填隙幂率流体下两刚性圆球相对错移时的粘性阻力

湿颗粒离散元模型以两球作用时填隙流体定常流动解为基础,其中切向作用是难点,国外仅有Goldman的牛顿流体渐近解.基于Reynolds润滑理论导出了两刚性球切向错动时填隙幂律流体的压力方程,并利用傅立叶级数展开简化,通过数值解法得到相应的压力分布、黏性阻力及阻力矩.该方程的解较之作者先前对速度场附加假定的结果精确,而当幂指数为1时等价于Goldman的牛顿流体渐近解.     

The determination of the refractive index of a photoelastic specimen by immersion technique

Conventional methods for determining the refractive index demand specimens of optical quality, the preparation of which is often very difficult. An indirect determination by matching the refractive indices of specimen and immersion liquid is a practical alternative for photoelastic specimen of nonoptical quality. An experimental arrangement used for this technique and observations made while matching the refractive indices of three different specimens are presented.     

An investigation of matched index of refraction technique and its application in optical measurements of fluid flow

Optical distortions caused by non-uniformities of the refractive index within the measurement volume is a major impediment for all laser diagnostic imaging techniques applied in experimental fluid dynamic studies. Matching the refractive indices of the working fluid and the test section walls and interfaces provides an effective solution to this problem. The experimental set-ups designed to be used along with laser imaging techniques are typically constructed of transparent solid materials. In this investigation, different types of aqueous salt solutions and various organic fluids are studied for refractive index matching with acrylic and fused quartz, which are commonly used in construction of the test sections. One aqueous CaCl₂·2H₂O solution (63 % by weight) and two organic fluids, Dibutyl Phthalate and P-Cymene, are suggested for refractive index matching with fused quartz and acrylic, respectively. Moreover, the temperature dependence of the refractive indices of these fluids is investigated, and the Thermooptic Constant is calculated for each fluid. Finally, the fluid viscosity for different shear rates is measured as a function of temperature and is applied to characterize the physical behavior of the proposed fluids.     

TEMPERATURE PROFILES OF LOCAL THERMAL NONEQUILIBRIUM FOR THERMAL DEVELOPING FORCED CONVECTION IN POROUS MEDIUM PARALLEL PLATE CHANNEL

Based on the two-energy equation model, taking into account viscous dissipation due to the interaction between solid skeleton and pore fluid flow, temperature expressions of the solid skeleton and pore fluid flow are obtained analytically for the thermally developing forced convection in a saturated porous medium parallel plate channel, with walls being at constant temperature. It is proved that the temperatures of the two phases for the local thermal nonequilibrium approach to the temperature derived from the one-energy equation model for the local thermal equilibrium when the heat exchange coefficient goes to infinite. The temperature profiles are shown in figures for different dimensionless parameters and the effects of the parameters on the local thermal nonequilibrium are revealed by parameter study.     

A Simple Model for a Fluid-Filled Open-Cell Foam

A simple microstructure model is used to describe a fluid-filled open-cell foam. In the simplest case it consists of parallel elastic plates with gaps between them, which are filled with a Newtonian fluid. We assume that the load applied to this model material is uniaxial. The constitutive equation is formulated with the pressure of the fluid as an inner variable. The model yields an evolutional equation for the fluid pressure which itself is a field equation, that is a partial differential equation in time and space coordinates. This differential equation is solved for an instantaneously applied constant load and for a harmonically oscillating load. The solution of the differential equation, in combination with the constitutive equation leads to a relation between mean applied load and global strain of the test specimen. Finally, we obtain the creep compliance and the complex modulus of the foam material, respectively. The influence of different geometries of the foam and of different material behaviour of the matrix and fluid on the creep compliance and the complex modulus is discussed.     

Particle image velocimetry in a variable density flow: application to a dynamically evolving microburst

A fondamental difficulty in the experimental study of gravity-driven flows using particle image velocimetry (PIV) and other optical diagnostic techniques is the problem associated with variations in thé refractive index within the fluid. This paper discusses a method by which the refractive indices of two fluids are matched while maintaining density differences of up to 4%. Aqueous solutions of glycerol and potassium phosphate are used to achieve precise index matching in the presence of mixed and unmixed constituents. The effectiveness of the method is verified in a PIV study of a laboratory-scale model of an atmospheric microburst where planes of two-dimensional velocity vectors are obtained in thé evolving flow field.This work was sponsored by the National Science Foundation under grant CTS-9209948. We also thank TSI, Inc. for the use of its facility     

Unobstructed particle image velocimetry measurements within an axial turbo-pump using liquid and blades with matched refractive indices

