Performance evaluation of Coriolis mass flow meter in laminar flow regime

In many fluid flow applications, mass flow rate is preferred over volume flow rate, as it is more beneficial in terms of cost and material balance calculations. Coriolis mass flow meter (CMFM) is accepted widely for mass flow measurement owing to its accuracy and reliability. However, it has been found to under-read the mass flow rate in laminar flow region [1], thus limiting its application in this region. The secondary flow in the curved tube section influences the generated Coriolis force and leads to a deviation in meter readings. Commercial CMFMs are available with various curved tube configurations and need to be analyzed for their application in laminar region. This paper presents comprehensive experimental and numerical investigations performed to evaluate the influence of tube configuration and other meter parameters, such as drive frequency, amplitude of vibration, and sensor position, on the performance of the CMFM in laminar region. The findings of this study have put forth a suitable combination of tube configuration, drive frequency, and sensor position while using the CMFM in laminar flow regime.     

Novel mass air flow meter for automobile industry based on thermal flow microsensor. II. Flow meter,test procedures and results

A prototype of mass air flow meter for automobile industry was developed on the basis of thermal flow microsensor. Design and manufacturing technology of the flow meter are described. Test procedure and results are presented. Developed prototype of flow meter can diagnose gas flow rates in a wide range.     

Multiphase flow measurements using coupled slotted orifice plate and swirl flow meter

Multiphase flow metering is a major focus for oil and gas industries. The performance of a modified version of a close coupled slotted orifice plate and swirl flow meter for multiphase flow was evaluated to provide further development of a new type of multiphase flow meter. The slotted orifice provides well homogenized flow for several pipe diameters downstream of the plate. This characteristic provides a homogeneous mixture at the inlet of the swirl meter for a wide range of gas volume fractions (GVF) and flow rates. In order to evaluate the performance of the designed flow-meter, its response was investigated for varying pressures and water flow rates. The proper correlations were established to provide high accurate two-phase flow measurements. The new proposed approach provides the GVF measurement with less than ±0.63% uncertainty for GVF range from 60% to 95%.     

Free transverse vibration of an axially loaded non-uniform spinning twisted Timoshenko beam using differential transform

This study investigates the vibration problems of an axially loaded non-uniform spinning twisted Timoshenko beam. First, using the Timoshenko beam theory and Hamilton's principle, we derive the governing equations and boundary conditions of the beam. Secondly, the differential transform method is used to solve these equations with appropriate boundary conditions. Finally, the effects of the twist angle, spinning speed, and axial force on the natural frequencies of a non-uniform Timoshenko beam are investigated and discussed.     

Deflections of Timoshenko beam with varying cross-section

Closed form solutions are presented for bending beams with linearly and (in the binomial form) parabolically varying depth and for bending beams with linearly varying width along the beam's length. The solutions are developed taking into account the shear deformation of the beam. The solutions are achieved, in an original way, by transforming the fourth-order differential equations with variable coefficients into fourth-order differential equations with constant coefficients. Though the solutions presented refer to three recurrent variations in the beam cross-section shape, the procedure outlined can be applied to beams with binomial variation (with any exponent) in the depth or width of the cross-section. Moreover, the solutions can be achieved for polynomial, exponential and sinusoidal load conditions. The solutions can be utilized to obtain the stiffness factors and the flexibility coefficients of beams in the analysis of frames. Closed form solutions for longitudinal displacements are also presented. The analytical solutions are applied to four recurrent beams commonly used in civil engineering practice and a comparison with a numerical procedure is made.     

Dynamic stability of a rotating pre-twisted asymmetric cross-section Timoshenko beam subjected to an axial periodic force

A finite element model is presented to study the static and dynamic stability of a pre-twisted Timoshenko beam having asymmetric aerofoil cross-section subjected to an axial periodic force. The change in the effects of coupling due to centre of flexure distance from the centroid and the shear coefficient on the stability due to the pre-twist angle is considered. It is concluded from the results that the pre-twist angle has an influence on the effects of coupling and the shear coefficient.     

