Passage of a liquid drop through a bifurcation

Numerical simulations of the motion of a viscous liquid drop through a two-dimensional bifurcating channel are conducted using a boundary-element method for Stokes flow. The drop viscosity is assumed to be equal to the ambient fluid viscosity and the drop interface is assumed to exhibit uniform surface tension. The mean fluid pressures are prescribed at the channel inlet and two outlets, and the corresponding flow rates are computed as part of the solution. Preliminary simulations show that the shape of a two-dimensional drop moving through a channel with parallel walls is similar to that of an axisymmetric drop moving along the centerline of a circular tube. The ability of a drop to remain intact as it passes through the bifurcation is determined by the drop size and capillary number expressing the significance of surface tension. For a given drop size and channel inlet and outlet pressures, there is a critical capillary number above which a drop splits into two pieces connected by a thinning bridge. The presence of the drop has a weak effect on the inlet and outlet flow rates throughout its passage. Simulations based on a boundary-element method for a rigid particle with circular or elliptical shape reveal a significantly stronger effect due to the absence of interfacial mobility.     

Transient heat conduction in a medium with multiple spherical cavities

This paper considers a transient heat conduction problem for an infinite medium with multiple non‐overlapping spherical cavities. Suddenly applied, steady Dirichlet‐, Neumann‐ or Robin‐type boundary conditions are assumed. The approach is based on the use of the general solution to the problem of a single cavity and superposition. Application of the Laplace transform and the so‐called addition theorem results in a semi‐analytical transformed solution for the case of multiple cavities. The solution in the time domain is obtained by performing a numerical inversion of the Laplace transform. A large‐time asymptotic series for the temperature is obtained. The limiting case of infinitely large time results in the solution for the corresponding steady‐state problem. Several numerical examples that demonstrate the accuracy and the efficiency of the method are presented. Copyright © 2008 John Wiley & Sons, Ltd.     

Transient Analysis of Elastic Wave Propagation in Multilayered Structures

In this article, explicit transient solutions for one-dimensional wave propagation behavior in multi-layered structures are presented. One of the objectives of this study is to develop an effective analytical method for constructing solutions in multilayered media. Numerical calculations are performed by three methods: the generalized ray method, numerical Laplace inversion method (Durbin's formula), and finite element method (FEM). The analytical result of the generalized ray solution for multilayered structures is composed of a matrix-form Bromwich expansion in the transform domain. Every term represents a group of waves, which are transmitted or reflected through the interface. The matrix representation of the solution can be used to calculate the transient response, without tracing the ray path manually. Numerical inversion of the Laplace transform by Durbin's formula is also used to construct transient responses. This numerical Laplace inversion technique has the advantage of calculating long-time transient responses for complicated multilayered structures. FEM results agree well with calculations obtained by the generalized ray method and numerical Laplace inversion.     

Nonlinear critical layers in the boundary layer on a rotating disk

The work of Gregory, Stuart and Walker (1955, Proc R Soc Ser A 406:93–106) and Hall (1986, Phil Trans R Soc London Ser A 248:155–199) is extended to include nonlinear effects for the stationary cross-flow vortex. It is shown that amplitude-dependent neutral modes are described by a forced Haberman equation. The corrections to the neutral wavenumbers and waveangles are derived and it is suggested that the nonlinear neutral modes can have wavenumbers decreased by an O(1) amount as compared to linear theory.     

On the shape of a rotating liquid drop in an electric field

Summary The axisymmetric relative equilibrium shape of a finite dielectric liquid mass held together by surface tension and rotating uniformly in a uniform axial electric field is determined by expressing the slope of its tangent in terms of confluent hypergeometric functions and following a numerical integration.

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Zusammenfassung Die axialsymmetrische, relative Gleichgewichtsfigur einer endlichen, dielektrischen, durch die Oberflächenspannung zusammengehaltenen Flüssigkeitsmasse, welche gleichförmig in einem axialen elektrischen Feld konstanter Feldstärke rotiert, wird untersucht. Die Steigung der Tangente wird mittels konfluenter hypergeometrischer Funktionen ausgedrückt, und die Gestalt des Flüssigkeitstropfens durch numerische Integration bestimmt.

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Presented at the Fifth United States National Congress of Applied Mechanics, University of Minnesota, Minneapolis, Minnesota, USA, June 1966; an abstract appears on page 764 of the proceedings.     

