Analysis of viscosity effect on turbine flowmeter performance basedon experiments and CFD simulations

Suna Guo a,b, Lijun Sun a,b,n, Tao Zhang a,b, Wenliang Yang a,b, Zhen Yang a,b

a School of Electrical Engineering & Automation, Tianjin University, Tianjin 300072, Chinab Tianjin Key Laboratory of Process Measurement and Control, Tianjin 300072, China

a r t i c l e i n f o

Article history:Received 27 May 2012Received in revised form17 April 2013Accepted 30 July 2013Available online 20 August 2013

Keywords:Flow measurementTurbine flowmeterViscosity effectComputational Fluid Dynamics (CFD)simulation

a b s t r a c t

Viscosity effect is one important factor that affects the performance of turbine flowmeter. The fluiddynamics mechanism of the viscosity effect on turbine flowmeter performance is still not fullyunderstood. In this study, the curves of meter factor and linearity error of the turbine flowmeterchanging with fluid viscosity variations were obtained from multi-viscosity experiments (the viscosityrange covered is 1.0�10–6 m2/s–112�10–6 m2/s). The results indicate that the average meter factor ofturbine flowmeter decreases with viscosity increases, while the linearity error increases. Furthermore,Computational Fluid Dynamics (CFD) simulation was carried out to analyze three-dimensional internalflow fields of turbine flowmeter. It was demonstrated that viscosity changes lead to changes of the wakeflow behind the upstream flow conditioner blade and the flow velocity profile before fluid enteringturbine rotor blade, which affect the distribution of pressure on the rotor blades, so impact the turbineflowmeter performance.

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1. Introduction

The turbine flowmeter is a very important kind of velocity typeflowmeters. It is widely used in industrial process control, oil andgas trade and other fields due to its high accuracy, good repeat-ability, wide range ability and other advantages.

The viscosity of fluid is one of the factors that affect theperformance of turbine flowmeter. The linear range of turbineflowmeter progressively decrease when viscosity is above 1 cSt, andvirtually disappeared between 50 cSt and 100 cSt [1]. Although lots ofeffort has been made, the fluid dynamics mechanism of the viscosityeffect on turbine flowmeter performance is still not fully understood.

Lee and Henning [2] held that any friction torque that is afunction of the viscosity affects the magnitude of turbine flow-meter linearity. Barry [3] pointed out that the viscous shear forceon the turbine rotor and the viscous friction force in bearingsincrease with the increase of fluid viscosity, and slow down theturn speed of rotor, while the flow velocity profile change makethe rotor accelerate. Salami [4] showed that fluid viscosity affectsturbine flowmeter performance because it affects the velocity ofgenerating swirl before fluid enter the rotor, and it also affects theaxial flow velocity distribution of fluid. Blows [5] thought thatReynolds number change induced by the viscosity change, at thesame flow rate, causes the variation of flow velocity profile inannular channel in front of the rotor, following the change of the

turn speed of the rotor, and then the meter factor. Fakouhi [6] andTan [7] demonstrated that increasing viscosity increases theresistance to flow in the blade tip clearance, and reduces the flowthrough the tip clearance, as a result of this, increases the flowthrough the blades, and increases the meter factor.

Some phenomena in the experiment process can be explainedby information extracted from the flow fields in the turbine flowsensor [8–10]. The investigations [11,12] have shown that theresults obtained from Computational Fluid Dynamics (CFD) simu-lation are close to that from experiment, and turbine flowmeterperformances can be predicted.

The K–qv curves of a turbine flowmeter at different fluid viscositypoints were obtained in this study, based on multi-viscosity experi-ments. The variation of its linearity error according to viscositychange was also obtained. CFD simulations were carried out toanalyze three-dimensional flow fields in the turbine flow sensor.Fluid dynamics mechanism of fluid viscosity change impactingturbine flowmeter performance was analyzed based on flow fields.This work makes a foundation for reducing the sensitivity of turbineflowmeter to viscosity changes.

2. Experiments

2.1. Structure parameters of tested turbine flowmeter

The tested prototype is LWGY (liquid turbine flowmeter indi-cated by the first letter combinations of Hanyu Pinyin) turbineflowmeter with diameter 10 mm made by Tianda Taihe CO., LTD.

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Flow Measurement and Instrumentation

0955-5986/$ - see front matter Crown Copyright & 2013 Published by Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.flowmeasinst.2013.07.016

n Corresponding author at: School of Electrical Engineering & Automation, TianjinUniversity, Tianjin 300072, China. Tel.: þ86 13622049756.

E-mail address: sunlijun@tju.edu.cn (L. Sun).

Flow Measurement and Instrumentation 34 (2013) 42–52

The structure and main geometrical dimensions of the turbineflow sensor tested are given in Fig. 1.

2.2. Properties of measured fluid

Experimental research was divided into three parts, that is,water flow experiment, diesel-oil mixture flow experiment, tur-bine oil flow experiment, limited by the viscosity of measuredfluid in the flow facility. The physical properties of measured fluidin the experiments are shown in Table 1.

