Development of a new calibration method for ...

International Flow Measurement Conference 2015 Advances and Developments in Industrial Flow Measurement

Coventry, UK 1-2 Jul, 2015

A New Calibration Method for Ultrasonic Clamp-on Flowmeters Bernhard Funck, Flexim GmbH, Berlin Erkan Kublay, Physikalisch-Technische Bundesanstalt, Braunschweig Rainer Engel, Physikalisch-Technische Bundesanstalt, Braunschweig Mathias Panicke, Flexim GmbH, Berlin

1

INTRODUCTION

Ultrasonic clamp-on flowmeters basically provide non-invasive flow metering capabilities. The ultrasonic transducers are installed on the outside of the pipe at the measurement location in the field. Therefore, a factory calibration of a clamp-on flowmeter cannot include a meter body. Conventionally, when a calibration for a clamp-on flowmeter is required, it is performed at a calibration facility designed for invasive flowmeters. This means that the pipe and the flow profile conditions of the calibration facility represent elements which cause impacts on the calibration results although the pipe is not delivered with the flow meter into the field. This is a valid method if the flow conditions can be assumed to be ideal and the uncertainty in the pipe geometry can be assumed negligible. While the pipe geometry in a flow lab usually is known very accurately, it is very difficult to provide ideal flow conditions. Therefore it is desirable to find a method that allows for calibrating a Clamp-on flow meter independently of the pipe and the flow profile which are not part of the meter that is delivered to the measurement location. The aim of this project is to investigate the transferability of such a new calibration technology into the field. The meter formula of an ultrasonic flowmeter includes an acoustic calibration factor, a fluid mechanic calibration factor for the flow profile influence and a geometric calibration factor which is identical to the inner cross sectional area of the pipe. Whereas the acoustic calibration factor is part of the flowmeter, the other two factors adhere to the measurement location in the field. The new calibration method determines the acoustic calibration factor directly and, thereby, enables the calibration of the clampon flow meter independently of the pipe. It also enables to replace or recalibrate transducers at any time after the initial installation without the need to recalibrate the meter. This paper covers the results of research cooperation, over three years, between the Physikalisch-Technische Bundesanstalt (PTB) and Flexim GmbH. The project was funded by the Federal Ministry of Economic Affairs and Energy. The aim of this cooperation was to investigate the transferability of the new calibration technology for ultrasonic clamp-on flowmeters into the field. Quantifying the transferability requires the realization of field conditions in a flow lab while keeping the uncertainty of the flow profile influences and the pipe geometry substantially lower than the uncertainty of the acoustic calibration factor. Such conditions can be provided by the hydrodynamic test field (HTF) of PTB in Braunschweig. The HTF represents the German national standard of liquid flow measurands. It is operated with the fluid "water" in a flowrate range from 0.3 m³/h to 2100 m³/h, at a level of expanded relative measurement uncertainty as low as 0.02 %. The investigations were conducted on three pipes with 50 mm, 100 mm and 300 mm nominal pipe diameter. The fluid mechanic calibration factor, in this project, was determined from the flow profile measured by means of a Laser Doppler anemometer (LDA).

1


2


THE MEASUREMENT PRINCIPLE

A main advantage of the new calibration method is that it enables the calibration of the transducers and the transmitter of a clamp-on ultrasonic flow meter without a metering tube being involved. This possibility can be derived from the meter formula which represents the physical model of the measurement principle[1]. The average path velocity along the sound path is calculated from the transit time difference ∆t and the transit time

= vl K a ⋅

t fl in the fluid as

∆t . 2t fl

(1)

Here the acoustic calibration factor calculated from the angle propagation angles

β

and

Ka

is a parameter of the transducers that can be

α and the sound speed cα in the coupling wedge. The γ in the pipe wall and the fluid are given by Snells law:

= K a c= c= cγ sin γ α sin α β sin β

(2)

The volumetric flow is calculated from the average path velocity by multiplying it with the pipe inner cross A section and the fluid mechanic calibration factor K Re :

∆t V =A ⋅ K Re ⋅ vl =A ⋅ K Re ⋅ K a ⋅ 2t fl

(3)

In this formula the properties of the measuring section, the flow profile, the transducers and the transmitter are represented by factors being independent of each other. Thus they can be determined independently of each other. The transducer and the transmitter are calibrated in the factory. The cross sectional area A of the measuring section is measured when installing the meter. The fluid mechanic calibration factor relates the mean velocity over the cross-section of the pipe to the average path velocity:

K Re =

Figure 1

vA vl

(4)

Calibration factors

The fluid mechanic calibration factor

K Re is calculated by the meter based on an em-

pirical model of the flow profile. This model describes a fully developed turbulent flow profile and is parameterized by the Reynolds number and the roughness of the inner pipe wall. 2


3


THE NEW CALIBRATION METHOD

In Equ. (3), the properties of the transducers are represented by the acoustic calibration factor K a defined by Equ. (2) which can be calculated from the geometry and sound velocity of the transducer coupling wedge. The uncertainty of

