Factors Influencing the Disturbed Flow Patterns Downstream of Curved Atherosclerotic Arteries

Pulsatile blood flows in curved atherosclerotic arteries are studied by com- puter simulations.Computations are carried out with various values of physiological parameters to examine the effects of flow parameters on the disturbed flow patterns downstream of a curved artery with a stenosis at the inner wall.The numerical re- suits indicate a strong dependence of flow pattern on the blood viscosity and inlet flow rate,while the influence of the inlet flow profile to the flow pattem in downstream is negligible.     

A two-dimensional model of pulsating flow in the basilar artery

The flow in the basilar artery is modelled by a pulsating flow of a viscous fluid in a plane straight semi-infinite channel with rigid walls. To model the merging flow from the two vertebral arteries, the prescribed initial velocity profile exhibits two separate maximum values. Numerical results are presented for the downstream velocity, the wall shear and the time-dependent inlet length. Finally, the biomechanical implications of the results are discussed.     

Significance of plaque morphology in modifying flow characteristics in a diseased coronary artery: Numerical simulation using plaque measurements from intravascular ultrasound imaging

The paper deals with numerical investigation of the effect of plaque morphology on the flow characteristics in a diseased coronary artery using realistic plaque morphology. The morphological information of the lumen and the plaque is obtained from intravascular ultrasound imaging measurements of 42 patients performed at Cleveland Clinic Foundation, Ohio. For this data, study of Bhaganagar et al. (2010) [1] has revealed the stenosis for 42 patients can be categorized into four types – type I (peak-valley), type II (ascending), type III (descending), and type IV (diffuse). The aim of the present study is to isolate the effect of shape of the stenosis on the flow characteristics for a given degree of the stenosis. In this study, we conduct fluid dynamic simulations for the four stenosis types (type I–IV) and analyze the differences in the flow characteristics between these types. Finely refined tetrahedral mesh for the 3-D solid model of the artery with plaques has been generated. The 3-D steady flow simulations were performed using the turbulence (k–ε) model in a finite volume based computational fluid dynamics solver. The axial velocity, the radial velocity, turbulence kinetic energy and wall shear stress profiles of the plaque have been analyzed. From the axial and radial velocity profiles results the differences in the velocity patterns are significantly visible at proximal as well as distal to the throat, region of maximum stenosis. Turbulent kinetic energy and wall shear stress profiles have revealed significant differences in the vicinity of the plaque. Additional unsteady flow simulations have been performed to validate the hypothesis of the significance of plaque morphology in flow alterations in diseased coronary artery. The results revealed the importance of accounting for plaque morphology in addition to plaque height to accurately characterize the turbulent flow in a diseased coronary artery.     

基于Schwarz-Christoffel变换的非圆截面血管流场分布研究

应用Schwarz-Christoffel(S-C)变换方法,实现从复平面单位圆到多边形区域的共形映射,结合圆形管道下完全发展脉动流的Womersley算法理论,建立了基于S-C映射的非圆入口截面下的Womersley速度边界模型.在边界模型建立的基础上,应用计算流体力学方法,对基于生理真实的人体肺动脉二级分支血管在一个心动周期内的血流流动情况进行了数值模拟,并与通过外接圆管法设定入口速度边界条件得到的流场模拟结果进行了对比分析.分析结果表明,两者的模拟结果高度一致,但考虑到模拟效率和数值模拟结果的确定性,基于S-C映射的Womersley速度边界模型优于外接圆管方法,对于血管血流动力学的模拟研究更具有现实意义.     

Numerical modeling on inlet aperture effects on flow pattern in primary settling tanks

Inlets should be designed to dissipate the kinetic energy or velocity head of the mixed liquor and to prevent short-circuiting, mitigate the effects of density currents, and minimize blanket disturbances. Flow in primary settling tank is simulated by means of computational fluid dynamics. The fluid is assumed incompressible and non-buoyant. A two-dimensional computational and one phase fluid dynamics model was built to simulate the flow properties in the settling tank including the velocity profiles, the flow separation area and kinetic energy. In this study, the RNG turbulent model was solved with the Navier–Stokes equations. In order to evaluate hydraulic influences on the velocity profile, separation length and kinetic energy, three different of opening positions and two and three aperture in inlets were simulated. The flow model uses to apply a fixed-grid of cells that are all rectangular faces; the fluid moves through the grid and free surfaces are tracked with the volume-of-fluid (VOF) technique. Effects of numbers and locations of inlet apertures on the flow field are presented and the results show the positions of inlet apertures are affected on the flow pattern in the settling basin and increasing the numbers of slots can reduce kinetic energy in the inlet zone and produce uniform flow.     