Transient Wave Propagation in a Functionally Graded Slab and Multilayered Medium Subjected to Dynamic Loadings

In this article, the transient response in a functionally graded material (FGM) slab is analyzed by Laplace transform technique. The numerical Laplace inversion (Durbin's formula) is used to calculate the dynamic behavior of the FGM slab. The slab is subjected an uniform loading at the upper surface, and the lower surface are assumed to be traction-free or fixed conditions. The analytical solutions are presented in the transform domain and the numerical Laplace inversion is performed to obtain the transient response in time domain. To take the accuracy and computational efficiency in consideration, Durbin's method is suitable for calculating the long-time response. In addition, the FGM slab is approximated as a multilayered medium with homogeneous material in each layer, and the transient responses of FGM formulation and multilayered solution are discussed in detail.     

Slow slumping of a very viscous liquid bridge

A layer of very viscous liquid (e.g. tar, molten glass) spans a chasm between two vertical walls. The slow fall or slump of this initially-rectangular liquid bridge is analysed. A semi-analytical solution is obtained for the initial motion, for arbitrary thickness/width ratios. The formal limits of large and small thickness/width ratios are also investigated. For example, the centre section of a thin bridge of liquid of density and viscosity µ, with width 2w and thickness 2h2w falls under gravity g at an initial velocity gw⁴/(32h²). A finite element technique is then employed to determine the slumping motion at later times, confirming in passing the semi-analytical prediction of the initial slumping velocity.     

NURBS-based isogeometric analysis for the computation of flows about rotating components

The ability of non-uniform rational B-splines (NURBS) to exactly represent circular geometries makes NURBS-based isogeometric analysis attractive for applications involving flows around and/or induced by rotating components (e.g., submarine and surface ship propellers). The advantage over standard finite element discretizations is that rotating components may be introduced into a stationary flow domain without geometric incompatibility. Although geometric compatibility is exactly achieved, the discretization of the flow velocity and pressure remains incompatible at the interface between the stationary and rotating subdomains. This incompatibility is handled by using a weak enforcement of the continuity of solution fields at the interface of the stationary and rotating subdomains. noli turbare circulos meos, “do not upset my circles (calculations)”, attributed to Archimedis, to a roman soldier who killed him, and was subsequently executed because he violated orders not to kill Archimedis, at the battle of Syracuse.     

Transient heat conduction analysis in functionally graded materials by the meshless local boundary integral equation method

Advanced computational method for transient heat conduction analysis in continuously nonhomogeneous functionally graded materials (FGM) is proposed. The method is based on the local boundary integral equations with moving least square approximation of the temperature and heat flux. The initial-boundary value problem is solved by the Laplace transform technique. Both Papoulis and Stehfest algorithms are applied for the numerical Laplace inversion to obtain the time-dependent solutions. Numerical results are presented for a finite strip and a hollow cylinder with an exponential spatial variation of material parameters.     

Transient heat conduction in a medium with multiple circular cavities and inhomogeneities

A two‐dimensional transient heat conduction problem of multiple interacting circular inhomogeneities, cavities and point sources is considered. In general, a non‐perfect contact at the matrix/inhomogeneity interfaces is assumed, with the heat flux through the interface proportional to the temperature jump. The approach is based on the use of the general solutions to the problems of a single cavity and an inhomogeneity and superposition. Application of the Laplace transform and the so‐called addition theorem results in an analytical transformed solution. The solution in the time domain is obtained by performing a numerical inversion of the Laplace transform. Several numerical examples are given to demonstrate the accuracy and the efficiency of the method. The approximation error decreases exponentially with the number of the degrees of freedom in the problem. A comparison of the companion two‐ and three‐dimensional problems demonstrates the effect of the dimensionality. Copyright © 2009 John Wiley & Sons, Ltd.     

