Flow Coefficient Research Articles

Numerical Investigation of Butterfly Valve Performance in Variable Valve Sizes, Positions and Flow Regimes

Reliability and efficiency of valves are necessary for precise control and sufficient heat-flow to heat application plants for the integrated energy systems of nuclear power plants (NPPs). Strategic Management Analysis Requirement and Technology (SMART) valves’ ability to control flow and assess environmental parameters stands out for these requirements. Their ability to sustain the downstream flow rate, prevent reverse flow, and maintain pressure in the heat transport loop is much more efficient with the integration of sensors and intelligent algorithms. For assessing valve performance and monitoring, mechanical design and operating conditions are two important parameters. In this study, the butterfly valves of three different sizes are simulated with water and steam using STAR-CCM+ in various flow regimes and positions to analyze performance parameters to strategize an automated control system for efficiently balancing the heat–transport network. Also, flow behavior is studied using velocity and pressure fields for valve–body geometry optimization. It can be observed, through performance parameters, that the valves are suitable for operation between 30° and 90° positions with significantly low loss coefficients and high flow coefficients, and the performance parameters follow a certain pattern in both water and steam flow in each scenario.

Effect of wettability on fracturing fluid microscale flow in shale oil reservoirs

The wettability of shale reservoirs has an important influence on the flow of external fluids. In this paper, the effect of wettability on the self-absorption of hydraulic fracturing fluid under different pore size conditions is first analyzed. Then, the mechanism of the influence of wettability pore size on the flow coefficient is elucidated. The results show that (a) as the pore size decreases, the importance of various forces acting on the fluid during the flow process changes, and the solid-liquid interaction will greatly affect the fluid flow in the nanopore. (b) When the radius is 5, the flow enhancement increases from 0.6331 to 0.998 as the radius increases from 0 to 3.141594.(c) The shale inorganic material contains a variety of minerals, and the interaction forces between different mineral surfaces and water molecules are different, resulting in different apparent viscosities.

A prediction model based on data-driven method for velocity and heat transfer coefficient of falling-film liquid on horizontal tube

The prediction of liquid film velocity and heat transfer coefficient of horizontal-tube falling-film flow is important for the investigation and enhancement of the flow and heat transfer behavior. To date, the prediction mainly relies on semi-empirical-semi-theoretical formulas based on data fitting. This prediction method has many limitations and assumptions on working conditions, and the error is large when it is extended to practical applications. In this paper, a support vector regression machine prediction method based on sine cosine algorithm optimization is proposed to improve the prediction accuracy of the liquid film velocity and heat transfer coefficient. And the database was established by conducting horizontal-tube falling-film flow and heat transfer experiments. Results show that the support vector regression model has the best prediction performance with small sample size in comparison with other four machine learning methods and traditional correlation based on Least Square method. The RMSEs of liquid film prediction model and heat transfer prediction model are only 0.0281 and 0.0117 respectively. And the MAPEs are 8.58 and 2.63 respectively. The liquid film velocity and heat transfer coefficient were accurately predicted based on relevant parameters. The importance of these parameters was also analyzed.

Variability of Double-Porosity Flow, Interporosity Flow Coefficient λ and Storage Ratio ω in Dolomites

Seventy-one pumping tests were carried out in various dolomites, revealing two of the less-studied hydrogeological parameters related to double-porosity flow: the interporosity flow coefficient λ and the ratio between storage in the fractures and storage in the whole system (ω). Conceptually, they are both tied to the flow properties of the fractures and matrix and define the communication between these two hydrogeological domains. Five different groups of dolomites were included in this study, with different diagenesis types, crystal sizes, bed thicknesses, fracture intensities and chert contents represented. The results of both parameters reflect variations in the sedimentological and resulting hydrogeological properties of dolomites. The largest values of the interporosity flow coefficient λ (6.53 × 10−1) are found in dolomites formed by late diagenesis, exhibiting the highest degree of fracturing, resulting in fast responses in fractures and large λ values. The values of the storage ratio ω also vary (the range of most values is from 3.32 × 10−4 to 2.14 × 10−1), with the overall range almost completely filling all the theoretical limits from zero to one. The greatest values of ω are found in dolomites with the largest storage, due to the large number of small fractures, and silica diagenesis probably reduces the matrix storage. The correlations among the parameters show some significant relationships, especially between λ and Km, λ and Sf, ω and Sf, and ω and Sm.