NEW METHOD FOR IMPROVED CALCULATIONS OF UNSTEADY COMPLEX FLOWS IN LARGE ARTERIES

Using an improved computational fluid dynamics (CFD) method developed for highly unsteady three-dimensional flows, numerical simulations for oscillating flow cycles and detailed unsteady simulations of the flow and forces on the aortic vessels at the iliac bifurcation, for both healthy and diseased patients, are analyzed. Improvements in computational efficiency and acceleration in convergence are achieved by calculating both an unsteady pressure gradient which is due to fluid acceleration and a good global pressure field correction based on mass flow for the pressure Poisson equation. Applications of the enhanced method to oscillatory flow in curved pipes yield an order of magnitude increase in speed and efficiency, thus allowing the study of more complex flow problems such as flow through the mammalian abdominal aorta at the iliac arteries bifurcation. To analyze the large forces which can exist on stent graft of patients with abdominal aortic aneurysm (AAA) disease, a complete derivation of the force equations is presented. The accelerated numerical algorithm and the force equations derived are used to calculate flow and forces for two individuals whose geometry is obtained from CT data and whose respective blood pressure measurements are obtained experimentally. Although the use of endovascular stent grafts in diseased patients can alter vessel geometries, the physical characteristics of stents are still very different when compared to native blood vessels of healthy subjects. The geometry for the AAA stent graph patient studied in this investigation induced flows that resulted in large forces that are primarily caused by the blood pressure. These forces are also directly related to the flow cross-sectional area and the angle of the iliac arteries relative to the main descending aorta. Furthermore, the fluid flow is significantly disturbed in the diseased patient with large flow recirculation and stagnant regions which are not present for healthy subjects.     

Calculating particle-to-wall distances in unstructured computational fluid dynamic models

Knowledge of particle deposition is relevant in biomedical engineering situations such as computational modeling of aerosols in the lungs and blood particles in diseased arteries. To determine particle deposition distributions, one must track particles through the flow field, and compute each particle's distance to the wall as it approaches the geometric surface. For complex geometries, unstructured tetrahedral grids are a powerful tool for discretizing the model, but they complicate the particle-to-wall distance calculation, especially when non-linear mesh elements are used. In this paper, a general algorithm for finding minimum particle-to-wall distances in complex geometries constructed from unstructured tetrahedral grids will be presented. The algorithm is validated with a three-dimensional 90° bend geometry, and a comparison in accuracy is made between the use of linear and quadratic tetrahedral elements to calculate the minimum particle-to-wall distance.     

弹性动脉血管中血液流动特性的模拟和分析

研究了两个不同的非牛顿血液流动模型:低粘性剪切简单幂律模型和低粘性剪切及粘弹性振荡流的广义Maxwell模型．同时利用这两个非牛顿模型和牛顿模型,研究了磁场中刚性和弹性直血管中血液的正弦型脉动．在生理学条件下,大动脉中血液的弹性对其流动性态似乎并不产生影响,单纯低粘性剪切模型可以逼真地模拟这种血液流动．利用高剪切幂律模型模拟弹性血管中的正弦型脉动流,发现在同一压力梯度下,与牛顿流体相比较,幂律流体的平均流率和流率变化幅度都更小．控制方程用Crank-Niclson方法求解．弹性动脉中血液受磁场作用是产生此结果的直观原因．在主动脉生物流的模拟中,与牛顿流体模型比较,发现在匹配流率曲线上,幂律模型的平均壁面剪切应力增大,峰值壁面剪切应力减小．讨论了弹性血管横切磁场时的血液流动,评估了血管形状和表面不规则等因素的影响．     

The effects of post-stenotic dilatations on the flow of a blood analogue through stenosed coronary arteries

Previous work on the resistance to flow ratio and wall shear ratio of non-Newtonian blood flow through arteries containing aneurisms and stenoses has considered only Power Law and Casson models of fluid behaviour. Here a Bingham fluid is used to model blood. Flow through both constrictions and dilatations is considered. The effects of both a single diseased portion and pairs of abnormal wall segments in close proximity to each other are investigated. Comparison is made with earlier studies. Particular attention is paid to the effects of a post-stenotic dilatation as the ameorlation of the increase in resistance to flow ratio caused by such a situation is clinically relevant.     

肾动脉变窄和流-固结构相互作用对非Newton脉动流的影响——一个真实的腹部主动脉和肾动脉模型

研究肾动脉狭窄(RAS)对血液流动和血管壁的影响.根据CT扫描图像,重建腹部主动脉和肾动脉的解剖模型,通过模型的脉动流进行了仿真计算,计算中考虑了流体-固体结构的相互作用(FSI).研究RAS对血管壁剪切应力和位移的影响,RAS使得肾动脉中流量减少,肾素-血管紧缩素系统可能被激活,从而导致严重的高血压.     