Theoretical and experimental investigation for developing a gas-liquid two-phase flow meter

Despite the intricacy, inline metering of two-phase flow has a significant impact in multitudinous applications including fusion reactors, oil, nuclear, and other cryogenic systems. Since measurement of individual flow rate is prominent in various systems, it warrants the establishment of a flow meter system that can monitor the mass flow rates of liquid. In this regard, an approach was taken towards the development of a two-phase flow meter system in the present study. The concept involves two-phase flow through narrow parallel rectangular channels resulting in laminar, stratified flow with a slope at the liquid-vapor interface. The height of the liquid column at specific channel locations is measured for determining the flow rate. However, the geometric configurations of the channels and fluid properties are pivotal in ensuring accurate measurement. Consequently, theoretical and experimental studies are performed to investigate the correspondence between flow rate and change in liquid height. Based on the governing equations, a theoretical model is established using MATLAB®. The model investigated the intricate influence of various flow and fluid properties in the estimation of the mass flow rate. The experimental investigation was done with various conditions under different liquid and vapor volume flow rates for validating the proposed supposition and the theoretical model. Both the theoretical and experimental analyses showed fair correspondence. The proposed system estimated the mass flow rate within a tolerance of ±10% and showed potential towards the development of the cryogenic two-phase flow meter.     

Model analysis for differential pressure two-phase flow rate meter in intermittent flow

Multiphase flow rate metering is a challenging problem, specially for flow patterns other than wet-gas. This paper brings forward a new comparative analysis of three differential pressure calibration models suited for liquid dominated two-phase flows, in a total of seven model configurations. First, the models are compared theoretically and classified in terms of the type of input data required. Then, experimental data of over 300 horizontal air–water experiments, for $1$” and $2$” pipe diameters, supports quantitative analyses of the prediction accuracies and sensitivity of the superficial velocities of gas and liquid to measurement errors in the model input variables. Finally, a method for assessing the decoupled measurement errors for the void fraction and gas velocity is shown, as these variables are typically subject to higher uncertainties. It results that, though the void fraction is shown to be systematically under evaluated in more than 10%, the total mass flow rate is estimated through the Paz et al. (2010) model with an overall root mean squared deviation (RMSD) of 5.75% for the $2$” data. Also, the use of gas velocity measurements, even if subject to considerable errors, decreased the RMSD for the gas superficial velocity by more than half for the $1$” data.     

Two-phase flow metering of heavy oil using a Coriolis mass flow meter: A case study

The use of Coriolis mass flow metering for two-phase (gas/liquid) flow is an emerging theme of both academic research and industrial application. The key issues are maintaining flow-tube operation, and modelling and correcting for the errors induced in the mass flow and density measurements. Experimentally-derived data is used to illustrate that these errors vary most notably with gas void fraction (GVF) and liquid flow rate, but other factors such as flow-tube geometry and orientation, and fluid properties such as viscosity are also influential. While undoubtedly a universal two-phase flow correction model is the ultimate research goal, there is currently no obvious candidate to explain the range of behaviours observed. This paper describes and demonstrates an empirical methodology that has proven effective in developing good correction models for a given choice of Coriolis flow-tube and flow mixture.

A growing proportion of the world’s oil reserves may be described as “heavy”, implying high density and high viscosity. Of the various metering challenges heavy oil poses, one of the most significant is its ready entrainment of gas, and the difficulties entailed in separating gas from the oil. Accurate two-phase measurement of heavy oil is therefore an especially desirable technical goal.

Trials were carried out at the National Engineering Laboratory (NEL), Scotland on a 75 mm flowmeter using a high viscosity oil. Flowrates from 1 kg/s to 10 kg/s were examined, with gas void fraction (GVF) up to 80%. The resulting models were tested online in a commercial Coriolis mass flow meter and demonstrated good performance for both steady and slugging two-phase flows, with the corrected measurements typically within 1%–5% of the nominal mass flow and density.

