Flow rate measurement by an orifice in a slowly reciprocating gas flow

It is shown that small density changes can give rise to misinterpretation of flow rate signals in unsteady (reciprocating) flows. Basically a flow rate measured at some point A cannot simply be assigned to a remote point B. Depending on the way of plotting a hysteresis appears which, in fact, does not exist. Unsteady conservation of mass is applied to a volume and orifice flow system to obtain an equation which explains and predicts the apparent hysteresis. The equation in dimensionless form contains a key parameter β which holds the flow determining quantities. Experiments are conducted with respect to a wide spread of β. It is shown that the equation predicts reality quite well.     

Discharge characteristics of orifice spillway under oblique approach flow

Orifice type spillways are provided in the dam at lower level for facilitation in flushing of the sediment from the reservoir in addition to spilling the flood water. However, in most of the hydraulic structures, particularly in the earthen and rockfill dams, the spillway is not a part of the dam and it is provided on either of the banks of the river which results in oblique approach flow to the spillway that likely to affect the discharging capacity of the spillway. Presented in this paper is an experimental study for discharge characteristics of orifice type spillway under straight and oblique approach flow. Analysis of data indicates that discharge through the spillway decreases with increase of obliquity of the flow. The effect of the obliquity has been quantified and discharge equations for one, two and three simultaneous opening of the bays have been proposed.     

Effect of conical angle on the hydraulic properties of orifice plate flows: A numerical approach

Orifice flowmeters are widely used in industry due to their simple design, ruggedness, and easy installation. However, high-pressure losses, measurement accuracy, and long pipe length requirements are still significant concerns. Typically, conical entry orifice plates at a 45-degree conical angle are recommended by orifice standards, especially for low Reynolds numbers instead of the sharp-edged orifice plates, which pose stability. The primary goal here is to develop the conical entry orifice plates further over a broader range of Reynolds numbers. In this case, a 45-degree conical angle may seem questionable since the optimization of conical angles has not been studied so far. To clarify that point and reach the new technical data about the conical entry orifice plates, orifice plates in different orifice diameter ratios (0.4, 0.5, 0.63) and beveled with different conical angles (15°, 30°, 45°) were tested numerically through water flow simulations inside a pipe with an inner diameter of 50.8 mm at different Reynolds numbers (5000,18,400, 91,100, 240,000).According to the analysis made, the 30-degree conical angle orifice plate was the best in reducing pressure losses, resulting in pressure losses 37–52% less than that of sharp-edged orifice plates in the min-max range. Furthermore, it reduced the pressure losses by 13–21 % more than that of the 45-degree conical angle. These last outcomes indicate that current orifice standards needs a modification into the recommended conical angles. Through these findings, pressure losses in multi-hole plate flow conditioners can be reduced considerably when the holes are beveled at the 30-degree conical angle.Also in the study, the axial characteristic lengths relevant to recirculation region, flow recovery and vena contracta were predicted approximately, along with the derived numerical correlations resulting with constants. Moreover, the effect of orifice plates exposed to an upstream distorted velocity profile on orifice flows was tested numerically. According to this evaluation, the lowest measurement errors were observed at the 30-degree conical angle orifice plate, about 30–70 % less than that of the sharp-edged orifice plate in the min-max range.     

The fractal flow conditioner for orifice plate flow meters

The sensitivity of orifice plate flow meters to the quality of the approaching flow continues to be a cause for concern in flow metering. The distortions caused by pipe fittings such as valves, bends, compressors and other devices located upstream of the orifice plate can lead to non-standard velocity profiles and give errors in measurement. The design of orifice plate meters that are independent of the initial flow conditions of the upstream is a major goal in flow metering. Either using a long straight pipe, or a flow conditioner upstream of an orifice plate, usually achieves this goal.The effect of a fractal flow conditioner for both standard and non-standard flow conditions was obtained in experimental work and also using simulations. The measurement of mass flow rate under different conditions and different Reynolds numbers was used to establish a change in discharge coefficient relative to a standard one. The experimental results using the fractal flow conditioner show that the combination of an orifice plate and a fractal flow conditioner is broadly insensitive to upstream disturbances.The simulation results also show that the device can be used as a part of a flow metering package that will considerably reduce installation lengths. Previous work with orifice plates has shown that a combination of flow conditioner and orifice plate was promising. The results of using a combination of the fractal flow conditioner and orifice plate for non-standard flow conditions including swirling flow and asymmetric flow show that this package can preserve the accuracy of metering up to the level required in the Standards.     