K a thus is

determined by the tolerances of the material properties and the manufacturing tolerances of the wedge. Better accuracy can be achieved by calibrating the acoustic calibration factor K a . This can be done indirectly by a flow calibration. Using Equ. (3), the transducer constant is determined by comparing the volume flow measured by the test instrument with the reference volume flow. This implies that the crosssectional pipe area A and the fluid mechanic calibration factor K Re have to be well known, as their uncertainty directly affects the calibration result. The new calibration method, however, permits a direct calibration of the acoustic calibration factor. The approach is explained, below, from the physical principle the transit time flowmeter is based on. The transit time flow measurement is based on the lateral displacement the ultrasonic signal experiences when traveling through a flowing fluid. The new calibration procedure makes use of the equivalence of this effect to a relative displacement of the transducers when the fluid is not flowing. Figure 2a shows the transducers mounted on the pipe and the sound signal without flow and with flow (dashed line). The ultrasonic signal is shifted in an axial direction by the flowing fluid by the amount ∆x . The part of the sonic path within the receiving transducer is reduced accordingly and thus the transit time is reduced by the transit time difference ∆t . As this is a relative displacement of the ultrasonic signal with respect to the transducer, the same effect will be achieved when one of the transducers is relocated relative to the other transducer when the fluid is not flowing (Figure 2b). The calibration consists of measuring the local displacement ∆x and the corresponding time difference ∆t . The transducer constant

K a is calculated as follows: ∆x Ka = ∆t

Figure 2

(5)

a) Sound path with and without flow b) Sound path without flow, transducer displaced

The calibration facility at FLEXIM GmbH that realises this method controls the displacement between the transducers with an accuracy of 1 μm. The uncertainty of the time difference measurement is below 1/5000 of the signal period length. The total uncertainty of the aperture calibration is therefore in the range 0.1 % ... 0.25 %, depending on transducer type.

3


4


QUANTIFICATION OF THE TRANSFERABILITY OF THE NEW CALIBRATION METHOD INTO THE FIELD

The task of verifying the transferability of the new calibration method into the field can be split into two subtasks: 1. Verifying the reproducibility of the calibration with various transducer specimens; 2. Verifying the independence of the factors in Equ. (3). For the first task a number of transducers of the same type were investigated under the same application conditions. The second task was achieved by determining the reproducibility with varying application conditions. These conditions were the pipe dimensions, temperature and Reynolds number. The reproducibility was quantified as the difference between the reference volumetric flow and the flow calculated from the path velocity of the ultrasonic meter by multiplying it with the cross sectional area A of the pipe and the fluid mechanic calibration factor K Re as determined from the LDA measurement:

 V − K ⋅ A ⋅ v ∆V= REF Re l _ DUT

(6)

When the ultrasonic flow meter is applied in the field, the fluid mechanical calibration factor

K Re is calculated by the meter. In order to exclude the flow profile influence in

this investigation, K Re here was determined from the flow profile measured by the LDA by a numerical evaluation of Equ. (4). With a fully developed flow profile the average velocity vl of the flow velocity along a path of length

L

can be derived from the axial

component of the velocity profile as follows:

vl =

1 vz ( l ) dl L ∫L

(7)

Assuming that the velocity profile does not change in axial direction within the measurement volume the path integral can be replaced by an integral along the radius of the pipe: R

vl =

1 vz ( r ) dr 2 R −∫R

The average velocity

vA =

(8)

v A over the cross-sectional area of the pipe is:

1 v ( r , ϕ ) dA A ∫A

(9)

Thus the fluid mechanical calibration factor

vA = K= Re vl

1 vz ( r , ϕ ) dA A ∫A R 1 vz ( r ) dr 2 R −∫R

K Re

results to:

(10)

4



With the area average and the path average of the velocity profile measured by the LDA, v A _ LDA and vl _ LDA , K Re is:

K Re =

v A _ LDA vl _ LDA

(11)

5

MEASUREMENT PROGRAM

5.1

Reproducibility with Various Transducer Specimen at the Same Location

A number of transducers of the same type were investigated at the same location. The reproducibility was quantified by the standard deviation of the error compared to the standard deviation of the acoustical calibration factors of the set of transducers. 5.2

Reproducibility with Varying Application Conditions

The independency of the calibration of the transducers was quantified with varying application conditions. The range of application conditions is listed in Table 1. 6

MEASUREMENT SETUP

6.1

Hydrodynamic Test Field

The measurements were conducted in the Hydrodynamic Test Field (HTF) of PTB in Braunschweig. The HTF can provide flow in the range of 0.3 m³/h through 2100 m3/h with a pressure range of 2 through 6 bar and a temperature range of 10 °C through 35 °C. Line A in the figure below is designed for diameters between 200 mm and 400 mm. Line B is optimized for diameters between 20 mm and 150 mm. 6.2

Location of Flow Measurement

The Figure 4 shows a principal drawing of the arrangement of the measurement sections (flow from left to right). There are two LDA chambers, one before and one after the location where the ultrasonic transducers were installed. The purpose of this was to quantify the profile change from before and after the measurement location (see section0). For the profile reference, the chamber directly downstream of the location of the transducers was used. Two pairs of transducers were installed simultaneously. Table 1

