Numerical investigation on the installation effects of electromagnetic flowmeter downstream of a 90° elbow–laminar flow case

An electromagnetic flowmeter installed downstream of a 90° elbow to measure the flowrate of laminar flow is numerically simulated to investigate installation effects by varying the location of the electromagnetic flowmeter at a distance up to 22D from the elbow, and the angle between the electrodes plane and the symmetry plane of the elbow at ϕ=0, 45 and 90°. Effects of the curvature radius (R_c) and the Reynolds number (Re) based on a diameter D are also scrutinized in the range of 400≤Re≤1500 and R_c=1.5D and 3.0D.For the simulation of an electromagnetic flowmeter, a commercial code FLUENT(ver. 4.4) is applied for flow field analyses and a three-dimensional numerical code is developed for analyzing the magnetic field. The developed code adopts a finite volume method to solve a Poisson-type voltage equation for the magnetic field.It is found that the deviations of the flow signal due to the disturbance from the elbow is strongly dependent on the pattern of axial velocity contours. Cases for ϕ=45° are found to permit significantly better measurement accuracy in comparison with ϕ=0° and ϕ=90°, and the effect of the curvature on the optimum installation distance depends on the Reynolds number. The present numerical simulation method is found to be a useful tool for the performance analysis of the electromagnetic flowmeter.     

Experimental verification and numerical simulation of a vortex flowmeter at low Reynolds numbers

This study presents experimental verification and numerical simulations of a vortex flow meter in the Reynolds number range between 8300 and 50,000. A custom-designed bluff body with a wedge back shape was used in the flowmeter. A shedding frequency of the flowmeter was measured in an air duct using a hot-film probe. To evaluate the accuracy of the flowmeter, a measurement uncertainty analysis was performed. Numerical simulations of the vortex flowmeter were performed with the open source code OpenFOAM. Transient simulations of periodic vortex shedding behind the bluff body were performed using different simulation methods depending on the pipe Reynolds number, such as Direct Numerical Simulation (DNS), Large Eddy Simulation (LES) and Unsteady Reynolds Averaged Navier Stokes (URANS) method. The simulated vortex shedding frequencies matched the experimental data very well. Experiments and simulations demonstrated a clear linear dependence of the shedding frequency on the volumetric flow rate over the entire range of Reynolds numbers. In addition, numerical simulations were used to study the main mechanisms of vortex formation and shedding behind the considered bluff body.     

Study on the design and performance of a bi-directional cone flowmeter

The present study explores a novel design of cone flowmeter for bi-directional flow metering application. Two identical cone shapes are machined with their base circle surfaces joined together with a small step in between them and differential pressure measurement is done across the apex of the cones. The bi-directional cone flowmeter is tested under fully developed flow conditions and its performance under double 90° bend (out-of-plane) is also evaluated. The bi-directional cone flowmeter is tested in a circular pipe (inside diameter of 101 mm) with water as the working medium for the flow Reynolds number ranging from 1.18×10⁵ to 5.48×10⁵. Influence of the half cone angle (α) and the location of static pressure taps on the coefficient of discharge (C_d) of a cone flowmeter are studied. Two cones with half cone angles α=30° and α=45° with a constant constriction ratio (β) of 0.75 are studied. Static pressure taps are located on both sides of the bi-directional cone. Two sets of locations of static pressure taps are studied. First set includes two static pressure taps on the pipe wall in the planes of apexes of the bi-directional cone—called apex taps. Second set includes pressure taps on the pipe wall in the planes at a distance D/4 away from the apexes of the bi-directional cone—called D/4 taps. Double 90° bend (out-of-plane) is placed at 1.5D, 5.5D, 9.5D and 13.5D upstream to the bi-directional cone flowmeter. It is observed that the apex static pressure taps located in the plane of apexes of the bi-directional cone result in statistically consistent coefficient of discharge for all Reynolds numbers covered in this study. The results suggest that the bi-directional cone flowmeter is insensitive to the swirl created by double 90° bend (out-of-plane) placed at the upstream of cone flowmeter, if placed at a distance of 9.5D or more.     

