Euler–Lagrange equations governing the flow of solids by extended slip with applications to plane torsion

The paper presents a variational principle based on a new physical law governing the rotationally continuous flow of a solid that flows by means of the recently identified mechanism of extended slip. The Euler–Lagrange equations derived from this principle are applied to the plane torsion problem. Theoretical results so obtained are compared to experimental measurements made using discs of cold-worked aluminium, and excellent agreement between experiment and theory is obtained. Interesting properties of plane torsion are revealed by this investigation. It is shown, for instance, that within the shear annulus in the disc, at each stage of its expansion, the rotation rate is independent of position. Moreover, if we consider the disc centre to be rotating relative to its edge, the rotation rate in the shear annulus is opposite to that in the rigid centre of the disc. At each stage, not only are the senses of rotation of the disc centre and the shear annulus opposite but the products of rotation rate and area for the two domains remain equal.     

中医滚法推拿对血液流动影响的数值研究

研究了中医滚法推拿的血液动力学机制．用狭窄轴向运动来模拟滚法推拿,通过轴对称非线性模型和含网格重分算法的任意欧拉-拉格朗日有限元方法研究狭窄轴向运动的轴对称刚性管中的粘性流动．流量和管壁切应力通过数值求解Navier-Stokes方程得到．数值结果表明,狭窄运动的频率,也就是滚法推拿的频率对流量和管壁切应力有很大的扰动作用．滚法推拿中另一个可变参数——刻划狭窄严重程度的狭窄度,对流量和管壁切应力同样表现出显著影响．这些数值结果可以为推拿的临床应用提供一些值得参考的数据．     

纤维悬浮剪切湍流中纤维旋转扩散系数的理论研究

对纤维悬浮剪切湍流中纤维旋转扩散系数进行了理论研究．首先建立了流场不同脉动速度梯度间的相关矩函数,然后推导出了纤维旋转扩散系数的表达式,该表达式依赖于特征长度、时间、速度和一个与壁面作用相关的无量纲参数．得到的纤维旋转扩散系数可以应用于非均匀和非各向同性的湍流场,此外还可以推广到三维湍流场,因而为纤维悬浮湍流场的研究提供了理论基础．     

Computational modelling of slug flow in a capillary microreactor

The benefits of slug flow capillary microreactor exhibit the ability to adjust two individual transport mechanisms, i.e., convection inside the slug and diffusion between two consecutive slugs. The mass transfer rate is enhanced by internal circulation, which arises due to the shear between slug axis and continuous phase or capillary wall. The knowledge of circulation patterns within the slug plays an important role in the design of a capillary microreactor. Apart from this, well defined slug flow generation is a key activity in the development of methodology to study hydrodynamics and mass transfer. In the present paper we discuss computational fluid dynamics (CFD) modelling aspects of internal circulations (single phase) and slug flow generation (two-phase).     

Dynamic deformation of a stationary rubber flow

The effect of dynamic deformation on the stationary flow of a rubber composition has been experimentally investigated for comparable values of the stationary and dynamic strain rates. The dependence of the effective viscosity on the stationary shear rate is not equivalent to its dependence on the periodic shear rate amplitude. An expression is given for calculating the effective viscosity in the case of combined stationary and dynamic shear deformation. The effectiveness of the dynamic deformation, estimated in terms of the effective viscosity, depends on whether it is superimposed on the stationary flow at constant stationary shear rate or at constant stress. It is proposed to estimate the effectiveness of dynamic deformation of a stationary non-Newtonian flow in terms of the change in the power of the stationary forces. When the effective viscosity is reduced by dynamic deformation of the stationary flow, the power of the stationary forces increases at constant shear stress and falls at constant stationary shear rate.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 489–496, May–June, 1971.     

