般不符合Darcy定律,为非Darcy渗流系统．峰后岩石非Darcy渗流系统的失稳和分岔是煤矿突水和煤与瓦斯突出动力灾害发生的根源．文中用谱截断方法建立了Ahmed-Sunada型非Darcy渗流系统的降阶动力学方程,再由变量代换得到以无量纲变量表示的平衡态附近的演化方程,分析了系统的分岔条件,给出了系统的各种吸引子图案,并结合采矿工程实际,用非线性数学的观点揭示了煤矿突水和煤与瓦斯突出的机理．研究表明：当非Darcy渗流系统渗流特性和边界压力的初始值满足一定条件时,系统由平衡转向不稳定,即存在跨临界Hopf分岔和切分岔,并且,系统的动力学响应不随渗透特性连续变化,即该系统存在突变性．     

Tomographic particle image velocimetry investigation of the flow in a modeled human carotid artery bifurcation

Hemodynamic forces within the human carotid artery are well known to play a key role in the initiation and progression of vascular diseases such as atherosclerosis. The degree and extent of the disease largely depends on the prevailing three-dimensional flow structure and wall shear stress (WSS) distribution. This work presents tomographic PIV (Tomo-PIV) measurements of the flow structure and WSS in a physiologically accurate model of the human carotid artery bifurcation. The vascular geometry is reconstructed from patient-specific data and reproduced in a transparent flow phantom to demonstrate the feasibility of Tomo-PIV in a complex three-dimensional geometry. Tomographic reconstruction is performed with the multiplicative line-of-sight (MLOS) estimation and simultaneous multiplicative algebraic reconstruction (SMART) technique. The implemented methodology is validated by comparing the results with Stereo-PIV measurements in the same facility. Using a steady flow assumption, the measurement error and RMS uncertainty are directly inferred from the measured velocity field. It is shown that the measurement uncertainty increases for increasing light sheet thickness and increasing velocity gradients, which are largest near the vessel walls. For a typical volume depth of 6 mm (or 256 pixel), the analysis indicates that the velocity derived from 3D cross-correlation can be measured within ±2% of the maximum velocity (or ±0.2 pixel) near the center of the vessel and within ±5% (±0.6 pixel) near the vessel wall. The technique is then applied to acquire 3D-3C velocity field data at multiple axial locations within the carotid artery model, which are combined to yield the flow field and WSS in a volume of approximately 26 mm × 27 mm × 60 mm. Shear stress is computed from the velocity gradient tensor and a method for inferring the WSS distribution on the vessel wall is presented. The results indicate the presence of a complex and three-dimensional flow structure, with regions of flow separation and strong velocity gradients. The WSS distribution is markedly asymmetric confirming a complex swirling flow structure within the vessel. A comparison of the measured WSS with Stereo-PIV data returns an acceptable agreement with some differences in stress magnitude.     

Numerical simulation of supersonic flow past reentry capsules

The flow fields over ARD (ESA's atmospheric reentry demonstrator), OREX (orbital reentry experiments) and spherically blunted cone-flare reentry configurations are numerically obtained by solving time-dependent, axisymmetric, compressible Navier–Stokes equations for freestream Mach numbers range of 1.2–6.0. The fluid dynamics are discretized in spatial coordinates employing a finite volume approach which reduces the governing equations to semi discretized ordinary differential equations. Temporal integration is performed using the multistage Runge–Kutta time-stepping scheme. A local time step is used to achieve steady-state solution. The numerical simulation is carried out on a structured grid. The flow-field features around the reentry capsule, such as bow shock wave, sonic line, expansion fan and recirculating flow in the base region are obtained. A good agreement is found between the calculated value of aerodynamic drag coefficient of the spherically blunted cone/fare reentry configuration with the experimental data. The effects of geometrical parameters, such as radius of the spherical cap, half cone angle, with sharp shoulder edge and with smooth shoulder edge on the flow-field have been numerically investigated for various reentry configuration which will be useful for optimization of the reentry capsule. PACS 47.11.Df, 47.40.Ki     

Effect of yield stress on the flow of a Casson fluid in a homogeneous porous medium bounded by a circular tube

