Instantaneous Squeeze-Film Force Between a Heat Exchanger Tube and a Support Plate for Arbitrary Tube Motion

The instantaneous squeeze-film force between a heat exchanger tube and a support plate is studied. Based on a two-dimensional rectangular plate model, a short-sleeve squeeze-film model for arbitrary tube motion is developed. The instantaneous squeeze-film force is expressed in normal and tangential directions. The normal squeeze-film force consists of four nonlinear terms, the viscous, unsteady inertia, convective inertia and centripetal inertia terms. Three nonlinear terms, the viscous, unsteady inertia and Coriolis inertia terms, make up the tangential squeeze-film force. An experimental apparatus was developed in order to evaluate the theoretical models against measurements of a finite length squeeze film. A modified model based on the experimental data is obtained where the viscous terms for both directions are multiplied by the instantaneous Reynolds number. All the inertia terms are multiplied by constant coefficients. The modified model is in good agreement with most experimental cases for unsymmetrical linear motion, approximate circular motion and elliptical motion. The form of the modified model is suitable for predicting instantaneous squeeze-film forces in the simulation of heat exchanger tube vibration. Further work using different sized components and fluid properties is required in order to finalize coefficient values.     

Leading-Order Dynamics of Gravity-Driven Flows in?Free-Standing Soap Films

We derive the leading-order equations that govern the dynamics of the flow in a falling, free-standing soap film. Starting with the incompressible Navier?CStokes equations, we carry out an asymptotic analysis using parameters that correspond to a common experimental setup. We account for the effects of inertia, surface elasticity, pressure, viscous stresses, gravity, and air drag. We find that the dynamics of the flow is dominated by the effects of inertia, surface elasticity, gravity, and air drag. We solve the leading-order equations to compute the steady-state profiles of velocity, thickness, and pressure in an experiment in which the film is in the Marangoni elasticity regime. The computational results, which include a Marangoni shock, are in good accord with the experimental measurements.     

DETERMINING MOTOR INERTIA OF A STRESS-CONTROLLED RHEOMETER

Viscoelastic measurements made with a stress-controlled rheometer are affected by system inertia. Of all contributors to system inertia, motor inertia is the largest. Its value is usually determined empirically and precision is rarely if ever specified. Inertia uncertainty has negligible effects on rheologic measurements below the coupled motor/plate/sample resonant frequency. But above the resonant frequency, G' values of soft viscoelastic materials such as dispersions, gels, biomaterials, and non-Newtonian polymers, err quadratically due to inertia uncertainty. In the present investigation, valid rheologic measurements were achieved near and above the coupled resonant frequency for a non-Newtonian reference material. At these elevated frequencies, accuracy in motor inertia is critical. Here we compare two methods for determining motor-inertia accurately. For the first (commercially-used) phase method, frequency responses of standard fluids were measured. Phase between G' and G" was analyzed at 5-70 Hz for motor inertia values of 50-150% of the manufacturer's nominal value. For a newly-devised two-plate method (10 mm and 60 mm parallel plates), dynamic measurements of a non-Newtonian standard were collected. Using a linear equation of motion with inertia, viscosity, and elasticity coefficients, G' expressions for both plates were equated and motor inertia was determined to be accurate (by comparison to the phase method) with a precision of ± 3%. The newly developed two-plate method had advantages of expressly eliminating dependence on gap, was explicitly derived from basic principles, quantified the error, and required fewer experiments than the commercially used phase method.     

Velocity fields around spheres and bubbles investigated by laser-doppler anemometry

An experimental investigation is presented in which the velocity fields around sheres and bubbles moving in a cylinder have been measured by laser-Doppler anemometry (LDA). Instabilities in the flow field at rather low Deborah numbers have been discovered and these instabilities are damped by inertia forces. It is shown that the wall correction factor K is a rapidly decreasing function of the Deborah number. The experimental measurements have been compared with numerical simulations, and on the basis of this comparison it has been possible to identify a time constant and a zero-shear-rate viscosity for the test liquid.     