2.3. Experimental facility

Water flow experiment was carried out on the water flow facilityin Flow Lab. of Tianjin University. The structure of the facility isshown in Fig. 2(a). Under the pressure of high water tank, waterflows past the tested turbine flowmeter, valve, then according to thestate of the diverter flow into the standard vessel, and then flow backinto the water pool through the bottom valve, or back into the pooldirectly. The computer controls the quantity of water flowing intothe standard vessel, collecting the number of pulse generatedby the tested turbine flowmeter when water flowing through it.

Nomenclature

A area of rotor blade pressure side [m2]Adriving parameter that represents the amount of fluid in

driving partAretarding parameter that represents the amount of fluid in

retarding partAi area of infinitesimal element face [m2]Ct driving torque coefficientd pipe diameter [m]Er repeatability errorEL linearity errorIi proportion of driving partJ rotational inertia of the rotational system [kg �m2]K meter factor [1/L]k coverage factor to expanded uncertaintyKij meter factor of each test run [1/L]Ki average meter factor of each flow rate [1/L]K average meter factor of whole flow rate range [1/L]Kimax maximum value of Ki in whole flow rate range [1/L]Kimin minimum value of Ki in whole flow rate range [1/L]Ks meter factor from simulation [1/L]L lead of blades [m]Mij reading of the electric balance [kg]Nij number of pulseN number of rotor bladesn number of infinitesimal elementsPi pressure on infinitesimal element face of rotor

blade [Pa]qv volume flow rate [L/h]ri radius corresponding to the center of infinitesimal

element [m]

Si sample standard deviation of the meter factor at theflow velocity point i

Tdr driving torque [N �m]Tb journal bearing retarding torque [N m]Th hub retarding torque due to fluid drag [N m]Tm retarding torque due to mechanical friction in journal

bearing and attractive force of magnetoelectricitydetector [N m]

Tt blade tip clearance drag torque [N �m]Tw both hub disks retarding torque due to fluid drag

[N �m]v instantaneous flow velocity at any point of the flow

field [m/s]v average flow velocity of the upstream straight pipe

entrance [m/s]v′ relative velocityxmax parameter represents the physical quantity at high

flow ratexmin parameter represents the physical quantity at low

flow rateα position of tested point [1]βi angle between the infinitesimal element and the axial

line of the rotor [1]δm relative deviation of proportion under different flow

velocities at same viscosityδr relative deviation of the physical quantity at high flow

rate from that at low flow rateρ fluid density [kg/m3]υ kinetic viscosity of fluid [m2/s]ω turn speed [rad/s]

Downstream Straight Pipe:Pipe diameter: 10mmPipe length: 10D

Upstream Flow Conditioner;Blade length: 25mmBlade number: 3Blade thickness: 0.8mm

Downstream Flow Conditioner:Blade length: 21mmBlade number: 3Blade thickness: 0.8mm

Upstream Straight Pipe:Pipe diameter: 10mmPipe length: 5D

Rotor:Blade number: 3Blade axial length: 2.5mmBlade normal thickness: 0.5mmBlade lead: 32mmTip radius: 4.8mmHub radius: 2mmShaft radius: 0.5mmShaft axial length: 9mm

Fig. 1. The rotor and the internal structure of turbine flowmeter.

S. Guo et al. / Flow Measurement and Instrumentation 34 (2013) 42–52 43

The quantity of water flow past tested turbine flowmeter is weighedby the electric balance. The valve is used to regulate the water flowrate in the pipeline. The calculation process of expanded uncertainty ofwater flow facility based on static weighing method is as following:

� Combined standard uncertainty of diverter: u(d)¼0.0103%;� Combined standard uncertainty of electric balance: u(e)¼

0.0106%;� Combined standard uncertainty of timer: u(t)¼0.015%;� Relative uncertainty of standard weights: u(w)¼0.011%;� Combined standard uncertainty:

u¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu2ðdÞþu2ðeÞþu2ðtÞþu2ðwÞ

p¼ 0:0238%;

� Expanded uncertainty: U¼u� k¼0.0476% (k¼2).

Diesel–oil mixture flow experiment was carried out on a vis-cosity variable oil flow facility in Flow Lab. of Tianjin University.

The structure of the facility is shown in Fig. 2(b). The temperature isadjusted to change the viscosity of the oil. The feedback controlsystem which controls the temperature of the oil within the tank ismade up of the DY2000 series intelligent controller, the heater in thetank, and temperature sensor. The control loop which includespressure sensor and frequency converter controls the flow rate inthe pipeline by regulating the turn speed of the pump motor. Thecalculation process of expanded uncertainty of viscosity variable oilflow facility based on static weighing method is as following:

� Combined standard uncertainty of diverter: u(d)¼0.0325%;� Combined standard uncertainty of electric balance: u(e)¼0.0162%;� Combined standard uncertainty of timer: u(t)¼0.005%;� Relative uncertainty of standard weights: u(w)¼0.0065%;� Uncertainty that brought by the temperature control system:

u(r)¼0.0046%;� Combined standard uncertainty:

u¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu2ðdÞþu2ðeÞþu2ðtÞþu2ðwÞþu2ðrÞ

p¼ 0:0375%;

� Expanded uncertainty: U¼u� k¼0.075% (k¼2).

