Flow Velocity Distribution Towards Flowmeter Accuracy: CFD ... - MDPI

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Flow Velocity Distribution Towards Flowmeter Accuracy: CFD, UDV, and Field Tests Mariana Simão 1, * , Mohsen Besharat 1 , Armando Carravetta 2 and Helena M. Ramos 1 1 2

*

CERIS, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal; [email protected] (M.B.); [email protected] (H.M.R.) Department of Hydraulic, Geotechnical and Environmental Engineering, Università di Napoli Federico II, via Claudio, 21, Napoli 80125, Italy; [email protected] Correspondence: [email protected]; Tel.: +351-218-418-151

Received: 22 October 2018; Accepted: 6 December 2018; Published: 8 December 2018







Abstract: Inconsistences regarding flow measurements in real hydraulic circuits have been detected. Intensive studies stated that these errors are mostly associated to flowmeters, and the low accuracy is connected to the perturbations induced by the system layout. In order to verify the source of this problem, and assess the hypotheses drawn by operator experts, a computational fluid dynamics (CFD) model, COMSOL Multiphysics 4.3.b, was used. To validate the results provided by the numerical model, intensive experimental campaigns were developed using ultrasonic Doppler velocimetry (UDV) as calibration, and a pumping station was simulated using as boundary conditions the values measured in situ. After calibrated and validated, a new layout/geometry was proposed in order to mitigate the observed perturbations. Keywords: experiments; ultrasonic Doppler velocimetry (UDV); flowmeters; computational fluid dynamics (CFD); pipe system efficiency

1. Introduction Worldwide, water companies use several flowmeters to measure the amount of water distributed. This equipment is quite vital for the management of water companies since important improvements are made according to the data provided by the available measures. The data provided by these devices also influences several performance indicators regarding the management of the system, such as non-revenue water (NRW) and water balances. The NRW is the volume of treated water that is not purchased. The water balances are important tools to detect leaks throughout the supply and distribution processes. Both these tools require accurate measurements [1]. The flow measurements can be correlated to the system efficiency. Usually, the systems are in part driven by gravity and by pressure differences, which require a pumping station. If the measurement accuracy is guaranteed, a higher energy efficiency level is possible to achieved, making possible a working period plan in the lower energy tariffs depending on the regularization ability and the water needs downstream [2,3]. Thus, the correct measurement by using flowmeters is an extremely important factor in terms of hydraulic system accuracy and management. Amongst other domains, the measured flow values are one of the key issues to detect leaks in pipe systems. Therefore, for any hydraulic system manager, the accuracy in flow measurements has significant impacts regarding both planning and investment decisions. Even when following all the constraints imposed by manufactures, incongruences can be identified in the field [4]. These irregularities suggested many times the occurrence of leaks in pipe systems. This conclusion raises a new problem that was not yet well identified [5].

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Hence, this toto analyze different variables, namely the the pipepipe layout and Hence, this research researchhas hasthe theobjective objective analyze different variables, namely layout the way it can disturb the the flowflow andand flowmeter accuracy. TheThe purpose is to how vertical or and the way it can disturb flowmeter accuracy. purpose is assess to assess how vertical horizontal curves, expansions and reductions, among other geometries can influence the flow and, or horizontal curves, expansions and reductions, among other geometries can influence the flow consequently the measurements. To fulfil the influence of several perturbations were and, consequently the measurements. To this fulfilgoal, this goal, the influence of several perturbations identified, using using an electromagnetic flowmeter and ultrasonic Doppler velocimetry (UDV), and were identified, an electromagnetic flowmeter and ultrasonic Doppler velocimetry (UDV), compared with the computed velocity profiles, using CFD models. The numerical model was and compared with the computed velocity profiles, using CFD models. The numerical model was calibrated and and validated validated using using the the same same conditions conditions as as the the experimental experimental facility. facility. The The numerical numerical calibrated simulations showed good approximation with the velocity measurements for two different simulations showed good approximation with the velocity measurements for two different geometries. geometries. To evaluate the accuracy of the numerical results, several experimental tests, using two To evaluate the accuracy of the numerical results, several experimental tests, using two different different geometries, were firstly developed, perturbations in the flow measurements, geometries, were firstly developed, identifyingidentifying perturbations in the flow measurements, followed by followed by analysis in a real case study. analysis in a real case study. 2. Electromagnetic Flowmeters Flowmeters are one of the most important and used devices to measure accurately, the volume flow rate [6]. Nowadays there there are are several several types types of flowmeters, flowmeters, but but the most important for flow [6]. Nowadays measurement are the electromagnetic and the ultrasonic ones. They are characterized for their high accuracy to to thethe authors of [1], electromagnetic flowmeters are only accuracy and andself-monitoring self-monitoring[7]. [7].According According authors of [1], electromagnetic flowmeters are disturbed by existing particles that may change the magnetic properties of each fluid.fluid. Properties like only disturbed by existing particles that may change the magnetic properties of each Properties temperature, viscosity and the fluid do not affect theaffect measurements. However, as mentioned like temperature, viscosity and thedensity fluid density do not the measurements. However, as in [8], a steady regime is a necessary guaranteetoaccurate measurements. mentioned in [8], a steady regime is acondition necessarytocondition guarantee accurate measurements. These flowmeters elements: thethe primary andand the the convertor (Figure 1). The flowmetershave havetwo twodifferent different elements: primary convertor (Figure 1). first The element corresponds to a hollow circular pipe with its length and isand set in pipeline [9,10]. first element corresponds to a hollow circular pipecoils withalong coils along its length is the set in the pipeline The flow through the section, createscreates an electromagnetic field which is proportional to the [9,10]. Thepassing flow passing through the section, an electromagnetic field which is proportional volume flow rate. convertor is the brain it creates magnetic field, reads thereads voltage, to the volume flowThe rate. The convertor is theelement: brain element: it acreates a magnetic field, the displays the data, the anddata, generates outputs. The convertor the volumethe flow rate and therate amount voltage, displays and generates outputs. The displays convertor displays volume flow and of through. thevolume amountpassed of volume passed through.

(a)

(b)

Figure Electromagnetic flowmeters components: (a) primary element; (b) convertor (adapted Figure 1.1.Electromagnetic flowmeters components: (a) primary element; (b) convertor (adapted from [1]). from [1]).

According to several manufactures, electromagnetic flowmeters assure an accuracy higher than several flowmeters an accuracy higher than 0.2%,According as long asto the flowmanufactures, velocities areelectromagnetic higher than 1 m/s and theassure installation requirements are 0.2%, as long as the flow velocities are higher than 1 m/s and the installation requirements areEquation fulfilled. fulfilled. The accuracy of electromagnetic flowmeters depends on the velocity, according to The accuracy electromagnetic flowmeters depends on the velocity, according to Equation (1) [1] and (1) [1] and as of represented in Figure 2. as represented in Figure 2. − 40𝑈 + 6% 𝑈 < 0.1 m/s  8(𝑈 − 0.55) + 0.38% 0.1 m/s ≤ 𝑈 ≤ 0.5 m/s  −40U + 6% U < 0.1 m/s  (1)   − 0.4𝑈 + 0.6% 0.5 m/s ≤ 𝑈 < 1 m/s  8(U − 0.55)2 + 0.38% 0.1 m/s ≤ U ≤ 0.5 m/s 0.2% 𝑈 ≥ 1 m/s (1)  − 0.4U + 0.6% 0.5 m/s ≤ U < 1 m/s     0.2% U ≥ 1 m/s

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Figure Figure2.2.Electromagnetic Electromagneticflowmeter flowmeteraccuracy accuracycurve curve[1]. [1].

In order order to to measure measure the the volume volume flow flow rate, rate, the the Faraday Faraday principle principle is is applied applied in in electromagnetic electromagnetic In flowmeters. In In1831, 1831,Michael MichaelFaraday Faradaydiscovered discovered that thatififan anelectric electricconductor conductorisismoving movingin inaamagnetic magnetic flowmeters. field, perpendicular perpendicular to the direction to field, direction of of the the motion, motion,an anelectrical electricalcurrent currentisisinduced inducedand andproportional proportional the magnetic field force, asaswell to the magnetic field force, wellasasthe thevelocity. velocity.IfIfthe theconductor conductorisiswater, water,the theflow flowpassing passingthrough througha current proportional to to thethe flow velocity. Figure 3 represents the amagnetic magneticfield fieldinduces inducesananelectrical electrical current proportional flow velocity. Figure 3 represents operating principle, which is important to understand the the following developments. the operating principle, which is important to understand following developments.