弹性动脉血管中血液流动特性的模拟和分析

研究了两个不同的非牛顿血液流动模型:低粘性剪切简单幂律模型和低粘性剪切及粘弹性振荡流的广义Maxwell模型．同时利用这两个非牛顿模型和牛顿模型,研究了磁场中刚性和弹性直血管中血液的正弦型脉动．在生理学条件下,大动脉中血液的弹性对其流动性态似乎并不产生影响,单纯低粘性剪切模型可以逼真地模拟这种血液流动．利用高剪切幂律模型模拟弹性血管中的正弦型脉动流,发现在同一压力梯度下,与牛顿流体相比较,幂律流体的平均流率和流率变化幅度都更小．控制方程用Crank-Niclson方法求解．弹性动脉中血液受磁场作用是产生此结果的直观原因．在主动脉生物流的模拟中,与牛顿流体模型比较,发现在匹配流率曲线上,幂律模型的平均壁面剪切应力增大,峰值壁面剪切应力减小．讨论了弹性血管横切磁场时的血液流动,评估了血管形状和表面不规则等因素的影响．     

Micro diffuser flow modeling for cold gas propulsion systems

The use of highly diluted and hypersonic gas flow is in the scope of application of cold gas thrusters for space applications. Satellites and small spacecrafts are navigated to their orbital trajectory with these nozzles. Inside these propulsion systems high density gradients are dominating the efficiency and the thrust steering behavior of the propulsion systems. Micro flows in the transient regime between free molecular flow and continuous flow are not able to be computed with trustworthy results by using a continuous model with no-slip boundary conditions. Therefore boundary slip-velocity models are used for modeling the reduced wall shear stress. Molecular shear stresses decrease the molecular mean velocity near the wall. With a Knudsen number depending slip-velocity model the effective shear stress is computed by the mean gradient of the velocity profile near the wall. In the present study a trans-sonic nozzle flow is computed by using a calibrated velocity slip model what depends on the Knudsen number. The Knudsen numbers are lower the Kn=1 at the nozzle neck of the propulsion system. The results are compared with simulation results of a uniform channel flow and computations of the corresponding no-slip approach. The differences in the hypersonic region are following discussed. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

壁面效应对剪切稀化流体内气泡上浮特性的影响

数值研究了壁面效应对剪切稀化流体内气泡上浮运动特性的影响,气液两相的界面捕捉采用流体体积(VOF)法,剪切稀化流体流变特性和气液相间表面张力的计算分别采用Carreau模型和连续表面张力模型.详细研究了不同流变指数下,壁面效应对气泡形状、液相流场和气泡终端速度的影响.结果表明,强的壁面效应或弱的剪切稀化程度会限制气泡的变形和尾涡的形成,使气泡的终端速度减小;气泡终端速度最易受壁面效应的影响;强的壁面效应和强的剪切稀化程度会导致高剪切速率区域出现在壁面附近,引起壁面附近液相表观黏度大幅度的下降.     

Modelling breakup process of a liquid drop in shear flow

The aim of this paper is to give a contribution within the mathematical modelling of the deformation and breakup of a droplet in a continuous immiscible liquid phase in impulsively started shear flow. Starting from the results of Cristini et al. [V. Cristini, S. Guido, A. Alfani, J. Blawzdziewicz, M. Loewenberg, Drop breakup and fragment distribution in shear flow, J. Rheol. 47 (5) (2003) 1283–1298] we extrapolate a general scheme for the whole breakage process, on the basis of which we formulate a procedure for the computation of the size distribution function at the end of the process.     

Optimization of the injection molding process for short-fiber-reinforced composites

A fast and effective methodology integrating the finite-element and Taguchi methods is presented to determine the optimal design conditions of the injection molding process for short-fiber-reinforced polycarbonate composites. The finite-element-based flow simulation software, M-flow, was employed to simulate the molding process to obtain the fiber orientation distributions required. The Taguchi optimization technique was used to identify the optimal settings of injection molding parameters to maximize the shear layer thickness. The effects of four main parameters — the filling time, melt temperature, mold temperature, and injection speed — on the fiber orientation or the shear layer thickness were investigated and discussed. It is found that the dominant parameter is the filling time. The best levels of the four parameters to acquire the thickest shear layer are also identified.     

Mathematical modeling of turbulent fiber suspension and successive iteration solution in the channel flow

The modified Reynolds mean motion equation of turbulent fiber suspension and the equation of probability distribution function for mean fiber orientation are firstly derived. A new successive iteration method is developed to calculate the mean orientation distribution of fiber, and the mean and fluctuation-correlated quantities of suspension in a turbulent channel flow. The derived equations and successive iteration method are verified by comparing the computational results with the experimental ones. The obtained results show that the flow rate of the fiber suspension is large under the same pressure drop in comparison with the rate of Newtonian fluid in the absence of fiber suspension. Fibers play a significant role in the drag reduction. The amount of drag reduction augments with increasing of the fiber mass concentration. The relative turbulent intensity and the Reynolds stress in the fiber suspension are smaller than those in the Newtonian flow, which illustrates that the fibers have an effect on suppressing the turbulence. The amount of suppression is also directly proportional to the fiber mass concentration.     