串联孔板的流量-压降计算探讨

基于气液两相流体流过孔板的压降理论提出串联孔板节流元件的计算方法，用实验数据进行计算分析和间接验证。结果表明，计算值与实验值有较好的一致性，说明该方法用于串联孔板节流元件的设计计算有一定的可行性。     

Transient shear flow of model lithium lubricating greases

This paper deals with the analysis of the transient shear flow behavior of lithium lubricating greases differing in soap concentration and base oil viscosity. The shear-induced evolution of grease microstructure has been studied by means of stress-growth experiments. With this aim, different lubricating grease formulations were manufactured by modifying the concentration of lithium 12-hydroxystearate and the viscosity of the base oil, according to a RSM statistical design. Moreover, atomic force microscopy (AFM) observations were carried out. The transient stress response can be successfully described by the generalized Leider-Bird model based on two exponential terms. Different rheological parameters, related to both the elastic response and the structural breakdown of greases, have been analysed. In this sense, it has been found that the elastic properties of lithium lubricating greases were highly influenced by soap concentration and oil viscosity. The stress overshoot, τ _max, depends linearly on both variables in the whole shear rate range studied, although the effect of base oil viscosity on this parameter is opposite at low and high shear rates. Special attention has been given to the first part of the stress-growth curve. In this sense, it can be deduced that the “yielding” energy density not only depends on grease composition, but also on shear rate. Moreover, an interesting asymptotic tendency has been found for both the “yielding” energy density and the stress overshoot by increasing shear rate. The asymptotic values of these parameters have been correlated to the friction coefficient obtained in a ball-disc tribometer.     

微细通道纳米制冷剂压降波动特性研究

为探究热流密度、质量通量和入口过冷度对微细通道流动沸腾压降波动特性的影响,以质量分数为0.8%的纳米制冷剂Al_2O_3-R141b及纯制冷剂R141b为工质在水力直径为1.33 mm的矩形微细通道内进行了流动沸腾实验。结果表明:热流密度从18.2 k W/m2增加到25.4 k W/m~2时,工质进出口压降波动更为剧烈;较大质量通量和较高入口过冷度一定程度上可以使压降波动更平缓;与纯制冷剂相比,质量分数为0.8%的纳米制冷剂Al_2O_3-R141b的压降波动较为平缓,其压降标准差最大降低了18%。     

基于液滴指纹图波形分析的液体识别方法

为了定量地描述“光电液滴指纹图”鉴别液体的功能,提出一种波形分析法来提取指纹图的特征参数。采用“邻域比较法”或“基于最大值和最小值的极值检测法”确定指纹图的峰谷位置,分别计算表征主峰、次峰和波谷的电容信号和光纤信号的参数,以及指纹图的曲线长度和曲线面积。实验证明,“曲线面积”是最有效的识别参数,不同种类液体的相对分辨率为7.45%;同一种类不同品牌的水、饮料、酒、醋和酱油的相对分辨率分别为1.96%,7.64%,14.39%,0.07%和3.65%。指纹图的“次峰”是相对较弱的特征,相对分辨率仅为0.07%。     

高压降迷宫套筒组合调节阀涡激振动仿真研究

针对高压降类调节阀涡激振动现象,设计多通道迷宫盘片和多级套筒组合高压降调节阀。基于计算流体动力学(CFD)和流固耦合模态分析法,计算调节阀内部瞬态流场及结构模态,得到其三种典型开度的流体流动情况,升力系数时域和频域特性曲线,以及模态频率和模态振型。分析结果表明:4s时刻,随调节阀开度减小,流体最大流速相应减小,第四级套筒外部流道区域的大涡逐渐形成小涡。调节阀全开时流体升力系数波动比70%和40%开度时更为剧烈,一阶模态频率、二阶模态频率均随开度的增大而增大。调节阀模态频率没有落在漩涡脱落主频率范围内,调节阀不会发生涡激振动锁定现象。     

Thermoelastic analysis of a functionally graded rotating disk

A semi-analytical thermoelasticity solution for hollow and solid rotating axisymmetric disks made of functionally graded materials is presented. The radial domain is divided into some virtual sub-domains in which the power-law distribution is used for the thermomechanical properties of the constituent components. Imposing the necessary continuity conditions between adjacent sub-domains, together with the global boundary conditions, a set of linear algebraic equations are obtained. Solution of the linear algebraic equations yields the thermoelastic responses for each sub-domain as exponential functions of the radial coordinate. Some results for the stress, strain and displacement components along the radius are presented due to centrifugal force and thermal loading. Results obtained within this solution are compared with those of a finite element analysis in the literature. Based on the results, it is shown that the property gradation correlates with thermomechanical responses of FG disks.     