Figure Figure3.3.Operating Operatingprinciple principleof ofan anelectromagnetic electromagneticflow flowmeter meter[1]. [1].

Throughmathematical mathematicalmanipulation, manipulation,the theelectrical electricalcurrent, current, UE, induced flow passage Through UE, induced byby thethe flow passage is is directly proportional to value the value ofvolume the volume flow Q, rate, or UAccording [1], the directly proportional to the of the flow rate, or Q, 𝑈 ~𝑄. to [1], the to electrical E ∼ Q. According electrical currentbyinduced flow is account taken into account the cross section defined by the current induced the flowby is the taken into only in the only crossin section defined by the electrodes, perpendicular to the flow. In words, only words, the parallel the velocity relevant foris electrodes, perpendicular to other the flow. In other only component the parallelof component of is the velocity the volume rate measurement [11]. This means thatmeans the tri-dimensional nature ofnature flow is relevant for flow the volume flow rate measurement [11]. This that the tri-dimensional of disregarded. flow is disregarded. The Theflow flowvelocity velocityprofile profileisis not not the the same same throughout throughoutthe theentire entire cross cross section. section. For Forthat thatreason, reason,to to prevent over ororunder-evaluations under-evaluations of the velocity, the suppliers of this equipment use a prevent over of the flowflow velocity, the suppliers of this equipment use a weighting weighting factor, 4W.represents Figure 4 represents the weighting factor distribution in a cross section. factor, W. Figure the weighting factor distribution in a cross section.

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Figure Figure4.4.Weighting Weightingfactor factordistribution distributionWWininthe theelectrode electrodeplane plane[1]. [1]. Figure 4. Weighting factor distribution W in the electrode plane [1].

InInFigure Figure4,4,each eachpoint pointininthe thecross crosssection sectionhas hasdifferent differentweighting weightingfactors factorsassociated. associated.The Thesum sum Figure 4, each point in the cross section has different weighting factors associated. The sum ofofIn the product between the velocity and the respective weighting factor corresponds to the electrical the product between the velocity and the respective weighting factor corresponds to the electrical of current, the product between the velocity the respective weighting factor to thetoto electrical which isisproportional totoand the flow Although ititiscorresponds determine current, which proportional thevolume volume flowrate. rate. Although isaagood goodmethod method determine current, which is proportional to the volume flow rate. Although it is a good method to determine the volume flow rate in a homogenous constant magnetic field along symmetric velocity profiles, the volume flow rate in a homogenous constant magnetic field along symmetric velocity profiles, this thethis volume flow rate in a homogenous constant magnetic field along symmetric velocity profiles, this itit formulation does not provide good results for non-symmetric velocity profiles. In these formulation does not provide good results for non-symmetric velocity profiles. In thesecases, cases, formulation does not provide goodand results forevaluate non-symmetric velocity profiles. In these cases, flow itflow would evaluate some under others leading totoaainaccurate volume wouldover over evaluate somevalues values and under evaluate others[1], [1], leading inaccurate volume would evaluate some values and under evaluate consider others [1],aaleading to induction ainduction inaccurate volume flow rate. To this, the ofofthe magnetic field, B,B,inversely rate.over Toavoid avoid this, thesuppliers suppliers theequipment equipment consider magnetic field, inversely rate. To avoid this, the suppliers of the equipment consider a magnetic induction field, B, inversely proportional proportionaltotothe theweighting weightingfactor factorW, W,Equation Equation(2): (2): proportional to the weighting factor W, Equation (2): (2) 𝑐𝑜𝑛𝑠𝑡 W𝑊××B𝐵==const (2) (2) 𝑊 × 𝐵 = 𝑐𝑜𝑛𝑠𝑡 According to Equation (2), for a cross section region in which the weighting factor is small, the According to Equation (2), a cross section region in which the weighting factor is small, According to Equation for afor cross section in which the weighting is even small, thenonmagnetic induction field (2), is increased, and vice region versa. This action ensures goodfactor results for the magnetic induction field is increased, and vice versa. This action ensures good results even for magnetic induction field profiles is increased, symmetrical velocity [2]. and vice versa. This action ensures good results even for nonnon-symmetrical [2]. symmetrical velocityvelocity profilesprofiles [2].

3. Equipment and Layout 3. Equipment and Layout 3. Equipment and Layout 3.1.Flow FlowMeter MeterInstallation Installation 3.1. 3.1. Flow Meter Installation Accordingtotoseveral severalauthors authors[1,2,4], [1,2,4],electromagnetic electromagneticflowmeters flowmeters(Figure (Figure5)5)are areonly onlydisturbed disturbed According According to several authors [1,2,4], electromagnetic flowmeters (Figure 5) are only disturbed bythe theexistence existenceofofparticles particlesthat thatmight mightchange changethe themagnetic magneticproperties propertiesofofthe thefluid. fluid.Thus, Thus,ititisis by by the existence of particles that mightofchange the magnetic properties of the fluid. Thus, it is necessary to guarantee the existence linear flow paths, to insure the measurement accuracy. necessary to guarantee the existence of linear flow paths, to insure the measurement accuracy. ItItisis necessary to guarantee the existence of linear flow paths, to insure the measurement accuracy. It is by thereforenecessary necessarytotomeet meetthe theminimum minimuminstallation installationrequirements requirementsfor foreach eachgeometry, geometry,specified specified therefore by therefore necessary to meet the minimumthe installation requirements forimposed each geometry, specifiedfor by the each manufacture. Figure 5 presents installation requirements by the suppliers each manufacture. Figure 5 presents the installation requirements imposed by the suppliers for the eachmost manufacture. Figure 5 presents the installation requirements imposed by the suppliers for the commongeometries. geometries. most common most common geometries.

Figure 5. Cont.

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Figure 5. Installation requirements for different pipe layouts. Figure 5. Installation requirements different pipe layouts. Figure 5. Installation requirements forfor different pipe layouts.

3.2. UDV Installation 3.2.3.2. UDV Installation UDV Installation The UDV operating principle is the MET-FLOW approach—an ultrasonic probe is placed near The UDV operating principle is the MET-FLOW approach—an ultrasonic probe is placed near The UDV operating principle is the MET-FLOW approach—an ultrasonic probe is placed near the pipe wall with a certain slope. The ultrasound is emitted and travels across the pipe cross section. thethe pipe wall with a certain slope. The ultrasound is emitted and travels across thethe pipe cross section. pipe wall with a certain slope. The ultrasound is emitted and travels across pipe cross section. When the ultrasound hits a fluid particle, some energy of the ultrasound disperses and produces an When thethe ultrasound hits a afluid produces an When ultrasound hits fluidparticle, particle,some someenergy energyof ofthe the ultrasound ultrasound disperses and produces echo, which reaches the probe. Then, by a mathematical manipulation, the equipment delivers a an echo, echo, which which reaches the probe. Then, by a mathematical manipulation, the equipment delivers a a the probe. Then, by a mathematical manipulation, the equipment delivers velocity value. Figure 6 presents the UDV operating principle. velocity value. Figure 6 presents thethe UDV operating principle. velocity value. Figure 6 presents UDV operating principle.

from [12]). [12]). Figure 6. Ultrasonic Doppler velocimetry (UDV) operating principle (adapted from Figure 6. Ultrasonic Doppler velocimetry (UDV) operating principle (adapted from [12]).

