A numerical study of pulsatile laminar flows in a pipe with a ring-type constriction

Numerical simulations have been carried out to study pulsatile laminar flows in a pipe with an axisymmetric ringtype constriction. Three types of pulsatile flows were investigated, namely a physiological flow, a pure sinusoidal flow and a non-zero mean velocity sinusoidal flow. The laminar flow governing equations were solved by the SIMPLE algorithm on a non-staggered grid and a modified Crank-Nicolson approximation was used to discretrize the momentum equations with respect to time. The maximum flow Reynolds numer (Re) is 100. The Womersley number (N_w) ranges from 0 to 50, with the corresponding Strouhal number (St) ranging from 0 to 3·98. The constriction opening ratio (d/D) and thickness ratio (h/D) are fixed at 0·5 and 0·1 respectively. Within the time period investigated, all these pulsatile flows include both forward and backward flows. The unsteady recirculation region and the recirculation points change in size and location with time. For N_w ≤ 1 and St≤ 1·56 x 10^?3 the three pulsatile flows have the same simple relation between the instantaneous flow rate and pressure loss (Δp) across the constriction and the pressure gradient in the axial direction (dp/dz) in the fully developed flow region. The phase angles between the flow rate and pressure loss and the pressure gradient are equal to zero. With increasing N_w and St, the phase angle between the flow rate and the dp/dz becomes larger and has its maximum value of 90° at N_w = 50 and St = 3·98. The three pulsatile flows also show different relations between the flow rate and the pressure gradient. The pure sinusoidal flow has the largest maximum pressure gradient and the non-zero mean velocity sinusoidal flow has the smallest. For larger N_w and St the fully developed velocity profiles in the fully developed flow region have a smaller velocity gradient along the radial direction in the central region. The maximum recirculation length increases for N_w ranging from 0 to 4·2, while this length becomes very small at N_w = 50 and St = 3·98. The deceleration tends to enlarge the recirculation region and this effect appears for N_w ≥ 3 and St ≥ 1·43×10^?2. Linear relations exist between the flow rate and the instantaneous maximum values of velocity, vorticity and shear stress.     

Numerical analysis of the transient conjugated heat transfer in a circular duct with a power-law fluid

We treat numerically in this paper, the transient analysis of a conjugated heat transfer process in the thermal entrance region of a circular tube with a fully developed laminar power-law fluid flow. We apply the quasi-steady approximation for the power-law fluid, identifying the suitable time scales of the process. Thus, the energy equation in the fluids is solved analytically using the well-known integral boundary layer technique. This solution is coupled to the transient energy equation for the solid where the transverse and longitudinal heat conduction effects are taken into account. The numerical results for the temporal evolution of the average temperature of the tube wall, _av, is plotted for different nondimensional parameters such as conduction parameter, , the aspect ratios of the tube, and ₀ and the index of power-law fluid, n.     

CALCULATION OF STEADY AND OSCILLATING FLOWS IN TUBES USING A VORTICITY TRANSPORT ALGORITHM

Steady and oscillating axisymmetric tube flows are modelled using a vorticity transport algorithm. The axisymmetric convective –diffusive Navier–Stokes equations are solved using a splitting technique. Axisymmetric ring vortex filaments are introduced on the walls and subsequently convected and diffused throughout the flow field. An axisymmetric equation similar to the Oseen diffusion equation is used to diffuse the ring vortex filaments. Vorticity is reflected from the tube walls using two techniques. Results are presented for the developing Poiseuille flow and for the developed flow in the form of the entrance length and the axial velocity and vorticity profiles. Good agreement is achieved with a finite difference method in the developing region of Poiseuille flow. The developed flow results are compared with the analytical solutions. The developed profiles of velocity and vorticity have errors of less than 0ċ3 per cent for both methods of dealing with reflection of diffusion at the bounding surfaces and similar accuracy is obtained for the velocity profiles in oscillating flow except at the wall. Oscillating flow is produced with a discretized sinusoidal piston motion. Velocity profiles, boundary layer thickness and entrance length are presented for oscillating flow. Good agreement is achieved for low-Womersley-number non-dimensional frequency. At higher values of this parameter, flows are inaccurately simulated, because the number of piston positions used to discretize the piston motion is inversely proportional to the non-dimensional frequency.     

Conjugated laminar forced convection in ducts with periodic variation of inlet temperature

Conjugated laminar forced convection with parabolic velocity is studied for flow inside both parallel-plate and circular ducts subjected to a periodically varying inlet temperature. The analysis of this classs of problems lead to a Sturm-Liouville type complex eigenvalue problem for which no known solution is available. In this work, a new methodology is presented for a direct solution of such complex eigenvalue problems in the complex domain using the shooting method along with the Runge-Kutta method. The methodology is applicable for solving both laminar and turbulent flow problems; here we consider only the laminar flow with a parabolic velocity profile. The results clearly show that the slug-flow assumption overestimates the phase lag and the Nusselt number. Some benchmark results are also presented for the eigenquantities in tabular form.     

Maxwell流体管内起动流的研究

对Maxwell流体管内起动流的振荡特性进行研究,得到了描述振荡特性的解析解,研究了黏弹性参数对各时刻速度剖面的影响,获得了轴心速度、平均速度和壁面摩擦力随时间的变化规律以及它们的频率特征. 结果表明振荡的基频成分决定了流动的主要特性,给出并分析了基频频率与振幅和黏弹性参数之间的关系.     