Turbine oil flow experiment was carried out on the viscosityvariable calibration facility in Shanghai Sinoto Instrument Co., Ltd.The master meter method was utilized during the experiment. Themaster meter was oval gear volume flowmeter, whose accuracy is0.5% based plants with flow temperatures from �10 1C to 120 1C,kinematic viscosity from 5.0�10–6 m2/s to 1.0�10–3 m2/s andflow rate between 0.15 m³/h and 6.4 m³/h. The calculation processof expanded uncertainty of facility is as following:

� Uncertainty of master meter: u(m)¼0.5%;� Combined standard uncertainty of timer: u(t)¼0.005%;� Uncertainty that brought by the temperature control system:

u(r)¼0.005%;� Uncertainty of data-collection process: u(c)¼0.05%;� Combined standard uncertainty:

u¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu2ðmÞþu2ðtÞþu2ðrÞþu2ðcÞ

p¼ 0:503%;

� Expanded uncertainty: U¼u� k¼1.006% (k¼2).

2.4. Data processing

Flow rates 0.2 m3/h, 0.3 m3/h, 0.48 m3/h, 0.84 m3/h and 1.2 m3/h were selected for DN10 turbine flowmeter test, in the flow raterange of 0.2 m3/h–1.2 m3/h. Each flow rate was tested three times.

The meter factor K of a turbine flowmeter is defined as a pulsegenerated by a blade rotation in contact with a pick-up coil. Underideal condition when there is no retarding torques, it is anapproximate constant. However, the ideal condition does not existin the practical application, and the meter factor K always changeswith volume flowrate qv. In order to understand the actual work-ing performance, the K–qv curve of a turbine flowmeter is obta-ined from factory calibration. The linearity error of K–qv curve, is

Table 1Physical properties of the measured fluid in each part of the experiment.

Fluid Temperature (1C) Kinematic viscosity (10–6 m2/s) Density (kg/m3) Dynamic viscosity (10–3 kg/m s)

Water 20 1.0 998.2 1.0Diesel–oil mixture 17 31.6 896.1 28.4

27 20.4 890.3 18.237 12.9 884.5 11.447 9.1 878.7 8.0

Turbine oil 13.9 112 843.7 94.830 49.2 832.9 41.036 37.9 828.9 31.447 24.7 821.6 20.3

StandardVessel

Water Pool

T P

Diverter

Turbine MeterFor Test

Computer

Balance and Weight Indicator Water Pump

HighWaterTank

Valve

Bottom valve

Bottom Valve

StandardVessel

Oil Tank

T P

Diverter

Turbine MeterFor Test

Computer

Balance and Weight Indicator

Oil Pump

T

IntelligentController

FrequencyConverter

Vale

Fig. 2. (a) Structure of water flow standard facility, and (b) Structure of viscosityvariable oil flow experiment facility.

S. Guo et al. / Flow Measurement and Instrumentation 34 (2013) 42–5244

defined as the closeness of a curve that approximates to a straightline throughout measurement range. It is an important index ofevaluating the turbine flowmeter performance.

The meter factor of each test run was

Kij ¼Nij

Mij=ρði¼ 1;2;3;4;5; j¼ 1;2;3Þ ð1Þ

where Nij is the number of pulse; Mij is the reading of the electricbalance; ρ is the density of the fluid; i is flow rate tested; j is thetest number of every flow rate. The average meter factor of thisflow rate was

Ki ¼13

∑3

j ¼ 1Kij ð2Þ

The average meter factor of turbine flowmeter in whole flow raterange K , the linearity error EL and the repeatability error Er werecalculated as follows.

K ¼ 12ðKimaxþKiminÞ ð3Þ

EL ¼ðKimax�KÞ

K� 100% ð4Þ

Er ¼ SiKi

� 100% ð5Þ

2.5. Results and analysis

The results of experiments were shown in Table 2. K–qv curvesof turbine flowmeter at different viscosities were shown in Fig. 3.It was shown by the curves that, the meter factor increases withflow rate increases, when fluid viscosity is higher (more than

24.7�10–6 m2/s), under the same viscosity condition. The largerthe fluid viscosity is, the more obvious this trend is. The meterfactor gradually rises with flow rate increase in the low flow ratesection, when viscosity is relatively lower (less than 12.9�10–6 m2/s). However, the meter factor tends to be stable and closeto a constant, as flow rate increases to a certain point. The meterfactor presents decline trend, as the flow rate continues toincrease.

The meter factor has a decreasing trend with viscosity increase, incomparison of low flow rate section under different fluid viscosity.The meter factors of minimum flow rate at the highest viscosity(112�10–6 m2/s) and the lowest viscosity (1.0�10–6 m2/s) are 1165.0(1/L) and 1643.5(1/L), respectively, and the relative variation of thesetwo meter factors is 29.11%. As flow rate increases, the difference ofmeter factor induced by the viscosity change decreases gradually. Therelative deviation of the meter factor is 16.06% between the highestand the lowest viscosity at the maximum flow rate.