Influence of cone angle on the performance of a wafer cone flowmeter

The present study explores the effect of upstream disturbances like a single 90°bend, double 90° bends (in plane and out of plane) on the performance of wafer cone flowmeters with same beta ratio (β) of 0.77 but different half cone angles (α) of 30° and 45°. The influence of these disturbances on the upstream and downstream axial velocity (u) profiles are studied experimentally. The orientation effects, if any, are also studied experimentally. The minimum upstream distances required to get a fully developed flow for these disturbances vary with type of upstream disturbance, beta ratio (β) and half cone angle (α) of the wafer cone flowmeter. The study is carried out for a single phase flow with air as working medium at high Reynolds number (Re_D = 144000). From the results obtained from this study, it may be concluded that the wafer cone flowmeter with a beta ratio (β) of 0.77 and a cone angle of 30° requires less upstream distance compared to the wafer cone flowmeter with a beta ratio (β) of 0.77 with a cone angle of 45° for all the disturbances under consideration.     

Pressure measurement technique and installation effects on the performance of wafer cone design

The present study explores novel pressure averaging technique for wafer cone flowmeter design and its robustness in the presence of double 90° bend (out-of-plane) and gate valve as a source of upstream flow disturbance. The wafer cone flowmeter is tested in a circular pipe (inside diameter of 101 mm) with water as the working medium for the flow Reynolds number ranging from 1.19×10⁵ to 5.82×10⁵. Influence of the half cone angle (α) on the coefficient of discharge (C_d) of wafer cone flowmeter is studied with this new pressure averaging technique. Half cone angles considered in this study are 30° and 45° with a constant constriction ratio (β) of 0.75. The upstream static pressure tap is located at 1D upstream of the wafer cone. The downstream pressure averaging technique comprises eight circumferential holes of diameter 2 mm on the maximum diameter step of the wafer cone. The pressure taps are communicated through the support strut which serves as a downstream static pressure tap. The disturbance causing elements are individually placed at 1.5D, 5.5D, 9.5D and 13.5D upstream to the wafer cone flowmeter. The wafer cone flowmeter is also tested with gate valve opening of 25%, 50% and 75% for all the arrangements considered. The 30° cone is found to be better than 45° cone for the range of Reynolds number covered in the present study. The results show that the 30° wafer cone flowmeter with novel downstream pressure averaging technique is insensitive to the swirl flow created by a double 90° bend (out-of-plane) and requires an upstream length of 9.5D with a gate valve as a source of flow disturbance.     

Methods to calibrate a critical nozzle and flowmeter using reference critical nozzles

Methods to calibrate a critical nozzle and a flowmeter against reference critical nozzles are developed to replace the time-consuming conventional procedures. The discharge coefficient of a critical nozzle at a low Reynolds number was measured in a series connection with a reference nozzle in the upstream position, and its Reynolds number dependence was obtained by changing the reference nozzle. The dependence of similar critical nozzles with negligible machining error measured at low pressures using the series connections and at atmospheric pressure using a constant volume tank system coincide within ±0.04%. The same configuration was employed to measure the stability of the choking flow rate, which revealed premature unchoking phenomenon. The discharge coefficient of a critical nozzle under a reference condition was measured by a combination of three series connections with two reference critical nozzles at the upstream positions. Reynolds number dependence of a critical nozzle was measured using a combination of three series connections with four reference critical nozzles. These two methods require only one pressure gauge whose sensitivity is constant in a narrow range. An air flowmeter was calibrated at various volumetric flow rates against only one critical nozzle by controlling the upstream pressure of the nozzle.     

