动脉局部狭窄时脉动流的有限元分析

本文利用有限元方法研究动脉局部狭窄下的脉动流流场,重点考查在50％与80％面积狭窄下的速度分布、压力分布、壁面剪应力分布及流动分离情况。几何形状及边界条件均模拟相应的脉动流实验模型。采用测得的随时间变化的速度分布作为入口端条件,并利用罚函数和逆风格式等计算技巧得出了光滑的与实验基本相符的速度、压力波形。本文讨论了不同狭窄下速度、压力、壁面剪应力的分布形态,给出了脉动流中狭窄处局部流动分离的间歇性变化规律,并结合实验与临床应用进行了讨论。     

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。     

Electrohydrodynamic peristaltic flow of a viscoelastic Oldroyd fluid with a mild stenosis: Application of an endoscope

The effect of a vertical alternating current, electric field, and heat transfer on a peristaltic flow of a dielectric viscoelastic Oldroyd fluid is studied. This analysis involves uniform and nonuniform annuli having a mild stenosis. The analytical solutions of equations of motion are based on the perturbation technique. This technique depends on two parameters: amplitude ratio and small wave number. Numerical calculations are performed to obtain the effects of several parameters, such as the electrical Rayleigh number, temperature gradient, Reynolds number, wave number, maximum height of stenosis, and Weissenberg numbers, on the distributions of velocity, temperature, electric potential, and wall shear stress. It is found that the above-mentioned distributions in the case of a convergent tapered tube are larger than those in the case of a non-tapered one as well as a diverging tapered tube.     

Numerical simulation of turbulent flow through series stenoses

The flow fields in the neighbourhoods of series vascular stenoses are studied numerically for the Reynolds numbers from 100 to 4000, diameter constriction ratios of 0.2–0.6 and spacing ratios of 1, 2, 3, 4 and ∞. In this study, it has been further verified that in the laminar flow region, the numerical predictions by k–ω turbulence model matched those by the laminar‐flow modelling very well. This suggests that the k–ω turbulence model is capable of the prediction of the laminar flow as well as the prediction of the turbulent stenotic flow with good accuracy. The extent of the spreading of the recirculation region from the first stenosis and its effects on the flow field downstream of the second stenosis depend on the stenosis spacing ratio, constriction ratio and the Reynolds number. For c₁ = 0.5 with c₂ ≤ c₁, the peak value of wall vorticity generated by the second stenosis is always less than that generated by the first stenosis. However, the maximum centreline velocity and turbulence intensity at the second stenosis are higher than those at the first stenosis. In contrast, for c₁ = 0.5 with c₂ = 0.6, the maximum values at the second stenosis are much higher than those at the first stenosis whether for centreline velocity and turbulence intensity or for wall vorticity. The peak values of the wall vorticity and the centreline disturbance intensity both grow up with the Reynolds number increasing. The present study shows that the more stenoses can result in a lower critical Reynolds number that means an earlier occurrence of turbulence for the stenotic flows. Copyright © 2003 John Wiley & Sons, Ltd.     

Peristaltic flow of Johnson-Segalman fluid in asymmetric channel with convective boundary conditions

This work is concerned with the peristaltic transport of the Johnson-Segalman fluid in an asymmetric channel with convective boundary conditions. The mathematical modeling is based upon the conservation laws of mass, linear momentum, and energy. The resulting equations are solved after long wavelength and low Reynolds number are used. The results for the axial pressure gradient, velocity, and temperature profiles are obtained for small Weissenberg number. The expressions of the pressure gra-dient, velocity, and temperature are analyzed for various embedded parameters. Pumping and trapping phenomena are also explored.     

