Statistics of ultrasonic speckles reflected from a rough surface

Summary  First- and second-order statistical properties of ultrasonic speckles reflected from a rough interface are studied theoretically and experimentally in this paper. A theoretical model for predicting statistical properties of ultrasonic speckles is constructed, based on the Fresnel-Huygens principle and three basic assumptions. Distributions of the amplitude and phase of ultrasonic speckles in a scattering space are studied; the study shows that they are in the form of Rayleigh and uniform distribution, respectively. Using the proposed model, the average transverse size of the speckles within a scattering domain, which are received by a focus probe, is investigated. The average transverse size is found to be dependent on the characteristics of the measuring system only, and does not vary with the position in the domain. To verify the applicability of the theoretical model, a special experimental set-up was designed. The corresponding experiments were conducted for measuring the sound pressure of the ultrasonic speckles reflected from a rough interface between water and aluminium alloy. The numerical results are compared with the experimental ones. The comparison demonstrates that the theoretical model and the three related assumptions are suitable for analysing statistical properties of ultrasonic speckles reflected from a rough interface. Received 26 January 2001; accepted for publication 27 November 2001 RID=" ID=" This work was supported by National Natural Science Foundation of China under project 10074017.     

Active control schemes for aseismic base-isolated structures

Summary  Active control schemes are used for the protection of base-isolated and seismically excited buildings. The desired control objective is to keep the whole structure arbitrarily close to its initial configuration prior to the earthquake. The proposed methods require control force application only at the base of the structure. The controllers developed may depend on information obtained from all the floors or just the first (base) floor alone. Received 13 September 2000; accepted for publication 26 June 2001 RID=" ID=" Dedicated to the memory of Professor P.D. Panagiotopoulos with our warmest prayers. RID=" ID=" The first author wishes to thank Prof. G. Leitmann and Prof. E. Papadopoulos for the numerous helpful discussions. The same author is supported in part by the Institute of Communication and Computer Systems, NTUA, under the program Archimedes 65/1017.     

Mixed-mode stress intensity factors and critical angles of cracks in bolted joints by weight function method

Summary   Mechanical joints, such as bolted or riveted joints, are widely used in structural components. Reliable determination of stress intensity factors for cracks in bolted joints is required to evaluate their safety and fatigue life. The weight function method is an efficient technique to calculate stress intensity factors for various loading conditions by the stress analysis of an uncracked model. In this paper, the mixed-mode stress intensity factors for cracks in bolted joints are analyzed by the weight function method, and coefficients included in the weight function are determined by finite element analysis for reference loadings. The critical angle at which mode I stress intensity factor becomes maximum is determined, and the effects of the amount of clearance and crack length on the critical angle are investigated. Received 28 February 2001; accepted for publication 22 June 2001 RID=" ID=" The authors are grateful for the support provided by a grant from the Korea Science & Engineering Foundation (KOSEF) and Safety and Structural Integrity Research Center at the Sungkyunkwan University.     

Analytical thermo-elastodynamic solutions for a nonhomogeneous transversely isotropic hollow sphere

Summary  The spherically symmetric dynamic thermoelastic problem for a special nonhomogeneous transversely isotropic elastic hollow sphere is formulated by introduction of a dependent variable and separation of variables technique. The derived solution can be degenerated into that for a homogeneous transversely isotropic hollow sphere, a nonhomogeneous isotropic hollow sphere or a solid sphere. The present method, allow to avoid integral transforms, is suited for a hollow sphere of arbitrary thickness subjected to arbitrary spherical symmetric thermal and mechanical loads, and is convenient in dealing with different boundary conditions of dynamic thermoelasticity . The numerical calculation involved is easy to be performed and its results are also presented. Received 30 October 2001; accepted for publication 21 February 2002 The work was supported by the National Natural Science Foundation of China (No. 10172075 and No. 10002016)     

Dynamic interaction between a moving vehicle and an infinite structure excited by irregularities – Fourier transforms solution

