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。     

THE COUPLE MOTION BETWEEN VESSEL WALL AN DBLOOD IN THE ENTRANCE REGION OF A TAPERED VESSEL

ＴＨＥＣＯＵＰＬＥＭＯＴＩＯＮＢＥＴＷＥＥＮＶＥＳＳＥＬＷＡＬＬＡＮＤＢＬＯＯＤＩＮＴＨＥＥＮＴＲＡＮＣＥＲＥＧＩＯＮＯＦＡＴＡＰＥＲＥＤＶＥＳＳＥＬＣｅｎＲｅｎ－ｊｉｎｇ（岑人经）ＱｉｎＣｈａｎ（秦婵）ＴａｎＺｈｅ－ｄｏｎｇ（谭哲东）（ＳｏｕｔｈＣ...     

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。     

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。     

Boundary layer development of pulsatile blood flow in a tapered vessel

Assuming that the tapered angle is small,the problems of developing flow under unsteady oscillatory condition are studied in this paper.The formula of velocity distribution is obtained.The analyses for the results show that the blood flow in a converging tapered vessel remains a developing flow throughout the length,and the effects of tapered angle on the developing flow are increased with the increment of the tapered angle.     

A calculation method for blood flow velocity distribution in smallep elocd vessels

The calculative method presented in this paper is based on an improvement of boundary conditions for a micro-continuum fluid model with blood flow assuming that the blood cell velocity at blood vessel wall is unequal to zero. As for steady state flood flow equation (flow in vitre—a rigid circular tube) presented by Eringen, the magnitude of the blood cell gyroscopic velocity at blood vessel wall and the slope of the blood cell gyroscopic velocity distribution curve at the axis of the blood vessel are assumed. From the above mentioned assumptions the calculating method of velocity distribution curve in blood vessel is derived. The curve calculated by this method is compared with the test curve measured by Bugliarello and Hayden. The results obtained by Turk, Sylvester and Ariman as well as with this method are compared with each other, too.     

The stress analysis of vessel wall in the entrance region of a tapered vessel

ＴＨＥＳＴＲＥＳＳＡＮＡＬＹＳＩＳＯＦＶＥＳＳＥＬＷＡＬＬＩＮＴＨＥＥＮＴＲＡＮＣＥＲＥＧＩＯＮＯＦＡＴＡＰＥＲＥＤＶＥＳＳＥＬＣｅｎＲｅｎ－Ｊｉｎｇ（岑人经）ＴａｎＺｈｅ－ｄｏｎｇ（谭哲东）ＣｈｅｎＺｈｅｎｇ－ｚｏｎｇ（陈正宗）（ＳｏｕｔｈＣｈｉｎ...     

Mathematical modeling and parametric investigation of blood flow through a stenosis artery

In this study, a mathematical model is formulated to examine the blood flow through a cylindrical stenosed blood vessel. The stenosis disease is caused because of the abnormal narrowing of flow in the body. This narrowing causes serious health issues like heart attack and may decrease blood flow in the blood vessel. Mathematical modeling helps us analyze such issues. A mathematical model is considered in this study to explore the blood flow in a stenosis artery and is solved numerically with the finite difference method. The artery is an elastic cylindrical tube containing blood defined as a viscoelastic fluid. A complete parametric analysis has been done for the flow velocity to clarify the applicability of the defined problem. Moreover, the flow characteristics such as the impedance, the wall shear stress in the stenotic region, the shear stresses in the throat of the stenosis and at the critical stenosis height are discussed. The obtained results show that the intensity of the stenosis occurs mostly at the highest narrowing areas compared with all other areas of the vessel, which has a direct impact on the wall shear stress. It is also observed that the resistive impedance and wall shear pressure get the maximum values at the critical height of the stenosis.

     

A Two-Layer Mathematical Model of Blood Flow in Porous Constricted Blood Vessels

In this paper, we discussed a mathematical model for two-layered non-Newtonian blood flow through porous constricted blood vessels. The core region of blood flow contains the suspension of erythrocytes as non-Newtonian Casson fluid and the peripheral region contains the plasma flow as Newtonian fluid. The wall of porous constricted blood vessel configured as thin transition Brinkman layer over layered by Darcy region. The boundary of fluid layer is defined as stress jump condition of Ocha-Tapiya and Beavers–Joseph. In this paper, we obtained an analytic expression for velocity, flow rate, wall shear stress. The effect of permeability, plasma layer thickness, yield stress and shape of the constriction on velocity in core & peripheral region, wall shear stress and flow rate is discussed graphically. This is found throughout the discussion that permeability and plasma layer thickness have accountable effect on various flow parameters which gives an important observation for diseased blood vessels.     

