局部狭窄血管中血液振荡流的速度和切应力

本文建立一种分析局部缓慢狭窄血管中血液振荡流的数学模型，给出了血液的轴向流速，径向流速和切应力的包含压力梯度项的解析表达式，并讨论了血管内由局部狭窄引起的压力梯度沿轴向变化的规律。文章以局部余弦狭窄为例进行数值计算，详细讨论上游均匀管段压力梯度的定常部分和不同次谐波对狭窄管段内流速和切应力的影响。数值结果表明，与均匀管情况相比，在狭窄段内，血液振荡流轴向流速无论平均值还是脉动幅值均明显增大，且径向流速不再为零。但径向流速仍远小于轴向流速。同时，切应力也不再仅由轴向流速梯度提供，径向流速梯度也将产生切应力，但是在计算管壁切向上的切应力时，径向流速梯度的贡献仍相当大。与均匀管管壁切应力沿流运方向保持恒定不同。狭窄管管壁切应力（平均值和脉动值）将随着狭窄高度的增大而增大，在狭窄最大高度处达到最大，因而沿流动方向产生了较大的切应力梯度。     

局部扩张动脉管血液振荡流的切应力分布

本文求解局部缓慢扩张动脉管中血液振荡流的基本方程，得到血管内血液的流速与压力梯度的关系。通过导出压力梯度沿局部扩张管轴向的变化特性。建立利用扩张段上游血管均匀段中心流速波形确定局部扩张管中血液流的速度和切应力分布的方法，文章以人体颈动脉余弦扩张为例进行分析。详细讨论了局部扩张对血管壁切应力及其梯度分布的影响。数值结果表明，在与刚性均匀管中管壁切应力沿轴向保持不变不同，在局部扩张段，管壁切应力将随着血管半径的增大而减小，因而管壁切应力梯度一般不为零，甚至在某些位置达到相当大的数值。另外，随着血管扩张程度的增加，管壁切应力还将进一步减小，而且管壁切应力梯度也将进一步增大，血管扩张导致管壁切应力的这些变化将直接影响血管壁的结构和功能，使其产生适应性的变化。     

动脉狭窄对血液流速的影响

为了定量计算动脉局部狭窄对动脉管中血液流动速度的影响，本文分别对狭窄区域内定常流和非定常流动进行了求解，得出了狭窄区域内定常流和脉动流的速度表达式。本文将均匀段的流速形经Ｆｏｕｒｉｅｒ分解成定常和脉动两部分，然后分别计算出狭窄区域内对应的定常和脉动流速，经Ｆｏｕｒｉｅｒ合成还原成流速时域波形，同时针对各种情况将不同狭窄对不同的流速波形的作了分析比较。     

刚性圆管中血液周期振荡流的切应力分布

本文通过求解圆管内血液振荡流的基本方程，求得圆管内血液流的压力梯度与切应力之间的关系式。在此基础上，详细讲座了圆管中轴向流速和切变率谐波的变化规律，指出流速谐波和切变率谐波的幅值都将随着谐波次数的增大而逐渐减小。为了使所得结果便于应用。文章通过管轴向中心线流速与压力梯度之间的关系式，进一步给出一种利用管轴向中心线流速计算管内切应力分布的简便方法。该方法用于检测活体血管内血液振荡流的切应力分布，具有操作简单，精度较高的优点。最后，以人体颈动脉为例，讨论血液周期振荡流的切应力的分布特性。发现在任意时刻，除了邻近管壁处切应力急剧增大到一定数值之外，沿管截面切应力分布相当均匀且接近于零，呈现出与定常流不同的切应力分布特征。     

动脉中非平稳流动壁面剪切力及其Hilbert-Huang变换

本文通过数值方法求解均匀动脉中的非平稳脉动流,给出了通过测量非平稳脉动血流量确定壁面切应力的方法.作为算例,采用实测的大鼠颈总动脉流量信号,求出了均匀动脉壁面切应力波形.进一步对求得的切应力波形进行经验模态分解(EMD),得到了切应力波形的各内在模态(IMF),以及Hilbert幅值谱.从切应力波形经Hilbert-Huang变换得到的IMF和Hilbert谱图可以明显地看出切应力各频率成分的物理意义.所得结果为进一步深入研究非平稳脉动切应力与血管重建的关系提供了一种方法学基础.     