The average meter factors K at different viscosities are differ-ent. The curve of the average meter factor and the fluid kinematicviscosity could be gotten, as shown in Fig. 4. It is indicated that theaverage meter factor decreases gradually with viscosity increase inthe whole viscosity range.

It was demonstrated by the data that, the linearity error wouldrise as fluid viscosity increase for the same turbine flowmeter. Thecurve of the linearity error and the fluid kinematic viscosity isshown in Fig. 5.

3. CFD simulations of flow fields and analysis

3.1. Three-dimensional simulation model of the turbine flowmeter

The CFD simulation software package FLUENT was adopted tostudy the three-dimensional internal flow fields of DN10 turbine

Table 2Experimental data of turbine flowmeter.

Temperature (1C) Kinematic viscosity (10–6 m2/s) K (1/L) EL (%)

Water flow experiment 20 1.0 1651.0 0.5Diesel–oil mixture flow experiment 17 31.6 1590.3 4.5

27 20.4 1612.8 3.037 12.9 1650.7 2.247 9.1 1623.2 1.7

Turbine oil flow experiment 13.9 112 1316.8 11.530 49.2 1398.8 10.236 37.9 1571.7 6.347 24.7 1610.3 3.8

Fig. 3. K–qv curves of turbine flowmeter at different viscosities.

0 15 30 45 60 75 90 105 1201300

1350

1400

1450

1500

1550

1600

1650

Ave

rage

Met

er F

acto

r of T

urbi

neFl

owm

eter

in W

hole

Flo

w R

ate

Ran

ge (1

/L)

Kinematic Viscosity(10-6m2/s)

Meter Factor Fitting Curve

Fig. 4. Viscosity effect on average meter factor of turbine flowmeter.

S. Guo et al. / Flow Measurement and Instrumentation 34 (2013) 42–52 45

flowmeter, under the same conditions as the experiment men-tioned above, in order to analyze the fluid dynamics mechanism ofturbine flowmeter performance affected by viscosity.

The three-dimensional simulation model of the DN10 turbineflowmeter was built using GAMBIT software, according to theactual structure of the turbine flowmeter, as shown in Fig. 1. 5Dand 10D length straight pipes were added at the upstream and thedownstream of the sensor, respectively, for making the flowregimes at the inlet and the outlet close to fully developedturbulence.

3.2. Model mashed

The model was divided into seven parts when meshed. Struc-tured grids were used at upstream straight pipe, downstreamstraight pipe, upstream flow conditioner, downstream flow con-ditioner which have relatively regular shape. The growth functionwas used to generate the volume mesh in upstream straight pipeand downstream straight pipe which have the maximum aspect-ratio 2, for reducing the number of cells but not affecting thequality of the grid. Unstructured grids were used at the regionbetween straight pipe and flow conditioner, the region betweenflow conditioner and rotor, and the region of rotor which havecomplicate structures.

The appropriate number of grids was determined based oncapturing the flow field details, predicting the performance ofturbine flowmeter correctly and saving computer resources appro-priately. Three different grids numbers were selected to simulatethe internal flow field of turbine flowmeter when the mediumwaswater at 20 1C in this study. The message of grids and simulationresults are shown in Table 3. The number 1.4 million is chosen dueto predicting the performance of turbine flowmeter closer toexperimental data and saving more computer resources, underthe condition that the flow field details can be captured using all of

the three methods. There are 5 grids in 0.5 mm thickness of bladeat the leading edge and the trailing edge and the tip of blade,2 grids in the blade tip clearance where the height is 0.2 mm.

3.3. Method for simulation

The entirely computational domain was divided into threeparts, i.e. the region of upstream straight pipe and upstream flowconditioner, the region of rotor, the region of downstream straightpipe and downstream flow conditioner. The motion type in theregion of rotor was set to the Moving Reference Frame (MRF), andthe two remaining regions were set to stationary. The rotationalregion and stationary regions are connected with two pairs ofinterface surfaces.

Pressure based steady solver was chosen. Linear pressure–strainof the Reynolds stress turbulence model and standard wall functionswere chosen when the fluid was water. When fluid viscosity washigher, Low-Re Stress-Omega in Reynolds stress turbulence modelwas chosen by virtue of the small Reynolds number.

Using FLUENT software to simulate the internal flow fields ofthe flowmeter was based on the torque balance equation, i.e. theangular acceleration of rotor is zero, when the turbine flowmeterwas in the steady state. The torque balance equation is as follow

Tdr�Tb�Th�Tm�T t�Tw ¼ Jdωdt

¼ 0 ð6Þ

where Tdr is the rotor driving torque; Tb is journal bearingretarding torque; Th is rotor hub retarding torque due to fluiddrag; Tm is retarding torque due to mechanical friction in journalbearing and attractive force of magnetoelectricity detector; Tt isthe blade tip clearance drag torque; Tw both hub disks retardingtorque due to fluid drag; J is rotational inertia of the rotationalsystem; ω is turn speed of the rotor.

