Uncertainty Of Flow Rate Research Articles

Reproducibility of inverse gas chromatography under infinite dilution: Results and interpretations of an interlaboratory study

Over the last years, inverse gas chromatography (IGC) proved to be a versatile and sensitive analytical technique for physicochemical properties. However, the comparability of results obtained by different users and devices remains a topic for debate. This is the first time, an interlaboratory study using different types of IGC instruments is reported. Eight organizations with different IGC devices defined a common lab measurement protocol to analyse two standard materials, silica and lactose. All data was collected in a standard result form and has been treated identically with the objective to identify experimentally observed differences and not potentially different data treatments. The calculated values of the dispersive surface energy vary quite significantly (silica: 22 mJ/m2 - 34 mJ/m2, lactose 37 mJ/m2 - 51 mJ/m2) and so do the ISP values and retention volumes for both materials. This points towards significant and seemingly undiscovered differences in the operation of the instruments and the obtained underlying primary data, even under the premise of standard conditions. Variations are independent of the instrument type and uncertainties in flow rates or the injected quantities of probe molecules may be potential factors for the differences. This interlaboratory study demonstrates that the IGC is a very sensitive analytical tool, which detects minor changes, but it also shows that for a proper comparison, the measurement conditions have to be checked with great care. A publicly available standard protocol and material, for which this study can be seen as a starting point, is still needed to judge on the measurements and the resulting parameters more objectively.

Numerical Simulations of Flow-Induced Deflections in MITR LEU Fuel Plate Due to Channel Size Disparity

The hydromechanical stability of the fuel plates in parallel coolant channels of a Materials Testing Reactor (MTR) fuel element design is of great importance to the safety of research and test reactors. Previous analytical, experimental, and numerical efforts focused on parallel channels with the same or similar size; also, in the prior numerical simulations, the fuel plate was often assumed to be perfectly flat. This work presents the results of a fluid-structure interaction simulation performed to evaluate the flow-induced deflections of the fuel plates in the low-enriched uranium (LEU, <20 wt% 235U) fuel element design for the conversion (from highly enriched uranium) of the Massachusetts Institute of Technology Reactor (MITR-II, also referred to as MITR). Various manufacturing and assembly tolerances of the MITR LEU elements are considered in the analysis, and the effects of channel size disparity, nonideal plate shape, and flow rate uncertainty are investigated. Results show that, for all cases analyzed, the deflection occurs toward the larger channel, and the change in any channel stripe remains small (less than 0.021 mm) compared to fabrication tolerances. In addition to simulation work, a hydraulic performance test of the MITR LEU fuel element is currently planned to support conversion to the use of LEU fuel.

Particle mass flow determination in dust-laden supersonic flows by means of simultaneous application of optical measurement techniques

Particle mass flow rate and particle mass concentration are key parameters for describing two-phase flows, especially for particle-induced heating augmentation analysis. This work addresses the question of how accurate particle mass flow rate can be determined with three non-intrusive measurement approaches, based on shadowgraphy, particle tracking velocimetry (PTV), and scattered light intensity, in supersonic flows. In terms of shadowgraphy and PTV, the particle mass flow rate was determined by measuring individual particle characteristics, namely particle size, velocity, and density, as well as the measurement volume. The presented shadowgraphy procedure is based on the commercial LaVision DaVis software and additional shadowgraphy corrections. Multiple tests were conducted in the experimental test facility GBK of DLR with varying flow conditions, at a Mach number of 2.1, unit Reynolds number (Re∞) ranging from 5e7 1/m to 1.5e8 1/m, total temperature (T0) ranging from 303 to 544 K, and particle materials, namely Al2O3, MgO, and SiO2, in the size range of 1 to 60 µm. Particle size distributions of Al2O3 and MgO particles could be reproduced with shadowgraphy quite well, while the PTV procedure resulted in non-similar distributions. Pycnometer measurements indicated MgO particle density to be significantly lower than reference values. A DaVis parameter variation analysis resulted in a particle mass flow rate uncertainty of shadowgraphy of up to 30%. The particle mass flow rate uncertainty of PTV is approx. 76%, and the respective uncertainty of scaled PTV and scattered light intensity approach is 28%. The particle mass flow rate, measured with shadowgraphy, is 58% higher than those of the semi-axisymmetric scattered light intensity approach, which can be explained by a higher particle concentration at the injection plane.