Performing PIV measurements within complex turbomachinery with multiple blade rows is difficult due to the optical obstruction to the illuminating sheet and to the camera caused by the blades. This paper introduces a refractive index matched facility that overcomes this problem. The rotor and stator blades are made of transparent acrylic, and the working fluid has the same optical refractive index as the blades. A 64% by weight solution of sodium iodide in water is used for this purpose. This liquid has a kinematic viscosity of about 1.1᎒^-6 m²/s, which is almost the same as that of water enabling operation at high Reynolds numbers. Issues related to operating with this fluid such as chemical stability, variations in transmittance and solutions to these problems are discussed. This setup allows full optical access to the entire rotor and stator passages both to the laser sheet and the camera. The experiments are conducted at different streamwise locations covering the entire flow fields around the rotor, the stator, the gap between them, and the wakes behind. Vector maps of the instantaneous and phase-averaged flow fields as well as the distribution of turbulent kinetic energy are obtained. Measurements at different magnifications enable us to obtain an overview of the flow structure, as well as detailed velocity distributions in the boundary layers and in the wakes.     

LATTICE BOLTZMANN SIMULATION OF POWER-LAW FLOW PAST AN ELLIPTIC CYLINDER

基于格子波尔兹曼方法(lattice Boltzmann method) 和幂律流体本构方程, 建立二维流动模型, 将充分发展的速度分布与理论解进行对比, 吻合良好. 对幂律流体的圆柱绕流进行模拟, 采用了反弹格式的无滑移圆柱边界, 并使用应力积分法计算阻力系数, 分析了稳态圆柱绕流时, 阻力系数随幂律指数n 以及雷诺数Re 的变化规律. 分析了椭圆横轴/纵轴长度比和幂律指数n, 对压力系数C_p 和黏度系数C_v 的影响. 得到的变化规律与有限元方法规律一致, 验证了格子波尔兹曼模型的可行性.     

Analytical modeling for nonlinear vibration analysis of partially cracked thin magneto-electro-elastic plate coupled with fluid

A nonlinear analytical model for the transverse vibration of cracked magneto-electro-elastic (MEE) thin plate is presented using the classical plate theory (CPT). The MEE plate material selected is fiber-reinforced \(\hbox {BaTiO}_{3}\)–\(\hbox {CoFe}_{2}\hbox {O}_{4}\) composite, which contains a partial crack at the center. The CPT and the simplified line spring model for crack terms are modified to accommodate the effect of electric and magnetic field rigidities. The analysis considers in-plane forces for the MEE plate, which makes the model nonlinear. The derived governing equation is solved by expressing the transverse displacement in terms of modal coordinates. An approximate solution for forced vibration of cracked MEE plate is also obtained using a perturbation technique. The effect of part-through crack, volume fraction of the composite on the vibration frequencies and structure response is investigated. The frequency response curves presented shows the phenomenon of hard or soft spring. Furthermore, the devised model is extended to the case of cracked MEE plate submerged in fluid. Velocity potential function and Bernoulli’s equation are used to incorporate the inertia effect of surrounding fluid. Both partially and totally submerged plate configurations are considered. The validation of the present results is carried out for intact submerged plate as to the best of the author’s knowledge the literature lacks in results for submerged-cracked plates. New results for cracked MEE plate show that the vibration characteristics are affected by volume fraction, crack length, fluid level and depth of immersion.     

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.     

A New Non-Darcy Flow Model for Low-Velocity Multiphase Flow in Tight Reservoirs

The pore and pore-throat sizes of shale and tight rock formations are on the order of tens of nanometers. The fluid flow in such small pores is significantly affected by walls of pores and pore-throats. This boundary layer effect on fluid flow in tight rocks has been investigated through laboratory work on capillary tubes. It is observed that low permeability is associated with large boundary layer effect on fluid flow. The experimental results from a single capillary tube are extended to a bundle of tubes and finally to porous media of tight formations. A physics-based, non-Darcy low-velocity flow equation is derived to account for the boundary layer effect of tight reservoirs by adding a non-Darcy coefficient term. This non-Darcy equation describes the fluid flow more accurately for tight oil reservoir with low production rate and low pressure gradient. Both analytical and numerical solutions are obtained for the new non-Darcy flow model. First, a Buckley–Leverett-type analytical solution is derived with this non-Darcy flow equation. Then, a numerical model has been developed for implementing this non-Darcy flow model for accurate simulation of multidimensional porous and fractured tight oil reservoirs. Finally, the numerical studies on an actual field example in China demonstrate the non-negligible effect of boundary layer on fluid flow in tight formations.     