The effect of Reynolds number on boundary layer turbulence

A new facility for studying high Reynolds number incompressible turbulent boundary layer flows has been constructed. It consists of a moderately sized wind tunnel, completely enclosed by a pressure vessel, which can raise the ambient air pressure in and around the wind tunnel to 8 atmospheres. This results in a Reynolds number range of about 20:1, while maintaining incompressible flow. Results are presented for the zero pressure gradient flat plate boundary layer over a momentum thickness Reynolds number range 1500–15?000. Scaling issues for high Reynolds number non-equilibrium boundary layers are discussed, with data comparing the three-dimensional turbulent boundary layer flow over a swept bump at Reynolds numbers of 3800 and 8600. It is found that successful prediction of these types of flows must include length scales which do not scale on Reynolds number, but are inherent to the geometry of the flow.     

Peristaltic transport of a Jeffrey fluid under the effect of magnetic field in an asymmetric channel

The peristaltic flow of a Jeffrey fluid in an asymmetric channel is studied under long wavelength and low Reynolds number assumptions. The fluid is electrically conducting by a transverse magnetic field. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phase. The flow is investigated in a wave frame of reference moving with the velocity of the wave. The expressions for stream function, axial velocity and axial pressure gradient have been obtained. The effects of various emerging parameters on the flow characteristics are shown and discussed with the help of graphs. The pumping characteristics, axial pressure gradient and trapping phenomenon have been studied. Comparison of various wave forms (namely sinusoidal, triangular, square and trapezoidal) on the flow is discussed.     

Noise Field in the Human Chest Due to Turbulent Flow in a Larger Blood Vessel

An acoustic model of a larger human blood vessel is developed. This model takes into account the main features of the acoustic generation and propagation of noise in the human chest from the source (turbulent pressure fluctuations in blood flow) to a receiver resting on the skin, and allows the consideration of a simple stenotic narrowing in the vessel. The low Mach number turbulent wall pressure models of Corcos, Chase, Ffowcs Williams, and Smol'yakov and Tkachenko are used to describe random sources in the vessel. The relationships obtained permit one to analyse the dependence of the resultant acoustic field in the thorax on the parameters of the blood flow and the vessel, and show the possibility of finding characteristic signs of the presence of a stenosis by comparison of noise fields from intact and diseased arteries. This revised version was published online in July 2006 with corrections to the Cover Date.     

Axial static pressure measurements of water flow in a rectangular microchannel

An experimental investigation of water flow through an aluminum rectangular microchannel with a hydraulic diameter of 169 μm was conducted over a Reynolds number (based upon mean velocity and hydraulic diameter) range from 230 to 4,740. Pressure measurements were simultaneously acquired at eight different axial locations within the channel along with pressure measurements in the inlet and outlet ports. The 27 μm pressure taps were more densely packed near the channel entrance in order to study the developing flow region. The average Poiseuille number for laminar flows was 86.4, which is in excellent agreement with the theoretical value of 86.9. The average critical Reynolds number was found to be 2,370. The limited turbulent friction factor data were in good agreement with the Haaland equation. The inlet to the channel was not well rounded and pressure distributions near the channel entrance show a region of pressure recovery. Entrance length and some minor loss coefficient data were not in agreement with theory, but the cause of these deviations were primarily a function of the inlet geometry and pressure recovery in the microchannel rather than a microscale effect.     

A two-phase model for laminar film condensation from steam-air mixtures in vertical parallel-plate channels

Detailed results are presented for laminar film condensation from steam-air mixtures flowing downward in vertical flat-plate channels. The mixture flow is laminar and saturation conditions prevail at the inlet. A fully coupled implicit numerical approach is used that achieves excellent convergence behavior, even for high inlet gas mass fractions. The detailed results include velocity, temperature, and gas mass fraction profiles, as well as axial variations of film thickness, pressure gradient and Nusselt number. The effects of a wide range of changes in the four independent variables (the inlet-to-wall temperature difference and the inlet values of gas concentration, Reynolds number, and pressure) on the film thickness, axial pressure gradient, and the local and average Nusselt numbers are carefully examined. It was found that increases in inlet concentration of noncondensable gas caused significant decreases in the film thickness, local Nusselt number, and axial pressure gradient. An analytical solution for the film thickness and velocity field at the end of condensation path was developed and shown to be the asymptotic value of the numerical results for large distances along the channel.     