Predicting oil flow rate through orifice plate with robust machine learning algorithms

Measuring fluid flow rate passing through pipelines is a basic strategy for developing the infrastructure of fluid-dependent industries. It is a challenging issue for trade, transportation, and reservoir management purposes. Predicting the flow rate of fluid is also regarded as one of the crucial steps for the development of oil fields. In this study, a novel deep machine learning model, convolutional neural network (CNN), was developed to predict oil flow rate through orifice plate (Qo) from seven input variables, including fluid temperature (T_f), upstream pressure (Pu), root differential pressure (√ΔP), percentage of base sediment and water (BS&W%), oil specific gravity (SG), kinematic viscosity (ν), and beta ratio (β, the ratio of pipe diameter to orifice diameter). Due to the absence of accurate and credible methods for determining Qo, deep learning can be a useful alternative to traditional machine learning methods. Justifying the promising performance of the developed CNN model over conventional machine learning models, three different machine learning algorithms, including radial basis function (RBF), least absolute shrinkage and selection operator (LASSO), and support vector machine (SVM), were also developed and their prediction performance was compared with that of the CNN model. A sensitivity analysis was also performed on the influence degree of each input variable on the output variable (Qo). The study outcomes indicate that the CNN model provided the highest Qo prediction accuracy among all the four models developed by presenting a root mean squared error (RMSE) of 0.0341 m3/s and a coefficient of determination (R²) of 0.9999, when applied to the dataset of 3303 data records compiled from oil fields around Iran. The Spearman correlation coefficient analysis results display that √ΔP, Pu, and Tf were the most influential variables on the oil flow rate in respect of the large dataset evaluated.     

Numerical simulations for multi-hole orifice flow meter

The measurement of flow rate is important in many industrial applications including rocket propellant stages. The orifice flow meter has the advantages of compact size and weight. However, the conventional single-hole orifice flow meter suffers from higher pressure drop due to lower discharge coefficient (Cd). This can be overcome by the use of multi-hole orifice flow meter. Flow characteristics of multi-hole orifice flow meters are determined both numerically and experimentally over a wide range of Reynolds numbers. Computational fluid dynamics (CFD) is used to simulate the flow in the single- and multi-hole orifice flow meters. Experiments are carried out to validate the CFD predictions. The discharge coefficients for the different orifice configurations are determined from the CFD simulations. It is observed that the pressure loss in the multi-hole orifice flow meter is significantly lower than that of single-hole orifice flow meter of identical flow area due to the early reattachment of flow in the case of the multi-hole orifice meter. The influence of different geometrical and flow parameters on discharge coefficient is also determined.     

Incompressible pulsating flow for low Reynolds numbers in orifice plates

A flow with periodic variations is known as a pulsating flow. A particularly important consequence of these flows occurs in the presence of orifice plates, which are devices related to the determination of discharge in pipes. Based on an experimental methodology, this work presents a study on the effects of pulsation variations and temporal inertia on the discharge coefficient. The work includes situations beyond those contained in the standards, particularly for liquid flows in small diameter pipes with low Reynolds numbers. The experiments were conducted on a flow bench, capable of producing pulsating flows inside pipes. For the experimental study of the transient flow, the propagation of a known flow fluctuation was related to a pressure fluctuation, allowing the dynamic calibration of the measuring system. The value of the dynamic discharge coefficient was determined, and the coefficients of static discharge and quasi-steady were compared. The results showed that the inertial effects significantly affect the value of the discharge coefficient of the orifice plate, reducing the discharge values.     