The UDV UDV uses usesan anultrasonic ultrasonicwave waveinin order provide velocity profile. a certain time order to to provide thethe velocity profile. At a At certain time (e.g., The UDV uses an ultrasonic wave in order to provide the velocity profile. At a certain time (e.g., (e.g., a burst is emitted. burst propagates inside liquid. timet2, t2,the theburst burst touches touches the t1), at1), burst is emitted. ThisThis burst propagates inside thethe liquid. AtAttime t1), a burst is emitted. This burst propagates inside the liquid. At time t2, the burst touches particle. If the sizes of the particle are much smaller than the wave length, only a very small echo isthe particle. If the sizeseffect). of the particle are much smaller than the wave length, only a very small echo is generated generated (scattering (scattering effect). This echo goes back in direction to the transducer, while the main energy generated propagation (scattering effect). This echo goes back inreaches direction the transducer, while of thethe main energy continues AtAt time t3, the thetotransducer. The depth particle, continues its its propagation[11,13]. [11,13]. time t3, echo the echo reaches the transducer. The depth of the continues its propagation [11,13]. At time t3, the echo reaches the transducer. The depth of the Depth = 𝐷𝑒𝑝𝑡ℎ C/2(t3=−𝐶t1 from thefrom traveling time (t3 time − t1),(t3where is theCsound ), can ⁄2(𝑡3 particle, − be 𝑡1)determined , can be determined the traveling - t1), C where is the ⁄ particle, 𝐷𝑒𝑝𝑡ℎ = 𝐶 2(𝑡3 − 𝑡1) , can be determined from the traveling time (t3 t1), where C is athe velocity of the acoustic wave in the in liquid. Following each emission, the echo signal is sampled at sound velocity of the acoustic wave the liquid. Following each emission, the echo signal is sampled sound velocity of the acoustic wave in the liquid. Following each emission, the echomoves signal between is sampled fixed delay after the emission. This delay the depth. it the particle at a fixed delay after the emission. This defines delay defines the However, depth. However, it the particle moves at a fixed delay after the emission. This delay defines the depth. However, it the particle moves the successive emissions the sampled values taken at time ts will change over the time [14]. Depending between the successive emissions the sampled values taken at time ts will change over the time [14]. between emissionsthese the sampledmay values taken at time tssignal. will change over the time [14]. of the shapethe of successive the emitted form a sinusoidal The frequency, , of Depending of the shape ofsignal, the emittedvalues signal, these values may form a sinusoidal signal.FdThe Depending of the shape of the emitted signal, these values may form a sinusoidal signal. The this sinusoidal which is named is directly connected to the velocity of the frequency, 𝐹 , signal, of this sinusoidal signal,Doppler which isfrequency, named Doppler frequency, is directly connected to frequency, 𝐹 , of this sinusoidal signal, which is named Doppler frequency, is directly connected to particle, which is given by the Doppler equation the velocity of the particle, which is given by the[14]: Doppler equation [14]: the velocity of the particle, which is given by the Doppler equation [14]: 𝐹 𝐶 = Fd C𝐹 𝐶 (3) V𝑉 = (3) 𝐶𝑜𝑠𝜃 2𝐹 𝑉 2F = e Cosθ (3) 2𝐹 𝐶𝑜𝑠𝜃 where 𝐹 is the frequency of the emitted burst. where Fe is𝐹 the frequency of the burst. where is the frequency of emitted the emitted burst. UDV offers instantaneously a complete velocity profile. Unfortunately, as the information is UDV offers instantaneously a complete velocity profile. Unfortunately, as the information is available only periodically, the maximum velocity (Vmax) exists for each pulse repetition frequency available only periodically, the maximum velocity (Vmax) exists for each pulse repetition frequency (𝐹 ) [11]: (𝐹 ) [11]:

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6 of 18 UDV offers instantaneously a complete velocity profile. Unfortunately, as the information is available only periodically, the maximum velocity (Vmax ) exists for each pulse repetition frequency 𝐹 𝐶 (Fpr f ) [11]: 𝑉 = (4) 4𝐹Fpr𝐶𝑜𝑠𝜃 fC Vmax = (4) 4Falso e Cosθ defined by the pulsed repetition frequency Thus, the maximum measurable depth (Pmax) is

Thus,(5), theand maximum measurable depth of (Pmax also defined by theand pulsed repetition frequency Equation consequently the product Pmax) is and Vmax is constant, is given by Equation (6) Equation (5), and consequently the product of Pmax and Vmax is constant, and is given by [13,14]: Equation (6) [13,14]: 𝐶 = C 𝑃 (5) Pmax = 2𝐹 (5) 2Fpr f 𝐶2 (6) ×𝑉 = 𝑃 C (6) Pmax × Vmax = 8𝐹 𝐶𝑜𝑠𝜃 8Fe Cosθ In the presence of air, the equipment signal is not able to read the signal, therefore, the probe In the presence of air, the equipment signal is not able to read the signal, therefore, the probe needs to be well installed. Thus, the probe is set in a specific probe holder (Figure 6), which is a plastic needs to be well installed. Thus, the probe is set in a specific probe holder (Figure 6), which is a plastic rectangle with several holes, where each of it has a certain angle associated. This probe holder has rectangle with several holes, where each of it has a certain angle associated. This probe holder has two two functions: to guarantee the stability to the probe, since it makes possible to attach it to the pipe; functions: to guarantee the stability to the probe, since it makes possible to attach it to the pipe; and and also make sure that there is no air between the pipe and the probe. This is accomplished by also make sure that there is no air between the pipe and the probe. This is accomplished by inserting a inserting a gel in the hole where the probe will be installed, always ensuring contact with it. gel in the hole where the probe will be installed, always ensuring contact with it. Moreover, since UDV uses very sensitive equipment, specially to electromagnetic noise, its Moreover, since UDV uses very sensitive equipment, specially to electromagnetic noise, its reading reading may be compromised by the electromagnetic field induced by the flowmeters. may be compromised by the electromagnetic field induced by the flowmeters.

3.3. 3.3. Experimental Experimental Facility Facility In computational results model, intensive In order order to to assess assess the the computational results provided provided by by the the CFD CFD model, intensive campaigns campaigns were developed in an experimental facility, schematically represented in Figure 7, and adapted were developed in an experimental facility, schematically represented in Figure 7, and adapted to to two operating conditions. conditions. Regarding two continuous continuous geometries geometries and and operating Regarding this this pipe pipe system system layout, layout, UVD UVD measurements measurements were were made made in in section section A A (in (in Figure Figure 7a). 7a).Two Twodifferent different volume volume flow flow rates, rates,corresponding corresponding 33/h were tested. In each UDV measurement, the velocity was captured in 100 different to 100 and 12 m to 100 and 12 m /h were tested. In each UDV measurement, the velocity was captured in 100 different points points in in aa total total of of 100 100 profiles. profiles.

(a) Figure 7. Cont.

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(b) (b) Figure 7. 7. System layouts 1 and 2: (a) facility scheme; (b) lab installation, with flow direction identified identified Figure Figure 7. System layouts 1 and 2: (a) facility scheme; (b) lab installation, with flow direction identified by the the blue blue arrow. by arrow. by the blue arrow.

1

The The results results obtained obtained are are presented presented in in Table Table 11 for for section section AA (Figure (Figure7). 7). The The flowmeter flowmeter error error 3 3 The results obtained are presented in Table 1 for section A (Figure 7). The flowmeter error decreases forboth bothlayouts. layouts. decreases as as the the velocity velocity increases, increases, as asitithappens happensfor forQ Q== 100 100 m m /h /h for 3/h for both layouts. decreases as the velocity happensA,for Q = 100 The velocity profilesincreases, measuredasinit section using the m UDV, are presented in Figure 8 for 100 1. m Test experiments andsection relativeA,errors in section A, for different volume 3/h,results: The profiles measured in usingachieved the UDV, are presented in Figure 8 for 100 m3/hTable and velocity 12 respectively. 3 3 flow rates. m /h and 12 m /h, respectively. Table 1. Test results: experiments and relative errors achieved in section A, for different volume flow Tests Results Error Table 1.Q Test results: experiments and relative errors achieved in section A, for different volume flow rates. theoretical Geometry V ND100 V reference ttheoretical Qreference ND100 (m3 /h) rates. treal (s) Re (-) (L) (L) (s) (m3 /h) (%) Tests Results Error

Qtheoretical

Tests Results Error 𝑽ND100 ttheoretical Qreference Re 5000 𝑽reference 180 173treal 104 −ND100 0.40% 365,631 3 𝑽(L) ND100 real Q reference Re 1018 𝑽reference 305 ttheoretical 285t(s) 13/h) −ND100 1.18% 45,704 (L) (s) (m (%) (-) (m³/h) 3/h) (L) (L) (s) (s) (m (%) (-) 4980 104 −0.40% 369,147 365,631 100 100 5026 5000 5000 180 180 172173 105 0.52% 21 12 1035 1020 306 295 12 1.47% 42,188 100 4980 5000 180 173 104 −0.40% 365,631 12 1006 1018 305 285 13 −1.18% 45,704 1 12 1006 1018 305 285 13 −1.18% 45,704 100 5026 5000 180 172 105 0.52% 369,147 2 3 100 5026 5000 180 172 105 0.52% 369,147 12 1035 1020 306 295 12 1.47% 42,188 The 2 velocity profiles measured in section A, using the UDV, are presented in Figure 8 for 100 m /h 12 1035 1020 306 295 12 1.47% 42,188 and 12 m3 /h, respectively.