弯曲动脉的血流动力学数值分析

利用计算流体力学的理论和方法对弯曲动脉中的血流动力学进行数值分析，是研究心血管疾病流体动力学机理的一种行之有效的方法。本文将升主动脉、主动脉弓和降主动脉联系起来作为弯曲动脉几何模型，给出了血液流动的边界条件以及计算条件。根据生理脉动流条件，对狗的弯曲动脉几何模型内发展中的血液流动进行了有限元数值模拟，并利用可视化方法对血液流动的轴向速度、二次流、壁面切应力等计算结果进行了分析。研究结果表明，在弯管内侧壁处，同时存在主流方向和二次流方向的回流，此处容易形成涡流。弯管内侧壁比外侧壁的壁面切应力具有更强的脉动性。     

用管轴流速确定动脉中血液振荡流的速度剖面

本文通过求解圆管内血液振荡流的基本方程，求得圆管内血液流的速度与压力梯度之间的关系式，文章提出一种利用管轴外流速计算管内压力梯度，进而确定血液振荡流动速度分布的方法，该方法用于检测活体血管内血液振荡流的速度剖面，具有操作简单，精度较高的优点，最后，以人体颈动脉为例，讨论血液周期振荡流的速度分布特征，发现在任意时刻，除了邻近管壁速度迅速降为零之外，沿管截面速度分布相当均匀，呈现出与定常流不同的速度分布特征。     

Taylor补丁对新型动脉旁路移植流场影响的数值分析

为了研究Taylor补丁对新型(S型)动脉旁路移植术中吻合口处流场的影响,使用数值方法研究了采用Taylor补丁和未采用该补丁的两个S型旁路移植模型内流场的血流动力学差异. 对流速、壁面切应力和切应力梯度等参数进行了比较分析. 结果表明,Taylor补丁对吻合口的流场有显著影响. 采用Taylor补丁的模型其下游吻合口处的流场分布较未采用补丁的模型更均匀,二次流平均流速减小约34.48%,壁面切应力梯度减小约52.22%,从壁面切应力梯度方面分析,这将有助于改善血流动力学分布,抑制动脉粥样硬化. 但从壁面切应力值分析,其动脉底部的壁面低切应力区明显增大,平均壁面切应力值减小30.33%,这又将促使动脉粥样硬化. 因此,Taylor补丁是否对S型搭桥术具有治疗优越性,仅从血流动力学分析尚不能定论,配合数值计算结果进行动物和临床实验研究是十分必要的.      

动脉中脉动流的准二维分析与数值计算

本文考虑了血液的菲牛顿流动特性,对血液在动脉管系中的脉动流建立了准二维流动模型。利用有限差分方法得到了动脉管系内非牛顿流体的准二维不定常流动的数值解。并以人体五根主要动脉所组成的动脉管系为例,进行了详细的数值计算。计算结果表明,在动脉的某些典型位置上。计算所得的理论波形与实测波形是相似的。     

分枝动脉脉搏流的数值模拟

本文考虑到血液粘度与动脉管壁的非线性特性,利用特征线法数值求解了主动脉和一根分枝动脉(桡动脉)中的脉搏流。得到的桡动脉压力波形与实测波形相似,而且改变某些生理参数能得到平缓脉、弦脉和滑脉所对应的波形,从而为解释中医脉象机理提供了一种方法,或许有可能通过脉搏波的分析求研究动脉系统的病变。     

Investigation of third-grade non-Newtonian blood flow in arteries under periodic body acceleration using multi-step differential transformation method

In this paper, a non-Newtonian third-grade blood in coronary and femoral arteries is simulated analytically and numerically. The blood is considered as the thirdgrade non-Newtonian fluid under the periodic body acceleration motion and the pulsatile pressure gradient. The hybrid multi-step differential transformation method (Hybrid-MsDTM) and the Crank-Nicholson method (CNM) are used to solve the partial differential equation (PDE), and a good agreement between them is observed in the results. The effects of the some physical parameters such as the amplitude, the lead angle, and the body acceleration frequency on the velocity and shear stress profiles are considered. The results show that increasing the amplitude, A_g, and reducing the lead angle of body acceleration, φ, make higher velocity profiles on the center line of both arteries. Also, the maximum wall shear stress increases when A_g increases.     