Electrokinetic flow and energy conversion in a curved microtube

Curved channels are ubiquitous in microfluidic systems. The pressuredriven electrokinetic flow and energy conversion in a curved microtube are investigated analytically by using a perturbation analysis method under the assumptions of the small curvature ratio and the Reynolds number. The results indicate that the curvature of the microtube leads to a skewed pattern in the distribution of the electrical double layer (EDL) potential. The EDL potential at the outer side of the bend is larger than that at the inner side of the bend. The curvature shows an inhibitory effect on the magnitude of the streaming potential field induced by the pressure-driven flow. Since the spanwise pressure gradient is dominant over the inertial force, the resulting axial velocity profile is skewed into the inner region of the curved channel. Furthermore, the flow rate in a curved microtube could be larger than that in a straight one with the same pressure gradient and shape of cross section. The asymptotic solutions of the axial velocity and flow rate in the absence of the electrokinetic effect are in agreement with the classical results for low Reynolds number flows. Remarkably, the curved geometry could be beneficial to improving the electrokinetic energy conversion (EKEC) efficiency.     

Behavior of shock trains in a diverging duct

A shock train inside a diverging duct is analyzed at different pressure levels and Mach numbers. Nonreactive pressurized cold gas is used as fluid. The structure and pressure recovery inside the shock train is analyzed by means of wall pressure measurements, Schlieren images and total pressure probes. During the course of the experiments, the total pressure of the flow, the back pressure level and the Mach number upstream of the compression region have been varied. It is shown that the Reynolds number has some small effect on the shock position and length of the shock train. However, more dominant is the effect of the confinement level and Mach number. The results are compared with analytical and empirical models from the literature. It was found that the empirical pseudo-shock model from Billig and the analytical mass averaging model from Matsuo are suitable to compute the pressure gradient along the shock train and total pressure loss, respectively.     

Study of laminar–turbulent flow transition under pulsatile conditions in a constricted channel

In this paper, direct numerical simulation is performed to investigate a pulsatile flow in a constricted channel to gain physical insights into laminar–turbulent–laminar flow transitions. An in-house computer code is used to conduct numerical simulations based on available high-performance shared memory parallel computing facilities. The Womersley number tested is fixed to 10.5 and the Reynolds number varies from 500 to 2000. The influences of the degree of stenosis and pulsatile conditions on flow transitions and structures are investigated. In the region upstream of the stenosis, the flow pattern is primarily laminar. Immediately after the stenosis, the flow recirculates under an adverse streamwise pressure gradient, and the flow pattern transitions from laminar to turbulent. In the region far downstream of the stenosis, the flow becomes re-laminarised. The physical characteristics of the flow field have been thoroughly analysed in terms of the mean streamwise velocity, turbulence kinetic energy, viscous wall shear stresses, wall pressure and turbulence kinetic energy spectra.     

Riblet modelling using a second-moment closure

A low Reynolds number second-moment closure has been used to calculate a turbulent boundary layer which develops over a riblet surface with zero pressure gradient. The calculated mean velocity distributions compare favourably with measurements. Calculated Reynolds stresses away from the riblet surface region are also in agreement with measurements. In the vicinity of the riblets, the model reflects the increased anisotropy of the Reynolds stress tensor inadequately. Possible reasons for this shortcoming are discussed and suggestions for improving the model are made.     