Influence of divergent section on flow fields and discharge coefficient of ISO 9300 toroidal-throat sonic nozzle

The effect of divergent section of ISO 9300 toroidal-throat nozzle on discharge coefficient was analyzed based on the inviscid transonic flow model and laminar boundary layer theory. A series of numerical simulations were conducted to verify the results of theory, and investigate the effect of divergent section length L and diffuser angle θ operated at different Reynolds numbers. Combined with the numerical results in this study and the experimental data reported by Nakao, it showed the discharge coefficient increases with the rise of diffuser angle θ or the drop of divergent section length L. A lot of new results about the effect of divergent section were obtained. It indicated that the effect of divergent section on discharge coefficient of ISO 9300 toroidal-throat nozzle should be considered when Re<1.1×10⁴. At last, a concept of effective critical flow was proposed to discuss the effect of divergent section on discharge coefficient.     

Effect of Reynolds number and boundary layer thickness on the performance of V-cone flowmeter using CFD

The effect of Reynolds number and boundary layer thickness on the performance of V-cone flowmeter has been evaluated using computational fluid dynamics (CFD). The shear stress transport k-ω (SST k-ω) turbulence model has been adopted for closure. The performance of two V-cone flowmeters with different beta ratios (β) viz., 0.6 and 0.7 for a fixed vertex angle (ϕ) of 60° has been analysed as a function of Reynolds number (Re). The results show that the coefficient of discharge (C_d) increases with Reynolds number in the laminar and transition flow regimes whereas it is nearly constant in turbulent flow regime. From the results, it can be concluded that C_d is independent of Re for values equal to 4000 and beyond. Further, it is also seen that the performance of the V-cone flowmeter is not affected by the upstream boundary layer thickness if the velocity profiles having different boundary layer thickness are extracted from an axial distance of 10D and more are fed at 5D upstream of the meter. However, the meter is sensitive to the extracted velocity profile from an axial distance of 5D and uniform velocity profile being fed at 5D upstream. The value of C_d may be sensitive as a result of the pressure variation due to the obstruction.     

Feedback fluidic flowmeters with curved attachment walls

Feedback fluidic flowmeters with curved attachment walls instead of conventional straight attachment walls were designed and machined. We experimentally investigated the effects of the dimensions of the jet nozzle and feedback channel on the oscillatory frequency, using water as the working fluid. The results reveal that in most cases, feedback fluidic flowmeters with curved attachment walls have a greater oscillatory frequency than those with straight attachment walls. A performance characteristic curve related to only the oscillatory frequency f and Reynolds number Re was found to be insensitive to the jet nozzle width and feedback channel width, even for asymmetric feedback channels [f(Hz)=7.67·exp(–α/2.56)+31.2·exp(–α/0.554)+0.757, where α=ln(Re)/f]. The characteristic curve can be used to measure the flow rates of liquids through a feedback fluidic flowmeter with curved attachment walls without the need for frequent calibrations.     

Approximate solution for discharge coefficient of the sonic nozzle with surface roughness

Sonic nozzle is widely used in the flow measurement and control. Nowadays, it has been applied to higher Reynolds number flow increasingly. The effect of surface roughness on discharge coefficient of the sonic nozzle should be discussed. An approximate analytic solution for discharge coefficient of the sonic nozzle with surface roughness was proposed in detail. The determination of this coefficient was based on universal logarithmic velocity-distribution law and the principle of equivalent velocity profile. Although there are some apparently approximations, this algebraic method accurately predicts the discharge coefficient of the sonic nozzle with surface roughness in Reynolds number range from 10⁴ to 10⁹, a relative equivalent roughness range of 10⁻⁶ to 10⁻². Some experiments of sonic nozzle conducted by others showed agreement with present algebraic method. Besides, the agreement between this method and the corresponding exact numerical calculation is also good. The present method provides an excellent tool to deeply investigate the roughness effect and promote further improvement of the standard.     