A mathematical formulation for robust targeting in heat integrated water allocation network

Resource conservation strengthens a process industry's competitiveness and sustainability. Process integration (PI) strategies conserve resources. Heat-integrated water allocation networks (HIWANs) conserve energy and water. Process systems engineering optimizes synthesis, design, planning, scheduling, control, and supply chain. Recent developments promote robust optimization (RO) for uncertain optimization. RO optimizes for uncertain parameters to deal with data uncertainty. This research introduces a RO-based HIWAN resource-targeting model. Flow, concentration, and temperature uncertainties are modelled. The budget parameter reflects robustness. The budget restricts RO's conservatism and uncertainty, generating unduly cautious solutions. This model is explained with an example with different scenarios. Three of the scenarios have a single parameter uncertainty like source flow, source concentration, or inlet temperature, while one has multiple. Parameter behaviors are examined from nominal to worst-case scenarios. For scenario 1 where flowrate uncertainty is accounted, the robust flowrate target is 53.8% higher than the nominal value for the worst case. Similarly, for the second scenario where concentration uncertainty is accounted, robust flowrate target is 5.594% higher than nominal. In the last scenario with multiple uncertainties, the targeted flowrate increases by 59.44% compared to the nominal state. Nominal to worst-case scenarios can be handled by this model.

Reduction of Signal Drift in a Wavelength Modulation Spectroscopy-Based Methane Flux Sensor.

Accurately quantifying unsteady methane venting from key oil and gas sector sources such as storage tanks and well casing vents is a critical challenge. Recently, we presented an optical sensor to meet this need that combines volume fraction and Doppler shift measurements using wavelength modulation spectroscopy with 2f harmonic detection to quantify mass flux of methane through a vent line. This paper extends the previous effort through a methodical component-by-component investigation of potential sources of thermally-induced measurement drift to guide the design of an updated sensor. Test data were analyzed using an innovative signal processing technique that permitted quantification of background wavelength modulation spectroscopy signal drift linked to specific components, and the results were successfully used to design a drift-resistant sensor. In the updated sensor, background signal strength was reduced, and stability improved, such that the empirical methane-fraction dependent velocity correction necessary in the original sensor was no longer required. The revised sensor improves previously reported measurement uncertainties on flow velocity from 0.15 to 0.10 m/s, while markedly reducing thermally-induced velocity drift from 0.44 m/s/K to 0.015 m/s/K. In the most general and challenging application, where both flow velocity and methane fraction are independently varying, the updated design reduces the methane mass flow rate uncertainty by more than a factor of six, from ±2.55 kg/h to ±0.40 kg/h. This new design also maintains the intrinsic safety of the original sensor and is ideally suited for unsteady methane vent measurements within hazardous locations typical of oil and gas facilities.

Simultaneous determination of particle size, velocity, and mass flow in dust-laden supersonic flows

The particle mass concentration and -mass flow rate are fundamental parameters for describing two-phase flows and are products of particle number, -size, -velocity, and -density. When investigating particle-induced heating augmentation, a detailed knowledge of these parameters is essential. In most of previous experimental studies considering particle-induced heating augmentation, only average particle mass flow rates are given, without any relation to measured particle sizes and -velocities within the flow or any indication of measurement uncertainty. In this work, particle number, individual particle sizes, and velocities were measured in a supersonic flow by means of shadowgraphy and particle tracking velocimetry (PTV). The goals are to determine measurement uncertainties, a particle velocity-size relation, and the spatial distribution of number, size, velocity, and mass flow rate across the nozzle exit. Experiments were conducted in a facility with a nozzle exit diameter of 30 mm, at Ma∞ = 2.1 and Re∞ = 8.2e7 1/m. Particles made of Al2O3 and up to 60 µm in size were used for seeding. Particle mass flow rates up to 50 kg/m2 s were achieved. It is shown that an additional correction procedure reduced common software uncertainties regarding shadowgraphy particle size determination from 14% to less than 6%. Discrepancies between calculated particle velocities and experimental data were found. In terms of spatial distribution, larger particles and a higher mass flow rate concentrate in the flow center. The determined particle mass flow rate uncertainty was up to 50% for PTV; for shadowgraphy, it was less than 17%.Graphical abstract