Based on Eq. (6), there should be a constant speed ω corre-sponding to a given inlet flow velocity. The driving torque on rotorwill change with the change of inlet flow velocity, and the torquebalance will be broken. ω should be adjusted to satisfy the torquebalance equation. If ω was set unreasonable, the total torque onthe rotor was not zero. During the process of numerical simula-tion, the value of ω was constantly adjusted according to the valueof the total torque on the rotor monitored, before the torques onrotor achieve balance. It was considered to achieve torque balancewhen total torque on the rotor less than 10�8 N m, and thecorresponding value ω was an appropriate turn speed of the rotor.The meter factor from simulation Ks can be calculated.

Ks ¼5:4ωπqv

ð7Þ

3.4. Analysis of fluid dynamics mechanism of viscosity effect

The viscosity effect on turbine flowmeter performance isanalyzed in two aspects, i.e. the effect of upstream flow condi-tioner wake flow and the force distribution on the rotor bladescaused by the flow velocity profile changes.

3.4.1. Effect of upstream flow conditioner wake flowThe flow fields of the turbine flowmeter at different viscosity

and different flow rates were studied, for analyzing the fluiddynamics mechanism of viscosity effect. However, the kinematicviscosity of 112�10–6 m2/s, 31.6�10–6 m2/s and 1.0�10–6 m2/swere chosen, and the flow fields at the maximum flow rate andthe minimum flow rate were enumerated in the paper, due tospace limitation. The flow velocity was normalized, in order tocompare the difference of flow velocity distributions betweenmaximum and minimum flow rate, and clearly analyze the effect

0 15 30 45 60 75 90 105 1200

2

4

6

8

10

12

Line

arity

Err

or (%

)

Kinematic Viscosity(10-6m2/s)

Linearity Error

Fitting Curve

Fig. 5. Viscosity effect on linearity error of turbine flowmeter.

Table 3The influence of different grids number on prediction results.

Case Minimum size(mm)

Total number(million)

Meter factorKs (1/L)

Linearityerror EL (%)

1 0.18 0.9 1642.5 1.62 0.15 1.4 1652.8 1.43 0.12 2.0 1654.9 1.5Experimental

data– – 1651.0 0.5

S. Guo et al. / Flow Measurement and Instrumentation 34 (2013) 42–5246

of wake flow on the meter factor.

v′¼ vv

ð8Þ

where v is the instantaneous flow velocity at any point of the flowfield, v is the average flow velocity at the cross-section of upstreamstraight pipe entrance.

Flow velocity distributions on the cylindrical surface (surface-1in Fig. 6) which is symmetry about the x-axis and with radius4 mm and on the plane (plane-1 in Fig. 6) at the center of rotorwere analyzed. As shown in Figs. 7 and 8, there is wake flowbehind the upstream flow conditioner blades which divides theflow region between two rotor blades into two parts distinctly. Theformer section on the pressure side of rotor blade has an impact of

driving the rotor, while the latter part on the suction side of theblade has an impact retarding the rotor.

The relative velocity information along Circumference-1 (theposition is shown in Fig. 8) was extracted from flow field and thecurve of velocity magnitude with position is shown in Fig. 9.Between two parts flow divided by the wake flow of upstreamflow conditioner, if the part acting on the pressure side of bladetake relatively large proportion and the other part take relativelysmall proportion, then the rotor get larger driving force andsmaller drag force, and have larger turn speed, so the meter factoris larger, and vice versa.

The proportion of driving part was

Ii ¼Aidriving

AiretardingþAidriving� 100% ði¼ 1; 2; …; 6Þ ð9Þ

where Aidriving, Airetarding are parameters that respectively repre-sent the amount of fluid in driving part and retarding part, andwere calculated by integrating the relative velocity in the corre-sponding region; i is the sequence number of conditions analyzed.

The relative deviation of proportion under different flowvelocities at same viscosity was

δm ¼ I2n�I2n�1

I2nþ I2n�1� 100% ðm¼ 1; 2; 3; n¼ 1; 2; 3Þ ð10Þ

wherem is the sequence number of viscosity analyzed; n is naturalnumbers; 2n is the sequence number corresponding to themaximum flow rate; 2n�1 is the sequence number correspondingto the minimum flow rate.

Results are presented in Table 4.

Line-1

Surface-1

Line-2

Line-3

Line-4 Plane-1

Line-5

Fig. 6. Positions of investigated objects.

Fig. 7. The distribution of relative velocity v′ around the rotor blades. (a) v¼112�10�6 m2/s, v¼0.7 m/s, (b) v¼112�10�6 m2/s, v¼4.2 m/s, (c) v¼31.6�10�6 m2/s,v¼0.7 m/s, (d) v¼36.6�10�6 m2/s, v¼4.2 m/s, (e) v¼1.0�10�6 m2/s, v¼0.7 m/s and (f) v¼1.0�10�6 m2/s, v¼3.9 m/s.