Transient modelling of flow distribution in automotive catalytic converters

The transient catalytic converter performance is governed by complex interactions between exhaust gas flow and the monolithic structure of the catalytic converter. Therefore, during typical operating conditions of interest, one has to take into account the effect of the inlet diffuser on the flow field at the entrance. Computational fluid dynamics (CFD) is a powerful tool for calculating the flow field inside the catalytic converter. Radial velocity profiles, obtained by a commercial CFD code, present very good agreement with respective experimental results published in the literature. However the applicability of CFD for transient simulations is limited by the high CPU demands.The present study proposes an alternative computational method for the prediction of transient flow fields in axi-symmetric converters time-efficiently. The method is based on the use of equivalent flow resistances to simulate the flow paths in the inlet and outlet catalyst sections. The proposed flow resistance modelling (FRM) method is validated against the results of CFD predictions over a wide range of operating conditions. Apart from the apparent CPU advantages, the proposed methodology can be readily coupled with already available transient models for the chemical reactions in the catalyst. A transient model for heat transfer inside the monolith is presented. An example of coupling between FRM and transient heat transfer inside the converter is included. This example illustrates the effect of flow distribution in the thermal response of a catalytic converter, during the critical phase of catalytic converter warm-up.     

A two-dimensional intake manifold flow simulation

A computer flow model of an intake manifold of a four cylinder engine has been developed using a computational fluid dynamic code. This code is base on the Conchas-Spray code developed at the Los Alamos National Laboratory. The flow inside the intake manifold is assumed to be two-dimensional, unsteady, compressible, and turbulent. A simple subgrid scale (SGS) turbulence model and hypothetical boundary conditions are employed in the simulation. Atmospheric pressure is specified at the inlet and the velocities are specified at the outlets of the manifold, together with the law of the wall at all the wall boundaries. Numerical results of the simulation are presented in the form of velocity, pressure, density, and temperature fields. The model is designed in such a way that different manifold geometries may be simulated with ease. A simulation of a concept manifold “the loop-manifold” is also presented.     

流固耦合作用下狭窄颈动脉内非Newton血流分析

采用计算流体力学方法分别对6种狭窄率的颈动脉内非Newton瞬态血流进行流固耦合数值分析.研究了狭窄率对颈动脉内血流动力学分布的影响,以探索狭窄率与颈动脉内粥样斑块形成的关系.结果表明,狭窄率不同的颈动脉内血流动力学分布特性明显不同,与0.05,0.1,0.2,0.3和04这5种狭窄率的颈动脉内血流动力学分布特性相比,狭窄率为0.5的颈动脉内血流动力学分布独特,狭窄部位附近区域存在面积较大的低速涡流区;复杂血流作用下,该区域分布低壁面压力,异常壁面切应力,较大管壁形变量和von Mises应力;血流速度低使血液中脂质、纤维蛋白等大分子易沉积,低壁面压力引起的明显“负压”效应引发脑部供血障碍,异常壁面切应力作用下粥样斑块易破裂与脱落,并堵塞脑血管,较大的von Mises应力易引起应力集中,导致血管破裂,为脑卒中发生提供有利条件.因此,狭窄率越大对颈动脉内血流动力学分布的影响越显著,促进颈动脉粥样斑块形成与发展,并引发缺血性脑卒中.     

Power law fluid model for blood flow through a tapered artery with a stenosis

In the present paper, blood flow through a tapered artery with a stenosis is analyzed, assuming the flow is steady and blood is treated as non-Newtonian power law fluid model. Exact solution has been evaluated for velocity, resistance impedance, wall shear stress and shearing stress at the stenosis throat. The graphical results of different types of tapered arteries (i.e. converging tapering, diverging tapering, non-tapered artery) have been examined for different parameters of interest. Some special cases of the problem are also presented.     

Optimization methodology assessment for the inlet velocity profile of a hydraulic turbine draft tube: part I—computer optimization techniques

In recent years, numerical and experimental investigations on the draft tube performance have confirmed the importance of the inlet swirling flow created by the runner vanes. The results indicate that it is still a challenge to get the optimal flow distribution at the draft tube inlet which gives the best machine performance over a range of operation points. Consequently, there is a need to adjust the runner-draft tube coupling to minimize the losses arising from the inlet flow distribution. This paper focus on establishing an optimization methodology for maximizing the draft tube performance as a function of the inlet velocity profile. The overall work is divides into two parts: The part one establish the inlet velocity parametrization, the numerical optimization set-up and the objective function definition. The part two validate the numerical CFD draft tube model. These steps are represented by the coupling of the commercial softwares MATLAB, FLUENT and iSIGHT. It is considered that this proved methodology will help to find a inlet velocity profile shape which will be able to suppress or mitigate the undesirable draft tube flow characteristics.     