计入油膜惯性作用椭圆接触弹流润滑性能研究

基于计入惯性项的Navier-Stokes方程和连续性方程，建立了计入油膜惯性作用的椭圆接触弹性流体润滑模型，研究了油膜惯性对椭圆接触弹流润滑性能的影响. 弹性变形通过快速傅里叶变换(FFT)计算，而油膜压力通过复合直接迭代法求解. 数值结果表明:在计入油膜惯性作用后，润滑膜的二次压力峰增大，入口区的油膜速度减小，且逆流区范围扩大；考虑油膜惯性作用后油膜厚度有所增大，当载荷从300 N增加到700 N时，中心膜厚最大增加了5.14%. 试验结果也表明，考虑油膜惯性作用后的中心膜厚数值解与试验结果更加接近.      

Axisymmetric vibrations of a cylindrical resonator measured by holographic interferometry

A circular, cylindrical, ultrasonic resonator excited at one of its resonant frequencies is studied by holographic interferometry. Displacement distributions associated with the axisymmetric oscillations of the resonator are measured with the aid of time-average holograms, and are compared with a simple one-dimensional theory of rod vibrations, corrected for radial inertia. Analysis shows the overall error bounds on measured displacements to be ±9 percent of the maximum displacement at the resonator tip. Although the accuracy of measurements could be increased by refinements in experimental techniques, the work reported here represents substantial improvement in measuring the vibratory motion characteristics of ultrasonic devices over the point-by-point technique used heretofore.     

3-PRS并联机器人惯量耦合特性研究

惯量是影响机器人动态性能的主要因素,并联机器人因其多支链耦合的结构特点,关节空间各驱动轴出现惯量耦合的动力学特性,在高速、高加速度运动时易引起控制超调、振动等现象,破坏机器人的动态性能,因此研究并联机器人惯量耦合特性具有重要意义. 以3-PRS 并联机器人为例,通过虚功原理求得惯量矩阵,提出惯量耦合指标,该耦合指标表征了并联机器人在工作空间不同位姿时各驱动轴的耦合惯量大小,并给出了该耦合指标在机器人工作空间内的分布规律. 进一步在一台3-PRS 并联机器人样机上进行了实验验证,结果表明耦合惯量会改变驱动轴负载,负载的改变将最终影响动态性能. 同时各驱动轴的负载变化量随着惯量耦合指标的变大而变大,与理论分析有较好的一致性. 研究成果可帮助评价并联机器人的动力学耦合特性,并可用于并联机器人的结构参数优化及伺服参数调试以提高机器人的动态性能.      

Transient filament stretching rheometer

The filament stretching device which is used increasingly as an apparatus for measuring extensional properties of polymeric liquids is analysed. A force balance that includes the effects of inertia and surface tension is derived. The force balance may be used to correct for the effects of inertia and surface tension, provided online measurements of the filament surface shape are available. In addition, the question of initial asymmetry due to gravity is addressed.     

Viscous dissipation with fluid inertia in oscillatory shear flow

For liquids with high viscosity and low thermal conductivity, viscous dissipation can cause appreciable errors in rheological property measurements. Here, the influences of both viscous dissipation and fluid inertia on the property measurements in oscillatory sliding plate rheometry are investigated. For Newtonian fluids, Bird (1965) solved the combined problem analytically, but only for high frequencies. Here his solution is extended to any frequencies. Also, the equations of motion and energy are solved for linear viscoelastic fluids, and new analytical solutions for the velocity and temperature profiles are given. In both Newtonian and linear viscoelastic fluids, the temperature rise in the gap increases with frequency. The location of the maximum temperature shifts from the mid-plane at low frequency towards the moving wall at high frequency. The fluid inertia increases the viscous dissipation in both fluids. By solving the combined problem, this paper simplifies rheometer design by providing one unified criterion for avoiding measurement errors. Operating limits are presented graphically for minimizing the effects of both fluid inertia and viscous dissipation in oscillatory sliding plate rheometry.     

NONLINEAR FLUID FORCES IN CYLINDRICAL SQUEEZE FILMS. PART II: FINITE LENGTH

Two nonlinear models of finite-length cylindrical squeeze films are developed. The first finite-length model is formed using length-correction factors on a short cylindrical model, while the second finite-length model is constructed using side-leakage factors with an infinitely long model. Each model has seven force terms which are nonlinear functions of instantaneous cylinder position. The two models are evaluated through experimental measurements using two geometrical configurations where 50·6 mm and 25 mm diameter cylinders undergo 160 cases of radial and offset-linear motions. Comparing the theoretical predictions of squeeze force waveforms with measurements, and also with previous models by Lu & Rogers, shows that the present finite-length models are quite reasonable. By investigating each force term, the present models are modified slightly and better predictions are obtained for most test cases. Without empirical corrections, the models tend to underestimate the unsteady inertia terms and are unable to predict the frequency dependence of the viscous terms.     