Design and construct unit to control fluid entering solar collectors during efficiency tests

This paper describes the development of an apparatus to control the fluids that enter a solar collector in experimental tests with respect to the Australian and New Zealand Standard AS/NZS 2535.1.2007. This standard explains the testing procedure, indicating that the inlet fluid should have specified temperature and flow rate uncertainties. The hardware components were constructed in the lab. A new sophisticated data acquisition system with an NI CompactDAQ was added to control the unit, and a new software application in LabVIEW was developed. The unit was operated in an open-loop to understand its behaviour as a multiple-inputs and multiple-outputs system (MIMO). A rule of thumb tuning method was used to design the proportional-integral PI controller for the heating system. Moreover, a custom decoupler with a PI controller was developed to reduce the interactions in the MIMO. The measured steady-state responses were analysed to determine the flow rate and temperature compared with the limited boundaries. The final results show that the system could supply water to the solar collector within the accuracy requirements. Achieving the fluid's absolute temperature and flow rate within the required constraints of the published standard has proven that the developed unit can be adapted to perform solar collector testing. However, additional steps are suggested for further work to enable the unit to provide field testing.

Each-Phase Metering with Gas-Liquid Stratified Flow Based on the Multi-Frequency Coriolis Principle

Gas-liquid two-phase flows generally have the characteristics of complex and variable flow patterns and flow rate uncertainty of each phase. The entrainment of gas increases errors of the existing non-separated multiphase metering. A novel metering method based on the multi-frequency Coriolis principle is proposed to solve the above problems. Compared to the conventional Coriolis mass flowmeter, the third-order mode of the measuring tube is used to improve the accuracy of the measurement. The influences of bubble effect and resonance effect on vibration responses in different vibrational modes were studied to determine the deviations of the apparent values of total density and mass flowrate by simulation. Simulation results with a single-frequency Coriolis flowmeter show that the maximum relative deviations of total density and total mass flowrate are −37.3% and −9.3%, respectively. Driven by different frequencies, the same two phase fluid in the measuring tube can have different responses of the primary mode and the higher vibrational modes. The vibrational responses characteristics corresponding to the first-order and third-order modes of measuring tube were selected and analyzed. Combined with advantages of high precision and multi-parameter measurement of traditional single-frequency Coriolis flowmeters, a multi-frequency correction model suitable for stratified flow was proposed. The results show that the corrected total density and mass flow deviations of gas-containing fluid are within ±4% and ±3%, respectively, which are significantly reduced. Corrected flowrate deviations of the gas-phase and liquid-phase are ±9.1% and ±7.2%, correspondingly, which also meet the metering requirements of the wellhead.

New approaches for modelling vortex flow meters

The paper proposes a new model of a vortex flow meter, which is developed on the basis of modification of the basic equations of incompressible fluid hydrodynamics. The article deals with the modification of the Euler equation and the continuity equation of the flow. In this paper, dependencies are obtained for estimating the final standard uncertainty of flow rate using a vortex transducer. A detailed analysis of the influence of incompressible fluid flow parameters and the geometric dimensions of the vortex transducer on the final uncertainty of flow rate is performed. Recommendations are given for improving the method of flow rate using vortex transducers.

Uncertainty analysis in the detection of trends, cycles, and shifts in water resources time series