Geometry 1 Geometry

100 Qtheoretical 4980 (m³/h) 12 1006

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(b) 3 3 Figure 3/h;(b) Figure8.8.UDV UDVprofiles profilesrelated relatedtotogeometries geometries1 1and and2:2:(a) (a)for for100 100mm/h; (b)for for12 12m m3/h. /h.

4. CFD Model 4. CFD Model 4.1. Governing Equations 4.1. Governing Equations Computational fluid dynamics (CFD) provide a qualitative and quantitative prediction of fluid fluid dynamicsand (CFD) providemethods. a qualitative and simulation quantitativetools prediction of fluid flowsComputational by means of mathematical numerical These represent an flows by means of mathematical and numerical methods. These simulation tools represent an important technological advance towards the detailed understanding of the flow, allowing theoretical important technological advance towards the detailed understanding of the flow, allowing considerations regarding the physical behavior of the flow, with mathematical formulations for theoretical considerations regarding the physical behavior of not theonly flow, withthe mathematical tri-dimensional modelling analyses [7]. These models make possible, to study behavior of formulations for tri-dimensional modelling analyses [7]. These models make possible, notvorticity only to turbulent and laminar flows, but also the multiple forms of exchanges of energy, flow phases, study the behavior of turbulent and laminar flows, but also the multiple forms of exchanges of and turbulence levels [9]. energy, andwork turbulence levels [9].Multiphysics 4.3.b, which presents accurate Theflow CFDphases, model vorticity used in this was COMSOL The CFD model used in this work was COMSOL Multiphysics 4.3.b,method which presents accurate results for several fluid flow problems [10]. COMSOL is a finite element (FEM) software, results for several fluid flow problems [10]. COMSOL is a finite element method (FEM) software, which uses the mass conservation and the RANS (Reynolds averaged Navier–Stokes) equations as which usesflow the equations: mass conservation and the RANS (Reynolds averaged Navier–Stokes) equations as governing governing flow equations: ∂ρ ∂(ρu) ∂(ρv) ∂(ρw) + + + =0 (7) ∂t𝜕𝜌 𝜕(𝜌𝑢) ∂x ∂y ∂z 𝜕(𝜌𝑣) 𝜕(𝜌𝑤) (7) + + =! 0 " + # 𝜕𝑡 𝜕𝑦 ∂u 𝜕𝑧 ∂u ∂ui ∂𝜕𝑥 j i = ρgi + − pδij + µ + − ρui0 u0j (8) ρu j 𝜕𝑢i 𝑗 𝜕𝑢 ∂x𝜕𝑢 ∂x j𝜕 ∂x j 𝑖 j 𝑖 ∂x 𝜌𝑢𝑗 = 𝜌𝑔𝑖 + [−𝑝𝛿𝑖𝑗 + 𝜇 ( + ) − 𝜌𝑢𝑖′ 𝑢𝑗′ ] (8) 𝜕𝑥𝑗 𝜕𝑥𝑗 𝜕𝑥𝑗 𝜕𝑥𝑖 FEM is a computational method that divides an object into smaller elements. Each element is FEMtoisaaset computational method that divides object intoas smaller Each element is assigned of characteristic equations that arean then solved a set ofelements. simultaneous equations assigned to a set of characteristic equations that are then solved as a set of simultaneous equations to to estimate the behavior of the object [15]. From the available turbulence models, the k-ε model was estimate the of [16] the object From the available turbulence models, the k-ε model selected. Thebehavior k-ε models are the[15]. most common and most used models worldwide mostly was for selected. The k-ε models [16] the most commonrate andand most used models worldwide mostly for industrial applications due to are its good convergence relatively low memory requirements. industrial due to its good rate and relatively requirements. This modelapplications solves two variables: k, theconvergence turbulence kinetic energy and ε,low thememory rate of dissipation of This modelkinetic solvesenergy. two variables: k, the turbulence kinetic energyassumptions, and ε, the rate dissipation of turbulence This turbulence model relies on several theof most important turbulence kinetic energy. This turbulence model relies on several assumptions, the most important of which is that the Reynolds number is high enough. It is also important that the turbulence of in which is that the high enough. It is the alsoproduction important that the the turbulence is in is equilibrium in Reynolds boundarynumber layers, iswhich means that equals dissipation. equilibrium in boundary layers, which means thatbecause the production equals the true, dissipation. These assumptions limit the accuracy of the model they are not always since it These does assumptions limit thetoaccuracy of the model becausegradients they are that not can always true, since it does not not respond correctly flows with adverse pressure result in under predicting respond toofflows with adverse gradients that result in of under predicting the the spatialcorrectly extension recirculation zonespressure [17]. Furthermore, in thecan description rotating flows, the spatialoften extension recirculation [17]. Furthermore, in the description of limited rotatingaccuracy flows, the model showsofpoor agreementzones with experimental data [18]. In most cases, the is often shows poor agreement with experimental data to [18]. In most cases, the limited accuracy amodel fair trade-off for computational resources saved compared more complex turbulence models. is a fair trade-off for computational resources saved compared to more turbulence models. While it is possible to modify the k-ε model so that it describes thecomplex flow in wall regions, this is While it is possible to modify the k-ε model so that it describes the flow in wall regions, this is not always desirable because of the very high resolution requirements. Instead, analytical expressions not used always very high[15]. resolution analytical are todesirable describe because the flowofatthe the walls These requirements. formulations Instead, are known as wallexpressions functions. are used to describe the flow at the walls [15]. These formulations are known as wall functions. Wall

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functions ignore the flow the in buffer region region and analytically compute a nonzero fluid velocity Wall functions ignore the field flowin field the buffer and analytically compute a nonzero fluid at the wall [17–19]. velocity at the wall [17–19]. + needs Thus, by byusing usingwall wallfunctions, functions, wall lift-off in viscous 𝛿 needs be checked. This Thus, thethe wall lift-off in viscous unitsunits δw to be to checked. This value value ifalerts if theat mesh at is thefine wall is fine enough should be 11.06 everywhere. If the mesh alerts the mesh the wall enough and shouldand be 11.06 everywhere. If the mesh resolution in resolution in normal the direction the wall isthen too this coarse, then thisbevalue willthan be greater thana11.06, the direction to thenormal wall is to too coarse, value will greater 11.06, and finer and a finerlayer boundary layer mesh toin bethese applied in these second should boundary mesh needs to be needs applied regions. Theregions. second The variable thatvariable should that be checked be checked using wall functions is theδwall lift-off 𝛿 (in length units) [18]. This variable is when using when wall functions is the wall lift-off (in length units) [18]. This variable is related to the w related to the assumed thickness of the viscous layer and should be small relative to the surrounding assumed thickness of the viscous layer and should be small relative to the surrounding dimensions of dimensions geometry. it is not,in then theregions mesh inmust these be refined, as well. the geometry.ofIfthe it is not, then Ifthe mesh these beregions refined,must as well. The wall wall functions functions in in COMSOL COMSOL are are such such that that the the computational computational domain domain is is assumed assumed to to start start aa The distance 𝛿 from the wall (Figure 9). distance δw from the wall (Figure 9).

Figure 9. 9. Computational Computational domain domain starts starts aa distance distance δ𝛿w𝑤 from Figure fromthe thewall wall[13]. [13].