落体法测刚体转动惯量的测量方法比较

用JIJG—I刚体转动惯量实验仪的同组数据，分别用测角加速度法和测时间法计算待测圆盘的转动惯量，结果表明，测角加速度法比测时间法的测量精度可提高1到2个数量级，具有明显优点；同时分析了测时间法产生误差的主要原因，也指出了使用测角加速度法的注意事项．     

Flow pattern analysis of linear gradient flow distribution

This paper uses the Oseen transformation to solve the differential equations governing motion of the vertical linear gradient flow distribution close to a wall surface. The Navier-Stokes equations are used to consider the inertia term along the flow direction. A novel contour integral method is used to solve the complex Airy function. The boundary conditions of linear gradient flow distribution for finite problems are determined. The vorticity function, the pressure function, and the turbulent velocity profiles are provided, and the stability of particle trajectories is studied. An L_x-function form of the third derivative circulation is used to to simplify the solution. Theoretical results are compared with the experimental measurements with satisfactory agreement.     

Measurement of inertial particle clustering and relative velocity statistics in isotropic turbulence using holographic imaging

We present the first measurements of relative velocity statistics of inertial particles in a homogeneous isotropic turbulent flow with three-dimensional holographic particle image velocimetry (holographic PIV). From the measurements we are able to obtain the radial relative velocity probability density function (PDF) conditioned on the interparticle separation distance, for distances on the order of the Kolmogorov length scale. Together with measurements of the three-dimensional radial distribution function (RDF) in our turbulence chamber, these statistics, in principle, can be used to determine interparticle collision rates via the formula derived by Sundaram and Collins (1997). In addition, we show temporal development of the RDF, which reveals the existence of an extended quasi-steady-state regime in our facility. Over this regime the measured two-particle statistics are compared to direct numerical simulations (DNS) with encouraging qualitative agreement. Statistics at the same Reynolds number but different Stokes numbers demonstrate the ability of the experiment to correctly capture the trends associated with particles of different inertia. Our results further indicate that even at moderate Stokes numbers turbulence may enhance collision rates significantly. Such experimental investigations may prove valuable in validating, guiding and refining numerical models of particle dynamics in turbulent flows.     

Predicting pressure drop in open-cell foams by adopting Forchheimer number

Interconnected struts arranged in 3-D foam structures pose a challenge in understanding fluid flow, which is significantly different from that in traditional porous media. Different flow regimes (Darcy, transition and weak inertia regimes) and thus, different flow laws in open-cell foams are used. The impact of characteristic lengths’ choices based on both, morphological and hydraulic parameters on flow law formulation has been studied. Ambiguities in definitions and measurements of several key parameters have been shown and limitations in the use of some parameters have been pointed out.An equivalent Reynolds number in the form of Forchheimer number (F_o) has been proposed to establish the friction factor relationship in order to avoid any morphological ambiguities. This number takes into account hydraulic characteristics of viscous and inertia regimes simultaneously. It has been observed that when F_o < 0.1, the flow through open-cell foams remains in the Darcy regime while the occurrence of weak inertia regime dominates when F_o > 1. Transition regime occurs in a narrow range of flow velocity when 0.1 < F_o < 1. The limits of transition for regime identification are found to be independent of foam morphologies. The form drag coefficient varies in relation with foam morphological parameters and is not a “universal” constant.Empirical correlations have been derived to predict hydraulic characteristics and friction factor data for different strut shapes and porosities. An excellent agreement has been obtained between predicted and numerical/experimental flow data.     

A Resistance Model for Newtonian and Power-Law Non-Newtonian Fluid Transport in Porous Media

A theoretical model based on the force balance between pressure, viscous force, and inertia force is proposed to predict the flow resistance of Newtonian and power-law non-Newtonian fluids through porous packed beds. The present model takes inertia effect into consideration, and the flow regime can be extended from Darcy flow to non-Darcy flow. It is demonstrated that the present model can predict most available experimental data well. The present results are also compared to the Ergun equation and other drag correlations.     