Effects of the Reynolds number on two-dimensional dielectrophoretic motions of a pair of particles under a uniform electric field

This paper presents two-dimensional direct numerical simulations to explore the effect of the Reynolds number on the Dielectrophoretic (DEP) motion of a pair of freely suspended particles in an unbounded viscous fluid under an external uniform electric field. Accordingly, the electric potential is obtained by solving the Maxwell’s equation with a great sudden change in the electric conductivity at the particle-fluid interface and then the Maxwell stress tensor is integrated to determine the DEP force exerted on each particle. The fluid flow and particle movement, on the other hand, are predicted by solving the continuity and Navier-Stokes equations together with the kinetic equations. Numerical simulations are carried out using a finite volume approach, composed of a sharp interface method for the electric potential and a direct-forcing immersed-boundary method for the fluid flow. Through the simulations, it is found that both particles with the same sign of the conductivity revolve and eventually align themselves in a line with the electric field. With different signs, to the contrary, they revolve in the reverse way and eventually become lined up at a right angle with the electric field. The DEP motion also depends significantly on the Reynolds number defined based on the external electric field for all the combinations of the conductivity signs. When the Reynolds number is approximately below Re_cr ≈ 0.1, the DEP motion becomes independent of the Reynolds number and thus can be exactly predicted by the no-inertia solver that neglects all the inertial and convective effects. With increasing Reynolds number above the critical number, on the other hand, the particles trace larger trajectories and thus take longer time during their revolution to the eventual in-line alignment.

     

Discharge coefficients of CFVN predicted for high Reynolds numbers based on low-Re-calibration

In 2016, PTB introduced a function for the representation of the discharge coefficient c_D of critical flow venturi nozzles (CFVN) (versus the Reynolds number Re) which covers the operating range for both laminar and turbulent boundary layers. It contains the parameters a for the impact of the core flow, b_lam for the Re-dependency in case of laminar and b_turb in case of turbulent boundary layers. These parameters are not independent from each other but have the fixed relation of b_turb = 0.003654b_lam^1.736.Furthermore, the parameter a and the parameter b_lam are both direct functions of the local curvature radius R_c,throat of the nozzle at the throat. These relationships to R_c,throat are described by theoretical models. Consequently, the overall dependency of the discharge coefficient c_D on Reynolds number Re can be derived from only one parameter.The paper describes how these relationships can be used to extrapolate the calibration values of a CFVN determined with atmospheric air to high pressure gas flow applications covering a Reynolds range of about 1:60. It is shown in detail by examples and the reliability is demonstrated by comparison data for low and high pressure for 33 nozzles. Finally, aspects of preconditions for such extrapolation and uncertainties are discussed.     

Research on the measuring characteristics of a new design butterfly valve flowmeter

Flowmeters and control valves are important components of flow measurement and control in heating, ventilating, and air conditioning (HVAC) system, which directly or indirectly impact building room comfort and energy costs. Valves as resistance components produce differential pressure which in turn can be used for flow measurement. This paper studies the function among valve opening position, pressure difference and flowrate of a new designed butterfly valve. The flow model of the butterfly valve is established based on the Bernoulli equation, the discharge coefficient C under different valve opening conditions are studied by CFD simulations and verified by experiments. The simulation results show that the discharge coefficient C reached a stable value of 0.67–0.70 as Reynolds number exceeded 5000, and the permanent pressure loss ratio is range from 0.95 to 0.37 corresponding to opening range from 10° to 70°. The correctness of the simulation results of C is verified by experiments, in which C is about 0.60. With the corrected values obtained from experiments, the simulation results are instructive to practice. The new designed butterfly valve flowmeter can be used efficiently in HVAC system, especially in variable air volume (VAV) air conditioning system. And the work of this paper offers a reference for other types of valve flowmeters in fluid control processes.     

