UNSTEADY ANALYSIS OF VISCOELASTIC BLOOD FLOW THROUGH ARTERIAL STENOSIS

A mathematical model of unsteady non-Newtonian blood flow in an artery under stenotic condition has been developed. The flowing blood is considered to be a viscoelastic fluid characterized by the Oldroyd-B model and the arterial wall is considered to be rigid, having cosine-shaped stenosis. The governing equations of motion accompanied by appropriate choice of the initial and boundary conditions are solved numerically by the MAC (marker and cell) method, and the results are checked, for numerical stability with desired degree of accuracy. The key factors like the wall shear stress, resistive impedance, and the other viscoelastic parameters are also examined for further qualitative insight into the flow through arterial stenosis. Comparison of the results reveals that dimensionless pressure drop for the viscoelastic model increases while it diminishes for the shear-thinning power law model over that of the Newtonian model. Moreover, the possibility of flow separation increases with increasing relaxation time (Deborah number), and in case of Newtonian fluid, delayed separation is observed. The grid independence study has also been performed successfully in order to validate the applicability of the methodology as well as the model used under consideration. Special emphasis has duly been made to compare the present theoretical results with the existing ones, and good agreement between them has been achieved both qualitatively and quantitatively.     

UNSTEADY CONVECTIVE DIFFUSION IN BLOOD FLOW THROUGH A TUBE

The paper presents an exact analysis of unsteady convective dispersion of a solute in a Casson fluid (assumed as the non-Newtonian behaviour of blood) flowing in a tube. Using a generalized dispersion model, which is valid for all time after the injection of the solute in the flow, we evaluate the axial dispersion coefficients as functions of time. The variation of the asymptotic dispersion coefficient K₂* with y₀ (the dimensionless radius of the plug flow region) shows that K₂* first increases with y₀, reaches a maximum and then decreases. The behaviour of the dimensionless dispersion coefficient K₂(T) - Pe^-2 with time T is also shown graphically.     

FLOW OF A SUSPENSION THROUGH A VERTICAL TUBE

Jiang el at. (1986) have developed the local volume averages of the equations of motion as well as the appropriate boundary conditions for a flowing suspension of non-neutrally buoyant, uniform spheres in an incompressible Newtonian fluid under conditions such that inertial effects can be neglected. Neither the equations nor the boundary conditions involve any free or undetermined parameters.

These local volume-averaged equations of motion have been solved for flow through a vertical tube and the results compared with available measurements of velocity profiles and of apparent viscosities. The predictions of measured apparent viscosities are in error by no more than 3%, when the volume fraction of solids is less than 0.20. The errors in representing the velocity profiles are comparable, but based upon fewer data.     

MASS TRANSFER IN RECIRCULATING BLOOD FLOW

An experimental investigation was done on oxygen transfer into laminar flows of whole blood and saline downstream of an abrupt pipe expansion. This was used as the experimental model for regions of separated flow in the arterial system. The flow was fully-developed prior to the tube expansion with Reynolds numbers between 160 and 850. The results showed high transfer rates over most of the region downstream of the step, with maximum transfer occurring near the reattachment point. In addition, oscillations of the transfer rate were measured at the larger Reynolds numbers of 450 and 850.     

水平直圆管内油气两相流的压降

对水平放置的内径为40 mm的有机玻璃管内的油气两相流进行了详细的实验研究,实验工质为46^＃机械油和空气.油相和气相折算速度分别为0.051～0.612 m•s^-1和0.024～50.64 m•s^-1,实验在室温下进行.采用Lockhart-Martinelli关联方法对各典型流型下的实验数据进行了整理,结合流动的具体情况对其中的关联参数C进行了重新定义,提出了基于典型流型的压力梯度计算模型,并对水平管内油气两相流的压降变化规律进行了分析和讨论.理论计算值与实验测量值吻合良好.     

BLOOD VISCOELASTICITY FOR CONDITIONS OF PHYSIOLOGICAL FLOW IN SMALL ARTERIES

The viscoelasticity of blood is quantified by studying the oscillatory flow of suspensions of RBC in plasma in 218 μm and 400 μm glass capillary tubes. The flow conditions are chosen to reflect normal physiological flow in small arterial vessels. Data are obtained for suspension hematocrits between 35 and 80 percent, and at physiological temperature (37°C) The results indicate that the elastic component of the viscoelasticity of blood is effectively negligible for the conditions of this study; the measured pressure gradient-flowrate relationship is dominated by the viscous component of blood viscoelasticity.     