Examination of disturbed pipe flow and its effects on flow measurement using orifice plates

In a great number of measurements the influence of a disturbed flow on the flow coefficient of a standard orifice plate was investigated. Single bends and double bends out of plane with and without spacer tubes were used as typical disturbances. Experiments were also performed using a combination with a star-shaped flow straightener. The necessary correction factors of the flow coefficient were determined for upstream straight length shorter than detailed in ISO 5167. The flow velocity profiles produced by the disturbances were examined and on this basis profile numbers were calculated. The examinations presented here show that the existing standard should be revised as regards the definition of the fully developed turbulent flow profile and the selection of the required upstream straight lengths.     

A new approach to gas flow calibration

Primary gas flow standards create calculable flow rates using two different techniques. Displacement systems rely upon the accurate determination of the first order change in position of an object being displaced by gas flowing at a constant pressure. Pressure, volume, temperature and time (PVTt) systems provide a nearly constant mass flow of gas to an accumulation tank of known volume over a fixed time interval. Measurements of pressure, temperature and time are used to calculate flow rate.     

Further investigation into a water flow rig related to calibration

In the development of a flow test rig as a tool for investigating manufacturing variation, we encountered various problems. We discussed some of these in an earlier paper (Baker et al. (2006) [1]). In this paper we report on tests aimed at identifying the limits of accuracy of the rig and the best obtainable uncertainty with this type of design. We consider: traceability issues relating to the calibration of the weigh scales, seasonal variation, and sources of uncertainty in the flow system, and we deduce from these the limits of uncertainty. We also include some observations relating to the effect on meters of flow oscillation due to flow rate change.     

Experimental research of single-hole and multi-hole orifice gas flow meters

As energy efficiency is becoming more important today due to limited energy resources as well as their rising prices and environment issues, it is crucial to have reliable measurement data of different fluids in production processes. Because of its simplicity, affordability and reliability, orifice flow meters are again becoming subject of numerous researches. Conventional single-hole orifice (SHO) flow meter has many advantages but also some disadvantages like higher pressure drop, slower pressure recovery, lower discharge coefficient etc. Some of these disadvantages can be overcame by multi-hole orifice (MHO) flow meter while still maintaining advantages of conventional SHO meter. Both SHO and MHO flow meters with same β ratios were experimentally tested and compared. Results showed better (lower) singular pressure loss coefficient and lower pressure drop in favour of the MHO flow meter. Experimental data indicates that MHO flow meter is superior to the conventional orifice flow meter, but further research is necessary to make the MHO a drop-in replacement for a SHO flow meter.     

Comparison of quantification strategies for one-point standard addition calibration: The heteroscedastic case

Two quantification strategies for one-point standard addition calibration have been compared mathematically. One strategy involved the extrapolation of measurement points to their intercept with the x-axis to determine the analyte content in the unknown sample, and the other strategy is based upon direct calculation of the analyte content in the unknown sample using the instrumental responses obtained during measurement. The cases of both conventional standard addition calibration (C-SAC) and sequential standard addition calibration (S-SAC) have been considered. The heteroscedastic situation has been considered, where the relative precision of instrumental responses is constant.     

Determining the flow correlation for an orifice with a non-dimensional number

Traditional devices like orifice meters play a crucial function as a flow measuring device because there is inaccuracy in the measurement of the flow measuring device concern. The pressure drop (Δp) between the upside and downsides of the orifice-pipe flow passage is calculated using Bernoulli's principle. Orifice meter produces errors and uncertainty in the downstream of the flow because of wake or backflow. The proposed study provides the procedure to calculate the Δp and flow characteristics for a circular orifice for a compressible fluid (Air) with CFD analysis. The numerical study was carried out by considering combined parameters such as area ratio (σ) and space ratio (s) as geometrical parameters and Reynolds number as flow parameters to minimize the errors of the numerical calculation. The input parameter σ varies from 0.2 to 0.6, and the s varies from 0.1 to 0.9. Whereas the Reynolds number (Re) varies from 10000 to 100000. A non-dimensional number is defined by the combined effect of σ and s to generated correlations with accuracy which is enhanced predicted results of the work. The correlation will make a significant contribution to the flow monitoring device design.     