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.     

FLOW STRUCTURE AND VARIATION OF WALL SHEAR STRESS IN ASYMMETRICAL ARTERIAL BRANCH

In the present study, the flow structure such as the velocity profile and the wall shear stress in an asymmetrical arterial branch in laminar steady flow has been experimentally studied. In the branch model, the daughter tube asymmetrically bifurcates from the parent tube at 45°. The axial and the transverse velocity components have been measured by two-dimensional laser Doppler velocimetry, and the wall shear stress is measured by the electrochemical method. Furthermore, the wall shear stress estimated from the velocity profile is compared with that measured by the electrochemical method. Consequently, it has been clarified that, as it approaches the entrance of the daughter tube, the core flow deflects into the daughter tube, and the variation of wall shear stress along the proximal wall results from the secondary motion which is transferred from the parent tube to the daughter tube.     

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.     

Performance modeling and analysis of blood flow in elastic arteries

Nomenclature　　τ　　wallshearstressγshearrateτy yieldstressηc Cassonviscosityktheconsistencyindexnnon_Newtonianindexτp shearstressofthepthelementωangularvelocityRvessel’sradiusCwavespeedM　　magneticparameter (Hartmannnumber)u,w　velocitycomponentinther_andz_directions,respectivelyP　　pressureα　　unsteadinessparameter k , R meanparametersTp relaxationtimeofthepthelementρ densityIntroductionTheimportancetoatherogenesisofarterialflowphenomenasuchasflowseparation ,recirculationands…     

The influence of flow-induced non-Newtonian fluid properties on turbulent drag reduction

Friction factors and velocity profiles in turbulent drag reduction can be compared to Newtonian fluid turbulence when the shear viscosity at the wall shear rate is used for the Reynolds number and the local shear viscosity is used for the non-dimensional wall distance. On this basis, an apparent maximum drag reduction asymptote is found which is independent of Reynolds number and type of drag reducing additive. However, no shear viscosity is able to account for the difference between the measured Reynolds stress and the Reynolds stress calculated from the mean velocity profile (the Reynolds stress deficit). If the appropriate local viscosity to use with the velocity fluctuation correlations includes an elongational component, the problem can be resolved. Taking the maximum drag reduction asymptote as a non-Newtonian flow, with this effective viscosity, leads to agreement with the concept of an asymptote only when the solvent viscosity is used in the non-dimensional wall distance.     

A method for estimating wall friction in turbulent wall-bounded flows

We describe a simple method for estimating turbulent boundary layer wall friction using the fit of measured velocity data to a boundary layer model profile that extends the logarithmic profile all the way to the wall. Two models for the boundary layer profile are examined, the power-series interpolation scheme of Spalding and the Musker profile which is based on the eddy viscosity concept. The performance of the method is quantified using recent experimental data in zero pressure gradient flat-plate turbulent boundary layers, and favorable pressure gradient turbulent boundary layers in a pipe, for which independent measurements of wall shear are also available. Between the two model profiles tested, the Musker profile performs much better than the Spalding profile. Results show that the new procedure can provide highly accurate estimates of wall shear with a mean error of about 0.5% in friction velocity, or 1% in shear stress, an accuracy that is comparable to that from independent direct measurements of wall shear stress. An important advantage of the method is its ability to provide accurate estimates of wall shear not only based on many data points in a velocity profile but also very sparse data points in the velocity profile, including only a single data point such as that originating from a near-wall probe.