BLOOD VISCOELASTICITY FOR CONDITIONS OF PHYSIOLOGICAL FLOW IN SMALL ARTERIES

The viscoelasticity of blood is quantified by studying the oscillatory flow of suspensions of RBC in plasma in 218 μm and 400 μm glass capillary tubes. The flow conditions are chosen to reflect normal physiological flow in small arterial vessels. Data are obtained for suspension hematocrits between 35 and 80 percent, and at physiological temperature (37°C) The results indicate that the elastic component of the viscoelasticity of blood is effectively negligible for the conditions of this study; the measured pressure gradient-flowrate relationship is dominated by the viscous component of blood viscoelasticity.     

A QUASI NEWTONIAN MODEL FOR SIMULATING THE FLOW OF DILUTE POLYMER SOLUTIONS THROUGH A SUDDEN CONTRACTION

The flow of a quasi Newtonian model fluid, which allows shear thinning as well as extension thickening, through a sudden planar 4:1 contraction is studied numerically. Comparing with numerical results for a purely shear thinning fluid differences show up which follow the trend of experimental data.     

THE LOCAL VOLUME-AVERAGED EQUATIONS OF MOTION FOR A SUSPENSION OF NON-NEUTRALLY BUOYANT SPHERES

The local volume averages of the equations of motion as well as the appropriate boundary conditions are developed for a flowing suspension of non-neutrally buoyant, uniform spheres in an incompressible Newtonian fluid under conditions such that inertial effects can be neglected. These equations do not represent an asymptotic theory with respect to the volume fraction of solids. Higher order terms have been retained everywhere, except where it has been necessary to estimate the velocity distribution within the immediate neighborhood of each sphere by neglecting the effects of the other spheres present. The resulting local volume-averaged equations of motion and boundary conditions involve no free or undetermined parameters.

For the special case of a very dilute suspension of neutrally buoyant spheres, the total local volume average of Cauchy's first law reduces to the form of the Navier-Stokes equation with the effective viscosity computed by Einstein (1906, 1956).

In two succeeding papers, we demonstrate for several flows [in vertical tubes, in a cone-plate viscometer, between rotating concentric cylinders (Couette flow), and between rotating parallel plates] that our general theory describes more concentrated neutrally buoyant suspensions than does its limiting case of very dilute suspensions.     

A QUASI NEWTONIAN MODEL FOR SIMULATING THE FLOW OF DILUTE POLYMER SOLUTIONS THROUGH A SUDDEN CONTRACTION

The flow of a quasi Newtonian model fluid, which allows shear thinning as well as extension thickening, through a sudden planar 4:1 contraction is studied numerically. Comparing with numerical results for a purely shear thinning fluid differences show up which follow the trend of experimental data.     

绝热层流泡状流运动的双流体模型

绝热层流泡状流是泡状流研究中的一个基础范例 .目前描述绝热层流泡状流常采用的双流体模型由于相间作用考虑欠缺而适用性差 .本文结合理论和实验研究结果导出了描述壁面“排斥”作用的表达式 ,并建立了一个封闭的双流体模型 .模型预测值和实验值的比较表明 ,由于相间作用的合理考虑 ,扩大了该模型的适用范围     

多通道流动电泳的pH值场模型

建立了描述制备多通道流动电泳pH值分布的理论模型,并进行了计算。结果表明,模型在较大范围内（操作电流20mA～80mA,进样流量1ml·min~(-1)～5ml·min~(-1),蛋白质浓度低于1.0mg·ml~(-1)）与实验值符合得很好。     

A MODEL FOR PULSING FLOW IN COCURRENT DOWN-FLOW TRICKLE-BED REACTORS

Based on macroscopic mass and momentum balances, a model is developed to characterize the hydrodynamic behavior of pulsing flow in cocurrent down-flow trickle-bed reactors. Predictions of the model regarding liquid saturation, length and velocity of both the liquid rich slug and gas rich pulse are reported. Also presented are experimental data of an air-water system for the effects of varying gas and liquid flow rates on pulse frequency, total pulse length and apparent slug velocity. To confirm the theory, predictions are compared with measured overall pressure gradient. Agreement is reasonably good.     

MULTI-SCALE MASS TRANSFER MODEL FOR GAS-SOLID TWO-PHASE FLOW

This article is devoted to analyzing the mass transfer in heterogeneous gas-solid flow by means of structure and process decomposition. A multi-scale mass transfer model was developed on the basis of the hydrodynamics calculated from the so-called EMMS model. This resulted in the predictions of the steady-state two-dimensional concentration distributions of sublimated substance as well as total mass transfer coefficient for circular concurrent gas-solid contactors. The predictions were validated by experimentally measured (via an on-line HP GC-MS system) axial concentration distributions of sublimated naphthalene in air in a circulating fluidized bed riser 3.0 m in height and 72 mm in diameter. The experiment also obtained mass transfer coefficients comparable to theoretical predictions under conditions with various gas velocities, solid circulation rates, particle sizes, and active material fractions in the particles. Both the theoretical and experimental results demonstrated that the heterogeneous flow structure prevailing in the concurrent gas-solid flow greatly influenced the flow's mass transfer.     

