The leakage flow rate represents an important input quantity in the measurement model for the gas flow rate in a clearance-sealed piston prover, especially when measuring small flow rates. This study ...deals with the experimental identification of leakage flow effects. The following influences were examined: the flow rate supplied to the piston prover, the inclination of the flow cell, the type of gas and the temperature of the gas. The leakage flow rate was measured during the typical operation of the piston prover using the dynamic summation method. The tests were carried out in a climate chamber to ensure stable and homogenous temperature conditions. It is demonstrated that the leakage flow rate is significantly affected by the piston prover's inclination and the viscosity of the gas, which depends mainly on the type and the temperature of the gas. Based on the experimental findings that confirm the leakage flow rate is inversely proportional to the gas viscosity, a correction model was proposed. The uncertainty analysis shows that reproducibility is the most important component in the combined uncertainty of the leakage flow rate.
•The piston provers are in general susceptible to non-stable ambient temperature.•The temperature inhomogeneity in the piston prover is related to the mass flow errors.•The magnitude of heat transfer ...effects decreases with the gas flow rate.•Covered flow cell shows systematic flow errors at stable temperature conditions.
This paper deals with the quantification of ambient temperature effects on the measured mass flow rate of a gas using a clearance-sealed piston prover. The variations of temperature were simulated by placing the piston prover in a climate chamber. The tests were made for flow rates of air between 13 mg/min and 15 g/min for three different flow cells. The temperature in the chamber and the piston prover, and the deviations of the piston prover’s readings from the flow source, were recorded. The results confirm that the temperature inhomogeneity in the piston prover can be related to the observed mass flow errors, which increase with the magnitude and the rate of temperature change and decrease with the gas flow rate. Placing the measurement cylinder under a protective cover reduces the sensitivity to variable ambient conditions, but introduces a systematic mass flow error, even in the case of a stable temperature.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPUK, ZAGLJ, ZRSKP
A piston prover measures the gas flow rate by determining the time interval that a piston needs to pass a known volume of gas at a defined pressure and temperature. In the clearance-sealed piston ...prover the leakage flow rate through the clearance between the cylinder and the piston represents the key contribution to the measurement uncertainty at the lowest measured gas flow rates. The article presents the measurement procedure for the leakage flow rate under operating conditions of the piston prover and evaluates some influence parameters on its magnitude; i.e., the measured flow rate, the gas viscosity and the flow cell inclination.
An understanding of the effects of flow pulsations on the dynamic behavior of Coriolis flowmeters is very important for their further development. In order to determine the phase difference between ...the vibrational signals, which represents the basic measurement effect of Coriolis flowmeters, there are many methods that include the proper filtering of all the signal components, except those with frequencies close to the drive frequency. Therefore, an understanding of the phenomenon of exciting the meter at its first natural frequency is very important. The results of a simple, linear, two-degree-of-freedom, lumped-parameter, dynamic model of a flowmeter show that the flow pulsations can degrade the accuracy of such a flowmeter as a result of indirect excitations of the measuring tube at the first natural frequency through the second-order perturbations by means of the Coriolis forces induced in pulsating flow conditions. In order to experimentally investigate these flow pulsation effects, a prototype of a straight-tube Coriolis mass flowmeter was developed to enable the processing of the response signals logged directly from the flow tube׳s sensors with the dual quadrature demodulation method, and therefore to provide the information available within the phase-difference data. The experimental results show that the flow pulsations upset the meter at its first natural frequency indirectly, as well as directly at the frequency of the pulsations due to the geometric imperfections of the measuring tube.
•Paper discusses the flow pulsation effects in Coriolis mass flowmeters.•Higher-order perturbation effect of the Coriolis force in the pulsating flow.•Beating effects between the flow pulsations and the driven motion of the meter.•Flow pulsations excite the meter at the drive frequency directly or indirectly.•Occurrence of the shaking forces due to the measuring-tube imperfections.
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This paper deals with heat exchange effects in a compact, high-speed, clearance-sealed version of a piston prover for gas flow measurements that has the temperature measurements limited to the ...time-averaged temperature of the gas flow. A lumped-element mathematical model is used to study the physical background of the heat exchange effects. Experimental testing is performed to validate the theoretical results, estimate the required temperature homogeneity in the piston prover and propose a modified measurement model that considers the heat exchange effects. These effects are almost linearly related to the temperature difference between the gas flow into the piston prover and the cylinder wall, with the sensitivity coefficient being dependent on the measured flow rate. The piston-prover configuration with the gas temperature sensor in the mixed inlet /outlet flow is found to be advantageous in comparison to a measurement of the inlet temperature.
Leakage flow rate is one of the most important contributions to the measurement uncertainty when measuring small gas flow rates with a clearance-sealed piston prover. Our previous study has shown ...that the systematic effects related to the change of the gas viscosity can be successfully corrected, whereas the effects related to the reproducibility of the leakage flow rate are poorly understood. This paper focuses on the interpretation and correction of the reproducibility related effects by analysing experimentally identified variations of the leakage flow rate and the gas pressure in the inclined piston prover. Small changes of the leakage flow in the inclined piston prover indicate that the position of the piston relative to the cylinder remains approximately the same. The obtained relationship between the leakage flow rate and the gas pressure below the piston led to the pressure-based correction of the leakage flow rate.
