Effect of asymmetric actuator and detector position on Coriolis flowmeter and measured phase shift

Coriolis flowmeters (CFM) are forced to vibrate by a periodic excitation usually applied midpipe through an electromagnetic actuator. From hands-on experience with industrial CFMs it appears, that the electromagnetic actuator has to be located as symmetric as possible. For CFM design and trouble-shooting it is of relevance to know how and if imperfections, related to the excitation location, influence the dynamic behavior of the vibrating fluid-conveying pipes employed in CFMs. A simple model of an imperfectly excited, simply supported, straight, single pipe CFM is investigated using a multiple time scaling perturbation analysis. The result is a simple analytical expression for the approximated phase shift, which offers a direct insight into how the location of the actuator influences the phase shift. It appears, that asymmetrical forcing combined with fluctuating pipe damping could be a factor contributing to lack of zero shift stability observed with some industrial CFMs. Tests of the approximated solution against results obtained by pure numerical analysis using Galerkin expansion show very good agreement. The effect of asymmetric detector positions is also investigated. Any asymmetry in the detectors position, e.g. due to manufacturing variations or improper handling of the CFM, induces a phase shift that leads to changes of the meter’s sensitivity, and could therefore result into erroneous measurements of the mass flow. This phase shift depends on the mass flow and does not contribute to a lacking zero-point stability. The validity of the hypotheses, which are assumed to be basically similar for more complicated geometries, e.g. bended and/or dual pipe CFMs, with or without multiple actuators, is suggested to be tested using laboratory experiments with purpose built non-ideal CFMs.     

Investigations on pressure dependence of Coriolis Mass Flow Meters used at Hydrogen Refueling Stations

In the framework of the ongoing EMPIR JRP 16ENG01 “Metrology for Hydrogen Vehicles” a main task is to investigate the influence of pressure on the measurement accuracy of Coriolis Mass Flow Meters (CFM) used at Hydrogen Refueling Stations (HRS). At a HRS hydrogen is transferred at very high and changing pressures with simultaneously varying flow rates and temperatures. It is clearly very difficult for CFMs to achieve the current legal requirements with respect to mass flow measurement accuracy at these measurement conditions. As a result of the very dynamic filling process it was observed that the accuracy of mass flow measurement at different pressure ranges is not sufficient. At higher pressures it was found that particularly short refueling times cause significant measurement deviations. On this background it may be concluded that pressure has a great impact on the accuracy of mass flow measurement. To gain a deeper understanding of this matter RISE has built a unique high-pressure test facility. With the aid of this newly developed test rig it is possible to calibrate CFMs over a wide pressure and flow range with water or base oils as test medium. The test rig allows calibration measurements under the conditions prevailing at a 70 MPa HRS regarding mass flows (up to 3.6 kg min⁻¹) and pressures (up to 87.5 MPa).     

Dynamic analysis of Coriolis flow meter using Timoshenko beam element

Coriolis mass flow meter (CFM) is used to measure the rate of mass flow through a pipe conveying fluid. In the present work, the Coriolis effect produced in the pipe due to a lateral excitation is modeled using the finite element (FE) method in MATLAB©. The coupled equation of motion for the fluid and pipe is converted to FE equations by applying Galerkin technique. The pipe conveying fluid is excited at its fundamental natural frequency. The time lag observed between symmetrically located measurement points which are equidistant from the point of excitation, is utilized to predict the mass flow rate. The results predicted by the present code is validated using the experimental, and numerical results published in the literature. The main contribution is the development of a FE model, using three node Timoshenko beam element to analyse the dynamics of fluid conveying pipes subjected to external excitation. The direction of the Coriolis force is perpendicular to the plane containing the velocity of flow vector and angular velocity vector of the pipe. Hence a three dimensional FE model is essential. This model can include curved geometry, damping, velocity and gyroscopic effects for three dimensional flexible tubes. The reduced integration used for overcoming shear locking in two node elements, will result in the formation of spurious modes leading to an incorrect prediction of natural frequencies and velocity. These modes will not occur while using three node elements. Influence of spatial as well as temporal discretisation on the time lag and frequency are also discussed. The sensitivity analysis shows that the time lag varies linearly with the mass flow rate.     