Scientists and water resources managers are increasingly worried about issues related to uncertainty. Although uncertainty analysis has been required in the decision-making processes, there is still a lack of knowledge on how to do it. The application of statistical methods for water resources research requires time series to be compliant with the hypotheses of randomness, homogeneity, independence, and stationarity (RHIS). Noncompliance may occur when trends, cycles, and/or shifts are present. However, the uncertainties and associated subjectivity in assessment and expression may make it difficult to detect these patterns of variability. In this research, synthetic time series (STS) were generated from the uncertainties in flow rates and a water quality parameter, and tested for RHIS by the Single-Sample Runs, Mann-Whitney, Wald and Wolfowitz, and Mann-Kendall tests, respectively. The tests were applied with an increasing number of elements (N). Three uncertainty scenarios were defined, the low level (LL: 10–30%), mid level (ML: 30–50%) and high level (HL: 50–70%). The Monte Carlo Method (MCM) was applied with uniform, normal and lognormal probability distributions. In each scenario, averages and standard deviations (std) were calculated as a measure of the p-values uncertainty. Although the complete series were compliant with the hypotheses, the p-values and std ranges varied from one extreme to the other (0.0–1.0) as N increased. The std ranges had an impact on the decisions when the p-value was close to the rejection limit. The randomness p-value for the flows in the uniform case was 0.04, while the STS p-values were ≈ 0.05 ± 0.04, 0.09 ± 0.10, and 0.18 ± 0.20 in the LL, ML and HL scenario respectively. However, the decision on significance should not be based only on p-values, since the actual existence and continuity of patterns of variability depends more on representativity-related issues. The results lead to the conclusion that efforts to reduce uncertainties should be directed towards the development of appropriate monitoring and data analysis/interpretation strategies.

Benders decomposition with integer sub-problem applied to pipeline scheduling problem under flow rate uncertainty

Important issues in a pipeline system are energy efficiency, reliability and throughput flexibility. Practically conventional pumps are not capable of operating at the highest attainable efficiency for long running time. This deficiency has prevented a pipeline system to operate close to its predefined program. A possible remedy is to take into account uncertainty due to pumps operations. In this paper, a stochastic two-stage mixed integer programming (MILP) model is developed for the multiproduct pipeline-scheduling problem under flow rate uncertainty. The problem arises in a number of settings, and the real-world applicability discussed and demonstrated. The stochastic MILP model involves many discrete variables that make it intractable for real-life cases. As a solution method, the sample average approximation is combined with a three-step solution approach based on Benders decomposition. The modeling and solving approach is evaluated in some case studies including a real-life problem from NIOPTC.

Propagation of uncertainty and sensitivity analysis in an integral oil‐gas plume model

AbstractPolynomial Chaos expansions are used to analyze uncertainties in an integral oil‐gas plume model simulating the Deepwater Horizon oil spill. The study focuses on six uncertain input parameters—two entrainment parameters, the gas to oil ratio, two parameters associated with the droplet‐size distribution, and the flow rate—that impact the model's estimates of the plume's trap and peel heights, and of its various gas fluxes. The ranges of the uncertain inputs were determined by experimental data. Ensemble calculations were performed to construct polynomial chaos‐based surrogates that describe the variations in the outputs due to variations in the uncertain inputs. The surrogates were then used to estimate reliably the statistics of the model outputs, and to perform an analysis of variance. Two experiments were performed to study the impacts of high and low flow rate uncertainties. The analysis shows that in the former case the flow rate is the largest contributor to output uncertainties, whereas in the latter case, with the uncertainty range constrained by aposteriori analyses, the flow rate's contribution becomes negligible. The trap and peel heights uncertainties are then mainly due to uncertainties in the 95% percentile of the droplet size and in the entrainment parameters.

An assessment of intra-patient variability on observed relationships between wall shear stress and plaque progression in coronary arteries.