Investigation of physiological pulsatile flow in a model arterial stenosis using large-eddy and direct numerical simulations

Physiological pulsatile flow in a 3D model of arterial stenosis is investigated by using large eddy simulation (LES) technique. The computational domain chosen is a simple channel with a biological type stenosis formed eccentrically on the top wall. The physiological pulsation is generated at the inlet using the first harmonic of the Fourier series of pressure pulse. In LES, the large scale flows are resolved fully while the unresolved subgrid scale (SGS) motions are modelled using a localized dynamic model. Due to the narrowing of artery the pulsatile flow becomes transition-to-turbulent in the downstream region of the stenosis, where a high level of turbulent fluctuations is achieved, and some detailed information about the nature of these fluctuations are revealed through the investigation of the turbulent energy spectra. Transition-to-turbulent of the pulsatile flow in the post stenosis is examined through the various numerical results such as velocity, streamlines, velocity vectors, vortices, wall pressure and shear stresses, turbulent kinetic energy, and pressure gradient. A comparison of the LES results with the coarse DNS are given for the Reynolds number of 2000 in terms of the mean pressure, wall shear stress as well as the turbulent characteristics. The results show that the shear stress at the upper wall is low just prior to the centre of the stenosis, while it is maximum in the throat of the stenosis. But, at the immediate post stenotic region, the wall shear stress takes the oscillating form which is quite harmful to the blood cells and vessels. In addition, the pressure drops at the throat of the stenosis where the re-circulated flow region is created due to the adverse pressure gradient. The maximum turbulent kinetic energy is located at the post stenosis with the presence of the inertial sub-range region of slope −5/3.     

Modeling of aerosol spray characteristics for synthesis of sensor thin film from solution

A model is developed of aerosol spray for synthesis of sensor film from solution. The synthesis technique considered involves atomization of a solution of mixed salts in methanol, spraying of solution droplets, droplet deposition on a heated substrate, evaporation and chemical reaction to produce mixed oxides, and subsequent film growth. The precise control of oxide nanoparticle size distribution and inter-particle spacing in the film is crucial to achieving high sensitivity. These in turn largely depend on the droplet characteristics prior to impingement on the substrate. This paper focuses on the development of a model to describe the atomization and spray processes prior to the film growth. Specifically, a mathematical model is developed utilizing computational fluid dynamics solution of the equations governing the transport of atomized droplets from the nozzle to the substrate in order to predict droplet characteristics in flight. The predictions include spatial distribution of droplet size and concentration, and the effect on these characteristics of swirling inlet flow at the spray nozzle.     

Numerical Modeling of Fluid-Structure Interaction of Blood in a Vein by Simulating Conservation of Mass and Linear Momentum with the Finite Element Method in FEniCS

In medicine a fundamental understanding for blood flow in human arteries is significantly important. In socalled hemodynamics engineers all over the world simulate blood flows in healthy and diseased vessels. Scientific findings in this area help to improve cardiovascular assisting devices and to plan surgical operations. The difficulty with such simulations is the interaction of the blood flow with the elastic vessel wall, which deforms due to changing flow conditions. We will present a two-dimensional model for blood flowing through an arterial vessel and investigate the balance of mass and the balance of linear momentum. We will adjust these balance equations appropriately and define time dependent boundary conditions. The necessary partial differential equations for the fluid-structure interaction will be solved by using the finite element method in FEniCS [1]. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An air sparging CFD model for heap bioleaching of chalcocite

A computational fluid dynamics (CFD) solver CFX4.4 is used to implement a steady state model of heap bioleaching of chalcocite, which includes air sparging (forced aeration) based on a previous model entirely under natural convection. The model assumes the oxygen supply limits the reaction rate. A parameter analysis is performed which shows that the factors important to copper leaching are liquid and air flow rates, permeability and fraction of pyrite to chalcocite leached (FPY). The ability to control which parts of the bed received the highest extraction as a function of the liquid and air flow rates was established. Sparging is found to increase the oxygen concentration throughout the heap compared to the circumstance with no sparging (natural convection), and consequently improves the copper extraction significantly. The results show that sparging does not provide any better copper extraction for very high heap permeabilities. The arrangement and spacing of air sparging inlets is analysed in regard to the existence of oxygen starved regions between the inlets.