S. Guo et al. / Flow Measurement and Instrumentation 34 (2013) 42–52 47

It can be found from Table 4 that, to the identical viscosity, theproportion of flow driving the rotor between the blades rises whenflow velocity increases, resulting in rotor turn speed increase andmeter factor growth. Therefore, for a certain kind of fluid, the meterfactor increases with flow rate increases.

To the identical flow rate at different viscosities, the influenceof wake flow is gradually increases accompanying the increase offluid kinematic viscosity, the proportion of the flow drivingthe rotor between the blades gradually decreases, causing thedecline of rotor turn speed and the meter factor. Therefore, fordifferent fluid viscosity, the meter factor decreases with viscosityincreases.

The difference of wake flow effect between maximum andminimum flow rate is different with viscosity change. FromTable 4, it can be observed that the relative deviation of proportionof driving part under different flow velocities is larger at highviscosity. That is, when viscosity is high, the difference betweenmeter factors at maximum and minimum flow rate is large; asviscosity is low, the difference is relatively small. Therefore, the

higher the viscosity of the fluid is, the larger linearity error is, andvice verse.

The structure of upstream flow conditioner could be changedbased on the analysis above, such as reducing blades thickness andlength, so that the fluid flow will be fully developed after theconditioner blades, the effect of their wake flow on the rotor turnspeed will be reduced.

3.4.2. Flow velocity profile effect on force distribution at rotor bladeSeparated flow appears near the leading edge when the fluid

flows through the blades, due to the shape of leading edge ofblades and the rotation of the rotor, as shown in Fig. 10. Therefore,there is a low pressure region appearing in front of the blades. Itextends gradually to the center of blades along the direction offlow, as shown in Fig. 11. When the flowmeter is running atdifferent viscosity or different flow rate, its inlet velocity profile ischanging, and the leading edge separation and reattachment flowsmust change accordingly [13].

Fig. 8. Flow velocity distribution between the rotor blades. (a) v¼112�10�6 m2/s, v¼0.7 m/s, (b) v¼112�10�6 m2/s, v¼4.2 m/s (c) v¼31.6�10�6 m2/s, v¼0.7 m/s,(d) v¼36.6�10�6 m2/s, v¼4.2 m/s, (e) v¼1.0�10�6 m2/s, v¼0.7 m/s and (f) v¼1.0�10�6 m2/s, v¼3.9 m/s.

S. Guo et al. / Flow Measurement and Instrumentation 34 (2013) 42–5248

Flow velocity profiles of the entrance of the rotor blades (theposition was Line-4 shown in Fig. 6) at the maximum and theminimum flow rate at the viscosity of 1.0�10–6 m2/s and112�10–6 m2/s were shown in Fig. 12(d), and the force on the

rotor blades generated by the fluid will change with the variationof flow velocity profile at the entrance of the rotor blades, asshown in Fig. 13. From Fig. 13, it can be concluded that, to the sameviscosity, the change is large as the flow rate is high, as shown inFig. 13(b) and (d), and vice versa, as shown in Fig. 13(a) and (c).

The size of low pressure region appearing in front of the bladesis also affected by the fluid viscosity. With high fluid viscosity andlow flow rate, the fluid flow near the blade is in laminar state andflows through the blades close to the wall of them, so there is nolow pressure area on the forepart of the blades, as show in Fig. 13(a). Due to the existence of shear stress force, the drag force onfluid flow is larger, so the impact force on the blades is gettingsmaller and smaller as the fluid flow downstream, and large areaof low pressure region exist near the tail of blades, as shown inFig. 13(a), which cause the driving torque on rotor smaller, theangular velocity smaller and the meter factor of turbine flowmetersmaller. With the flow rate increase, the size of low pressure areareduces, while the high pressure area moves up to the blade tip,resulting in the increase of the driving torque, the angular velocityof rotor and the meter factor of turbine flowmeter.

Since viscous friction is small, there is no low pressure regionnear the tail on the blades when viscosity is low. With flow rateincreasing, the low pressure region on the forepart of bladesmoves downstream, the high pressure area in the blade will movetoward the tail and toward the tip of the blades, resulting in theincrease of the driving torque, the angular velocity of the rotor andthe meter factor of turbine flowmeter.

Five different locations were compared at the maximum andthe minimum flow rate at the viscosity of 1.0�10–6 m2/s and112�10–6 m2/s, respectively. The five locations (Line-1–Line-5shown in Fig. 6) are at the upstream straight pipe where the flowregime is close to fully developed turbulence, the central of theupstream flow conditioner, the axial central of the gap betweenthe upstream flow conditioner and the rotor, the entrance of therotor blades, the axial central position of the rotor. As shown inFig. 12, both the fluid viscosity and the flow rate affect the flowvelocity profile. To the same viscosity, the corresponding flowvelocity profile change with the average flow velocity. Under thesame fluid condition, the velocity profiles are not the same atdifferent locations, due to the internal structure of turbine flow-meter change with location. So, changing the structure of theinside wall of the turbine flowmeter shell could control the flowvelocity profile of the fluid in front of the rotor, and decrease theimpact of the pressure distribution on turbine flowmeter perfor-mance due to viscosity change.