BackgroundWall shear stress (WSS) has been associated with sites of plaque localization and with changes in plaque composition in human coronary arteries. Different values have been suggested for categorizing WSS as low, physiologic or high; however, uncertainties in flow rates, both across subjects and within a given individual, can affect the classification of WSS and thus influence the observed relationships between local hemodynamics and plaque changes over time. This study examines the effects of uncertainties in flow rate boundary conditions upon WSS values and investigates the influence of this variability on the observed associations of WSS with changes in VH-IVUS derived plaque components.MethodsThree patients with coronary artery disease underwent baseline and 12 month follow-up angiography and virtual histology-intravascular ultrasound (VH-IVUS) measurements. Coronary artery models were reconstructed from the data and models with and without side-branches were created. Patient-specific Doppler ultrasound (DUS) data were employed as inflow boundary conditions and computational fluid dynamics was used to calculate the WSS in each model. Further, the influence of representative coronary artery flow waveforms upon WSS values was investigated and the concept of treating WSS using relative, rather than actual, values was explored.ResultsModels that included side-branch outflows and subject-specific DUS velocities were considered to be the reference cases. Hemodynamic differences were caused by the exclusion of side-branches and by imposing alternative velocity waveforms. One patient with fewer side-branches and a scaled generic waveform had little deviation from the reference case, while another patient with several side-branches excluded showed much larger departures from the reference situation. Differences between models and the respective reference cases were reduced when data were analyzed using relative, rather than actual, WSS.ConclusionsWhen considering individual subjects, large variations in patient-specific flow rates and exclusion of multiple side-branches in computational models can cause significant differences in observed associations between plaque evolution and ranges of computed WSS. These differences may contribute to the large variability typically found among subjects in pooled populations. Relative WSS may be more useful than actual WSS as a correlative variable when there is a large degree of uncertainty in flow rate data.

Primary standard for liquid flow rates between 30 and 1500 nl/min based on volume expansion.

An increasing number of microfluidic systems operate at flow rates below 1 μl/min. Applications include (implanted) micropumps for drug delivery, liquid chromatography, and microreactors. For the applications where the absolute accuracy is important, a proper calibration is required. However, with standard calibration facilities, flow rate calibrations below ~1 μl/min are not feasible because of a too large calibration uncertainty. In the current research, a traceable flow rate using a certain temperature increase rate is proposed. When the fluid properties, starting mass, and temperature increase rate are known, this principle yields a direct link to SI units, which makes it a primary standard. In this article, it will be shown that this principle enables flow rate uncertainties in the order of 2-3% for flow rates from 30 to 1500 nl/min.

Valve-Induced Water Hammer and Column Separation in a Pipeline Apparatus

A flexible experimental apparatus for investigating water hammer and column separation in an unsteady friction-dominated pipelines has been developed and designed. The apparatus has been tested for steady and unsteady flow conditions. Transient cavitation and column separation phenomena have been observed in a number of experimental runs. Water hammer has been triggered by both the closing and opening of electro-pneumatic (EV) and hand-operated (HV) valves. The experimental data have been compared with results given from in-house numerical code written in Visual Fortran based on the method of the characteristics (MOC) with a convolution-based unsteady friction model (CBM) included. The column separation and transient cavitation phenomena are modelled via a discrete gas cavity model (DGCM). There is good agreement between the experimental and numerical results; the model is robust and, therefore, it is recommended for engineering practice. In addition, the influence of variations of the pressure wave speed and the uncertainty in flow rate measured by the electromagnetic flow meter are also investigated.

Development and evaluation of the calibration facility for high-pressure hydrogen gas flow meters

The calibration facility with the multi-nozzle calibrator was developed for the calibration of flow meters to be used with high-pressure, high-flow-rate hydrogen gas. The critical nozzles installed in the multi-nozzle calibrator were calibrated with traceability to the national standard. The relative standard uncertainty of the mass flow rates produced from the calibration facility is 0.09% when the flow rate is between 150g/min and 550g/min. In this study, the Coriolis flow meter was calibrated for a pressure range of 15–35MPa. The relative standard uncertainty of the flow rates obtained from the Coriolis flow meter was 0.44% for the case of the worst fluctuations in the output of the flow meter; based on the calibration curve, this is 0.91%. The present result shows that there is a maximum 3% difference between the output of the Coriolis flow meter and the mass flow rates of the multi-nozzle calibrator, even though the Coriolis flow meter was calibrated using water. Therefore, for the development of a calibration facility that can calibrate a flow meter under the same conditions as those encountered in actual use, it will be important to develop a new flow meter.