Identification of the Ten Inertia Parameters of a Rigid Body

Standard experiments for identifying inertia parameters of a rigid body only provide a subset of the inertia parameters of the body [1–10]. In addition, they do not use in the estimation process the complete information included in the equations of motion of the rigid test body. The objective of the work described in this paper is the simultaneous, automatic experimental identification of the ten inertia parameters of a rigid body using the complete information hidden in the nonlinear model equations of the test body. This task has been solved in several steps:– mathematical modelling of the special motions of a rigid body in space. These model equations have been mapped into a form suitable for identification purposes (identification hypothesis)– design of a special measurement robot for performing the identification experiments– laboratory experiments providing test data used for the identification experiments– identification of the inertia parameters and accuracy tests.The accuracy of the identified parameters is satisfactory.     

Fluid inertia effects on a Controlled Stress Rheometer in its oscillatory mode

This paper is concerned with the effect of fluid inertia on experimental oscillatory stress data taken from a Controlled Stress Rheometer. A linear viscoelastic theory is developed which includes the effect of fluid inertia for cone and plate, parallel plate and concentric cylinder geometries. This theory is used to interpret dynamic data for both a slightly elastic and a highly viscoelastic fluid. It is shown that intertial effects are very small for both a cone and plate and parallel plate geometries. Inertial effects, however, can be important in the concentric cylinder geometry.     

Dynamic pre-strain and inertia effects on the fracture of metals

A combined experimental and theoretical study is described which examines the influence of strain-rate and dynamic pre-strain on the ductile fracture of thin cylinders. The thin-cylinder configuration is particularly important in this case because it allows inertia terms to be directly incorporated into the theory of plastic instability. A series of quasi-static and dynamic tests is conducted on three materials with differing degrees of strain-rate sensitivity and strain-hardening. The experimental observation that fracture is inhibited at high strain-rates is in accord with the theory when inertia can no longer be considered insignificant. It is also shown that dynamic pre-strain has little or no effect on the flow stress or the strain at fracture in materials which-are essentially strain-rate insensitive, but does reduce the fracture strain in the strain-rate sensitive materials.     

Can extensional viscosity be measured with opposed-nozzle devices?

Opposed-nozzle devices are widely used to try to measure the extensional viscosity of low-viscosity liquids. A thorough literature survey shows that there are still several unanswered questions on the relationship between the quantity measured in opposed-nozzle devices and the true extensional viscosity of the liquids. In addition to extensional stresses, opposed nozzle measurements are influenced by dynamic pressure, shear on the nozzles, and liquid inertia. Therefore the ratio of the apparent extensional viscosity that is measured to the shear viscosity that is independently measured is greater than three even for Newtonian liquids. The effect of inertia on the extensional measurements is analyzed by computer-aided solution of the Navier-Stokes system, and by experiments on low-viscosity Newtonian liquids(1 mPa sS 800 mPa s). The effect of nozzle separation-to-diameter ratio on the average residence time of the liquid is analyzed under the assumption of simple extensional flow kinematics. The average residence time of the liquid is independent of this ratio unless the radial inflow section of the extensional flow volume is related to the nozzle separation. Experiments indicate that in some cases widening the gap lowers the apparent extensional viscosity that is measured, whereas in other cases the opposite is true. In the light of these theoretical considerations and experimental observations, the use of systematic corrections to extensional viscosity measurements on non-Newtonian liquids is not recommended. Thus opposed nozzle devices should be considered as useful indexers rather than rheometers. Finally, measurements on a series of semi-dilute solutions of high molecular weight poly(ethylene oxide) in. water are also reported.Dedicated to the memory of Anastasios C. Papanastasiou     

Matched eigenfunction expansions for slow flow over a slot

We solve the problem of plane flow of a second-order fluid over a rectangular slot when inertia is neglected by matching biorthogonal eigenfunction expansions in different regions of flow. The method appears to be cheaper and more accurate than direct numerical methods. The effect of normal stresses on pressure measurements at the bottom of the slot is discussed.