From the results of discussion above, it was concluded thatboth the upstream flow conditioner wake flow and the flowvelocity profile affect the value of the driving torque on the rotor.It was verified quantificationally through the data extracted fromthe flow fields, as shown in Table 5.

The driving torque Tdr on the rotor was

Tdr ¼N∑n

iPiAiri cosβi ¼N∑

n

iPiAiri cos arctg

2πriL

� �� �

The former section hasan impact on the pressure side

0 40 80 120 160 200 240 280 320 3600.0

0.5

1.0

1.5

2.0

2.5

v=0.7 m/sv=4.2 m/s

v'

α(° )

0 40 80 120 160 200 240 280 320 360α(° )

0 40 80 120 160 200 240 280 320 360α(° )

The latter part hasan impact on the suction side

The centre of wake flow

The position of rotor blade

0.0

0.5

1.0

1.5

2.0

v=0.7 m/sv=4.2 m/s

'v

The former section hasan impact on the pressure side

The latter part hasan impact on the suction side

The centre of wake flow

The position of rotor blade

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

v=0.7 m/sv=3.9 m/s

v'

The former section hasan impact on the pressure side

The latter part hasan impact on the suction side

The centre of wake flow

The position of rotor blade

Fig. 9. Relative velocity information along Circumference-1. (a) v¼112�10�6 m2/s,(b) v¼31.6�10�6 m2/s and (c) v¼1.0�10�6 m2/s,

Table 4The analysis data of upstream flow conditioner wake flow effect.

i Viscosity (m2/s) Velocity (m/s) Aretarding Adriving Ii (%) δm (%)

1 1 0.7 85.5 58.9 40.8 2.52 1 3.9 78.8 59.1 42.93 31.6 0.7 112.4 57.9 34 3.54 31.6 4.2 98.2 56.5 36.55 112 0.7 129.5 55.8 30.1 8.16 112 4.2 110.7 60.7 35.4

S. Guo et al. / Flow Measurement and Instrumentation 34 (2013) 42–52 49

¼N∑n

iPiAiri �

Lffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4π2ri2þL2

q ð11Þ

where Pi is the pressure on infinitesimal element face of rotorblade; Ai is the area of infinitesimal element face; ri is the radiuscorresponding to the center of infinitesimal element; βi is theangle between the infinitesimal element and the axial line of therotor; L is the lead of blades; N is the number of rotor blades; n isthe number of infinitesimal elements.

The driving torque coefficient Ct was calculated throughfollowing equation.

Ct ¼ Tdr

ð1=2Þρv2Adð12Þ

where v is the average velocity of the upstream straight pipeentrance; ρ is the density of fluid; A is the area of rotor bladepressure side; d is the pipe diameter.

The relative deviation is

δr ¼xmax�xmin

xmaxþxmin� 100% ð13Þ

where xmax represents the physical quantity at high flow rate; xmin

represents the physical quantity at low flow rate.As shown in Table 5, the driving torque Tdr on the rotor is

affected by fluid viscosity and flow rate: to different kind fluid, thedriving torque rises with viscosity decreases; to the same kindfluid, the driving torque rises with flow rate increases; the relative

Fig. 10. The velocity vectors in the flow separation region near the leading edge of the blade.

Fig. 11. The relative pressure contours distribution around the rotor blades.

S. Guo et al. / Flow Measurement and Instrumentation 34 (2013) 42–5250

deviation between Tdr at high viscosity is larger than that at lowviscosity.

4. Conclusions and advices

Through multi-viscosity experiment of turbine flowmeter, CFDsimulation of three-dimensional flow fields in the turbine flowsensor, the analysis of flow fields, several conclusions were gottenas follows.

(1) The average meter factor of the turbine flowmeter decreases asthe fluid viscosity increase, while the linearity error rises withthe increase of viscosity. When the fluid kinematic viscosityincreases from 1.0�10–6 m2/s to 49.3�10–6 m2/s, the averagemeter factor decreases from 1651.0 (1/L) to 1398.8 (1/L),meanwhile, the linearity error increases from 0.45% to 10.24%.

(2) The wake flow of upstream flow conditioner affects the flowvelocity distribution between turbine rotor blades which

changes the performance of the turbine flowmeter. As fluidviscosity increases, the effect of the wake flow of upstreamflow conditioner becomes larger.

(3) The change of the fluid viscosity impacts the flow velocityprofile of fluid entering the rotor blades, which affects thepressure distribution on the rotor blades and then the rotorturn speed. The performance of the turbine flowmeter isaffected as the fluid viscosity changes the flow velocity profilein front of the rotor.