MULTI-SCALE MASS TRANSFER MODEL FOR GAS-SOLID TWO-PHASE FLOW

This article is devoted to analyzing the mass transfer in heterogeneous gas-solid flow by means of structure and process decomposition. A multi-scale mass transfer model was developed on the basis of the hydrodynamics calculated from the so-called EMMS model. This resulted in the predictions of the steady-state two-dimensional concentration distributions of sublimated substance as well as total mass transfer coefficient for circular concurrent gas-solid contactors. The predictions were validated by experimentally measured (via an on-line HP GC-MS system) axial concentration distributions of sublimated naphthalene in air in a circulating fluidized bed riser 3.0 m in height and 72 mm in diameter. The experiment also obtained mass transfer coefficients comparable to theoretical predictions under conditions with various gas velocities, solid circulation rates, particle sizes, and active material fractions in the particles. Both the theoretical and experimental results demonstrated that the heterogeneous flow structure prevailing in the concurrent gas-solid flow greatly influenced the flow's mass transfer.     

油气混输管道联合传热模型推导

本文所提出的联合传热模型的管道倾斜范围为-90°到＋90°。联合传热模型所需的参数由Zhang等人提出的气液混输管道联合水动力学模型计算得到。用本模型计算管道内的对流换热系数与实验得到的对流换热系数相一致。     

液固循环流化床两相流动模型

引　言流化床换热器具有防、除垢和强化传热等优点 ,在化工、食品、海水淡化、废水处理等领域具有广阔的应用前景[1].目前 ,流化床换热器历经散式流化床、内循环流化床 ,已发展到外循环流化床换热器[2 ],它要求在较稀的颗粒浓度 (颗粒浓度小于 5% )、较高的流速 ( 1～ 3ｍ·ｓ- 1)下操作 .流化床换热器中液体流动及颗粒运动状态的研究对流化床换热器的设计和操作具有重要意义 ,但人们对循环流化床换热器中颗粒运动情况的研究还很缺乏 .考虑到循环流化床换热器中的每根换热管都可作为一个独立的循环流化床对待[3].本文试图建立一滑移速度模型…     

A PORE NETWORK MODEL FOR THE CALCULATION OF NON-DARCY FLOW COEFFICIENTS IN FLUID FLOW THROUGH POROUS MEDIA

A computational method was developed to determine the correlation between permeability and the Forchheimer (non-Darcy) coefficient and to investigate numerically the factors that affect this correlation. The method is based on the construction of a 2-D random pore network. The porous medium is represented as a network of cylindrical pipes with randomly generated size, orientation, and connectivity. Probability density functions are used to characterize the orientation, length, diameter, and connectivity properties of the pipes that form the pore space. In this article the development and validation of the computational method are discussed. The computational procedure provides an expected value for the medium properties and a variation around this expected value, which is a measure of the uncertainty associated with the calculation of porous media properties. It was found that the porous medium structure has a strong effect on the flow properties. Specifically, the splitting of the pores is mostly responsible for non-Darcy flow behavior. Examination of the behavior of the medium properties under compaction shows that there is a unifying correlation for the behavior of the permeability. However, each type of porous medium exhibits different non-Darcy flow behavior under compaction. Finally, a statistical model, which correlates the structure characteristics of the porous medium to the measured properties, is presented.     

VAPOR-LIQUID FLOW THROUGH SPRING LOADED RELIEF VALVES

The behavior of a relief valve with a short throat has been studied. Measurements of discharge rates when the unit was fed with a two-phase mixture have been made at moderate pressure differentials. These experiments show that the valve behavior is similar to that of an orifice and that flashing does not occur until downstream of the flow restriction. Design techniques which enable valve discharge rates to be computed under these conditions are developed

Other data show that, when fed with a two-phase mixture and subject to high pressure differentials, relief valves with longer throats exhibit critical flow rates close to these preducted by the homogeneous-equilibrium model (HEM). Additional data are needed in order to define the transition between orifice-like and HEM choking behavior.     

气液两相流流经环形狭缝通道的流动特性

引言动力、能源、石油化工等领域中广泛应用着各类管壳式换热器,此类换热器的管子与折流板之间、折流板与壳体之间在制造与装配中存在着一定的间隙。这些间隙对壳侧的压降及换热系数有较大影响。对于单相流体,这些间隙产生的泄漏量可占总流量的15％～60％~［1～4]．根据文献报道~［5],大约有50％以上的管壳式换热器涉及气液两相流,迄今为止对气液两相流体流经环形狭缝通道的流动特性研究尚未见有文献报道．本文在水平放置环形狭缝通道中,对空气一水两相混合物流经3种不同间隙环形狭缝通道的流动特性进行了研究,并应用分相模型提出了计…