The effect of yield stress on the flow characteristics of a Casson fluid in a homogeneous porous medium bounded by a circular tube is investigated by employing the Brinkman model to account for the Darcy resistance offered by the porous medium. The non-linear coupled implicit system of differential equations governing the flow is first transformed into suitable integral equations and are solved numerically. Analytical solution is obtained for a Newtonian fluid in the case of constant permeability, and the numerical solution is verified with that of the analytic solution. The effect of yield stress of the fluid and permeability of the porous medium on shear stress and velocity distributions, plug flow radius and flow rate are examined. The minimum pressure gradient required to start the flow is found to be independent of the permeability of the porous medium and is equal to the yield stress of the fluid.     

Plaque components affect wall stress in stented human carotid artery: A numerical study

Carotid artery stenting presents challenges of in-stent restenosis and late thrombosis, which are caused primarily by alterations in the mechanical environment of the artery after stent implantation. The present study con-structed patient-specific carotid arterial bifurcation models with lipid pools and calcified components based on magnetic resonance imaging. We numerically analyzed the effects of multicomponent plaques on the distributions of von Mises stresses (VMSs) in the patient-specific models after stenting. The results showed that when a stent was deployed, the large soft lipid pool in atherosclerotic plaques cushioned the host artery and reduced the stress within the arterial wall;how-ever, this resulted in a sharp increase of VMS in the fibrous cap. When compared with the lipid pool, the presence of the calcified components led to slightly increased stresses on the luminal surface. However, when a calcification was located close to the luminal surface of the host artery and the stenosis, the local VMS was elevated. Overall, compared with calcified components, large lipid pools severely dam-aged the host artery after stenting. Furthermore, damage due to the calcified component may depend on location.     

Numerical simulation of the process of autoregulation of the arterial blood flow

For describing the autoregulation of the blood flow in an artery under constant transmural pressure a mathematical model that takes into account the multilayer structure of the arterial wall, the diffusion and kinetic processes in the wall, and the nonlinear viscoelastic properties of the wall material is proposed. The limiting case of a thin-walled artery is studied analytically. The arterial-wall viscosity range on which the equilibrium state of the system is stable is estimated. Accurate stationary distributions of the nitric oxide, calcium and myosin concentrations in the arterial wall are found. Numerical simulation of the autoregulation process demonstrated the possibility of arterial adaptation to radius perturbations, the existence of slow oscillations, and system transition to a new equilibrium state with change in blood flow level. The results are in good agreement with the experimental data.     

Numerical simulation of gas-solid flow with two fluid model in a spouted-fluid bed

The flow characteristics in a spouted-fluid bed differ from those in spouted or fluidized beds because of the injection of the spouting gas and the introduction of a fluidizing gas. The flow behavior of gas-solid phases was predicted using the Eulerian-Eulerian two-fluid model （TFM） approach with kinetic theory for granular flow to obtain the flow patterns in spouted-fluid beds. The gas flux and gas incident angle have a significant influence on the porosity and particle concentration in gas-solid spouted-fluid beds. The fluidizing gas flux affects the flow behavior of particles in the fountain. In the spouted-fluid bed, the solids volume fraction is low in the spout and high in the annulus. However, the solids volume fraction is reduced near the wall.     

Numerical simulation of the extrusion of strongly compressible Newtonian liquids

The axisymmetric and plane extrusion flows of a liquid foam are simulated assuming that the foam is a homogeneous compressible Newtonian fluid that slips along the walls. Compressibility effects are investigated using both a linear and an exponential equation of state. The numerical results confirm previous reports that the swelling of the extrudate decreases initially as the compressibility of the fluid is increased and then increases considerably. The latter increase is sharper in the case of the exponential equation of state. In the case of non-zero inertia, high compressibility was found to lead to a contraction of the extrudate after the initial expansion, similar to that observed experimentally with liquid foams and to decaying oscillations of the extrudate surface. The time-dependent calculations show that the oscillatory steady-state solutions are stable. These steady-state oscillatory solutions are not affected by the length of the extrudate region nor by the boundary condition along the wall.     