An application of holography to complete stress analysis of photoelastic models

A new procedure is proposed by which holographic principles may be extended to include stress analysis of three-dimensional photoelastic models. A sixth independent equation can be obtained to permit a complete stress solution by using the double-exposure hologram technique in conjunction with an immersion tank. The salient feature of the method is that no stress relieving is necessary between exposures of the hologram. Two experiments were performed to compare the stress-relieving method to the immersion method. In both experiments, a two-dimensional model was used to simplify the demonstration of the general techniques, which are also applicable to slices from frozen-stress models.     

On axisymmetric flow of Sisko fluid over a radially stretching sheet

This study presents an analysis of the axisymmetric flow of a non-Newtonian fluid over a radially stretching sheet. The momentum equations for two-dimensional flow are first modeled for Sisko fluid constitutive model, which is a combination of power-law and Newtonian fluids. The general momentum equations are then simplified by invoking the boundary layer analysis. Then a non-linear ordinary differential equation governing the axisymmetric boundary layer flow of Sisko fluid over a radially stretching sheet is obtained by introducing new suitable similarity transformations. The resulting non-linear ordinary differential equation is solved analytically via the homotopy analysis method (HAM). Closed form exact solution is then also obtained for the cases n=0 and 1. Analytical results are presented for the velocity profiles for some values of governing parameters such as power-law index, material parameter and stretching parameter. In addition, the local skin friction coefficient for several sets of the values of physical parameter is tabulated and analyzed. It is shown that the results presented in this study for the axisymmetric flow over a radially non-linear stretching sheet of Sisko fluid are quite general so that the corresponding results for the Newtonian fluid and the power-law fluid can be obtained as two limiting cases.     

The convective instability of Maxwell fluid-saturated porous layer using a thermal non-equilibrium model

A linear stability analysis is carried out to study viscoelastic fluid convection in a horizontal porous layer heated from below and cooled from above when the solid and fluid phases are not in a local thermal equilibrium. The modified Darcy–Brinkman–Maxwell model is used for the momentum equation and two-field model is used for the energy equation each representing the solid and fluid phases separately. The conditions for the onset of stationary and oscillatory convection are obtained analytically. Linear stability analysis suggests that, there is a competition between the processes of viscoelasticity and thermal diffusion that causes the first convective instability to be oscillatory rather than stationary. Elasticity is found to destabilize the system. Besides, the effects of Darcy number, thermal non-equilibrium and the Darcy–Prandtl number on the stability of the system are analyzed in detail.     

Evaluation of the effect of variable refraction index on the path of a laser beam

The use of a laser-Doppler anemometer to measure velocities in a fluid with a larger variation in its refractive index perpendicular to the laser beams may introduce appreciable errors. This situation is commonly encountered in convective heat transfer studies. The beams are refracted as they pass through the fluid and the distance of the intersection of the beams, control volume, from the surface may be significantly different than the distance of the beams from the surface when they entered the fluid. If the flow is unsteady or turbulent, the relative movement of the beams may be such that the size and location of the control volume is constantly changing causing appreciable errors.     

Characteristics of flow field and water concentration in a horizontal deadleg

Deadlegs are defined as the inactive portion of the pipe where the flow is stagnant. Corrosion in deadlegs occurs as a result of water separation due to the very low flow velocity. The present work provides an investigation of the effect of deadleg geometry and average flow velocity on flow field and oil/water separation in deadlegs. The investigation is based on the solution of the mass and momentum conservation equations of an oil/water mixture together with the volume fraction equation for the secondary phase. A fluid flow model based on the time-averaged governing equations of 3-D turbulent flow has been developed. An algebraic slip mixture model is utilized for the calculation of the two immiscible fluids (water and crude oil). The model solves the continuity and momentum equations for the mixture, and the volume fraction equation for the secondary phase utilizing an algebraic expression for the relative velocity. Flow visualization experiments were conducted in order to validate the numerical procedure. Good agreement was obtained between the calculated and measured flow patterns. Results are obtained for different lengths of the deadleg. The considered fluid mixture contains 90% oil and 10% water (by volume). The inlet flow velocity ranges from 0.2 to 10 m/s and the deadleg length to diameter ratio (L/D) ranges from 1 to 10. The results showed that the size of the stagnant fluid region increases with the increase of L/D and decreases with the increase of inlet velocity. The results also indicated that the water volumetric concentration increases with the increase of L/D and influenced by the deadleg geometry.     