Estimating Demands with a Markov Chain Monte Carlo Approach

The use of drinking water distribution system models has been around for decades, and demand estimation has been a key component in the model development process. Existing techniques utilized by consultants/utilities have been capable of representing the general hydraulics for assessing typical objectives such as maintaining adequate pressure. However, these models are generally not appropriate, or simply do not work, when attempting to recreate the observed hydraulics and operational conditions associated with a specific time horizon. In general, these limitations in recreating demands have become even more important when attempting to assess the ability of models to represent complex water quality dynamics. In this paper, a Bayesian demand estimation algorithm is presented, and estimated water demand multipliers are compared with synthetically generated “observed” demand multipliers in a water distribution system network. Using two different data scenarios − an “ideal” case assuming all flow and pressure data are available for the estimation process and a more realistic “limited” case using only flow rates at the sources and tank levels − the Markov chain Monte Carlo (MCMC) method demonstrated an increase in demand estimate uncertainty for the “limited” data scenario. Using the “limited” data set only resulted in a moderate increase in the underlying flow rate uncertainty. These results demonstrate the potential feasibility of the MCMC algorithm for recreating adequate demand estimates that will provide an improved approach for evaluating water quality models.

Metrological performances of mass flow controllers for dynamic gas dilution

The method of dynamically generating reference mixtures of volatile organic compounds at trace levels requires the uninterrupted blending of the component flows during the generation time. The target flow rate uncertainty depends on the application and the range of the concentration generated. Accurate air flow rates used for dilution can be realized by mass flow controllers (MFCs). The short-term stability of MFCs has been measured in order to assess their usefulness in dynamic gas dilutors. As shown here, MFCs are appropriate for the dynamic preparation of diluted gas mixtures provided they are calibrated prior to each use, because their calibration is not stable over longer time periods. The calibration results of the low pressure drop MFC proved its applicability in a wide range of pressure drop. The uncertainty of the dilution flow rate resulted mainly from the limited short-term stability of the MFC at low dilution flow rate or at short generation time. Consequently, MFCs can provide highly accurate dilution air flow rates with a relative uncertainty of 0.2 %, for flow rates larger than 70 % of the MFC’s maximum flow rate and generation times longer than 5 min.

Uncertainty analysis of the diffusion rate in the dynamic generation of volatile organic compound mixtures

The measurement of volatile organic compound (VOC) concentration changes, in the range of 10 ppt–1ppb, is essential in several applications. The World Meteorological Organization has identified a set of VOCs that are critical because of their long-term instability. The measurement of such changes demands generation of reference mixtures at a high accuracy and stability level. The dynamic preparation of gas mixtures based on diffusion is a suitable way of generating accurate reference mixtures, particularly of unstable VOCs. Diffusion rate and dilution gas flow rate uncertainties are the main contributors to the overall VOC concentration uncertainty. This paper presents a comprehensive overview of the uncertainty of the diffusion rate. Stress is laid on the advantages offered by a modified measurand equation. The validity of this analysis and the modified equation has been confirmed experimentally. Temperature variability and mass difference uncertainty make the main contributions to the uncertainty: a 0.01 °C variability results in a 0.2% uncertainty. The new measurand equation provides both a better indication of the systematic effects at a narrow temperature variability and a more realistic calculation of the uncertainty. The modified equation enhances calculation of uncertainty at the low diffusion rates needed to generate very low VOC concentration mixtures.

엔진 고공 시험에서 연료 유량 측정용 터빈 유량계의 측정 불확도 분석

Measurement uncertainty analysis of fuel flow using turbine flowmeter was performed for the case of altitude engine test. SAE ARP4990 was used as the fuel flow calculation procedure, as well as the mathematical model for the measurement uncertainty assessment. The assessment was performed using Sensitivity Coefficient Method. 11 parameters involved in the calculation of the flow rate were considered. For the given equipment setup, the measurement uncertainty of fuel flow was assessed in the range of 1.19~1.86 % for high flow rate case, and 1.47~3.31 % for low flow rate case. Fluctuation in frequency signal from the flowmeter had the largest influence on the fuel flow measurement uncertainty for most cases. Fuel temperature measurement had the largest for the case of low temperature and low flow rate. Calibration of K-factor and the interpolation of the calibration data also had large influence, especially for the case of very low temperature. Reference temperature, at which the reference viscosity of the sample fuel was measured, had relatively small contribution, but it became larger when the operating fuel temperature was far from reference temperature. Measurement of reference density had small contribution on the flow rate uncertainty. Fuel pressure and atmospheric pressure measurement had virtually no contribution on the flow rate uncertainty.