Equations and methodologies of inlet drainage system discharge coefficients: A review

Abstract Accurate determination of grate inlet discharge coefficients is crucial in reducing modeling uncertainties and mitigating urban flooding hazards. This review critically examines the methods, equations, and recommendations for determining the weir/orifice discharge coefficients, based on the inlet parameters and flow conditions. Reviewing previous studies for inlets showed that the discharge coefficient of rectangular inlets under subcritical flow ranges from 0.53 to 0.6 for weirs and from 0.4 to 0.46 for orifices, while in grated circular inlets, it falls between 0.115 and 0.372 for weirs and between 0.349 and 2.038 for orifices. For circular non-grated inlets under subcritical flow, the weir and orifice coefficients are in the range of 0.493–0.587 and 0.159–0.174, respectively. However, the orifice discharge coefficients of grated and non-grated inlets with unknown Froude number range between 0.14–0.39 and 0.677–0.82, respectively. For supercritical flow, the weir and orifice discharge coefficients of grated and non-grated rectangular inlets are 0.03–0.47 and 1.67–2.68, respectively. Previous studies showed that it is recommended to correlate the discharge coefficients with the approaching flow and Froude number under subcritical and supercritical flows, respectively. Yet, additional studies are recommended for a better understanding of the limits and parameters governing the flow transitional stage between weir and orifice and between subcritical and supercritical conditions. Moreover, further research is required to determine the weir and orifice discharge coefficients of circular inlets under supercritical flow as well as the orifice discharge coefficient range of rectangular non-grated inlets under subcritical flow. Finally, it is recommended to increase the road surface roughness to reduce Froude number, and thereby, increase discharge coefficients of street inlets. The aim of this review is to help inlet designers and authorities promote sustainable cities with resilient urban drainage systems and reduce the environmental, economic, health, and social impacts of urban drainage failure.

A combined experimental and computational investigation of an inducer’s characteristics with gas-water two-phase flow

The objective of the paper is to investigate the internal flow characteristics inside the inducer under the gas-water condition using a combination of experiment and numerical simulations. Gas-water mixing is achieved by an annular gas mixing device and visualized by high-speed imaging technology. Meanwhile, the shear stress transport (SST) k- ω model coupled with the VOF model is applied to investigate the gas phase distribution. Numerically simulated inducer energy characteristics and internal gas-phase distribution are in good agreement with experimental data. The results show that the mixed gas-liquid flow inside the inducer exhibits three flow patterns: wavy flow, bubbly flow, and plug flow. For the wavy flow, a series of wavy structures on the blade surface and gas-pocket bubbles near the blade rim are observed. From wavy flow to bubbly flow, uniform bubble streams on the blade surface and spiraling strip bubbles near the edge of the blade are observed. For plug flow, bubble accumulation results in a bullet-shaped plug, and the strip-shaped bubbles near the blade rim are more obvious. In the same axial position of the inducer, the proportion of gas phase is increasing as the flow coefficient increases, thus affecting the inducer performance. The main frequency amplitude of the pressure pulsations gradually rise when the flow pattern changes from wavy to plug flow.

Performance Envelope of a 538-Series High-Speed Helico-Axial Pump for High-Gas-Volume-Fraction Operation