海洋地震工程流固耦合问题统一计算框架

海底地震动的模拟以及海洋工程结构的地震反应分析中,涉及到海水、饱和海床、弹性基岩、结构之间的相互耦合.传统的方法分别采用声波方程描述理想流体、Biot方程描述饱和海床、弹性波方程描述基岩和结构,分别考虑相互之间的耦合,十分不便.本文基于理想流体、固体分别为饱和多孔介质的特殊情形(孔隙率分别为1和0),由饱和多孔介质的Biot方程可退化得到理想流体的声波方程和固体的弹性波方程.然后,以饱和多孔介质方程为基础,经集中质量有限元离散,考虑不同孔隙率的饱和多孔介质之间耦合的一般情形,建立了该耦合情形的求解方法.进一步论证了该一般情形的耦合计算方法可分别退化到流体与固体、流体与饱和多孔介质、固体与饱和多孔介质之间的耦合计算,从而将流体、固体、饱和多孔介质间的耦合问题纳入到统一计算框架,并编制了相应的三维并行分析程序.以P-SV波垂直入射时,半无限层状海水-饱和海床、海水-弹性基岩、海水-饱和海床-弹性基岩三种情形的动力分析为例,采用统一计算框架结合透射边界条件进行求解,并与传递矩阵方法得到的解进行对比,验证了该统一计算框架的有效性以及并行计算的可行性.      

Error estimation of laser-Doppler anemometry measurements in fluids with spatial inhomogeneities of the refractive index

We report a combined experimental and theoretical investigation of the influence of spatial non-uniformities of the refractive index on the accuracy of laser Doppler anemometry (LDA) measurements in transparent fluids. One LDA beam is guided through heated air of a thermal boundary layer near a heated vertical flat plate. It is found that the hot air is deflecting the beam because of a modification of the refractive index n in the fluid. This deflection causes three effects: (1) spatial displacement of beam intersection, (2) waist mismatch in the measurement volume and (3) variation in interference fringe distance. With the help of a rotating disk calibration system the resulting displacement of the LDA measurement volume and the Doppler frequency variation is systematically studied at different temperatures. Using a simple model of beam propagation under the influence of well-defined temperature inhomogeneities, the displacement of measurement volume and change in Doppler frequency are calculated and are found to be in agreement with the experimental observations. The results provide a rational framework for an assessment of the accuracy of LDA data in arbitrary transparent fluids with non-uniform refractive index.     

幂律流体圆柱绕流的格子波尔兹曼模拟简

基于插值补充格子波尔兹曼方法和幂律流体的本构方程,建立了贴体坐标系下适用于幂律流体的格子波尔兹曼模型,模拟了幂律流体的圆柱绕流问题,采用非平衡外推格式处理圆柱表面的速度无滑移边界,利用应力积分法确定曳力系数和升力系数,并与基于标准的格子波尔兹曼方法和有限容积法获得的数值数据进行对比,吻合良好. 进行了网格无关性验证之后,分析了稳态流动时,不同雷诺数下幂律指数对于尾迹长度、分离角、圆柱表面黏度分布、表面压力系数及曳力系数的影响,以及非定常流动中,幂律指数对于流场、曳力系数、升力系数和斯特劳哈尔数的影响. 获得的变化规律与基于其他数值模拟方法得到的结果相一致,充分验证了模型的有效性和正确性. 结果表明：插值补充格子波尔兹曼方法可以用来模拟幂律流体在具有复杂边界流场内的流动问题,通过引入不同的非牛顿流体本构方程,该方法还可以进一步应用于其他类型的非牛顿流体研究中.     

幂律流体圆柱绕流的格子波尔兹曼模拟

基于插值补充格子波尔兹曼方法和幂律流体的本构方程,建立了贴体坐标系下适用于幂律流体的格子波尔兹曼模型,模拟了幂律流体的圆柱绕流问题,采用非平衡外推格式处理圆柱表面的速度无滑移边界,利用应力积分法确定曳力系数和升力系数,并与基于标准的格子波尔兹曼方法和有限容积法获得的数值数据进行对比,吻合良好. 进行了网格无关性验证之后,分析了稳态流动时,不同雷诺数下幂律指数对于尾迹长度、分离角、圆柱表面黏度分布、表面压力系数及曳力系数的影响,以及非定常流动中,幂律指数对于流场、曳力系数、升力系数和斯特劳哈尔数的影响. 获得的变化规律与基于其他数值模拟方法得到的结果相一致,充分验证了模型的有效性和正确性. 结果表明:插值补充格子波尔兹曼方法可以用来模拟幂律流体在具有复杂边界流场内的流动问题,通过引入不同的非牛顿流体本构方程,该方法还可以进一步应用于其他类型的非牛顿流体研究中.