Summary  A new approach to calculate the dynamic interaction between a moving vehicle and an infinite structure is presented. Its main characteristics are: use of Fourier transformed domains (leading to a very general formulation of the problem), correct consideration of the motion of all components of the model; consideration of all kinds of mutual dynamic interactions between the vehicle and the track, and the possibility to include a layered half-space for the subgrade, instead of the elastic Winkler foundation used here. Examples of a single axle and a bogie model passing an irregular track illustrate characteristic effects. Received 13 December 1999; accepted for publication 21 September 2001 RID=" ID=" The research reported here was done at the Lehrstuhl für Baumechanik, (TUM). The authors are greatly indebted to Harry Grundmann for his interest and advice.     

Simulation of the sedimentation of aggregating particles

The methods of the thermodynamics of irreversible processes are used to construct a three-phase model of a suspension that takes into account the formation of aggregates from suspended particles and the trapping of part of the carrier fluid in the aggregates. The model makes it possible to describe both the motion of the aggregates relative to the carrier fluid as well as the flow of the fluid through the structure of the aggregate, and also the elastic properties of the aggregates. In the framework of the model, a study is made of the problem of one-dimensional sedimentation of aggregating particles in a finite tube under the influence of gravity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 71–78, May–June, 1983.I thank S. A. Regirer for interest in the work and valuable discussions.     

Influence of unsteady wake on a turbulent separation bubble

 An experimental study was made of turbulent separated and reattaching flow over a blunt body, where unsteady wake was generated by a spoked-wheel type of wake generator with cylindrical rods. The influence of unsteady wake was scrutinized by altering the rotation direction (clockwise and counter-clockwise) and the normalized passing frequency (0 ≤ St _H  ≤ 0.20). The Reynolds number based on the cylindrical rod was Re _d =375. A phase-averaging technique was employed to characterize the unsteady wake. The effect of different rotation directions, which gave a significant reduction of x _R , was examined in detail. The wall pressure fluctuations on the blunt body were analyzed in terms of the spectrum and the coherence. Received: 15 January 2001 / Accepted: 17 July 2001     

The rule of affine similitude for the force coefficients of a body oscillating in a uniformly stratified fluid

 This paper presents a study on affine similitude for the force coefficients of an arbitrary body oscillating in a uniformly stratified fluid. A simple formula is derived that gives a relation between the force coefficients for a body oscillating in homogeneous and uniformly stratified ideal fluids. In particular, it implies the existence of a universal nondimensional similitude criterion for a family of affinely similar bodies, namely, the bodies that can be transformed into each other by vertical dilation of the initial coordinate system. Theoretical results are verified by experiments with a set of spheroids having different length-to-diameter ratios. The experimental technique for evaluation of the frequency-dependent force coefficients is based on Fourier analysis of the time-history of damped oscillation tests. Received: 25 September 2000 / Accepted: 6 July 2001 Published online: 29 November 2001     

一种考虑液相惯性的一维准静力固结模型

经典Terzaghi一维固结理论不考虑孔隙流体惯性影响,且该理论在不同时期模型推导和表述结果差别较大,导致当前仍存在诸多困惑甚至认识混乱的现象. 在笔者前期研究大变形动力固结理论框架内,忽略固相惯性而重点考虑液相惯性影响,经过合理简化建立反映孔隙流体惯性的一维小变形固结波动模型. 该固结波模型具有频散和耗散特性. 采用分离变量法,可得到单面排水和瞬时加载条件下无量纲形式固结波解析解答. 算例分析结果表明:固结波发展规律受无量纲数D_{\mathrm{c}}变化影响而呈现不同性态;D_{\mathrm{c}}数值较大时固结波响应会出现阶跃和正负波动现象;当D_{\mathrm{c}}值较小时,可能出现Mandel-Cryer效应等特殊现象. 通过对早期和后期Terzaghi固结模型的分析和对比,初步探明Terzaghi固结理论模型内部的矛盾性,在普通土体坐标和固相体积坐标两种不同解读条件下,早期Terzaghi (1923,1925)模型可以分别诠释为具有小变形和大变形属性的不同固结模型. 在经典一维固结理论模型的不同诠释背景下,固结波模型也可以据此作出相应拓展和表述. 固结波理论揭示缩尺固结试验中土体物理力学参数与固结波响应两种因素之间存在一种不确定性矛盾,据此建议微观土力学研究重视尺度效应. 固结波模型的意义还在于,可为Terzaghi经典固结模型理论精度分析提供新的依据.      