Comparison of flow characteristics around an equilateral triangular cylinder via PIV and Large Eddy Simulation methods

The flow structures around an equilateral triangular cylinder, which is commonly used as a vortex shedder in the vortex flowmeter, were investigated experimentally and numerically. Flow characteristics such as vorticity contours, patterns of sectional streamlines, velocity vectors, velocity fields, Reynolds stress correlations, Strouhal numbers and drag coefficients were examined using the Particle Image Velocimetry (PIV) technique and the Large Eddy Simulation (LES) turbulence model. Experimental studies were performed in an open water channel for Re=2.9×10³, Re=5.8×10³ and Re=1.16×10⁴ based on the equilateral triangle edge. A sharp-tip corner of the cylinder with a triangle cross-section was exposed to the upstream side while the other two sharp-tip corners were placed on the downstream side. Numerical studies were also completed at Reynolds numbers in the range of 2.9×10³≤Re≤1.16×10⁵ to obtain the changes in the Strouhal numbers and drag coefficients. When the results of PIV and LES are considered in the same interval of Reynolds numbers, the maximum and minimum values of each flow pattern were nearly the same. The time-averaged patterns had considerable symmetry with respect to the axis line passing through the sharp-tip corner of the cross-section of the triangular cylinder. The Strouhal number was independent of the Reynolds number and was found to be approximately 0.22. The drag coefficient decreased with increasing Reynolds numbers while increasing the Power Spectral Density (PSD) and the vortex shedding frequency. For the same Reynolds numbers, the experimental and numerical results were in good agreement. Therefore, the LES turbulence model is recommended for applications of flow around this type of bluff body that is generally used in the design of vortex flowmeters to generate vortex shedding.     

Influence of blockage and shape of a bluff body on the performance of vortex flowmeter with wall pressure measurement

Experimental and numerical investigations are carried out with various bluff body shapes to identify an appropriate shape which can be used for vortex flowmeter application. In both the cases vortex shedding frequency is inferred from the fluctuation of wall pressure. The numerical simulations are carried out with cylindrical and triangular bluff bodies to understand the vortex shedding phenomenon and to identify an appropriate turbulence model for this class of flows with wall pressure measurement. The simulations reveal that the k-ε RNG model predicts the Strouhal number closer to the experimental results than other models. The experimental investigations are carried out with several bluff body shapes, such as triangular, trapezoidal, conical, cylindrical and ring shapes, with water as the working medium. In this context, the effects of sampling rate, tap location and blockage effects are explored. The results suggest that the axisymmetric tapping is better than differential pressure tapping in terms of signal amplitude. The non-dimensional location of the static pressure tap is found to be 0.714 times diameter of pipe times blockage. The trapezoidal bluff body is found to be the best among all the bluff bodies investigated in terms of signal amplitude and constancy of Strouhal number. The vortex flowmeter performance is also measured under disturbed flow conditions created by using gate valve and bends. These results are significant because they provide an optimum bluff body shape and blockage, and also present the performance of vortex flow meter under disturbed flow conditions which is rather seldom reported in the literature.     

Flow distribution in manifolds for low Reynolds number flow

This paper addresses the fundamental flow distribution question of how to design manifolds of low Reynolds number flow with both numerical analysis and experiments. The present study introduces new parameters of α_c and α_d, defined as the ratio of header diameter to header length in combining and dividing manifolds, the parameters which are not clearly considered in the previous studies of flow distribution in manifolds. The parameters of α_c and α_d were found to govern the flow distribution independently of each other. varying α_c, α_d and the Reynolds number respectively, a correlation of optimal flow distribution is obtained for laminar fow in manifolds as follows; α_d·Re _w ^m =K where acu _c≥1/4. The proposed correlation makes predictions possible for wide ranges of α_d and Re_w. Also, the present numerical results show satisfactory agreements with those of flow visualization. From the flow visualization. recirculating flow regime was observed at the inlet of each channel, in which hot spots may occur due to small velocities. The size of recirculating flow regime is strongly dependent on the Reynolds number and is smaller for optimal cases than others.     