Imperfect interface effect for nano-composites accounting for fiber section shape under antiplane shear

This paper investigates the elastic responses of fibrous nano-composites with imperfectly bonded interface under longitudinal shear. The proposed imperfect interface model is the shear lag (or the spring layer) model; the presented nano interfacial stress model is the Gurtin–Murdoch surface/interface model; and the three-phase confocal elliptical cylinder model is the geometry model accounting for the fiber section shape. By virtue of the complex variable method, a generalized self-consistent method is employed to derive the closed from solution of the effective antiplane shear modulus of the fibrous nano-composites with imperfect interface. Five existing solutions can be regarded as the limit form the present analytic expression. The influences of the interface elastic constant, the interfacial imperfection parameter, the size of the elliptic section fiber, the fiber section aspect ratio, the fiber volume fraction and the fiber elastic property on the effective antiplane shear modulus of the nano-composites are discussed. Particularly, numerical results demonstrate that the interfacial elastic imperfection will always cause a significant reduction in the effective antiplane shear modulus; and the fiber interface stress effect on the effective modulus of the fibrous nano-composites will weaken with the interfacial imperfection increases.     

Instability of power-law fluid flows down an incline subjected to wind stress

In this paper we investigate the effect of a prescribed superficial shear stress on the generation and structure of roll waves developing from infinitesimal disturbances on the surface of a power-law fluid layer flowing down an incline. The unsteady equations of motion are depth integrated according to the von Kármán momentum integral method to obtain a non-homogeneous system of nonlinear hyperbolic conservation laws governing the average flow rate and the thickness of the fluid layer. By conducting a linear stability analysis we obtain an analytical formula for the critical conditions for the onset of instability of a uniform and steady flow in terms of the prescribed surface shear stress. A nonlinear analysis is performed by numerically calculating the nonlinear evolution of a perturbed flow. The calculation is carried out using a high-resolution finite volume scheme. The source term is handled by implementing the quasi-steady wave propagation algorithm. Conclusions are drawn regarding the effect of the applied surface shear stress parameter and flow conditions on the development and characteristics of the roll waves arising from the instability. For a Newtonian flow subjected to a prescribed superficial shear stress, using an analytical theory, we show that the nonlinear governing equations do not admit roll waves solutions under conditions when the uniform and steady flow is linearly stable. For the case of a general power-law fluid flow with zero shear stress applied at the surface, the analytical investigation leads to a procedure for calculating the characteristics of a roll waves flow. These results are compared with those yielded by the numerical procedure.     

Mathematical modeling of pulsatile flow of non-Newtonian fluid in stenosed arteries

The pulsatile flow of blood through mild stenosed artery is studied. The effects of pulsatility, stenosis and non-Newtonian behavior of blood, treating the blood as Herschel–Bulkley fluid, are simultaneously considered. A perturbation method is used to analyze the flow. The expressions for the shear stress, velocity, flow rate, wall shear stress, longitudinal impedance and the plug core radius have been obtained. The variations of these flow quantities with different parameters of the fluid have been analyzed. It is found that, the plug core radius, pressure drop and wall shear stress increase with the increase of yield stress or the stenosis height. The velocity and the wall shear stress increase considerably with the increase in the amplitude of the pressure drop. It is clear that for a given value of stenosis height and for the increasing values of the stenosis shape parameter from 3 to 6, there is a sharp increase in the impedance of the flow and also the plots are skewed to the right-hand side. It is observed that the estimates of the increase in the longitudinal impedance increase with the increase of the axial distance or with the increase of the stenosis height. The present study also brings out the effects of asymmetric of the stenosis on the flow quantities.     