Modeling the response of filled elastomers at finite strains by rigid-rod networks

Summary  A constitutive model is developed for the isothermal response of particle-reinforced elastomers at finite strains. An amorphous rubbery polymer is treated as a network of long chains bridged to permanent junctions. A strand between two neighboring junctions is thought of as a sequence of rigid segments connected by bonds. In the stress-free state, a bond may be in one of two stable conformations: flexed and extended. The mechanical energy of a bond in the flexed conformation is treated as a quadratic function of the local strain, whereas that of a bond in the extended conformation is neglected. An explicit expression is developed for the free energy of a network. Stress–strain relations and kinetic equations for the concentrations of bonds in various conformations are derived using the laws of thermodynamics. In the case of small strains, these relations are reduced to the constitutive equation for the standard viscoelastic solid. At finite strains, the governing equations are determined by four adjustable parameters which are found by fitting experimental data in uniaxial tensile, compressive and cyclic tests. Fair agreement is demonstrated between the observations for several filled and unfilled rubbery polymers and the results of numerical simulation. We discuss the effects of the straining state, filler content, crosslink density and temperature on the adjustable constants. Received 3 January 2001; accepted for publication 12 July 2001     

Contribution to the theory of stationary separation zones

Experiment shows that the stationary flow pattern about a bluff body with closed separation zone, in the case of laminar flow about the body and in the separation zone, breaks down for a subsonic stream velocity in the Reynolds number range from 10¹ to 10². However, experiment shows that for a supersonic stream velocity a stable stationary flow pattern is observed with the existence of laminar stagnant zones adjacent to the body (the stagnant zone behind an aft-facing step on the body surface, the stagnant zone ahead of a gradual forward-facing step on the body surface, the forward separation zone formed by the tip of a spike, the stagnant zone formed when a shock impinges on a body surface) at high Reynolds numbers of the order of 10⁴–10⁶.Thus, experiments indicate that in certain ranges of variation of M and R, under certain boundary condition, stationary solutions of the viscous fluid equations of motion exist and are stable. Outside these ranges and under other boundary conditions the flow about a body with a closed separation zone has a more (Karman vortex street for M1) or less (pulsating flow in the near wake behind the body for M>1) marked unsteady nature, indicating instability of the stationary solutions of the equations of motion under these conditions. To date no theoretical justification has been presented for the existence of stable stationary flows with separation zones in the ranges indicated.In the following an attempt is made to find the region of existence of possible stationary flows with a closed separation zone in that range of Reynolds numbers in which the flow in the viscous mixing region may be described by the Prandtl equations. In so doing the boundary conditions for the flow within the separation zone are selected so that the flow pattern within the zone is significantly simplified and use of the analysis methods applicable in hydrodynamics becomes possible. In the first part (§§1–4) we study the field of possible stationary flows for the case of an incompressible fluid. It is shown that only under special boundary conditions within the separation zone (ideal dissipator) does the flow about a flat plat as R approach the Kirchhoff flow with fluid at rest within the zone. In this case the drag coefficient of the system consisting of the plate plus the ideal dissipator c_x/(^{+ +}4), i.e., it approaches a value which is half that obtained by Kirchhoff for an ideal fluid.A qualitative study of the field of possible stationary flows in the c_xR plane made it possible to discover the existence of a region, having an upper bound at R10², which degenerates into a line. In this region the stationary flows have a singular flow configuration with inviscid vortical-type attachment.The existence of a connection between the flow configuration in the inviscid vortical attachment region and the stability of the stationary solutions is investigated in the second part (§§6–7), both for the case of individual solutions obtained by the method of linear hydrodynamic stability theory and on the basis of the available experimental data obtained over a wide range of Reynolds numbers for both subsonic and supersonic flow velocities. This investigation makes it possible to formulate a rule for finding stable stationary flows with separation zones and to apply this rule to analyze separation-type flows, both laminar and in certain special cases turbulent.     

