A device for measuring the velocity of ultrasonic waves: An application to stress analysis

In this paper we present a device for the practical application of an ultrasonic critical-angle refractometry (UCRfr) technique. UCRfr is a technique for measuring the velocity of longitudinal, shear and Rayleight waves, developed to improve the traditional ultrasonic methods for measuring the stress level in materials by means of acousto-elasticity. The technique consists of relating the variations in wave propagation velocity to variations in the angle of refraction at the interface with a second medium. Variations in the angle of refraction are determined on the basis of delay in receiving of the same wave at two different points. The study deals with the measurements of velocity changes of longitudinal wave due to uniaxial stress. In the present work the effects of stress on aluminum and steel specimens have been studied. Experimentation has show the potential of the technique for stress measurement; on the other hand, when the applied stress is known, it allows the measurement of the acoustoelastic constants of longitudinal waves. As regards measuring variations in velocity induced by stress, using this method it is possible, with a suitable choice of the material the device is made of, to isolate the effects of stress on velocity from the possible effects of temperature.     

温度场作用下输流悬臂碳纳米管的颤振失稳分析

以非局部弹性理论为基础，采用欧拉-伯努利梁模型，考虑碳纳米管的小尺度效应，应用哈密顿原理获得了温度场作用下的输流悬臂单层碳纳米管（SWCNT）的振动控制方程以及边界条件，依靠微分变换法（DTM法）对此高阶偏微分方程进行求解，通过数值计算研究了温度场中悬臂单层输流碳纳米管的振动与颤振失稳问题。结果表明：管内流体流速、温度场中温度变化情况与小尺度参数都会对系统振动频率以及颤振失稳临界流速产生影响。其中，小尺度效应将会降低悬臂输流系统的稳定性，使系统更为柔软；而高温场与低温场对系统动态失稳的影响不同，低温场中随温度变化值的增加，系统的稳定性提高；高温场这一作用效果恰好与之相反。     

磁场对不同温度场中输流悬臂碳纳米管动态特性的影响

本文在采用经典欧拉-伯努利梁模型的基础上,引入考虑小尺度效应的非局部弹性理论,着重研究不同温度场中输流悬臂单层碳纳米管系统（SWCNT）在外加纵向磁场作用下的颤振失稳问题。基于哈密顿原理获得了该流固耦合系统的振动控制方程及相应的边界条件,应用微分变换法（DTM法）求解此高阶偏微分方程,通过数值计算研究了不同温度场中施加纵向磁场对系统动力学特性的影响。结果表明：施加纵向磁场在不同温度场中都将增强输流悬臂碳纳米管的动态稳定性。然而,这种增强程度却与温度场的变化量有关,在不同温度变化量下,磁场对系统稳定性的增强程度有一个峰值,这意味着,实际应用中,为了提高这类流固耦合系统的动态稳定性,一味提高纵向磁场强度并不可取。     

Application of the ultrasonic velocity profile method to the mapping of liquid metal flows under the influence of a non-uniform magnetic field

An ultrasonic velocity profile (UVP) method has been successfully applied to the investigation of a liquid metal channel flow under the influence of an inhomogeneous magnetic field. Using velocity profiles obtained by the ultrasonic velocimeter and their numerical post processing, two-dimensional time-averaged flow maps were efficiently produced. A single transducer immersed directly into the working fluid was used in order to simplify alignment of measurement lines and avoid the undesirable refraction of the acoustic beam on the walls. An M-shaped flow and wake behind a magnetic obstacle were reconstructed as the patterns of shear and large-scale vortical flows.     

Effect of measurement volume size on turbulent flow measurement using ultrasonic Doppler method

This paper presents the results of an investigation on the effects of measurement volume size on the mean velocity profile and the Reynolds stress for fully developed turbulent pipe flows. The study employs the ultrasonic velocity profile method, which is based on the ultrasonic Doppler method. The ultrasonic Doppler method offers many advantages over conventional methods for flow rate measurement in the nuclear power plant piping system. This method is capable of measuring the instantaneous velocity profile along the measuring line and is applicable for opaque liquids and opaque pipe wall materials. Furthermore, the method has the characteristic of being non-intrusive. Although it is applicable to various flow conditions, it requires a relatively large measurement volume. The measurement volume of the present method has a disk-shape determined by the effective diameter of the piezoelectric element and the number of the wave cycles of the ultrasonic pulse. Considering this disk-shaped measurement volume and expressing the time-averaged velocity in a truncated Taylor series expansion around the value at the center of the measuring control volume, the value of the velocity can be obtained. The results are then compared with the data obtained from DNS and LDA measurements. The result shows that the effect of the measurement volume size appears in the buffer region and viscous sublayer.     