Numerical computation of pulsatile flow through a locally constricted channel

This paper deals with the numerical solution of a pulsatile laminar flow through a locally constricted channel. A finite difference technique has been employed to solve the governing equations. The effects of the flow parameters such as Reynolds number, flow pulsation in terms of Strouhal number, constriction height and length on the flow behaviour have been studied. It is found that the peak value of the wall shear stress has significantly changed with the variation of Reynolds numbers and constriction heights. It is also noted that the Strouhal number and constriction length have little effect on the peak value of the wall shear stress. The flow computation reveals that the peak value of the wall shear stress at maximum flow rate time in pulsatile flow situation is much larger than that due to steady flow. The constriction and the flow pulsation produce flow disturbances at the vicinity of the constriction of the channel in the downstream direction.     

Simulation of bed load transport in turbulent open channel flow

The paper reports on direct numerical simulations of a particle-laden open channel flow carried out to investigate the interaction between the dispersed and the continuous phase. The dispersed phase is represented by an immersed boundary method. The particle-particle collisions are accounted for by a physically motivated collision model. Two cases, one with shear stress below the threshold of mobilization and the other with shear stress above the threshold are considered. The different density ratios lead to different types of modification of the flow field by the formation of density-specific patterns of the particles. Light particles do not attain resting states but saltate evenly distributed in span-wise direction. Heavy particles tend to form stream-wise clusters of inactive particles. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Sinai–Bowen–Ruelle Measures on Horocycles of 3-D Anosov Flows

Let ^t be a topologically mixing Anosov flow on a 3-D compact manifold M. Every unstable fiber (horocycle) of such a flow is dense in M. Sinai proved in 1992 that the one-dimensional SBR measures on long segments of unstable fibers converge uniformly to the SBR measure of the flow. We establish an explicit bound on the rate of convergence in terms of integrals of Hölder continuous functions on M.     

An extension of Banerjee and Rahim's model for economic design of moving average control chart for a continuous flow process

In this paper, we propose a model of a moving average control chart (MA control chart) with a Weibull failure mechanism from an economic viewpoint. When the process-failure mechanism follows a Weibull model or other models having increasing hazard rates, it is desirable to have the decreasing sampling interval with the age of the system. The MA control chart is used to monitor quality characteristics of raw material or products in a continuous process. A cost model utilizing a variable scheme instead of fixed sampling lengths in a continuous flow process is studied in this research. The variable sampling scheme is used to maintain a constant integrated hazard rate over each sampling interval. Optimal values for the design parameter, the moving subgroup size, the sampling interval, and the control limit coefficient are determined by minimizing the loss-cost model. The performance of the loss cost with various Weibull parameters is studied. A sensitivity analysis shows that the design parameters and loss cost depend on the model parameters and shift amounts.     

Flow characteristics of filled rubber compounds

It is shown that carbon-black extended rubber compounds are characterized by two flow mechanisms: 1) by the stationary flow of non-Newtonian liquids common to all polymers and described by a common "reduced viscosity-reduced shear rate" curve referred to a single temperature; 2) by flow specific to black compounds associated with the destruction of carbon-black structures during the nonstationary period of deformation and manifested in a dependence of the stationary-flow activation energy on the shear rate and stress.Mekhanika Polimerov, Vol. 3, No. 3, pp. 511–516, 1967     

Nonlinear mathematical analysis for blood flow in a constricted artery under periodic body acceleration

This study analyses the pulsatile flow of blood through mild stenosed narrow arteries, treating the blood in the core region as a Casson fluid and the plasma in the peripheral layer as a Newtonian fluid. Perturbation method is employed to solve the resulting coupled implicit system of non-linear partial differential equations. The expressions for shear stress, velocity, wall shear stress, plug core radius, flow rate and longitudinal impedance to flow are obtained. The effects of pulsatility, stenosis depth, peripheral layer thickness, body acceleration and non-Newtonian behavior of blood on these flow quantities are discussed. It is noted that the plug core radius, wall shear stress and longitudinal impedance to flow increase as the yield stress and stenosis depth increase and they decrease with the increase of the body acceleration, pressure gradient, width of the peripheral layer thickness. It is observed that the plug flow velocity and flow rate increase with the increase of the pulsatile Reynolds number, body acceleration, pressure gradient and the width of the peripheral layer thickness and the reverse behavior is found when the yield stress, stenosis depth and lead angle increase. It is also recorded that the wall shear stress and longitudinal impedance to flow are considerably lower for the two-fluid Casson model than that of the single-fluid Casson model. It is found that the presence of body acceleration and peripheral layer influences the mean flow rate and mean velocity by increasing their magnitude significantly in the arteries.