Field trials in Venezuela have confirmed the performance of this two-phase solution.

While research continues into the development of a generic two-phase correction, this case study demonstrates that the current state of the art can provide, for economically important fluids, tailored models with good two-phase flow performance.     

Active disturbance rejection boundary control of Timoshenko beam with tip mass

In this paper, the active disturbance rejection control (ADRC) is utilized to stabilize the vibration of perturbed Timoshenko beam model with tip mass. The boundary control design is based on a hybrid PDE–ODE model, and is accompanied with designing a high-gain extended state observer (ESO) that is used to estimate the boundary disturbances. By transforming the model into the appropriate state space, the semigroup theory is employed to prove the well-posedness of the closed-loop system. To this end, it is proved by a frequency domain method that the semigroup generated by the system operator is exponentially stable, which allows to conclude the boundedness of perturbed closed-loop system response. The stability of the closed-loop system is further analyzed using the Lyapunov approach. Simulation results are presented to illustrate the efficacy of the suggested method.     

The dynamic performance of a new ultra-fast response Coriolis flow meter

The paper identifies the requirements for both a Coriolis flow-tube and the associated flow-transmitter, to achieve an ultra-fast dynamic response. A ‘new’ meter was assembled using a commercially available straight flow-tube, selected for its high drive (fundamental resonant) frequency of about 750 Hz (water-filled) and this was interfaced with a newly extended version of Oxford’s digital transmitter technology. This new transmitter gives measurement updates that are calculated every half drive-cycle, at 1.5 kHz, and are output via a high precision frequency pulse signal. Dynamic response tests in the laboratory and during a field trial have shown the ‘new’ meter to have a response time at least an order of magnitude faster than was reported previously [Clark C, Cheesewright R. Experimental determination of the dynamic response of Coriolis mass flow meters. Flow Measurement and Instrumentation 2006;17:39–47] from tests on the fastest response commercially available Coriolis meters. The ‘new’ meter shows a typical delay of 3.8 ms between a change in fluid flow rate and the corresponding change in the frequency output. Suggested further developments of the new transmitter technology indicate a route that could be followed to produce transmitters suitable for the newly emerging micro-machined Coriolis flow-tubes, which have fundamental resonant frequencies in the range 10–30 kHz.     

新型正弦行星齿轮流量计的三维实现及流量脉动分析

根据正弦函数曲线类比推导出了正弦齿轮的直角坐标方程,利用CAXA电子图板2007的公式曲线功能和Pro/E软件建立了正弦齿轮和流量计的三维模型。为了探究正弦行星齿轮流量计的测量精确性,进行了流量脉动分析,分析结果表明:该流量计比渐开线齿轮流量计具有更小的流量脉动率。     

电磁流量计的使用及电磁兼容性分析

介绍利用面板及智能终端进行电磁流量计参数设置和组态的方法,以及提高电磁流量计的电磁兼容性技术。电磁流量计的干扰源主要包括工频电磁干扰、流体电化学干扰噪声和电源干扰噪声。目前电磁流量计主要采用低频或双频矩形波励磁技术、同步采样技术、输入保护、接地技术等来降低干扰。实际应用表明,这些技术有较好的抗干扰效果。     

浅谈石化装置流量仪表的选用

石化行业生产所用的原料及产品种类繁多。根据这些流体特点,需要采用不同的流量计进行测量。该文浅谈了针对不同性能的流体所采用的测量方法和流量计的选型。     

Free vibration of Timoshenko beam with finite mass rigid tip load and flexural–torsional coupling