Measurements of pulsating and oscillating flows of non-Newtonian fluids through concentric and eccentric cylinders

The unsteady flow of non-Newtonian fluids through concentric and eccentric cylinders was investigated experimentally. Two experiments were carried out; one was pulsating flow and the other was flow under a constant pressure gradient with the inner cylinder oscillating longitudinally. The flow enhancement was examined and its dependence on the frequency of the oscillations and the eccentricity of the apparatus was determined.     

基于分形导数对非牛顿流体层流的数值研究

非牛顿流体具有复杂的流变特性,揭示该流变特性可以更加合理地指导非牛顿流体在工农业生产中的应用.经典的非牛顿流体本构模型往往形式复杂,仅能应用于某些特定的情况.分数阶导数模型具有参数少和形式简单的特点,己成功地应用于描述非牛顿流体的运动.Hausdorff分形导数作为一个备选的建模方法,相比分数阶导数具有更简单的形式以及更高的计算效率.本文基于Hausdorff分形导数改进现有牛顿黏性模型,提出分形黏壶模型.通过研究分形黏壶在常应变率下表观黏度的变化情况,以及在加、卸载条件下的蠕变及恢复特性,发现分形黏壶模型适合于描述具有黏弹性的非牛顿流体(本文称之为分形流体).结合连续性方程及运动微分方程,推导出分形流体在平行板间层流的基本方程.按是否拖动上板和是否存在水平的压力梯度分为3种工况,分别用数值方法计算这3种工况下流速在板间的分布及其随时间变化的情况.通过分析不同工况下的流速分布,发现水平的压力梯度会改变流速随时间变化的形状,且会推迟流速到达稳定的时间.在水平压力梯度不存在的情况下,不同阶数的分形流体具有相同的流速分布或是演变过程.另外,在水平压力梯度存在的情况下,上板速度不影响不同阶数分形流体间稳定速度的差值.     

Laminar shear flow of plastic viscoelastic fluids

Summary The theory of plastic viscoelastic fluids was developed by the author to represent the rheological behavior of polymer melts and solutions with high loading of small particles. The present paper develops an asymptotic formulation of the general theory which applies to laminar shear flows. The formulation is analogous to Criminale, Ericksen and Filbey's theory for viscoelastic fluids. We apply this to study plane Poiseuille and Couette flow.With 2 tables     

幂律流体两平行圆板间径向扩散层流进口段流动阻力的分析

在文献￣［２,３］的基础上,将其方法推广到幂律流体流动,首先导出幂律流体两平行圆板间径向扩散层流边界层的动量积分方程和能量积分方程。通过对动量积分方程的求解,对幂律流体的进口段长度以及进口段效应压力损失和流量修正系数进行了分析计算,并且讨论了幂律流体的流动指数ｎ与进口处修正雷诺数Ｒｅ＿１对进口段长度和压力损失系数的影响。特别是当ｎ＝１时,本文的解与文献￣［３］中的解完全一致,因而间接验证了本文结果的可靠性。     

幂率流体圆管非定常流动的数值分析

本文讨论水平圆管中幂率流体的起动问题。用显式和隐式两种格式,我们得到了问题的数值解并从而得到流动建立时间的近似公式。     

振荡管流换热的理论解

本文从流体在管内振荡的运动方程和流体及管壁的能量方程出发,经过变量转换对常微分方程组进行求解,得到了计及管壁影响的振荡流体轴向换热的一般理论解。由这解,可以导出各种特殊条件下的表达式,包括已有的各种解析解。本解经数字化而制成各种图线,它们与已有的实验数据基本吻合。     

Effect of the pattern of initial perturbations on the steady pipe flow regime

The influence of the inlet flow formation mode on the steady flow regime in a circular pipe has been investigated experimentally. For a given inlet flow formation mode the Reynolds number Re* at which the transition from laminar to turbulent steady flow occurred was determined. With decrease in the Reynolds number the difference between the resistance coefficients for laminar and turbulent flows decreases. At a Reynolds number approximately equal to 1000 the resistance coefficients calculated from the Hagen-Poiseuille formula for laminar steady flow and from the Prandtl formula for turbulent steady flow are equal. Therefore, we may assume that at Re > 1000 steady pipe flow can only be laminar and in this case it is meaningless to speak of a transition from one steady pipe flow regime to the other. The previously published results [1–9] show that the Reynolds number at which laminar goes over into turbulent steady flow decreases with increase in the intensity of the inlet pulsations. However, at the highest inlet pulsation intensities realized experimentally, turbulent flow was observed only at Reynolds numbers higher than a certain value, which in different experiments varied over the range 1900–2320 [10]. In spite of this scatter, it has been assumed that in the experiments a so-called lower critical Reynolds number was determined, such that at higher Reynolds numbers turbulent flow can be observed and at lower Reynolds numbers for any inlet perturbations only steady laminar flow can be realized. In contrast to the lower critical Reynolds number, the Re* values obtained in the present study, were determined for given (not arbitrary) inlet flow formation modes. In this study, it is experimentally shown that the Re* values depend not only on the pipe inlet pulsation intensity but also on the pulsation flow pattern. This result suggests that in the previous experiments the Re* values were determined and that their scatter is related with the different pulsation flow patterns at the pipe inlet. The experimental data so far obtained are insufficient either to determine the lower critical Reynolds number or even to assert that this number exists for a pipe at all.