Nevertheless, with constant density and viscosity equal to Nevertheless, in inall allsimulations simulationsthe thefluid fluidwas waswater, water, with constant density and viscosity equal 3 − 6 2 3 and 999.62 Kg/m 1.0097 × 10 respectively. to 999.62 Kg/mand 1.0097 × 10m /s, m2/s, respectively. In the CFD model, three types of boundary In the CFD model, three types of boundary conditions conditions were were assigned: assigned: inlet, inlet, outlet outlet and and solid solid walls. walls. For For the the inlet inlet boundary boundary condition, condition, the the pressure pressure was was set, set, as as for for the the outlet outlet condition, condition, the the average average velocity. Thus, velocity. The The no-slip no-slip condition condition was was considered, considered, which which stated stated that that the the walls walls were were impermeable. impermeable. Thus, the boundary conditions used to defined the inlet condition, are governed by the set of the following the boundary conditions used to defined the inlet condition, are governed by the set of the following equations equations [16]: [16]: p = p0 i h  𝑝=𝑝 (µ + µ T ) ∇u + (∇u)T − 23 ρkl × n = 0 (9)  2 2 3/2 3/4 k× (𝜇 k+=𝜇 3)(∇𝑢 (∇𝑢) ) + − 𝜌𝑘𝑙 𝑛 = 0 ε =3 Cµ LT (9) 2 Ure f IT / where p0 is the input value (of pressure), 3IT is the turbulent intensity, L T corresponds to the turbulence / 𝑘 𝜀=𝐶 𝑘= 𝑈 𝐼 2 by [20], and Ure f is the 𝐿 reference velocity scale. length scale, l is the mixing length defined For the outlet condition, the boundary conditions are expressed by Equation (10), where U0 𝐿 corresponds to the where 𝑝 is the input value (of pressure), 𝐼 is the turbulent intensity, corresponds to the average velocity (input value) and, the first equation represents the normal outflow turbulence length scale, l is the mixing length defined by [20], and 𝑈 is the reference velocity scale. velocity Formagnitude: the outlet condition, the boundary conditions are expressed by Equation (10), where 𝑈 u = U0 nand, the first equation represents the normal corresponds to the average velocity (input value) (10) ∇k × n = 0 ∇ε × n = 0 outflow velocity magnitude:

4.2. Mesh Definition and Solution Convergence

𝑢=𝑈 𝑛

(10) ∇𝑘 × 𝑛was = 0 discretized ∇𝜀 × 𝑛 =into 0 smaller units, called mesh elements. As for the mesh definition, the geometry Its resolution and element quality are important aspects to take into account, when validating the model, since the decreasing of resolution can originate low accuracy results [21]. Meanwhile, low mesh 4.2. Mesh Definition and Solution Convergence element quality can lead to convergence issues [22–24]. As calculations for the mesh definition, the geometry discretized into smaller mesh All have been performed on a PCwas (Intel 5, CPU 3.90 GHz, RAMunits, 8 GB) called with 4 cores elements. Its resolution and element quality are important aspects to take into account, when and threads running in parallel. The model default uses a physic controlled mesh, which defines, validating thethe model, since the and decreasing of sequences resolution necessary can originate low aaccuracy resultsto[21]. automatically, size attributes operations to create mesh adapted the Meanwhile, low mesh element quality can lead to convergence issues [22–24].

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All calculations have been performed on a PC (Intel 5, CPU 3.90 GHz, RAM 8 GB) with 4 cores All calculations been performed ondefault a PC (Intel 3.90 GHz, RAM 8 GB) withdefines, 410cores Water 10, 1807 of 18 and 2018, threads runninghave in parallel. The model uses 5,a CPU physic controlled mesh, which and threads running parallel.and Theoperations model default uses anecessary physic controlled defines, automatically, the sizein attributes sequences to create amesh, mesh which adapted to the automatically, the size attributes andcreated operations sequences to create a mesh adapted to the problem. This mesh is automatically and adapted fornecessary the model’s physics settings. The default problem. This mesh isisautomatically created and adapted for the model’s physics settings. The default problem. This mesh automatically created and adapted for the model’s physics settings. The default physics-controlled meshing sequences create meshes that consist of different element types and size physics-controlled meshing sequences create meshes that consist of element types and physics-controlled sequences consist ofdifferent different element types andsize size features, which canmeshing be used as a startingcreate pointmeshes to add, that move, disable, and delete meshing operations. features, which can be used as aa starting point to add, move, disable, and delete meshing operations. features, which can be used as starting point to add, move, disable, and delete meshing operations. Each meshing operation is built in the order it appears in the meshing sequence to produce the final Each operation isisbuilt in order in the sequence to the Eachmeshing meshing operationthe built inthe thesequence orderititappears appears themeshing meshing toproduce produce thefinal final mesh [23]. Customizing meshing helps to in reduce memorysequence requirements by controlling mesh [23]. Customizing the meshing sequence helps to reduce memory requirements by controlling mesh [23]. Customizing the meshing sequence helps to reduce memoryand requirements by controlling the number, type, and quality of elements, thereby creating an efficient accurate simulation [25]. the type, and quality of elements, thereby creating an efficient and accurate simulation [25]. thenumber, number, type, and quality of elements, thereby creating an efficient and accurate simulation [25]. For the fluid-flow model, since the mesh is adapted to the physic setting, the mesh is finer than For the fluid-flow model, since the mesh isisadapted to the physic setting, the mesh isisfiner than For the fluid-flow model, since the mesh adapted to the physic setting, the mesh finer than the default one, with a boundary layer (Figure 10a) in order to solve the thin layer near the solid walls the one, aaboundary layer 10a) thedefault default one,with withof boundary layer(Figure (Figure 10a)in inorder orderto tosolve solvethe thethin thinlayer layernear nearthe thesolid solidwalls walls where the gradients the flow variables are high [26–29]. where the gradients of the flow variables are high [26–29]. where the gradients of the flow variables are high [26–29].

(a) (a)

(b) (b)

Figure 10. Physics-controlled mesh used: (a) Boundary layer mesh; (b) Refinement near a curve. Figure10. 10. Physics-controlled Physics-controlledmesh meshused: used: (a) (a) Boundary Boundarylayer layermesh; mesh;(b) (b)Refinement Refinementnear nearaacurve. curve. Figure

To ensure a proper and acceptable accuracy of the results, COMSOL uses an invariant form of Toensure ensure proper and acceptable accuracy the results, COMSOL an invariant form of To a aproper and acceptable the results, COMSOL usesuses invariant form of the the damped Newton method. Starting accuracy with 𝑍 , of theof linear model (MUMPS) isansolved for the Newton the damped Newton method. Starting with 𝑍 , the linear model (MUMPS) is solved for the Newton damped method. Starting with Z0 , the linear model (MUMPS) solved for Newton step (𝛿𝑍)Newton [16]. Afterwards, a new iteration is calculated, according to is Equation (7),the where 𝜆 isstep the step[16]. (𝛿𝑍) Afterwards, [16]. Afterwards, new iteration is calculated, according to Equation 𝜆 is the (δZ) a new aiteration is calculated, according to Equation (7), where(7), λ0 where is the damping damping factor: damping factor: factor: +λ𝜆0 δZ 𝛿𝑍 Z𝑍1 ==Z𝑍0 + (11) (11) 𝑍 = 𝑍 + 𝜆 𝛿𝑍 0 |λ |𝜆||< < 11 (11) |𝜆 | < 1 The error of the newnew iteration and,and, if theiferror of theof current iteration is bigger Themodel modelestimates estimatesthe the error of the iteration the error the current iteration is than the previous one, the code decreases the damping factor and a new iteration process restarts. The model estimates one, the error of the new iteration and, if the error current iteration is bigger than the previous the code decreases the damping factor andofathe new iteration process This procedure will occur until either the error is smaller than the error calculated in the previous bigger than the previous one, the code decreases the damping factor and a new iteration process restarts. This procedure will occur until either the error is smaller than the error calculated in the iteration theprocedure damping factor reaches minimum value 1× 10−14the ).× 10 When acalculated successful restarts. or This will occur untilits either theminimum error is (i.e., smaller than error instep the previous iteration or the damping factor reaches its value (i.e., ). When a successful is reached, the algorithm computes the next iteration. The iteration process finish the relative previous iteration or algorithm the damping factor reaches its minimum valueiteration (i.e., 1 ×process 10 ). when When a successful step is reached, the computes the next iteration. The finish when the tolerance exceeds the relative computed error. The model stops the iteration when the relative error is step is reached, the algorithm computes the next iteration. The iteration process finish when the relative tolerance exceeds the relative computed error. The model stops the iteration when the relative −3 and the smaller than 1 × 10 damping factor is equal to 1. Otherwise the solution would not converge relative tolerance exceeds the relative computed error. The model stops the iteration when the relative error is smaller than 1 × 10 and the damping factor is equal to 1. Otherwise the solution would not and the would 11 presents convergence solution the reached. error is iteration smaller than 1 ×continue. 10would andFigure the damping factor is equal to 1. convergence Otherwise solution would not converge and the iteration continue. Figure 11the presents the solution reached. converge and the iteration would continue. Figure 11 presents the convergence solution reached.