Flow instability due to cryogenic cavitation in the downstream of orifice

Flow instability in LRE (liquid rocket engine) occurs due to various reasons such as flow interactions with valve, orifice and venturi, etc. The inception of cavitation, especially in the propellant feeding system, is the primary cause of mass and pressure oscillations because of the cyclic formation and depletion of cavitation. Meanwhile, the main propellant in a liquid rocket engine is the cryogenic fluid, which properties are very sensitive to temperature variation. And the change of propellant properties to temperature variation by thermodynamic effect needs to be properly taken into account in the flow analysis in order to understand basic mechanisms for cryogenic cavitation. The present study focuses on the formation of cryogenic cavitation by using the IDM model suggested by Shyy and coworkers. The flow instability was also numerically investigated in the downstream of orifice with a developed numerical code. Calculation results show that cryogenic cavitation can be a primary source of flow instability, leading to mass fluctuations accompanied by pressure oscillations. The prediction of cavitation in cryogenic fluid is of vital importance in designing a feeding system of an LRE. This paper was recommended for publication in revised form by Associate Editor Jun Sang Park Changjin Lee received his B.S. and M.S. degrees in Aeronautical Engineering from Seoul National University in 1983 and 1985. He then went on to receive his Ph.D. degree from University of Illinois at Urbana- Champaign in 1992. Dr. Lee is currently a Professor at the department of Aerospace Engineering at Konkuk University in SEOUL, Korea. His research interests are in the area of combustion instabilities of hybrid, liquid rocket and jet propulsions. Tae-Seong Roh received his B.S. and M.S. degrees in Aeronautical Engineering from Seoul National University in 1984 and 1986. He then went on to receive his Ph.D. degree from Pennsylvania State University in 1995. Dr. Roh is currently a Professor at the department of Aerospace Engineering at Inha University in Incheon, Korea. His research interests are in the area of combustion instabilities, rocket and jet propulsions, interior ballistics, and gas turbine engine defect diagnostics.     

Data-based estimation and simulation of compressible pulsating flow with reverse-flow through an orifice

Highly compressible pulsating flows are often encountered in devices where knowledge of the flow rate is required but elimination of pulsations is not an option. The current work is a continuation of a previous investigation that characterized the orifice discharge coefficient C_d as a function of dimensionless groups based on pulsation characteristics. The experimental apparatus has been rebuilt in the current work to mitigate temperature and vibration problems, allowing pressure and ΔP measurements to be made very close to the test section with 159-mm of nylon tubing. Data was acquired for 77 operating conditions spanning a range of pulsation frequencies, mass flow rates and system pressures. They confirm previously reported low C_d's in 0.20 range (calculated from time-averaged pressures) at some high-pressure low-flow operating conditions. Computational Fluid Dynamics (CFD) simulations of 12 of these data points suggest that the low C_d's result from reverse flow. Flow direction changed several times during each pulsation cycle closely tracking the orifice ΔP. A ‘core-and-sheath’ phenomena was observed for reverse-flow operating conditions: a positive core flow surrounded by a sheath of negative flow transitioned to a negative core and positive sheath several times during each pulsation cycle. The simulations also suggested that velocity profiles at the orifice stay stable and similar to steady-state profiles except for periods of rapid transitions. Based on these results a data-based quasi-steady method of estimating pulsating flow has been proposed. A pair of forward and reverse flow C_d's chosen by the data are used to predict instantaneous forward and reverse flows using the steady-state orifice discharge equation for compressible flow. The instantaneous values are then summed up over the pulsation cycle to estimate average mass flow rate. Average prediction errors were within 6%. A previously proposed method where regression was used to model C_d as a function of dimensionless groupings was shown to produce similar results. Both methods are designed to extract information from experimental data in order to overcome theoretical limitations and experimental error. The data is available upon request for further understanding of the flow physics.     