Based on the research and analysis above, for the optimizationof the structure of the turbine flowmeter to reduce the sensitivityof the turbine flowmeter to the fluid viscosity change, followingadvices were given:

(1) Reduce the impact of the wake flow behind upstream flowconditioner. Change the structure of the upstream flow con-ditioner, such as reducing blades thickness and length, so thatthe fluid flow will be fully developed after the conditioner

-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5

0.0

0.2

0.4

0.6

0.8

1.0

Rel

ativ

e V

eloc

ity (v

/vm

ax)

Rel

ativ

e V

eloc

ity (v

/vm

ax)

Rel

ativ

e V

eloc

ity (v

/vm

ax)

Rel

ativ

e V

eloc

ity (v

/vm

ax)

Rel

ativ

e V

eloc

ity (v

/vm

ax)

r/D

-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5

r/D

-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5

r/D

-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5

r/D-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5

r/D

0.0

0.2

0.4

0.6

0.8

1.0

0.0

0.2

0.4

0.6

0.8

1.0

0.0

0.2

0.4

0.6

0.8

1.0

0.0

0.2

0.4

0.6

0.8

1.0

Fig. 12. Flow velocity profiles at different locations of turbine flowmeter. (a) Line-1, (b) Line-2, (c) Line-3, (d) Line-4 and (e) Line-5.

S. Guo et al. / Flow Measurement and Instrumentation 34 (2013) 42–52 51

blades, the effect of its wake flow on the rotor turn speed willbe reduced.

(2) Control the flow velocity profile of the fluid in front of therotor, by changing the structure of the inside wall of theturbine flowmeter shell, such as changing pipeline diameter,changing roughness of pipeline's internal wall or changing theshape of rotor blade, to decrease the impact of the pressuredistribution on turbine flowmeter performance due to viscos-ity change.

References

[1] Watson GA, Furness RA. Development and application of the turbine meter.Proc. Transducer 77 Conf. Flow Measurement Session (June 1977).

[2] Lee WF, Henning ZK. A study of viscosity effect and its compensation onturbine-type flowmeters. Transactions of ASME Journal of Basic Engineering1960:717–28.

[3] Barry AE. Turbine meters for liquid measurement. Mechanical Engineering1983:52–6.

[4] Salami LA. Analysis of swirl, viscosity and temperature effects on turbineflowmeters. Transactions of the Institute of Measurement and Control 1985;7(4):183–202.

[5] Blows LG. Towards a better turbine flowmeter in ‘international conference onthe advance in flow measurement techniques, Warwick, English’. BHRA FluidEngineering Cranfield, England; 1981. p. 307–18.

[6] Fakouhi A. The influence of viscosity on turbine flow meter calibration curves.University of Southampton; 1977 ([Ph.D. thesis]).

[7] Tan PAK. Theoretical and experimental studies of turbine flowmeter. Depart-ment of Mechanical Engineering University of Southampton; 1973 ([Ph.D.thesis]).

[8] Sun LJ. Research on reducing turbine flowmeter's sensitivity to viscositychange. Tianjin University; 2004 ([Ph.D. thesis] (in Chinese).

[9] Wang Z, Zhang T. Computational study of the tangential type turbineflowmeter. Flow Measurement and Instrumentation 2008;19(5):233–9.

[10] Lavante EV, Thomas H, Schieber WM. Numerical investigation of the flow fieldin a 2-stage turbine flowmeter, In: Proceedings of the international conferenceon flow measurement; 2001.

[11] Lavante EV, Kettner T and Lazaroski N. Numerical simulation of unsteadythree-dimensional flow fields in a turbine flowmeter, In: Proceedings of theinternational conference on flow measurement; 2003.

[12] Lavante EV, Banaszak U, Kettner T. Numerical simulation of Reynolds numbereffects in a turbine flowmeter, In: Proceedings of the international conferenceon flow measurement; 2004. p. 575–582.

[13] Xu Y. Calculation of the flow around turbine flowmeter blades. Flow Measure-ment and Instrumentation 1992;3(1):25–35.

Fig. 13. The pressure distribution on pressure side of the rotor blades. (a) v¼112�10�6 m2/s, v¼0.7 m/s, (b) v¼112�10�6 m2/s, v¼4.2 m/s, (c) v¼1.0�10�6 m2/s,v¼0.7 m/s and (d) v¼1.0�10�6 m2/s, v¼3.9 m/s,

Table 5The data extracted from the flow fields.

Viscosity (10–6 m2/s) Flow velocity (m/s) Meter factor from experiment (1/L) Meter factor from CFD simulation (1/L) Tdr (N �m) Ct

1.0 3.9 1654.9 1681.3 2.6E-05 2.5E-021.0 0.7 1643.5 1627.5 8.3E-07 2.2E-02δr (%) 68.2 0.4 1.6 93.8 5.3112 4.2 1438.4 1404.9 1.3E-05 1.2E-02112 0.7 1163.8 1009.5 2.0E-07 6.7E-03δr (%) 71.1 10.6 16.4 96.8 27.8

S. Guo et al. / Flow Measurement and Instrumentation 34 (2013) 42–5252