Transient numerical simulation of buoyancy driven flow adjacent to an elliptic tube

In this paper the problem of laminar, transient, two-dimensional free convective heat transfer from the surface of a horizontal elliptic tube is considered. The tube, whose surface is suddenly subjected to uniform heat flux, is placed in a quiescent Boussinesq Newtonian fluid with its major axis horizontal. The details of both flow and thermal fields are obtained by solving the full governing Navier–Stokes and energy equations. These equations, expressed in terms of stream function, vorticity and temperature, are numerically solved using an implicit spectral finite difference procedure. The parameters involved are the modified Rayleigh number, Prandtl number and axis-ratio. The investigation covers a Rayleigh number range up to 10⁷. The minor–major axis ratio of elliptic cylinder ranges between 0.05 and 0.998 and Prandtl number ranges between 0.1 and 10. The effects of these parameters on the surface temperature distribution and heat transfer coefficients are determined and the different aspects of the results are discussed for some selected cases.     

Numerical simulation of plate autorotation in a viscous fluid flow

A general formulation of the plane coupled dynamical and aerodynamical problem of the motion of a rigid body with a rotational degree of freedom in a viscous incompressible fluid flow is given. A computation technique for solving the Navier-Stokes equations based on the meshless viscous vortex domain method is used. The autorotation of a single plate and a pair of plates is investigated. The effect of the reduced moment of inertia and the Reynolds number on the angular rotation velocity is determined. The time dependences of the hydrodynamic loads are compared with the corresponding instantaneous flow patterns. The increased the autorotation velocity of two plates in tandem is detected.     

Upscaling the flow of generalised Newtonian fluids through anisotropic porous media

The homogenisation method with multiple scale expansions is used to investigate the slow and isothermal flow of generalised Newtonian fluids through anisotropic porous media. From this upscaling it is shown that the first-order macroscopic pressure gradient can be defined as the gradient of a macroscopic viscous dissipation potential, with respect to the first-order volume averaged fluid velocity. The macroscopic dissipation potential is the volume-averaged of local dissipation potential. Using this property, guidelines are proposed to build macroscopic tensorial permeation laws within the framework defined by the theory of anisotropic tensor functions and by using macroscopic isodissipation surfaces. A quantitative numerical study is then performed on a 3D fibrous medium and with a Carreau–Yasuda fluid in order to illustrate the theoretical results deduced from the upscaling.     

On the dispersion of soluble matter in a channel flow of non-Newtonian fluid

Summary An analysis of the dispersion of a solute in Rivlin-Ericksen third-order fluid in a parallel plate channel is carried out. It is seen that the solute which is dispersed relative to a plane moving with the mean speed of the flow has its effective Taylor diffusion coefficient which decreases with increasing the non-Newtonian parameter With 1 table     

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 hybrid RANS/LES simulation of high-Reynolds-number channel flow using additional filtering at the interface

A hybrid method combining large eddy simulation (LES) with the Reynolds-averaged Navier-Stokes (RANS) equation is used to simulate a turbulent channel flow at high Reynolds number. It is known that the mean velocity profile has a mismatch between the RANS and LES regions in hybrid simulations of a channel flow. The velocity mismatch is reproduced and its dependence on the location of the RANS/LES interface and on the type of RANS model is examined in order to better understand its properties. To remove the mismatch and to obtain better velocity profiles, additional filtering is applied to the velocity components in the wall-parallel planes near the interface. The additional filtering was previously introduced to simulate a channel flow at low Reynolds number. It is shown that the filtering is effective in reducing the mismatch even at high Reynolds number. Profiles of the velocity fluctuations of runs with and without the additional filtering are examined to help understand the reason for the mismatch. Due to the additional filtering, the wall-normal velocity fluctuation increases at the bottom of the LES region. The resulting velocity field creates the grid-scale shear stress more efficiently, and an overestimate of the velocity gradient is removed. The dependence of the velocity profile on the grid point number is also investigated. It is found that the velocity gradient in the core region is underestimated in the case of a coarse grid. Attention should be paid not only to the velocity mismatch near the interface but also to the velocity profile in the core region in hybrid simulations of a channel flow at high Reynolds number. PACS47.27.Eq; 47.27.Nz; 47.60.+i