Development of an accurate method to prognosticate choke flow coefficients for natural gas flow through nozzle and orifice type chokes

One of the main components in oil and gas production system is choke valve. The choke valve role is maintaining sufficient back pressure to prevent water gas coning and formation damage and also stabilizing fluid flow to reach the optimum production scenario. Chokes can be employed either on surface or subsurface to control the fluid flow characteristics to the downstream processing facilities such as flow rate, pressure, and velocity. Malfunction of choke may results in severe damages in safety, facilities, and environment.In this study, a rigorous method based on artificial intelligence is developed to predict the choke flow coefficient for subsonic natural gas flow through nozzle and orifice type chokes. Reynolds number and ratio of choke diameter to pipe diameter was utilized as input parameters. The method used in this study is radial basis function neural network coupled with genetic algorithm. The results showed great agreement with experimental data. In addition, the proposed method was compared with classic correlations. This comparison demonstrated the robustness and superiority of the GA-RBF model.     

A novel calibration procedure for dynamically tuned gyroscope designed by D-optimal approach

Effective calibration and compensation of the deterministic errors of Dynamically Tuned Gyroscope (DTG) are crucial in improving the application precision and performance of DTG. However, conventional calibration procedures used empirical parameter-setting and provided no evidence on optimization in terms of accuracy and calibration time. In this paper, D-optimal experimental designs were constructed to propose a practical 12-position calibration procedure of DTG which can be implemented by the medium-precision turntable. The proposed procedure was tested by a tactical-grade DTG. Test results show that, the fit uncertainty is reduced about 62% for the ox axis and 39% for the oy axis respectively. Furthermore, the new calibration procedure achieves D-optimal accuracy with half of the calibration time of the widely adopted 24-position calibration procedure.     

A unique test facility for calibration of domestic flow meters under dynamic flow conditions

In the early nineties a hot water test facility was planned and constructed for calibration and testing of volume and flow meters at the National Volume Measurement Laboratory at RISE (formerly SP Technical Research Institute of Sweden). The main feature of the test facility is the capability to measure flow in a wide temperature and flow range with very high accuracy. The objective of the project, which was initiated in 1989, was to design equipment for calibration of flow meters with stable flow and temperature conditions.After many years of international debate whether static testing is adequate to represent the later more dynamic application of domestic water meters, the EMPIR project 17IND13 Metrology for real-world domestic water metering (“Metrowamet”) was launched in 2018. The project investigates the influence of dynamic flow testing on the measurement accuracy of different types of domestic flow meters. One of the main objectives of the project is the development of infrastructure to carry out dynamic flow measurements. The existing test facility at RISE was at the time of construction one of the best hot and cold-water test facilities in the world. Due to the Metrowamet project the test facility has been upgraded to meet the needs of an infrastructure for dynamic flow investigations. The first findings from dynamic consumption profile measurements are reported in this paper.     

A novel approach based on artificial neural network for calibration of multi-hole pressure probes

Imperfections in the manufacturing process of flow measuring probes affect their measuring behavior. Nevertheless, in order to provide the highest possible accuracy, each individual multi-hole pressure probe has to be calibrated before using them in turbomachinery. This paper presents a novel method based on artificial neural networks (ANN) to predict the flow parameters of multi-hole pressure probes. A two-stage ANN approach using multilayer perceptron (MLP) is proposed in this study. The two-stage prediction approach involves two MLP networks, which represent the calibration data and the prediction error. For a given set of inputs, outputs from both networks are combined to estimate the measured value. The calibration data of a 5-hole probe at RWTH Aachen was used to develop and validate the proposed ANN models and two-stage prediction approach. The results showed that the ANN can predict the flow parameters with high accuracy. Using the two-stage approach, the prediction accuracy was further improved compared to polynomial functions, i.e. a commonly used method in probe calibration. Furthermore, the proposed approach offers high interpolation capabilities while preventing overfitting (i.e. failure to fit new data). Unlike polynomials, it is shown that the ANN based method can provide accurate predictions at intermediate points without large oscillations.