Effect of surface slip on Stokes flow past a spherical particle in infinite fluid and near a plane wall

The motion of a spherical particle in infinite linear flow and near a plane wall, subject to the slip boundary condition on both the particle surface and the wall, is studied in the limit of zero Reynolds number. In the case of infinite flow, an exact solution is derived using the singularity representation, and analytical expressions for the force, torque, and stresslet are derived in terms of slip coefficients generalizing the Stokes–Basset–Einstein law. The slip velocity reduces the drag force, torque, and the effective viscosity of a dilute suspension. In the case of wall-bounded flow, advantage is taken of the axial symmetry of the boundaries of the flow with respect to the axis that is normal to the wall and passes through the particle center to formulate the problem in terms of a system of one-dimensional integral equations for the first sine and cosine Fourier coefficients of the unknown traction and velocity along the boundary contour in a meridional plane. Numerical solutions furnish accurate predictions for (a) the force and torque exerted on a particle translating parallel to the wall in a quiescent fluid, (b) the force and torque exerted on a particle rotating about an axis that is parallel to the wall in a quiescent fluid, and (c) the translational and angular velocities of a freely suspended particle in simple shear flow parallel to the wall. For certain combinations of the wall and particle slip coefficients, a particle moving under the influence of a tangential force translates parallel to the wall without rotation, and a particle moving under the influence of a tangential torque rotates about an axis that is parallel to the wall without translation. For a particle convected in simple shear flow, minimum translational velocity is observed for no-slip surfaces. However, allowing for slip may either increase or decrease the particle angular velocity, and the dependence on the wall and particle slip coefficients is not necessarily monotonic.     

Pressure drop reduction phenomenon of slush nitrogen flow in a horizontal pipe

Cryogenic slush fluids, such as slush hydrogen and slush nitrogen, are two-phase single-component fluids containing solid particles in a liquid. Their density and refrigerant capacity are greater than those of a liquid-state fluid alone. Owing to these advantages, there are high expectations for use of slush fluids in various applications such as a clean-energy fuel, fuel for space-planes to improve the efficiency of transportation and storage, and as a refrigerant for high-temperature superconducting power machines. Experimental tests were performed with slush nitrogen to obtain the frictional pressure drop flowing in a horizontal pipe with an inner diameter of 15 mm and a length of 400 mm. The primary objective of the study was to investigate the pressure drop reduction phenomenon according to changes in velocity and solid fraction. The pressure drop correlation between the friction factor and the Reynolds number was obtained, and an empirical correlation between them was derived. The flow pattern for slush nitrogen inside a pipe and the behavior of solid particles were observed using a high-speed video camera and the PIV method. From the experimental results, the pressure drop reduction phenomenon emerged clearly when the flow velocity was higher than 3.6 m/s and the flow pattern of solid particles inside the pipe was pseudo-homogeneous.     

Hydromagnetic couette flow of an Oldroyd-B fluid in a rotating system

The motion of electrically conducting, Oldroyd-B and incompressible fluid between two infinitely extended non-conducting parallel plates under a uniform transverse magnetic field, fixed relative to the fluid has been considered. The lower plate is at rest and the upper plate is oscillating in its own plane. The governing partial differential equation of this problem, subject to boundary conditions are solved analytically. The expressions for the steady and unsteady velocity fields for the conducting Oldroyd-B fluid are obtained. The graphs are plotted for different values of dimensionless parameters of the problem and the analysis of the results showed that the flow field is appreciably influenced by the applied magnetic field, the rotation and the material parameters of the fluid.     

不同填料旋转床功耗与气体压降特性对比研究

采用同心环波纹碟片填料和不锈钢波纹丝网两种填料，在气液逆流CO2吸收操作时，对旋转床的功耗及气体压降进行了对比实验分析。功耗特性对比结果表明，当液流量不变，旋转床转速低于38rad／s时，丝网填料旋转床吸收器消耗的功率大于碟片填料旋转床吸收器消耗的功率；转速高于38rad／s时则相反。气体压降特性对比结果表明，在液流量和旋转床转速不变的操作条件下，碟片填料旋转床的气体压降要大于丝网填料旋转床的气体压降约50Pa；在气流量和转速不变的操作条件下，当液流量较小时，丝网填料旋转床的气体压降大于碟片填料旋转床的气体压降；当液流量较大时则相反。在相同气流量和液流量下，碟片旋转床气体压降要大于丝网填料旋转床气体压降。研究结果为AIP系统旋转床吸收器的填料优选及全系统的优化设计提供了重要的依据。