Summary Operating at high speeds can have the benefit of increasing the capability of pumps to enhance surface or downhole production of fluids with high gas volume fraction (GVF). This study presents the performance envelope of a high-speed helico-axial pump (HAP) operating at high GVFs (>80%). The ultimate aim of the physical tests was to ascertain the operating capabilities of the pump for potential scaleup to a field prototype. The HAP housing outer diameter was 5.38 in. and operated at a rotational speed of 6,000 rev/min. Air and water were the test fluids, with an average pump intake and a discharge temperature of 28°C. The fluid volume flow rates were varied while maintaining 46 psig at the HAP intake. The liquid and total intake volume flow rates varied from 128 B/D to 664 B/D and 4,941 B/D to 7,593 B/D, respectively. The corresponding dimensionless pressure boost (DPB), GVF, liquid flow coefficients (LFCs), and total flow coefficients (TFCs) were recorded. Additional parameters noted were the percentage of electric current draw to full-load motor current by the HAP motor and the percentage of electric power input to full load power to the HAP motor. The results showed that the HAP had a stable operation during the tests for intake GVF range of 91–98%. The corresponding pump DPB was in the range of 0.0138–0.0751. These values being positive indicated the capability of the HAP to boost fluid pressure even for such high intake gas content and avoid pump gas lock. The results also showed that for a given intake GVF, the HAP DPB increased with decreasing LFC. For a given LFC, the DPB decreased with increasing intake GVF. The percent electric input power to the HAP motor varied between 28% and 64% of full-load motor power. It was observed to strongly increase with decreasing LFC at a given intake GVF and very strongly decrease with increasing intake GVF at a given LFC. The associated percent electric current draw by the HAP motor was seen to vary between 24% and 53% of full-load motor current. Its variation with LFC and intake GVF was similar to those of the percent electric power input. The DPB, percent electric current, and power draw by the HAP motor variations with TFC for a given intake GVF were similar to those of the LFCs. In conclusion, the HAP demonstrated the capability to boost fluid pressure when handling high GVF flows. It is being scaled up to a field prototype to handle higher volume flow rates of high GVF gas-liquid mixtures. This study mainly highlights the method to extend the gas-handling capability of a HAP by operating it at high speeds. Optimal hydraulic design and proper conditioning of the inlet flow components were also incorporated into the HAP architecture. Expanding the HAP operating envelope to handle high-GVF flows significantly unlocks the potential for field operators to maximize hydrocarbon production from high-gas content applications. This, in turn, increases the economic bottom line from the field asset.

Numerical Study of Cavitation Characteristics through Butterfly Valve under Different Regulation Conditions

Butterfly valves are widely used in the pipeline transportation industry due to their safety and reliability, as well as their low manufacturing and operation costs. Cavitation is a common phenomenon in the butterfly valve that can lead to serious damage to a valve’s components. Therefore, it is important to investigate the generation and evolution of cavitation in butterfly valves. In this study, LES and the Zwart model were used as the turbulence and cavitation models, respectively, to simulate cavitation through a butterfly valve. The influence of the valve opening degree and inlet flow velocity on dynamic cavitation through the butterfly valve were studied. Furthermore, the cavitated flow field was examined, along with the performance coefficients of the butterfly valve. With the increase in the incoming flow velocity, the high-speed jet zone over a large-range and low-pressure zone appeared inside the downstream of butterfly valve, which affected its stability and the cavitation generation through the valve. Furthermore, the flow coefficient decreased with the increase in vapor volume. In addition, the results indicated that cavitation was more easily induced for smaller valve opening degrees, and the interaction between cavitation and solid walls was stronger. Due to the existence of cavitation, the flow characteristics of butterfly valves are seriously affected.

Identification of spatially distributed rheological parameters for viscoplastic gravity currents

The rheology of a fluid is often difficult to measure in situ and in real time. This work investigates whether it is possible to recover rheological information from direct field observations. We present a closed-form analytical solution for inverse problem of identification of the mobility coefficient in gravity-driven fluid flowed down an inclined plane. The lubrication approximation is used to model the three-dimensional thin film of fluid and the governing equation is solved numerically by the explicit finite difference method to calculate the fluid thickness. We show in this study that using very straightforward measurements of fluid thickness at only a few points and only two successive instants, the mobility coefficient of fluid flow can be estimated accurately. Then as an important application in Bingham fluids we show that the knowledge of the mobility coefficient together with velocity measurement at only one point and instant enable us to estimate temperature-dependent viscosity and yield stress of the Bingham fluid. Unlike other methods, the proposed method allows the local identification of the rheology which is particularly useful when the rheological parameters are functions of the local temperature and/or composition. The proposed inverse analysis is a non-iterative approach with negligible computational cost since our analysis revealed closed form formulae relating the rheological parameters to the local flow depth, its derivatives, and the local free surface velocity.