•The leakage flow rate represents important uncertainty contributions at low gas flows.•The study tries to explain the effects related to the reproducibility of the leakage flow rate.•The flow cell inclination is not a significant uncertainty contribution to the leakage flow rate.•The variations of the leakage flow rate can be linked to the pressure difference acting on the piston.•The pressure correction reduces the uncertainty of the leakage flow related to its reproducibility.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPUK
The paper presents a coupled numerical model built to simulate the operation of Coriolis flowmeters, which exploit the alteration of the vibration mode shape of the measuring tube for the mass flow ...rate measurement. The explained measuring effect is a consequence of the interaction between the motion of the tube, vibrating at its natural frequency, and the fluid flow in it. The numerical model is realized by coupling of a finite volume (FV) code for fluid flow analysis with a finite element (FE) code for structural analysis using the conventional staggered solution procedure, with added inner iterations to achieve strong coupling. The simulation algorithm is divided into two steps. A free vibration of the measuring tube considered in the first step is complemented in the second step, after the numerical free vibration response is properly stabilized, with the harmonic excitation force actuating the measuring tube at its resonant frequency of several hundreds of Hertz to resemble the operation of actual Coriolis flowmeters. Different scenarios using zero-order or three-point fluid load predictor and soft application of the fluid load in the initial stages of the simulation are compared to yield a simulation strategy, which will minimize the time needed to obtain the stabilized steady-state response of the vibrating measuring tube. The proposed simulation procedure was applied on a straight-tube Coriolis flowmeter and used for the estimation of the velocity profile effect. The results exhibit sufficient stability (low scatter) to be used for the estimation of sensitivity variations of order of magnitude around tenths of a percent.
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A coupled finite-volume (FV)/finite-element (FE) numerical model of the straight-tube Coriolis flowmeter is considered. It uses the staggered partitioned algorithm with additional pressure predictor ...and interfield iterations to minimize the time lag in the fluid–structure coupling procedure. The solutions were evaluated in terms of the fundamental natural frequency of the vibrating system and the corresponding phase difference between the motion of the symmetrically located sensing points on the measuring tube, which are actually exploited as the measuring effects of the Coriolis flowmeter for the fluid density and the mass flowrate, respectively. The FV/FE numerical model was validated by comparison with the solutions of the Euler beam and one-dimensional flow model, as well as with the solutions of the Flügge shell and potential flow model. The respective simulations were performed for different lengths of the measuring tube.
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This paper presents a study of the axisymmetric velocity profile effects in the shell-type Coriolis flowmeter with a second circumferential mode, which exploits the results of computational fluid ...dynamics simulations. Simulations were carried out for viscous fluid flow in the vibrating measuring tube, whose mode shape remained fixed during the transient simulation process. We observed time responses of the integral anti-symmetric fluid forces acting on the inner wall of the measuring tube. Their magnitudes and their relative variations with the mass flow rate of the fluid were used for the integral estimation of the velocity profile effect. Simulation results are presented for different fluid velocities through the measuring tube and show considerable loss of flowmeter’s sensitivity in the range of lower Reynolds numbers. The results are also compared with the weight vector estimations of the velocity profile effect and are evaluated for two different turbulent models.
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•Traceability for high pressure gaseous hydrogen and liquified hydrogen.•High-pressure measurements with critical flow Venturi nozzles up to 100 MPa.•Computational fluid dynamics simulations ...describing the nozzle flow.•Experimental speed-of-sound data for new equation of state (for hydrogen).•Three-pronged approach to enable traceable flow measurement of liquified hydrogen.
This paper gives an overview of the ongoing Joint Research Project (JRP) 20IND11 “Metrology infrastructure for high pressure gas and liquefied hydrogen flows” (MetHyInfra), which will ensure traceability in the hydrogen distribution chain. For this purpose, very precise nozzles with well-defined geometries have been produced. In this project, Critical Flow Venturi Nozzles (CFVNs) will be traceably calibrated for the first time with hydrogen and pressures up to 100 MPa using a Coriolis Flow Meter (CFM) as a secondary standard. A CFM has been successfully calibrated with hydrogen against a gravimetric primary standard.
Equations of State (EoS) are important for the high-pressure calibration of the nozzles, but also for Computational Fluid Dynamics (CFD) simulations. With regard to CFD, a numerical model has been developed to simulate high pressure hydrogen flow in the CFVN. In a parameter study, non-ideal nozzle shapes are investigated using a shape variation parameter. New Speed of Sound (SoS) measurements were conducted at temperatures from 273 to 323 K and pressures from 1 to 100 MPa. These new data were then used to develop a new EoS for normal hydrogen, optimized for gas phase calculations. In addition to gaseous hydrogen, the project has a strong focus on liquefied hydrogen. Here a three-pronged approach allows traceable measurements. Each of the approaches presented is based on a unique flow calibration principle and relies on independent traceability schemes. The results of the project will ensure traceable measurements and thus a higher level of confidence among end users.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPUK, ZAGLJ, ZRSKP
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