Numerical solution of oscillatory flow of Maxwell fluid in a rectangular straight duct

A numerical analysis is presented for the oscillatory flow of Maxwell fluid in a rectangular straight duct subjected to a simple harmonic periodic pressure gradient.The numerical solutions are obtained by a finite difference scheme method. The stability of this finite difference scheme method is discussed. The distributions of the velocity and phase difference are given numerically and graphically. The effects of the Reynolds number, relaxation time, and aspect ratio of the cross section on the oscillatory flow are investigated. The results show that when the relaxation time of the Maxwell model and the Reynolds number increase, the resonance phenomena for the distributions of the velocity and phase difference enhance.     

Hydrodynamic and heat transfer characteristics of laminar flow past a parabolic cylinder with constant heat flux

 Steady, two-dimensional, symmetric, laminar and incompressible flow past parabolic bodies in a uniform stream with constant heat flux is investigated numerically. The full Navier–Stokes and energy equations in parabolic coordinates with stream function, vorticity and temperature as dependent variables were solved. These equations were solved using a second order accurate finite difference scheme on a non-uniform grid. The leading edge region was part of the solution domain. Wide range of Reynolds number (based on the nose radius of curvature) was covered for different values of Prandtl number. The flow past a semi-infinite flat plate was obtained when Reynolds number is set equal to zero. Results are presented for pressure and temperature distributions. Also local and average skin friction and Nusselt number distributions are presented. The effect of both Reynolds number and Prandtl number on the local and average Nusselt number is also presented. Received on 5 July 2000     

Modeling low Reynolds number incompressible flows with curved boundaries using SPH

In this paper, a method that can be used to model low Reynolds number incompressible flows with curved boundaries using SPH was presented. In contrast to that usually used for the flows with flat and straight boundaries, the hydrostatic pressure gradient is treated as a variable body force in this method, and thus, it can be applied to simulate the flows with curved boundaries. Three numerical examples of low Reynolds number incompressible flows, including Poiseuille flow, flow in a section of blood vessel with a local expansion, and flow between inclined plates were calculated to test the method. The results obtained with the proposed method were in good agreement with the analytical solutions. It implies that the method presented in this paper can be successfully used to simulate low Reynolds number incompressible flows not only with flat and straight boundaries but also with curved boundaries. Copyright © 2011 John Wiley & Sons, Ltd.     

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.

     

An experimental study into the effects of streamwise and spanwise acceleration in a turbulent boundary layer

We compare two turbulent boundary layers produced in a low-speed water channel experiment. Both are subjected to an identical streamwise pressure gradient generated via a lateral contraction of the channel, and an additional spanwise pressure gradient is imposed on one of the layers by curving the contraction walls. Despite a relatively high streamwise acceleration, hot-film probe measurements of the mean-velocity distributions show that the Reynolds number increases whilst the coefficient of friction decreases downstream. Visualization of the viscous layers using hydrogen bubbles reveal an increase in the non-dimensional streak spacing in response to the acceleration. Changes in statistical moments of the streamwise velocity near the wall suggest an increased dominance of high-velocity fluctuations. The near-wall streaks and velocity statistics have little sensitivity to the boundary layer three-dimensionality induced by the spanwise pressure gradient, with the boundary-layer crossflow velocity reaching 11 % that of the local freestream velocity.     

Laminar heat transfer characteristics of internally finned tube with sinusoidal wavy fin

Comparative numerical study of laminar heat transfer characteristics of annular tubes with sinusoidal wavy fins has been conducted both experimentally and numerically with Re = 299–1,475. The uniform heat flux is imposed on the tube outside wall surface. Two tube materials (copper and stainless steel) are considered. It is found that the fluid temperature profile is not linear but convex along the flow direction due to the axial heat conduction in tube wall, and the effects of axial heat conduction on the heat transfer decreases with an increase in Reynolds number or decrease in tube wall thermal conductivity. The axial distributions of local Nusselt number could reach periodically fully developed after 3–5 cycles. The convectional data reduction method based on the traditional method should be improved for tube with high thermal conductivity or low Reynolds numbers, Otherwise, the heat transfer performance of internally finned tube may be underestimated.