In this paper, the free vibration of a cantilever Timoshenko beam with a rigid tip mass is analyzed. The mass center of the attached mass need not be coincident with its attachment point to the beam. As a result, the beam can be exposed to both torsional and planar elastic bending deformations. The analysis begins with deriving the governing equations of motion of the system and the corresponding boundary conditions using Hamilton's principle. Next, the derived formulation is transformed into an equivalent dimensionless form. Then, the separation of variables method is utilized to provide the frequency equation of the system. This equation is solved numerically, and the dependency of natural frequencies on various parameters of the tip mass is discussed. Explicit expressions for mode shapes and orthogonality condition are also obtained. Finally, the results obtained by the application of the Timoshenko beam model are compared with those of three other beam models, i.e. Euler–Bernoulli, shear and Rayleigh beam models. In this way, the effects of shear deformation and rotary inertia in the response of the beam are evaluated.     

Effect of axial force on free vibration of Timoshenko multi-span beam carrying multiple spring-mass systems

The situation of structural elements supporting motors or engines attached to them is usual in technological applications. The operation of machine may introduce severe dynamic stresses on the beam. It is important, then, to know the natural frequencies of the coupled beam-mass system, in order to obtain a proper design of the structural elements. The literature regarding the free vibration analysis of Bernoulli–Euler single-span beams carrying a number of spring-mass system and Bernoulli–Euler multi-span beams carrying multiple spring-mass systems are plenty, but that of Timoshenko multi-span beams carrying multiple spring-mass systems with axial force effect is fewer. This paper aims at determining the exact solutions for the first five natural frequencies and mode shapes of a Timoshenko multi-span beam subjected to the axial force. The model allows analyzing the influence of the shear and axial force effects and spring-mass systems on the dynamic behavior of the beams by using Timoshenko Beam Theory (TBT). The effects of attached spring-mass systems on the free vibration characteristics of the 1–4 span beams are studied. The calculated natural frequencies of Timoshenko multi-span beam by using secant method for non-trivial solution for the different values of axial force are given in tables. The mode shapes are presented in graphs.     

Large amplitude free vibration analysis of Timoshenko beams using a relatively simple finite element formulation

Free vibration analysis of uniform isotropic Timoshenko beams with geometric nonlinearity is investigated through a relatively simple finite element formulation, applicable to homogenous cubic nonlinear temporal equation (homogenous Duffing equation). Geometric nonlinearity is considered using von-Karman strain displacement relations. The finite element formulation begins with the assumption of the simple harmonic motion and is subsequently corrected using the harmonic balance method. Empirical formulas for the non-linear to linear radian frequency ratios, for the boundary conditions considered, are presented using the least square fit from the solutions of the same obtained for various central amplitude ratios. Numerical results using the empirical formulas compare very well with the results available from the literature for the classical boundary conditions such as the hinged–hinged, clamped–clamped and clamped–hinged beams. Numerical results for the beams with non-classical boundary conditions such as the hinged-guided and clamped-guided, hitherto not studied, are also presented.     

别克汽车空气流量计故障分析与维修

针对别克汽车动力下降、油耗增大、怠速不稳等情况,对产生这些故障的原因逐条排查,最后锁定是由于空气流量计电阻丝受到空气中尘埃的污染造成的。通过清除附着在电阻丝上的污染物,是汽车功能恢复正常,圆满地解决了以上问题;同时,由于修复了故障元件,避免了更换部件总成,节省了费用。     

The dynamic stability of a rotating pre-twisted asymmetric cross-section Timoshenko beam subjected to lateral parametric excitation

A finite element model is presented to study the dynamic stability of a pre-twisted Timoshenko beam having asymmetric aerofoil cross-section subjected to lateral parametric excitation. Solutions referred to as combination resonance are investigated. The effects of shear deformation and rotary inertia are included in the analysis. The effects of coupling due to centre of flexure distance from the centroid and the shear coefficient on the stability are considered. The change in these effects due to pre-twist angle is investigated. It is concluded from the results that the pre-twist angle has an influence on the effects of coupling and the shear coefficient.