An improved in situ measurement of offset phase shift towards quantitative damping-measurement with AFM

An improved approach is introduced in damping measurement with atomic force microscope (AFM) for the in situ measurement of the offset phase shift needed for determining the intrinsic mechanical damping in nanoscale materials. The offset phase shift is defined and measured at a point of zero contact force according to the deflection part of the AFM force plot. It is shown that such defined offset phase shift is independent of the type of sample material, varied from hard to relatively soft materials in this study. This improved approach allows the self-calibrated and quantitative damping measurement with AFM. The ability of dynamic mechanical analysis for the measurement of damping in isolated one-dimensional nanostructures, e.g. individual multiwalled carbon nanotubes, was demonstrated.     

A finite element model for the analysis of flexible tube Coriolis mass flow meter using first order shear deformation shell theory

The numerical modelling of Coriolis Mass flow Meter (CFM) is essential for predicting its outcomes accurately in terms of sensitivity as well as exact mass flow rates. In the majority of mathematical and numerical modelling concerning the flexible structures, the authors neglect the dimensional and shape variation of the structure due to self-weight. The shell based on the First-order shear deformation shell theory (FSDST) is preferred in modelling shells compared to the beam model. The current work includes numerical modelling of CFM using eight noded isoparametric shell elements and twenty noded Acoustic fluid elements. The fluid energy describes as the potential, and the dynamic boundary condition is assumed utilising the displacement of structure and potential of the fluid. The fluid dynamic equation combining suitable numerical model, fluid-structure interaction module and cross-correlation technique helps to achieve the numerical modelling of CFM. The numerical model of CFM utilises the Newmark Beta method of numerical integration, and the response of two equidistant locations from the point of tube excitation is acquired. For the flexible tube conveying fluid, there exists sagging of tube due to the weight of tube and fluid. The Coriolis force and the external excitation force cause the fluid conveying tube to bend and twist, and as a result, the velocity responses picked from two equidistant points shows a difference in phase. The effect of sagging leads to a lower phase shift and time decay, and hence the sensitivity of the CFM is low for low pre-stretched flexible tubes. The pre-stretching of flexible tubes reduces the effect of sagging, facilitates to regain the cylindrical shape of the tube and increases the sensitivity of CFM. The result reveals that the shell element along with the three-dimensional acoustic fluid element provides the most accurate numerical model for the CFM and the change in sensitivity, as well as the change in mass flow measurements, can appropriately be analysed with the help of this numerical model. The amplitude of the velocity of the structure, measured from the two equidistant points, shows a difference. The severe variation in amplitude of velocity measured from two points is an implication of the out of plane deflection of the tube. For a CFM made up of metal tubes, the amplitude of velocity variation is minimal and ignored by the authors.     

Design of a Low-Cost Thermal Dispersion Mass Air Flow (MAF) Sensor

There is a need for a low-cost sensor to be used in many practical applications, such as the control of the air–fuel ratio in combustion burners, which measures the mass flow rate of fluid. This paper focuses on the design, calibration, and testing of a mass flow sensor operating on the principle of thermal dispersion. The developed sensor implements a digital proportional-integral controller which regulates the body temperature of a heated element, recognized as a thermistor, located in the stream of the fluid flow to a constant difference with respect to the ambient air temperature. The power dissipated by this heated element was referenced to known mass flow rates of air to determine the relationship between the dissipated power and ambient temperature to the measured mass flow rate. The inclusion of air flow conditioners, which filtered unwanted debris and delivered a more laminar air flow, was imperative to the success of the design. The designed sensor was proven to measure the incoming mass air flow through a duct, in the presence of moderate disturbances in the intake air pipe and for a wide range of ambient air temperatures, with a maximum full-scale error of 5.5% and a range up to 80 kg/h.     