A study of swirl flow measurements in a cylinder under an intake flow similar to an engine operating condition using a rotating slit disk valve

A new swirl measurement system was developed by installing bevel gears and a slit rotary valve into an impulse- type swirl measurement system of the type traditionally used to measure the swirl ratio and flow coefficient of engine intake ports. When operating this new swirl measurement system, it was confirmed that the characteristics of the intake air flow rate to the cylinders were similar to those of a typical operating engine condition. When the valve lift was limited to the cam angle range of 160 to 200 (the valve lift is maximized at a cam angle of 180°), the flow coefficient Cf increased as the cam angle increased under a constant camshaft rotation speed. Moreover, as the rotation speed of the camshaft increased, the Cf value decreased slightly. The swirl ratio NR in the cam angle range of 160 to 200 showed a nearly constant value with an increase of the cam angle at a constant camshaft rotation speed. There were also no significant changes in Cf with an increase in the camshaft rotation speed. NR measurement results while changing the camshaft rotation speed cannot be obtained by the traditional impulse swirl measurement method. NR measurement results with the new swirl measurement system can be used as basic data when calculating spray dispersion characteristics considering the engine rotation speed.

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Long- and short-range correlations for pairs of charged particles are studied via two-particle angular correlations in pp collisions at s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 13 TeV and p–Pb collisions at sNN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s_{\ extrm{NN}}} $$\\end{document} = 5.02 TeV. The correlation functions are measured as a function of relative azimuthal angle ∆φ and pseudorapidity separation ∆η for pairs of primary charged particles within the pseudorapidity interval |η| < 0.9 and the transverse-momentum interval 1 < pT< 4 GeV/c. Flow coefficients are extracted for the long-range correlations (1.6 < |∆η| < 1.8) in various high-multiplicity event classes using the low-multiplicity template fit method. The method is used to subtract the enhanced yield of away-side jet fragments in high-multiplicity events. These results show decreasing flow signals toward lower multiplicity events. Furthermore, the flow coefficients for events with hard probes, such as jets or leading particles, do not exhibit any significant changes compared to those obtained from high-multiplicity events without any specific event selection criteria. The results are compared with hydrodynamic-model calculations, and it is found that a better understanding of the initial conditions is necessary to describe the results, particularly for low-multiplicity events.

MATHIMATICAL MODEL TO PREDICT THE DESIGN ANI) PERFORMANCE OF HIGH.SPEED TURBOPUMPS

In this work a high-speed turbopumps of (22000 rpm) rotational speed, which are oxidizer and fuel turbopumps, are designed. The design requirement for mass flow rate and outlet pressure are (12.5 kg/s) and (113×10 Pa) respectively for the oxidizer turbopump, and (3.5 kg/s) and (95x10 Pa) respectively for the fuel turbopump. The design work of centrifugal pump is divided into impeller and volute design works. The impeller design work is performed by the streamline curvature and quasi-orthogonal technique based on hub-to-shroud mean stream surface between two blades with assistance of experimental design coefficients and relations for first prediction. The volute is designed by using the method of constant angular momentum, where in this method the tangential and radial velocities are considered uniform around the impeller. The numerical results are compared with experimental data of the actual pumps, and it is found that these results agree well with the real designs. The output of the design program is used as an input to the performance program. The performance prediction is achieved by three dimensional, steady, incompressible and viscous flow analyses through the blade passage. The ANSYS program has been employed to solve these equation in order to predict the flow characteristics at design and off-design conditions. The analysis is done at many operation conditions, which have the range of flow coefficient ratio (ФФ) from (0.4) to (1.8), and the results are compared with experimental results for previous work to make sure the validity of the analysis program at design and off-design conditions.