Influence of wall roughness on discharge coefficient of sonic nozzles

To research the influence of roughness on discharge coefficient of axisymmetric sonic nozzles systematically, a turbulence model was established, and standard k–ε model was used in the turbulent core region while Wall Functions was carried out in the boundary layer region. A series of numerical simulations were conducted to research discharge coefficients of 6 critical flow Venturi nozzles with throat diameter ranging from 0.5 to 100 mm when Reynolds numbers ranges from 10⁴ to 10⁹ and relative roughness from 10⁻² to 10⁻⁶. The validity of the simulation model was confirmed by both the experimental data of Stewart and ISO 9300 empirical equation. According to the simulation results and theoretical analysis, the relations between discharge coefficient and relative roughness were obtained. It is recommended that the dimensionless parameter relative roughness should be used in ISO 9300 rather than absolute roughness. Additionally, when the machining of nozzle cannot satisfy the ISO 9300 requirement or the Reynolds numbers exceed the upper limits of the ISO 9300 equation, the effect of roughness should be considered, and the relative roughness of sonic nozzle should be provided clearly in the further experiment of discharge coefficient.     

Study on the effect of vertex angle and upstream swirl on the performance characteristics of cone flowmeter using CFD

Computational Fluid Dynamics (CFD) has emerged as a revolutionary tool for optimizing the design of any flowmeter for given conditions. The flow features obtained with CFD are more extensive compared to experiments. In the present study, CFD code ‘FLUENT” after validation has been used to investigate the effect of cone vertex angle and upstream swirl on the performance of cone flowmeter. The values of discharge coefficient ($C_d$) evaluated for different vertex angles shows that the value of discharge coefficient is independent of Reynolds number and its value decreases with increase in vertex angle. In the presence of upstream disturbance in the form of swirl, the value of discharge coefficient is also independent of Reynolds number and its value is only marginally affected by the magnitude of swirl. The flow in a longitudinal plane shows the presence of a pair of contra-rotating vortices in the recirculation region just downstream of the cone. The velocity profile downstream becomes stable after a distance of about 5D.     

Analysis of externally pressurized gas-lubricated conical bearings

An analysis is presented of externally pressurized conical gas bearings with discrete point pressure sources in the form of orifices located around the circumference at quarter stations from the end of the bearing. The governing Reynolds equation over the developed bearing area is solved by a direct numerical method to determine the pressure distribution. Numerical results are presented in the form of non-dimensional charts for load capacity, flow rate and stiffness for a conical bearing having L/D_M = 1 and semicone angles from 10° to 40°.     

Structure and dynamics of the turbulent flow through a central baffle

Central baffle flume (CBF) can be utilized as a control structure to measure flow discharge in irrigation channels under free and submerged flow conditions. Stage-discharge relationship has been extensively studied for various geometrical parameters and flow conditions, whereas internal structure of the flow around a baffle has not been investigated in the literature. To address this need, the present work investigates the turbulent flow around a central baffle through high-resolution numerical simulations using an open source computational model. Velocity measurements were conducted in a laboratory flume to setup and validate the numerical model. Comparison of the numerical results with the experimental measurements proves that the present numerical model can predict water depth and velocity field. Longitudinal distance from the apex to the intersection point of water and critical depths can be estimated as L_xc = 2L_e, where L_e is the longitudinal length of the guide walls. A horseshoe vortex system identified in front of the baffle produces a significant bump on the free-surface and rib vortices generated from the baffle extend up to the sidewalls of the channel. The vertical separation layer observed downstream of the baffle results in a reverse flow and a vortex pair is formed by the impingement of the resulting reverse flow on the back of the baffle. Reverse flow, plunging flow structure, splash and rebounding wave events observed at the downstream produce substantial hydrodynamic effects on the baffle. Geometry of the central baffle was modified to suppress recirculation effects based on the insights into the complete flow structure around the baffle. Eventually, vortex structures were suppressed and the length of the recirculation zone was reduced by 76%.