Importance of induced magnetic field and exponential heat source on convective flow of Casson fluid in a micro-channel via AGM

The study of the natural convective flow of a fluid in the presence of an induced magnetic field has always been of considerable importance due to its many applications in various areas of science, technology, and industry, such as the operation of magnetohydrodynamic generators. This study addresses an analysis of exponential heat source and induced magnetic field on the second-class convection of Casson fluid in a microchannel. The flow is in a vertical microchannel organized by two vertical plates. The answer to governing equations has been grabbed for temperature field, induced magnetic field, and velocity via Akbari-Ganji's method (AGM). Nusselt number, skin friction coefficient, and current density are approximated. Graphs that describe the conclusion of influential physical variables on velocity, temperature, current density, induced magnetic field, and skin friction coefficient distributions are shown. Comparison of results with numerical method (Runge-Kutta-Fehlberg, RKF-45), homotopy perturbation method, and AGM confirms the accuracy of answers obtained with AGM.     

Quantitative NMR velocity imaging of a main-chain liquid crystalline polymer flowing through an abrupt contraction

 The flow of isotropic and liquid crystalline (LC) hydroxypropylcellulose (HPC) aqueous solutions into an abrupt axisymmetric contraction has been quantitatively measured by pulsed-field-gradient NMR techniques. Steady-state axial velocity profiles, acquired upstream of the contraction, reveal a large contraction entry length for the LC solution. This entry flow field exists over an order of magnitude change in flow rate and is attributed to elasticity that is associated with polydomain liquid crystallinity. Pronounced, off-centerline velocity maxima (in an axisymmetric flow field) were present upstream of the contraction, in the entry flow region. Apparently, a more viscous and elastic core of fluid was present along the centerline; this fluid resisted elongational strain more than the fluid closer to the walls. Quantitative velocity profiles were extracted from displacement distributions and corrected for elongational dispersion. The isotropic solution velocity profiles matched those obtained from viscoelastic simulations using an approximate Doi-Edwards model, parameterized with independent rheological data. Received: 29 April 1999/Accepted: 30 August 1999     

Fluid structure interaction of cantilever micro and nanotubes conveying magnetic fluid with small size effects under a transverse magnetic field

Micro and nanotubes have found major application in fluidic systems as channels for conveying fluid. In some micro and nanofluidic applications such as drug delivery, a transverse magnetic field can be used to guide the fluid flow by generating an axial force in the flow direction. An important issue in the design of micro and nanofluidic systems is the structural vibration caused by the fluid flow. In the current study, we investigate the effect of transverse magnetic field on the vibration of cantilever micro and nanotubes conveying fluid by considering the small size effects. We couple the nonlocal Euler–Bernoulli beam model with Navier–Stokes theory to determine a fluid structure interaction (FSI) model for the vibration analysis of the system. We modify the FSI governing equation by driving a velocity correction factor to consider the effect of transverse magnetic field on the fluid flow’s pattern through the tube. Then, we use the Galerkin’s method to obtain the frequency diagrams for the instability analysis of the system. We show that the transverse magnetic field can have a substantial effect on the dynamics of tube conveying fluid by increasing the system’s natural frequencies and critical flow velocity which contributes to the flutter instability. We also discover that although the transverse magnetic field plays a crucial role on dynamics of microstructures, its effect on the dynamics of nanotubes is not significant and can be ignored.     

3D particle streak velocimetry by defocused imaging

Particle streak velocimetry (PSV) has become one of the important branches of flow filed measurements. It extracts velocity information from particle trajectories captured by single frame long exposure images. Since the defocus of moving particle is inevitable during a long exposure time and under a large magnification, a novel three-dimensional (3D) velocity measurement method named defocusing particle streak velocimetry (DPSV) is proposed in this paper. On the one hand, an extension from two-dimensional (2D) to 3D velocity measurement with a monocular system is carried out. The depth information of the particle, which reflects the position in the third dimension, is indicated by the defocusing degree (characteristic parameter σ) of the particle images. The variation of σ along the trajectory is recognized by surface fitting of the gray value distribution of particle images, assuming that σ varies linearly along the trajectory. On the other hand, based on the linear fitting for the straight trajectory, an arc fitting model is developed for curved trajectories which are commonly captured in turbulent flow. The relationship between σ and the particle depth position z is experimentally calibrated using a LED light and a diaphragm. Finally, the DPSV method is verified in a submerged jet flow field as well as in a microchannel flow field to obtain the 3D velocity field with single monocular system.     

Exact Averaging of Stochastic Equations for Transport in Random Velocity Field

We present new examples of exactly averaged multi-dimensional equation of transport of a conservative solute in a time-dependent random flow velocity field. The functional approach and a technique for decoupling the correlations are used. In general, the averaged equation is non-local. We study the special cases where the averaged equation can be localized and reduced to a differential equation of finite-order, where the problem of evolution of the initial plume (Cauchy problem) can be solved exactly. We present in detail the results of the analyses of two cases of exactly averaged problems for Gaussian and telegraph random velocity with an identical exponential correlation function, which are informative and convenient models for continuous and discontinuous random functions. The problems in which the field has sources of solute and boundaries are also examined. We study the behavior of different initial plumes for all times (evolutions and convergence) and show the manner in which they approach the same asymptotic limit for two stochastic distributions of flow-velocity. A comparison between exact solutions and solutions derived by the method of perturbation is also discussed.