Figure 11. 11. Convergence Convergence solution. solution. Figure Figure 11. Convergence solution.

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4.3. Calibration and Validation 4.3. Calibration and Validation According presented in in Table 2 and in Figure 12, According to to the theinput inputdata dataand andthe therespective respectivegeometries, geometries, presented Table 2 and in Figure According to the input data andand thecompared respective geometries, presented in Table 2 and in Figure 12, numerical simulations were made the experimental tests. numerical simulations were made and compared withwith the experimental tests. 12, numerical simulations were made and compared with the experimental tests. Table 2. 2. Boundary, Boundary, mesh mesh and and study study conditions. conditions. Table 2. Boundary, mesh and study conditions. Characteristics 100 Characteristics 100 m3m /h3/h 1212 m3m /h3/h

Characteristics 100 m3/h 12 m3/h Inlet Inlet 5.65.6 barbar 5.85.8 barbar Inlet 5.6 bar 5.8 bar Outlet 0.59 m/s m/s Outlet 0.59 m/s 0.07 0.07 m/s Outlet 0.59 m/s 0.07 m/s Wall No-slip Wall No-slip Wall No-slip Mesh Physics-controlled Mesh Physics-controlled Mesh Physics-controlled Flow conditions Steady state Flow Steady Flowconditions conditions Steady state state

(a)(a)

(b) (b)

Figure Modelconfiguration: configuration:(a) (a)geometry geometry 1; 1; (b) (b) geometry Figure 12.12. Model geometry2. 2. Figure 12. Model configuration: (a) geometry 1; (b) geometry 2.

Figure 13 presents velocity profilesobtained obtainedin inthe the CFD CFD model model and Figure profiles obtained andin inthe theexperimental experimentaltests, tests, Figure 13 presents thethe velocity profiles for the same section of the UDV measurements. section of of the the UDV UDV measurements. measurements. for the same section

(a)

(a)

0.7 U (m/s)

U (m/s)

0.6 0.5 0.4

1

0.7

0.9

1 0.8 0.9 0.7 0.8 0.6 0.7 0.5

0.6 0.5

U (m/s)U (m/s)

0.8

0.8

0.4

0.6 0.4 0.5 0.3

0.3 0.2

0.4 0.2

0.3 0.2

0.1

0.3 0.1

0

0.20

0.1

0.1

0

0

(b) Figure 13. Comparison of velocity distribution through CFD and (b) profiles Figure 13. Comparison of velocity distribution profiles obtainedobtained through CFD model and model experiments: experiments: (a) for 100 m33/h; (b) for 12 m3/h. 3 (a) for 100 m /h; (b) for 12 m /h. Figure 13. Comparison of velocity distribution profiles obtained through CFD model and experiments: (a) for 100 m3/h; (b) for 12 m3/h.

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The velocity profiles Figure13, 13,related relatedto to UDV, UDV, presents some is is justified The velocity profiles ininFigure somespikes. spikes.This Thisbehavior behavior justified The velocity profiles in Figure 13, related to UDV, presents some spikes. This behavior is justified presence fluctuationsininthe thevelocity velocity and and the the existence existence of of of by by thethe presence ofof fluctuations of vortexes, vortexes,both bothcharacteristic characteristic by the presence of fluctuations in the velocity and the existence of vortexes, both characteristic of deviations on the flow direction. Despite this, the results present a good approximation between the deviations on the direction. Despite this, goodapproximation approximation between deviations onflow the flow direction. Despite this,the theresults results present present aagood between the the experimental data and the CFD results. In Figure 14 is represented the velocity contours in the pipe experimental data and the CFD results. In Figure 14 is represented the velocity contours in the experimental data and the CFD results. In Figure 14 is represented the velocity contours in the pipepipe cross section the two different volume flow rates. cross section forfor the two different volume flow cross section for the two different volume flowrates. rates.

(a)

(a)

(b)

(b) Figure 14. Velocity contours in the pipe cross section: (a) for 100 m3/h; (b) for 12 m3/h. Figure 14. Velocity contours in the pipe cross section: (a) for 100 m3 /h; (b) for 12 m3 /h. Figure 14. Velocity contours in the pipe cross section: (a) for 100 m3/h; (b) for 12 m3/h.

In order to assess the associated errors of the volume flow rate measured by the flowmeter, if

In order to assess the associated errors of the volume flow rate measured by the flowmeter, if the the is equal to the numerical model, several automaticbyprocedures were if In velocity order to distribution assess the associated errors of the volume flow rate measured the flowmeter, velocity distributionThe is equal to the numerical model, of several automatic procedures were implemented. implemented. first step involves the definition limits presented in Figure 4. The relevant the velocity distribution is equal to the numerical model, several automatic proceduresdata were The first involveswas the the definition of limits in Figure section 4. The relevant data for The this data analysis for step this analysis one associated topresented the electrodes the flowmeter. implemented. The first step involves the definition of limitscross presented inofFigure 4. The relevant data was the one associated to theis electrodes section of the flowmeter. The redrawn from from the aassociated plan with cross the three coordinates, x, ysection and z and thedata average velocity, U. the for redrawn this analysis wasmodel the one to the electrodes cross of the flowmeter. The data modelEach is a plan with the three y and and z and thelimit average U. EachTherefore, two coordinates two coordinates are coordinates, associated a x, velocity each to a velocity, certain weight. the redrawn from the model is a plan with the three coordinates, x, y and z and the average velocity, U. velocity ata points located near limit the limits a maximum error of 0.5%) was multiplied by located the areEach associated velocity and each to a (with certain weight. Therefore, the velocity at points two coordinates are associated a velocity and each limit to a certain weight. Therefore, the corresponding weighting factor (Figure 15). near the limits (with alocated maximum of 0.5%) was multiplied error by theofcorresponding weighting velocity at points near error the limits (with a maximum 0.5%) was multiplied by factor the (Figure 15). corresponding weighting factor (Figure 15).

Figure 15. Weighting function distribution of uniform magnetic field point electrode electromagnetic flowmeter. Calculated limits (black continuous lines) analogous to Figure 4. Data provided by the model the blue ticks. Figure 15.represented Weighting by function distribution of uniform magnetic field point electrode electromagnetic

Figure 15. Weighting function distribution of uniform magnetic field point electrode electromagnetic flowmeter. Calculatedlimits limits(black (blackcontinuous continuous lines) lines) analogous analogous to byby thethe flowmeter. Calculated toFigure Figure4.4.Data Dataprovided provided model represented the blueticks. ticks. model represented byby the blue

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The step isisthe theinterpolation interpolationofofpoints points between limits, which were multiplied by The subsequent subsequent step between limits, which were multiplied by the the correspondent weighting factor. This procedure was made for all limits except the ones that are correspondent weighting factor. This procedure was made for all limits except the ones that are closer closer the electrodes. The limits electrodes were very difficulttotoassess, assess,since sinceclosely closely to to the to thetoelectrodes. The limits nearnear the the electrodes were very difficult the electrodes the weight was not entirely known. Thus, another assumption was taken, i.e., the weighting electrodes the weight was not entirely known. Thus, another assumption was taken, i.e., the factor was calculated Figure 16.toThis function wasfunction defined was and defined validated through the weighting factor was according calculatedtoaccording Figure 16. This and validated available experimental data. The x variable is the value resulted from the subtraction of the number of through the available experimental data. The x variable is the value resulted from the subtraction of the total data point with the ones in the region near to the electrodes section. the number of the total data point with the ones in the region near to the electrodes section.

Figure Figure 16. 16. The The best best function function for for the the calculus calculus of the the factor factor for the the region region near near the the electrodes electrodes to to fit fit the the experiments (blue marks represent the experimental data used). experiments (blue marks represent the experimental data used).

Knowing Knowing the the remaining remaining factor, factor,the thevelocity velocitywas was obtained obtained through throughthe the sum sum of of the the velocity velocity of of each each point, thethe corresponding weighting factor,factor, and then by the sum weighting point,multiplied multipliedbyby corresponding weighting anddivided then divided by of thethesum of the factors. Thefactors. error was (Table 3) by(Table applying Equation (12). weighting Thethen errordetermined was then determined 3) by applying Equation (12).