Unsteady potential and viscous flows between eccentric cylinders

This paper presents a newly developed spectral collocation method for the study of the unsteady annular flow between two eccentric cylinders. In order to predict the stability of a system in a confined flow, the formulae and results of added mass and fluid damping are provided in the present paper when a cylinder undergoes oscillatory motion in the plane of symmetry and normal to the plane of symmetry in an eccentric annulus. The potential flow theory has been developed to obtain the added mass for incompressible, inviscid and irrotational fluid. For the viscous fluid, the added mass and the viscous damping are presented. This method is validated by comparison with the available analytical solutions obtained for the unsteady potential flow in the eccentric annular space. Excellent agreement was found between the solutions obtained with the present spectral method and the available analytical solutions. In the present study, the viscous effect on the added mass can be evaluated, comparing the results obtained by potential flow theory with those obtained by the viscous flow theory, and viscous damping is investigated.     

An analytical estimation of the Coriolis meter’s characteristics based on modal superposition

The aim of this paper is to derive approximate, analytically expressed, theoretical characteristics for a straight, slender-tube Coriolis meter, which can be applied to any of its working modes. The mathematical model is based on the theories of the Euler beam and one-dimensional fluid flow, and includes the effects of axial force, added masses, damping and excitation. The analytical approximations are evaluated by applying a Taylor-series expansion to the solutions of the Galerkin method, which are considered as a superposition of the Euler-beam modal functions. On the basis of the obtained analytical expressions, the properties of the meter’s characteristics are discussed, with the emphasis being on particular nonidealities.     

Effect of flow on a dual Helmholtz resonator

The acoustic characteristics of a dual Helmholtz resonator in the presence of flow is investigated theoretically and experimentally. A lumped parameter model is introduced, including the damping effect and neck inertia, and the predicted transmission loss (TL) is compared with experiments performed with a flow-impedance tube setup. ^Predicted and measured results with flow exhibit a good agreement, while capturing the key variations in peak TL magnitude and the shifts in peak TL frequency. Theoretical approach demonstrates that the damping of the first neck inertia of the dual Helmholtz resonator has a marked impact not only on the magnitude of the first peak TL but also the second peak TL.     

Combustion of a single droplet in the presence of an oscillating flow

The two-dimensional, unsteady, laminar conservation equations for mass, momentum, energy and species transport in the gas phase are solved numerically in spherical coordinates. This is to study the heat and the mass transfer, and the combustion around a single spherical droplet. The droplet mass and momentum equations are also solved simultaneously with the gas phase equations in order to investigate the effects of droplet entrainment in the oscillating flow with and without a steady velocity. The numerical solution for a single droplet combustion gives the droplet diameter variation as well as the gas phase velocity, temperature and species concentrations as a function of time. The effects of frequency, amplitude of oscillating flow, velocity ratio of oscillating flow amplitude to the steady velocity, ambient temperature and initial droplet diameter on the droplet combustion are also investigated. The droplet burning history is not governed by thed ²-law in the presence of oscillating flow, unlike to the case under quiescent ambient conditions.     

气力输送分支管路流量分配特性的研究

在水平T形分支管道中，用压缩空气作为输送气体，对不同粒径的砂石进行气力输送试验。分别通过试验和改进型BP神经网络预测两种方法对表观气速和分支管路流量控制阀开度变化时，固相在分支管路中的分配特性进行了研究。结果表明，随着表观气速减小和两分支管路流量控制阀开度差值变大，固相流量在两分支管中的分配产生较大差异。试验值和改进型BP网络预测值的对比结果表明，二者相互吻合较好，说明采用改进型的BP网络来模拟固相在分支管路中的分配特性适应性较好。     

管内螺旋导流板引发的气液两相旋流场

用数值模拟的方法研究某种螺旋导流板结构引发的管内气液两相旋流的流动特点。空气为主相,水为次相,入口为雾状流。研究旋转给流型转变、气液相分布、速度分布及旋流衰减带来的影响。发现雾状流在螺旋导流板的作用下,转变为环状流。螺旋导流板内有二次涡的生成,且二次涡结构不断发展变化,离心力分布不均匀而形成沿管壁周向不连续的液膜;流出螺旋导流板后,二次涡会衰减消失,流体做螺旋向前运动,液膜沿圆管周向逐渐分布均匀。管中心处气相切向速度小,气相切向速度较大的区域远离旋流中心区,旋流中心与圆管中心存在小的偏心距;与直管及螺旋纽带相比,螺旋导流板引发的气液两相旋流在圆管中心的气相轴向流速远高于光管和螺旋纽带;与螺旋纽带相比,螺旋导流板引发的旋流强度更大且衰减减慢。     