Dynamic simulation of sedimentation of solid particles in an Oldroyd-B fluid

In this paper we present a two-dimensional numerical study of the viscoelastic effects on the sedimentation of particles in the presence of solid walls or another particle. The Navier-Stokes equations coupled with an Oldroyd-B model are solved using a finite-element method with the EVSS formalism, and the particles are moved according to their equations of motion. In a vertical channel filled with a viscoelastic fluid, a particle settling very close to one side wall experiences a repulsion from the wall; a particle farther away from the wall is attracted toward it. Thus a settling particle will approach an eccentric equilibrium position, which depends on the Reynolds and Deborah numbers. Two particles settling one on top of the other attract and form a doublet if their initial separation is not too large. Two particles settling side by side approach each other and the doublet also rotates till the line of centers is aligned with the direction of sedimentation. The particle-particle interactions are in qualitative agreement with experimental observations, while the wall repulsion has not been documented in experiments. The driving force for lateral migrations is shown to correlate with the pressure distribution on the particle's surface. As a rule, viscoelasticity affects the motion of particles by modifying the pressure distribution on their surface. The direct contribution of viscoelastic normal stresses to the force and torque is not important.     

A correlation for yield stress fluid flow through packed beds

Relatively few correlations are available for non-Newtonian fluid flows through packed beds, even though such fluids are frequently used in industry. In this paper, a correlation is presented for yield stress fluid flow through packed beds. The correlation is developed by introducing the yield stress model in place of the Newtonian model used in deriving Erguns equation. The resulting model has three parameters that are functions of the geometry and roughness of the particle surfaces. Two of the parameters can be deduced in the limit as the yield stress becomes negligible and the model reduces to Erguns equation for Newtonian fluids. The third model parameter is determined from experimental data. The correlation relates a defined friction factor to the dimensionless Reynolds and Hedstrom numbers and can be used to predict pressure drop for flow of a yield stress fluid through a packed bed of spherical particles. Conditions for flow or no-flow are also determined in the correlation. Comparison of model calculations, between a Newtonian and a yield stress fluid for flow penetration into a packed bed of spheres, shows the yield stress fluid initially performs similar to the Newtonian fluid, at large Reynolds numbers. At lower Reynolds numbers the yield stress effect becomes important and the flow rate significantly decreases when compared to the Newtonian fluid.     

Electrohydrodynamic method of determining the particle size of the dispersed phase in a magnetic fluid

A mathematical model of the process of passing an alternating electric current through a magnetic fluid is proposed. The process has been experimentally investigated at different frequencies for various concentrations of the dispersed phase. So far this effect has been investigated mainly experimentally (for example, in [1, 2]), and the experimental results have been qualitatively interpreted. An expression is obtained for the impedance of the part of the circuit containing the cell with the magnetic fluid in the case of high frequencies. This expression makes it possible to determine, from the ratio of the amplitudes and phases of the current and the voltage in the circuit, the conducbivity and dielectric constant of the magnetic fluid. It is shown that in the particular case of low volume concentration of the dispersed phase the conductivity of the magnetic fluid depends on two parameters: the volume concentration of the dispersed phase a and the dimensionless frequency of variation of the potential difference applied to the cell containing the magnetic fluid . The passage of an alternating electric current through a cell containing a magnetic fluid has been experimentally investigated at different frequencies for various volume concentrations of the dispersed phase. A new method of determining the particle size of the dispersed phase in a magnetic fluid is proposed on the basis of a comparison of the theoretical and experimental results.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 157–164, September–October, 1987.     