Film cooling performance under plasma aerodynamic actuation and spoiler ribs of an internal cooling channel based on Suzen model

In this paper, a plasma actuator (PA), treated by the Suzen model, is introduced into film cooling, and four rows of rectangular ribs are employed in internal cooling. Combined action and individual action of film cooling and internal cooling are then investigated at four blowing ratios (M = 0.25; 0.5; 0.75; 1.0). Results show that (no PA, no ribs) the coolant is ejected from the film hole in a spiral form under the action of internal crossflow, and its distributions are inclined to crossflow direction. When the plasma actuator is opened (no ribs), the strength and scale of the counter-rotating vortex pairs are weakened, and the motion of coolant is accelerated, the average cooling effectiveness shows an increase of 82.4% (M = 0.25), 98.9% (M = 0.5), 33.4% (M = 0.75) and a decrease of 2.1% (M = 1.0), the spanwise cooling effectiveness is raised by 57.3–143.3% for each streamwise position, the flow coefficient is lowered by 1.8–3.2%. Ribs (no PA) interfere with the coolant flow in the internal channel, reducing the rotation degree and exit momentum of the coolant, and greatly eliminate the uneven distribution of coolant along the spanwise direction, resulting in an enhancement of 50.4–162.8% in the spanwise cooling effectiveness and of 59.2% (M = 0.25) and 79.5% (M = 0.5) in average film cooling effectiveness. The effect of combined action (PA plus ribs) is lower than those effects of individual factors, and wall average film cooling effectiveness with PA and ribs exhibits a 62.4% (M = 0.25) and 49.4% (M = 0.5) higher to PA off a case (no PA, no ribs); however, a local or global heat transfer deterioration appears at M = 0.75 and 1.0.

A new heat transfer correlation based on flow patterns for hydrocarbon refrigerants condensation flow

To accurately predict heat transfer coefficients for hydrocarbon refrigerants condensation flow in heat exchangers is imperative for designing efficient systems. While various studies have proposed numerous correlations for predicting heat transfer coefficients, some of these correlations are based on fitted experimental data and are limited to predicting specific conditions. The prediction accuracy and capability for different working fluids remain to be evaluated. Currently, most researches mainly focus on pure working fluids, with relatively little attention given to mixed working fluids. In this study, six commonly used heat transfer correlations are evaluated and a new heat transfer correlation based on flow patterns is proposed. The research results indicate that the existing correlations have poor universality for predicting hydrocarbon refrigerants, and the prediction accuracy needs to be improved. The correlation developed in this study demonstrates good prediction performance for condensation heat transfer coefficients of 413 sets of hydrocarbon refrigerants, including methane, propane, ethane/propane, and methane/propane. The overall mean relative deviation (MRD) is −1.77%, and mean absolute relative deviation (MARD) is 8.12%. The correlation developed in this study can provide theoretical guidance for predicting condensation heat transfer coefficient for pure and mixed hydrocarbon refrigerants, aiding in the design of efficient heat exchangers.

Mapping performance of a marine energy harvesting turbine for flow coefficient and Reynolds number with varying Mach number through an automated optimization technique

Mapping performance of a marine energy harvesting turbine for flow coefficient and Reynolds number with varying Mach number through an automated optimization technique

Experimental investigation of rectangular nozzle aspect ratio effects on high-pressure helium leakage characteristics

High-pressure hydrogen leakage is one of the bottlenecks restricting the development of the hydrogen energy industry. In this study, a high-pressure helium leakage experimental system with stable pressure was built to research the influence of aspect ratio on concentration decay rate and mass flow rate. Similar to the circular nozzle, the centerline helium concentration of the rectangular jet is also inversely proportional to the distance from the nozzle. For the rectangular nozzles with aspect ratio of 1–4, the helium concentration decay rate is consistent with the circular nozzle when the leakage pressure is lower than 6.5 MPa. However, the decay rate is obviously larger for rectangular nozzles with aspect ratio of 10 when the leakage pressure is greater than 5.0 MPa. The aspect ratio has a greater influence on the flow coefficient, which increases with the aspect ratio under the same leakage pressure. To comprehensively consider the effects of nozzle size and shape, a weighted characteristic diameter of equivalent diameter and rectangular width, dc=αde+1−αdw, was proposed in this study. The results indicate that the equivalent diameter has greater impact on the centerline concentration decay rate, while the width of nozzles has substantial influence on the flow coefficient.