Effects of Fluid Inertia on Finite-Length Squeeze-Film Dampers

The influence of fluid inertia on the SFD force response to circular-centered motions of arbitrary amplitude is analyzed in detail, For finite length, locally sealed SFDs, integro-differential equations are derived in terms of the mean flow components. Numerical predictions, using the finite-element method, show that the damping and added mass coefficients remain invariant as the Reynolds number increases from small values to a moderate Reynolds number equal to 10. An approximate, finite-length, solution for the fluid-film forces has been analytically obtained which accounts for the fluid-inertia effect as well as local end seal effects in symmetric SFD configurations. The approximate solution, strictly valid for small Reynold numbers (Re < 1), agrees well with the results from the numerical solution for most SFD configurations and orbit radii considered.     

Vibration and dynamic stability of pipes conveying fluid on elastic foundations

The paper deals with the vibration and dynamic stability of cantilevered pipes conveying fluid on elastic foundations. The relationship between the eigenvalue branches and corresponding unstable modes associated with the flutter of the pipe is thoroughly investigated. Governing equations of motion are derived from the extended Hamilton’s principle, and a numerical scheme using finite element methods is applied to obtain the discretized equations. The critical flow velocity and stability maps of the pipe are obtained for various elastic foundation para-meters, mass ratios of the pipe, and structural damping coefficients. Especially critical mass ratios, at which the transference of the eigenvalue branches related to flutter takes place, are precisely determined. Finally, the flutter configuration of the pipe at the critical flow velocities is drawn graphically at every twelfth period to define the order of the quasi-mode of flutter configuration.     

Semi-analytical derivation of approximate non-linear eigenvalues and eigenvectors for general non-linear MDOF systems

This work introduces a novel theoretical formulation for the evaluation of approximate eigenvalues and eigenvectors for general non-linear MDOF systems using the so-called “approximate non-linear mode evaluation” (ANME) method. The approach is based on analytically derived quasi-linear expressions which relate the change in modal parameters to physical non-linear elements that can be added anywhere in the system. Subject to assuming that the change in the mode shape is small, expressions for non-linear eigenvalues and eigenvectors become fully determined for a general MDOF system, even within typical experimental constraints. The errors arising from this assumption can be minimized via an iterative procedure. Preliminary results indicate that the rate of convergence is quite fast for systems with medium to high damping but more effort is required for lightly damped systems. The derived expressions provide a theoretical basis for observations made by previous researchers from an inspection of their experimental and/or numerical results: these indicate that an invariant relationship exists between a non-linear eigenvalue and its associated modal response.     

Damping forces of vibrating cylinder in confined viscous fluid by a simplified analytical method

The simplified analytical solutions for viscous damping have been formulated, considering the results obtained by an existing numerical method, for relatively narrow annular configurations: (i) when a rigid cylinder executes translational oscillation in the plane of symmetry, and (ii) a flexible cylinder vibrates in its first mode as a clamped-clamped beam subject to axial flow. For narrow annular passages, the viscous damping has significant effects on fluid-dynamic forces. In such a case, an inviscid fluid model is acceptable for estimating added mass. This theory is developed for both relatively high and low oscillatory Reynolds numbers. In terms of computational efficiency, it is useful to obtain the viscous damping forces using this approximate method. Also this method has important benefit for the future study of stability analysis of system; since, the viscous damping forces obtained by the present method can be expressed in terms of the oscillatory Reynolds number explicitly. To validate this theory, the results are compared with the ones obtained by the full viscous theories in the previous works. These results were found to be in reasonably good agreement with the results of the full theories.     