Transient dislocation emission from a crack tip under dynamic mode III loading

Summary  Transient dislocation emission from a crack tip under dynamic mode III loading is analyzed. By taking into account the dynamic interaction between the crack and dislocation, the governing equation for the dislocation motion is derived under the quasi-steady assumption. The behavior of dislocation emission is explored in detail by solving this equation numerically. A critical initial speed can be determined, which must be exceeded by dislocations to escape from the crack tip. The dislocation emission process is found to be completed in such a short time period that the applied load may be approximately treated as constant during dislocation emission. Based on this fact, an asymptotic criterion for transient dislocation emission is developed, from which the critical initial speed can be evaluated. In the case that the dislocation is emitted from rest, we recover the quasi-static criterion of dislocation emission. Received 22 November 2000; accepted for publication 20 March 2001     

Existence of Weak Solutions for the Unsteady Interaction of a Viscous Fluid with an Elastic Plate

The purpose of this work is to study the existence of solutions for an unsteady fluid-structure interaction problem. We consider a three-dimensional viscous incompressible fluid governed by the Navier–Stokes equations, interacting with a flexible elastic plate located on one part of the fluid boundary. The fluid domain evolves according to the structure’s displacement, itself resulting from the fluid force. We prove the existence of at least one weak solution as long as the structure does not touch the fixed part of the fluid boundary. The same result holds also for a two-dimensional fluid interacting with a one-dimensional membrane.     

A numerical model for thermal systems with helically-coiled tubes and its experimental verification

 A conjugate numerical model proposed by Nakayama et al. for the steady problem of cooling a fluid flowing through a coiled tube, has been successfully extended to investigate two distinctive thermal problems, namely, the transient cooling processes associated with a beer dispenser, and the transient processes of heat storage and recovery associated with a packed bed saturated with a molten salt. An axisymmetric numerical procedure is adopted for determining the velocity and temperature fields within the chilled water bath of the beer dispenser. A simplified one-dimensional heat transfer model is introduced for coupling the tube flow with the recirculating flow in the bath. A similar axisymmetric finite difference procedure is applied for the heat transfer analysis of the packed bed saturated with a molten salt. For the heat recovery process, a one-dimensional heat balance equation for the two-phase flow with a helically-coiled tube is introduced to update the wall surface temperatures, which are needed to calculate the temperature field in the saturated packed bed. The numerical results for both thermal systems associated with coiled tubes agree very well with the corresponding velocity and temperature data obtained from the experiments. Received on 28 August 2000 / Published online: 29 November 2001     

Modeling particle sedimentation in viscous fluids with a coupled immersed boundary method and discrete element method

Numerical techniques have increasingly been used to model fluid–particle two-phase flows. Coupling the immersed boundary method (IBM) and discrete element method (DEM) is one promising approach for modeling particulate flows. In this study, IBM was coupled with DEM to improve the reliability and accuracy of IBM for determining the positions of particles during the sedimentation process within viscous fluids. The required ratio of the particle diameter to the grid size (D/dx) was determined by comparing the simulation results with the analytical solution and experimental data. A dynamic mesh refinement model was utilised in the IBM model to refine the computational fluid dynamics grid near the particles. In addition, an optimum coupling interval between the IBM and DEM models was determined based on the experimental results of a single particle sedimentation within silicon oil at a Reynolds number of 1.5. The experimental results and the analytical solution were then utilised to validate the IBM–DEM model at Reynolds numbers of 4.1, 11.6, and 31.9. Finally, the validated model was utilised to investigate the sedimentation process for more than one particle by modeling the drafting-kissing-tumbling process and the Boycott phenomenon. Benchmark tests showed that the IBM–DEM technique preserves the advantages of DEM for tracking a group of particles, while the IBM provides a reliable and accurate approach for modeling the particle–fluid interaction.