Flow discharge coefficient of crest weirs with covered vegetation

The flow data of mountainous rivers is very important in hydrological forecasting. Crest weirs with smooth surface have been widely used and studied, while there is little information on the weir covered with vegetation. In this experiment, the flow coefficient reduction are systematically investigated by different density flexible artificial vegetation, in addition to the changes of discharge, crest length and height. The equivalent roughness height of vegetation on the weir was calculated. It was found that the flow coefficient with vegetation is smaller than smooth crest. According to the ratio of upstream water head to the length of vegetation weir crest, the experimental flow can be divided into broad-crested weir flow rate of H/L < 0.4 and narrow-crested weir flow rate of H/L > 0.4. The flow coefficient reduction rate of both types of weir flow rates varies to a certain extent. Experimental data showed that the crest weir height H/P played a different law for the broad-crested weir and narrow-crested weir. Taking into account the influence of vegetation, crest length and height, empirical formula for flow coefficient was proposed for flow estimation correction.

Study of the Carreau fluid over a linearly curved stretching sheet: A numerical approach

Carreau fluid flow over a linearly curved stretching surface has significant applications in manufacturing industries. This study focuses on the impact of various parameters on the velocity, temperature, pressure skin friction, and heat transfer coefficient of a 2D Carreau flow. Both shear thinning (pseudoplastic) and shear thickening (dilatant) behaviors are considered. The parameters include suction, non-dimensional radius of curvature, Weissenberg number, magnetic parameter, power-law index, Eckert number (viscous dissipation parameter), and Prandtl number. The effects of viscous dissipation, magnetic field, convective boundary conditions, and suction are also taken into account. The study reveals that the flow velocity decreases with increasing magnetic parameter, curvature factor, and suction, but increases with the Weissenberg number and power law index. The heat transfer rate is reduced by the curvature factor, Weissenberg number, suction, power-law index, and Prandtl number, while the magnetic parameter has the opposite effect. The boundary value problem is simplified through appropriate similarity transformation and solved numerically using the shooting method and Matlab’s built-in function bvp4c. The results obtained from these two methods show good agreement. The findings also align well with existing literature in some limiting cases, confirming the validity of the study.

Interpreting pore-scale fluctuations: Predicting transport coefficients in multiphase flow through porous media using the Green–Kubo formulation—An experimental investigation

Flow fluctuations that are commonly associated with multiphase flow in porous media are studied using concepts from non-equilibrium thermodynamic and statistical mechanics. We investigate how the Green–Kubo formulation of the fluctuation dissipation theorem can be used to predict the transport coefficient from the two-phase extension of Darcy's law. Flow rate-time series data are recorded at the millisecond timescale using a novel experimental setup that allows for the determination of flow fluctuation statistics. By using Green–Kubo relations, a transport coefficient is predicted based on the integrated autocorrelation function. Notably, this coefficient aligned closely with the total effective phase mobility computed using Darcy's equation for multiphase flow, particularly in scenarios where a linear relationship between flow rate and pressure gradient was observed. Our results open a new field of coefficient explorations where microscale fluctuations during multiphase flow are directly linked to macroscale parameters.

Research on multi-objective parameter optimization of split flow dual flash thermodynamic cycle

In addition to considering the intermediate pressure variables, the split flow double flash thermodynamic cycle also needs to consider the operating conditions and split flow coefficient of the cycle. Traditional algorithms require too much computation and have a longer response time. Faced with sudden operating conditions or changes in production conditions, it is difficult to quickly re-optimize the intermediate parameters of the split flow double flash thermal cycle and carry out corresponding system control. This article uses intelligent optimization algorithms instead of global search methods to optimize multi-objective parameters in a split flow double flash thermodynamic cycle. By summarizing and analyzing the characteristics of algorithms such as SIO, EA, and ANN, it is believed that the GWO algorithm in the SIO class is the most suitable for multi-objective parameter optimization of the split flow double flash thermal cycle. It is combined with the SA optimization algorithm to propose the SA-GWO algorithm with faster optimization speed and higher optimization accuracy, taking the initial position of the wolf pack as the optimization objective. Combined with the cycle thermodynamic model, a multi-objective parameter optimization model for the split flow double flash thermal cycle is established.