Developing flows and developed flows

This paper puts emphasis on the problem of the developing flows in the circular tube under oscillatory conditions. According to the Navier-Stokes' equations and using the method of Bessel function of imaginary argument, a system of formulas is obtained. Comparing the formulas obtained in this paper with Atabek's formulas, it may be seen that the former is simpler and more convenient. When both the formulas obtained in this paper and Atabek's formulas are reduced to the representation of developed flows, both of them are consistent. Numerical calculation results show that the computed results obtained in this paper are rather consistent with both Atabek's computed results and the experimental results.     

计算动脉血管发展流动的新差分格式

在引用守恒型N—S方程和SIMPLE方法的基础上，对血管发展流动的控制方程提出了新的差分格式。算例结果表明：本差分格式对血管发展流动的数值研究是可行的。     

Free oscillations of a liquid rotating in a cylindrical vessel under conditions of weightlessness

The plane problem of determination of the natural frequencies of small oscillations of a viscous liquid rotating in a partially filled cylindrical vessel under conditions of weight-lessness is examined. If the angular velocity of vessel rotation is sufficiently low, surface forces acting on the liquid-gas boundary prove to be of the same order as the centrifugal forces and significantly affect the oscillatory frequencies. Asymptotic formulas expressing the dependence of the oscillatory frequencies on the parameters of the problem are obtained by the boundary layer method, with the assumption that the ratio of viscous to centrifugal forces is low.Khar'kov. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkostii Gaza, No. 4, pp. 3–9, July–August, 1972.     

Two-pass countercrossflow heat exchangers with both fluids unmixed throughout

The aim of this paper is to present the formulas for computing the effectiveness and spatial temperature distribution of each stream and the wall of the two-pass countercrossflow heat exchangers with both fluids unmixed throughout for all possible flow arrangements. Making the usual idealizations for analysis of any heat exchanger flow arrangement and giving the coupling conditions for each pass, the problem of finding the spatial temperature distributions in the crossflow heat exchanger core is reduced to the solution of Fredholm's second order integral equation. By using the collocation method the solution of this integral equation is obtainable in the form of power series. The explicit formulas for the spatial temperature distributions and effectiveness are then obtained by simple integrations. The new relations are particularly helpful for computer-aided design procedures of two-pass countercrossflow heat exchangers.     

Oscillatory flow of second grade fluid in cylindrical tube

The unsteady oscillatory flow of an incompressible second grade fluid in a cylindrical tube with large wall suction is studied analytically. Flow in the tube is due to uniform suction at the permeable walls, and the oscillations in the velocity field are due to small amplitude time harmonic pressure waves. The physical quantities of interest are the velocity field, the amplitude of oscillation, and the penetration depth of the oscillatory wave. The analytical solution of the governing boundary value problem is obtained, and the effects of second grade fluid parameters are analyzed and discussed.     

用流体双折射的位相差积分法定量分析具有对称平面的三维流场

本文对流体双折射方法做了简单的回顾。用位相差积分理论导出了具有对称平面双折射介质所适用的公式。作为实例,我们定量分析了扩张和收缩管中的剪应变率分布。     

Numerical study of flow and heat transfer during oscillatory blood flow in diseased arteries in presence of magnetic fields

A problem motivated by the investigation of the heat and mass transfer in the unsteady magnetohydrodynamic(MHD) flow of blood through a vessel is solved numerically when the lumen of the vessel has turned into the porous structure.The time-dependent permeability and the oscillatory suction velocity are considered.The computational results are presented graphically for the velocity,the temperature,and the concentration fields for various values of skin friction coefficients,Nusselt numbers,and Sherwood numbers.The study reveals that the flow is appreciably influenced by the presence of a magnetic field and also by the value of the Grashof number.     

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。     

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。     

Red blood cell partitioning and blood flux redistribution in microvascular bifurcation

This paper studies red blood cell (RBC) partitioning and blood flux redistribution in microvascular bifurcation by immersed boundary and lattice Boltzmann method. The effects of the initial position of RBC at low Reynolds number regime on the RBC deformation, RBC partitioning, blood flux redistribution and pressure distribution are discussed in detail. It is shown that the blood flux in the daughter branches and the initial position of RBC are important for RBC partitioning. RBC tends to enter the higher-flux-rate branch if the initial position of RBC is near the center of the mother vessel. The RBC may enter the lower-flux-rate branch if it is located near the wall of mother vessel on the lower-flux-rate branch side. Moreover, the blood flux is redistributed when an RBC presents in the daughter branch. Such redistribution is caused by the pressure distribution and reduces the superiority of RBC entering the same branch. The results obtained in the present work may provide a physical insight into the understanding of RBC partitioning and blood flux redistribution in microvascular bifurcation.