𝐸𝑟𝑟𝑜𝑟[%] = Error [%] =

𝑈boundary conditon 𝑈calculated −−U U 100 ××100 𝑈boundary condition U

(12) (12)

The theoretical error of the flowmeters ought to increase with the decrease in the volume flow The theoretical error of the flowmeters ought to increase with the decrease in the volume flow 3/h are bigger than 100 m3/h (Table 3). For the rate. Thus, it is clear that the error associated to 12 m 3 /h rate. Thus, it is clear that the error associated to 12 m are bigger than 100 m3 /h (Table 3). For the volume flow rate of 100 m33/h it is verified that the error associated to geometry 1 is the smallest one. volume flow rate of 100 m /h it is verified that the error associated to geometry 1 is the smallest one. From the two experimental tests, geometry 2 corresponds to the worst scenario, since the pipe is not From the two experimental tests, geometry 2 corresponds to the worst scenario, since the pipe is not long enough to dissipate the flow perturbations caused by the profile vertical curves. long enough to dissipate the flow perturbations caused by the profile vertical curves. The difference between CFD and the lab tests is twofold: minor installation problems, such as The difference between CFD and the lab tests is twofold: minor installation problems, such as the the position of the gasket inserted in between flanges causing obstructions to the reading, and the position of the gasket inserted in between flanges causing obstructions to the reading, and the level of level of detail of the CFD model. detail of the CFD model. Table 3. 3. Summary Summary of of the the errors errors calculated calculated with with the the volumetric volumetric method methodfor forboth bothgeometries. geometries. Table 3 3 Qm=312 QQ==100 100 m m3/h /h Q = 12 /h m /h Geometry Error Error Geometry Error Error Experimental Model Experimental Model Experimental Model Experimental Model 1 −0.40% −0.48% −1.18% −1.27% 1 − 0.40% −0.48% −1.18% 2 0.52% 1.11% 1.47% −1.27% 1.61%

2

0.52%

1.11%

1.47%

1.61%

The error associated to the position of the gasket is important and, in several situations, The error associated the positionitof gasket is important and, in avoidable avoidable errors. In theseto experiments is the mathematically improbable to several assumesituations, that the errors could errors. In these experiments it is mathematically improbable to assume that the errors could be be preventable. However, in practice, since the number of gaskets is much smaller, these errors can preventable. However, in practice, the number of gaskets is much smaller, these errors can be be disregarded if engineering goodsince practices are follow. disregarded if engineering good practices are follow. 5. Case Study 5.1. Geometry Layout The pumping station layout is presented in Figure 17, where almost 90% of the total water volume is pumped. The flow arrives by the drive pipe, i.e., right to left side of Figure 17c, and follows

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5. Case Study 5.1. Geometry Layout WaterThe 2018,pumping 10, x FOR PEER REVIEW 14 of 18 station layout is presented in Figure 17, where almost 90% of the total water volume

is pumped. The flow arrives by the drive pipe, i.e., right to left side of Figure 17c, and follows through through the pump (represented by the green section) by a vertical pipe in the top of the drive pipe. the pump (represented by the green section) by a vertical pipe in the top of the drive pipe. Afterwards, Afterwards, the flow reaches the delivery pipe with a 30° angle, sidewise, after passing two 90° the flow reaches the delivery pipe with a 30◦ angle, sidewise, after passing two 90◦ curves. curves.

(a)

(b)

(c) Figure 17. 17. Pumping Pumping station station layout layout (a); (a); photographs photographs of of the the different different parts parts of of the the hydraulic hydraulic system system (b); (b); Figure modelling geometry—pump geometry—pump location location identified identified by by the the green green pipe pipe section, section, flowmeter flowmeter identified identified by by the the modelling red line, line, flow flow direction direction identified identified by bythe the blue bluearrow arrow(plan (planview viewon onthe theleft left and and 3D 3Dview viewon onthe theright) right) (c). (c). red

5.2. 5.2. Simulations Simulations The The problems problems detected detected in in situ situ were were assumed assumed to to be be correlated correlated to to the the flowmeters flowmeters in in the the pumping pumping station. station. As As the the flow flow passes passes through through the the pump, pump, the the disturbances disturbances from from upstream upstream can can be be disregarded, disregarded, i.e., caused byby thethe pump. Thus, since the the pressure is measured just i.e., considering consideringonly onlythe theperturbations perturbations caused pump. Thus, since pressure is measured downstream of theof pump, the geometry used forused simulating the disturbances is presented in Figure 18 just downstream the pump, the geometry for simulating the disturbances is presented in and the related characteristics of the pipe and the flowmeter are presented in Table 4. Figure 18 and the related characteristics of the pipe and the flowmeter are presented in Table 4.

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Figure 18. System layout modelling geometry—with the flowmeter section identified by the red arrow andSystem flow directionmodelling identifiedgeometry—with by the blue arrow. Figure the the flowmeter section identified by theby redthe arrow Figure18. 18. Systemlayout layout modelling geometry—with flowmeter section identified red and flow direction identified by the blue arrow. arrow and flow direction identified by the blue arrow. Table 4. Characteristic of the main pipe and flowmeter. Table 4. Characteristic of the main pipe and flowmeter. Table 4. Material Characteristic of the main pipeSteel and flowmeter. Material Steel Expansion ND700 to ND800

Material Expansion Remaining pipes Expansion Remaining pipes Flowmeter Remaining pipes Flowmeter

Steel

ND700 to ND800 ND800 ND700 to ND800 ND800 ND800 ND800 ND800

Flowmeter ND800 The simulations were performed by first defining the geometry, after which was necessary to The the simulations were performed firstwater) defining which was necessary to identify characteristics of the fluidby (i.e., andthe thegeometry, boundaryafter conditions. Lastly the mesh The simulations were performed by first defining the geometry, after which was necessary to identify the were characteristics of the fluid (i.e., water) and the boundary conditions. Lastly the mesh definitions chosen. The boundary conditions and other important features are described in identify the characteristics of the fluid (i.e., water) and the boundary conditions. Lastly the mesh definitions chosen. The boundary conditions and other important features are described in Table 5. were definitions were chosen. The boundary conditions and other important features are described in Table 5. Table 5. Table 5. System layout existing situation: simulation input values and characteristics. Table 5. System layout existing situation: simulation input values and characteristics. Table 5. System layout values Inlet existing situation: simulation input 9.5 barand characteristics. Inlet 9.5 bar Outlet 1.5 m/s

Inlet 9.5 bar Outlet 1.5 m/s No-slip Wall Outlet 1.5 m/s Wall No-slip Mesh Physics-controlled Wall No-slip Mesh Physics-controlled Flow Mesh conditions Steady state Flow conditions Steady state Physics-controlled Flow conditions Steady state Figure 19 presents the streamlines velocities and the velocity distribution in the cross section of Figure 19 presents the streamlines velocitiessection, and the the velocity distribution in the cross sectiontoofeach the the flowmeter, respectively. In the flowmeter streamlines appear to the be parallel Figurerespectively. 19 presents thethe streamlines velocities andstreamlines the velocity distribution in cross section of flowmeter, In flowmeter section, the appear to be parallel to each other. other. the flowmeter, respectively. In the flowmeter section, the streamlines appear to be parallel to each other.

(a)

(b)

(a) simulation (b) Figure 19. 19. Streamlines Streamlines simulation along along the the hydraulic hydraulic circuit circuit for for the the pipe pipe branch system system layout layout Figure branch (flowmeter section identified by the red arrow), in m/s (a); Velocity distribution in the cross section of (flowmeter identified by the red arrow), in m/s (a);circuit Velocity in the cross section of Figure 19. section Streamlines simulation along the hydraulic fordistribution the pipe branch system layout theflow flowmeter meter(b). (b). the (flowmeter section identified by the red arrow), in m/s (a); Velocity distribution in the cross section of the flow meter (b).