无阀微泵动态特性的固液耦合分析

根据无阀微泵的工作原理,对泵膜－流体耦合振动过程进行理论分析,推导出此状态下的非线性耦合振动方程,并采用伽辽金加权最小余量法得出方程的近似解。在此基础上讨论阻尼系数、驱动力及薄膜固有频率与薄膜振幅、相位差及无阀泵流量的关系。理论分析表明在阻尼系数较小时,在一阶固有频率附近还存在振幅增大的现象,随着阻尼系数的增大,流体对泵膜的阻力逐渐增大,振幅随着频率的增大迅速衰减,相位差也越来越快地靠近90°;驱动力一定的情况下,薄膜的固有频率越低,薄膜在低频段振动可以达到的振幅越大;对于流量而言,在低频段,流量很快就达到极大值,而且阻尼系数越大、泵膜固有频率越低、驱动力越大,流量越快到达极大值。     

Measurement of velocity profiles in multiphase flow using a multi-electrode electromagnetic flow meter

This paper describes an electromagnetic flow meter for velocity profile measurement in single phase and multiphase flows with non-uniform axial velocity profiles. A Helmholtz coil is used to produce a near-uniform magnetic field orthogonal to both the flow direction and the plane of an electrode array mounted on the internal surface of a non-conducting pipe wall. Induced voltages acquired from the electrode array are related to the flow velocity distribution via variables known as ‘weight values’ which are calculated using finite element software. Matrix inversion is used to calculate the velocity distribution in the flow cross section from the induced voltages measured at the electrode array. This paper presents simulations and experimental results including, firstly the effects of the velocity profile on the electrical potential distribution, secondly the induced voltage distribution at the electrode pair locations, and thirdly the reconstructed velocity profile calculated using the weight values and the matrix inversion method mentioned above. The flow pipe cross-section is divided into a number of pixels and, in the simulations, the mean flow velocity in each of the pixels in single phase flow is calculated from the measured induced voltages. Reference velocity profiles that have been investigated in the simulations include a uniform velocity profile and a linear velocity profile. The results show good agreement between the reconstructed and reference velocity profiles. Experimental results are also presented for the reconstructed velocity profile of the continuous water phase in an inclined solids-in-water multiphase flow for which the axial water velocity distribution is highly non-uniform. The results presented in this paper are most relevant to flows in which variations in the axial flow velocity occur principally in a single direction.     

Theoretical investigation of the thermal performance of evacuated heat pipe solar collector with optimum tilt angle under various operating conditions

The thermal performance of an individual pipe in an evacuated tube solar collector with a heat pipe is investigated by an analytical method based on the energy balance of the collector. A simulation method was developed and compared to experimental results under different operating conditions, such as different ambient temperature and changes in weather. After comparing the simulation and experimental results, a discrepancy of about 0–6% is observed due to the simple assumptions in the simulation process and unavoidable human factors. The results show that under conditions of poor radiation and low ambient temperature, the efficiency changes rapidly, while it is relatively steady in high-radiation situations, and is influenced by differences in the ambient temperature and the collector inlet temperature. In addition to the change in the tilt angle of the solar collectors, the solar radiation collected by the absorber unit varies, which leads to differences in the outlet temperature and the efficiency.

     

On the Fluid Flow and Thermal Analysis of a Compliant Surface Foil Bearing and Seal

Foil gas bearings have been applied successfully to a wide range of high-speed rotating machinery such as air cycle machines (ACMs) and auxiliary power units (APUs). The performance of these bearings are based on the high pressure gas in a very thin layer between the journal and the bearing governed by the Reynolds equations. Generation of heat in these bearings especially at high journal rotating speed and high loads or at high ambient temperature directly affect their performance. Thermal and fluid flow analysis of an advanced compliant foil journal bearing/seal are presented. The side flow (known as leakage) and the approximate temperatures are the results of this analysis. The result of preliminary analysis shows that the major portion of the heat is carried through conduction and using the modified Couette flow approximation for the present working fluid, air, helped in analysis of the temperature magnitude, which can be related to the gas viscosity behavior and thin gas film thicknesses.