The velocity velocity changes largely within the in The the cross cross section, section,from fromzero zeronear nearthe thewall walltotoover over1.7 1.7m/s m/s thethe right lower side, where the velocity attains the highest value. This behavior not expected in right lower side, where the velocity attains the highest value. This was not expected The velocity changes largely within the cross section, from zero near the wall to over 1.7 m/s in ◦ curves because the flowside, passes through two90 90° curves after after the pump, pump, therefore, wouldwas be reasonable reasonable to because flow passes through two the therefore, itit would be to the rightthe lower where the velocity attains the highest value. This behavior not expected anticipate that the perturbations induced would be, in practice, neglected, according to manufactures anticipate that the perturbations induced would be, in practice, neglected, according to manufactures because the flow passes through two 90° curves after the pump, therefore, it would be reasonable to anticipate that the perturbations induced would be, in practice, neglected, according to manufactures

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experience. Nevertheless, Nevertheless,ititisisimportant importantnot not forget that second curve presents a rotation in toto forget that thethe second curve presents rotation in axis axis experience. Nevertheless, it is important not to forget that the second curve presents aa rotation in axis z. Therefore, the non-symmetric velocity is due to the existing geometry (Figure 19b). z. Therefore, Therefore, the the non-symmetric non-symmetric velocity velocity is is due due to to the the existing existing geometry geometry (Figure (Figure 19b). 19b). z. For each point, provided by the numerical model, the correspondent weighting factor was each point, provided by the numerical model, the correspondent weighting factor was was For each point, provided by the numerical model, the correspondent weighting factor estimated. The velocity measured by the flowmeter was calculated dividing the product of the velocity estimated. The The velocity velocity measured measured by by the the flowmeter flowmeter was was calculated calculated dividing dividing the the product product of of the the estimated. with the weighting factors by the sumby of all the weighting factors. The error associated to the flowmeter velocity with the weighting factors the sum of all the weighting factors. The error associated to velocity with the weighting factors by the sum of all the weighting factors. The error associated to was about 0.71%, determined according to Equation (8).to The error calculated by the manufacture, the flowmeter was about 0.71%, determined according Equation (8). The error calculated by the the flowmeter was about 0.71%, determined according to Equation (8). The error calculated by the through waterthrough balances,water was close to −1%. errors are alike, the model is considered to be manufacture, balances, wasSince closethe to −1%. −1%. Since Since the errors errors are alike, alike, the model model is manufacture, through water balances, was close to the are the is validated and thevalidated results accurate. considered to be and the results accurate. considered to be validated and the results accurate. 5.3. Solution 5.3. Solution Solution 5.3. In order to achieve solution that that presents presents aa lower lower error, error, 33 different different procedures procedures can can be be adopted: adopted: In order order to to achieve achieve aaa solution solution In that presents a lower error, 3 different procedures can be adopted: (1) changing the geometry but maintaining the values of volume flow rate and pressure; (2) changing (1) changing changing the the geometry geometry but but maintaining maintaining the the values values of of volume volume flow flow rate rate and and pressure; pressure; (2) (2) changing changing (1) the inlet and outlet conditions but maintaining the geometry; and (3) using both solutions. The chosen the inlet and outlet conditions but maintaining the geometry; and (3) using both solutions. The chosen the inlet and outlet conditions but maintaining the geometry; and (3) using both solutions. The chosen procedure was the first one, since the volume flow rate and pressure demanded downstream remain procedure was the first one, since the volume flow rate and pressure demanded downstream remain procedure was the first one, since the volume flow rate and pressure demanded downstream remain the same. the same. same. the The previous results showed that the existing layout would not be to the The previous previous results results showed showed that that the the existing existing layout layout would would not not be be enough enough to to guarantee guarantee the the The enough guarantee dissipation effects and the flow uniformity. For that reason, a new pipe with 20 m of length was added dissipation effects effects and and the the flow flow uniformity. uniformity. For For that that reason, reason, aa new new pipe pipe with with 20 20 m m of of length length was was dissipation in orderintoorder maketopossible the complete dissipation of disturbances. Considering the flowmeter in the added make possible the complete dissipation of disturbances. Considering the flowmeter added in order to make possible the complete dissipation of disturbances. Considering the flowmeter same as the as previous simulation (i.e., the flowmeter located between 24 m of straight pipe in the thelocation, same location, location, the previous previous simulation (i.e., the flowmeter flowmeter located between 24 m m of of straight straight in same as the simulation (i.e., the located between 24 upstream and 4and m downstream), the new geometry corresponds to Figure 20. 20. pipe upstream upstream m downstream), downstream), theproposed new proposed proposed geometry corresponds to Figure Figure pipe and 44 m the new geometry corresponds to 20.

20. System Systemlayout layoutproposed proposedmodelling modelling geometry—the flowmeter section represented by red the Figure 20. geometry—the flowmeter section represented by the Figure 20. System layout proposed modelling geometry—the flowmeter section represented by the red arrow; flow direction identified by the blue arrow (added pipe in red). arrow; flow direction identified by the blue arrow (added pipe in red). red arrow; flow direction identified by the blue arrow (added pipe in red).

For the same boundary conditions and mesh features, presented in Table 5, same boundary boundary conditions 5, the the streamlines streamlines For the same and mesh features, presented in Table 5, the streamlines obtained are presented in Figure 21a as well as the velocity distribution across the electrodes plan as well as the velocity distribution across the electrodes plan obtained are presented in Figure 21a as well as the velocity distribution across the electrodes plan (Figure 21b). (Figure 21b). (Figure 21b).

(a) (a)

(b) (b)

Figure 21. 21. Streamlines Streamlines simulation simulation along the the hydraulic circuit circuit for the the proposed system system layout Figure Figure 21. Streamlines simulation along along the hydraulic hydraulic circuit for for the proposed proposed system layout layout (flowmeter section identified identified by the the red arrow), arrow), in in m/s m/s (a); (a); velocity velocity distribution distribution in in the the electrodes electrodes cross cross (flowmeter (flowmeter section section identifiedby by thered red arrow), in m/s (a); velocity distribution in the electrodes section for the proposed geometry (b). section for thefor proposed geometry (b). (b). cross section the proposed geometry

This profile profile presents presents minor minor perturbations perturbations compared compared to to the the one one in in Figure Figure 18b. 18b. However, However, the the This velocity distribution is not exactly symmetric. The perturbation is still noticeable several meters velocity distribution is not exactly symmetric. The perturbation is still noticeable several meters ahead of of the the last last singularity. singularity. For For this this amount amount of of volume volume flow flow rate rate and and pressure, pressure, the the error error associated associated ahead

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This profile presents minor perturbations compared to the one in Figure 18b. However, the velocity distribution is not exactly symmetric. The perturbation is still noticeable several meters ahead of the last singularity. For this amount of volume flow rate and pressure, the error associated to this simulation is 0.37%, which is closer to the reference value that the flowmeters suppliers assure for a flow velocity higher than 1 m/s (i.e., 0.2%). 6. Conclusions The measurement problem has a significant influence in the correct management of technical, hydraulic and economic efficiency of water companies. Since the hydraulic circuits have, normally, two flowmeters, a water balance is possible. These balances are important tools to detect leaks throughout the supply and distribution processes. If the measurement is not accurate enough, the balances do not match and, subsequently, these tools loss their importance. The procedure used to analyze the associated errors, revealed to be enough showing good results for the experiments and the case study. Nevertheless, more scenarios need to be studied in order to assess if the procedure developed can be applied for every case. Regarding the simulation results, the model presented an error very similar to the one verified in the experimental tests developed by [30]. According to the results achieved, the errors calculated are very significant for an equipment with high accuracy. Consequentially, errors associated to the installation and the geometry are very important with relevant issues that are not always taken into account by engineers, responsible for the design, nor by teams responsible for the installation of this equipment. If these factors are not addressed properly, the flow measurement is not accurate. Regarding the proposed solution, the geometry to minimize the installation errors is not feasible, since the facility is already built according to manufacturer’s conditions. This could be overcome if well-defined automatic tools were applied to estimate the uncertainty of flow measurements. Using CFD models, a faster error approximation from a certain type of geometry, volume flow rate, and pressure could be obtained. Moreover, this research intends to assess that the installation requirements proposed by the manufactures are not sufficient to dissipate such uncertainties. Thus, it is reasonable to emphasize the importance of flow measurement for water companies, regarding more efficient and rational water use and management. Author Contributions: The author H.M.R. has contributed with the idea, in the revision of the document and in supervising the whole research. M.S. and M.B. developed the experimental tests and the CFD modelling and the analysis of the results between CFD and experiments. H.M.R. and A.C. revised the final document. Funding: This research was funded by REDAWN, EAPA_198/2016. Acknowledgments: The authors wish to thank to the project REDAWN (Reducing Energy Dependency in Atlantic Area Water Networks) EAPA_198/2016 from INTERREG ATLANTIC AREA PROGRAMME 2014–2020 and CERIS-IST and the Hydraulic Laboratory, for the support in the conceptual developments and experiments. Conflicts of Interest: The authors declare no conflict of interest.

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