Range of parameter variations

Parameter

Range

Nominal pipe diameter

50 mm

100 mm

300 mm

Transducer frequency

2 MHz, 4 MHz

2 MHz, 4 MHz

1 MHz, 2 MHz

Fluid temperature

10°C … 35°C

Fluid point velocity

0.5 m/s … 5 m/s

Reynolds number (Re)

30E+03 … 2.5E+06

Characteristics of flow profile

Non-disturbed

5


Figure 3

Cut-away view of PTB’s Hydrodynamic Test Field (HTF)

Installation area for the transducers

Inlet flow section 40D

Measurement section 4 m LDA chamber

Figure 4 6.3


>3D

Outlet 10D LDA chamber

Measurement pipe section

LDA Path Velocity Measurement

Laser Doppler Anemometry (LDA) is a non-invasive optical method for measuring the flow velocity fields [2][3][4][5][6][7]. In this project the LDA was used to measure the flow velocity along the ultrasonic path. The aim was to provide a reference for the fluid mechanical calibration factor. The access to the pipe flow was provided by a glass chamber. LDA uses the Doppler shift in a laser beam to measure the velocity in transparent or semi-transparent fluid flows. The LDA, applied here, crosses two beams of collimated, monochromatic, and coherent laser light in the flow of the fluid being measured. The two coherent beams are obtained by splitting a single beam. A transmitting optics focuses the beams to intersect at their focal points, where they interfere and generate a set of straight fringes. As particles entrained in the fluid pass through the fringes, they reflect light that is then collected by a receiving optics and focused on a photodetector (see Figure 5). 6


Figure 5


Principle of LDA measurement

The reflected light fluctuates in intensity, the frequency of which is equivalent to the Doppler shift between the incident and scattered light, and is thus proportional to the component of particle velocity which lies in the plane of two laser beams. If the sensor is aligned to the flow such that the fringes are perpendicular to the flow direction, the electrical signal from the photo detector will then be proportional to the flow velocity, assuming that the particle are moving with flow velocity. 6.4

Ultrasonic Transducers

The transducer types applied were selected according to the pipe sizes as shown in the figure below. Due to overlapping application ranges it was possible to use two different transducer sizes on each pipe size. The transducers were mounted on the 4m long section of pipe between the two LDA chambers as shown in Figure 6. Four pairs of transducers of the same type were tested simultaneously. Each two of them were installed at the same axial position oriented at +-45° measured along the pipe circumference (see Figure 6). Table 2

Transducer selection for the tests

Nominal diameter

50 mm

100 mm

300 mm

Transducer type

FSP

FSQ

FSP

FSQ

FSP

FSM

Transducer frequency

2 MHz

4 MHz

2 MHz

4 MHz

2 MHz

1 MHz

6.5

Geometry of the Measuring Pipe

The 100 mm pipe and the 300 mm pipe were standard stainless steel welded pipes. The 50 mm pipe was a standard stainless steel seamless pipe. The wall thickness was measured by an ultrasonic probe that was calibrated to the sound speed of the pipe wall. The outer diameter was measured by a pipe circumference tape measure.

7



-45° +45°

Figure 6

6.6

Setup with LDA chamber and 2 different transducer types, each one in 2 planes +-45°, at a pipe 100 mm pipe.

Geometry of the LDA Glass Pipe

The geometry parameters of the glass pipe according to the specification given by the manufacturer are shown in Table 3. Table 3

Geometrical parameter of the LDA glass pipe Type

50 mm

100 mm

300 mm

Uncertainty of inner diameter

+/- 0.05 mm

+/- 0.05 mm

+/- 0.1 mm

Inner diameter

55.0 mm

107.3 mm

299.5 mm

Wall thickness

2.2 mm

3.1 mm

7.0 mm

6.7

Inflow Conditions

To confirm that the flow profile at the location of the ultrasonic transducers was the same as at the LDA chamber, the profile was measured both, at the inlet and at the outlet of the measurement section. The difference between these two measurements was used as a measure for the change of the profile along the measurement section. This investigation was done for a range of flow velocities and temperature. Examples of the profile plots for two of the three measurement sections are shown in Figure 7 and Figure 8.

8



Figure 7

Flow profile at the inlet (left) and the outlet (right) of the measurement section, Pipe nominal diameter 100 mm

Figure 8

Flow profile at the inlet (left) and the outlet (right) of the measurement section, Pipe nominal diameter 300 mm.

The numerical evaluation of the fluid mechanic calibration factor

K Re from the profile

measurement is shown in Table 5 to Table 10. It can be seen that there is a difference between inlet and outlet of up to 1.3 %. There is also a difference between the two planes at +45° and -45° of up to 0.6 %. This shows that the inflow conditions were not completely ideal. The best conditions were achieved at the 50 mm pipe. Table 4

K Re in two planes at the inlet and the outlet of the measurement section, pipe nominal diameter 100 mm

K Re

Inlet

Outlet

Difference

Path 1 -45°

0,924

0,9353

-1,248 %

Path 2 +45°

0,921

0,9330

-1,337 %

Difference

-0,331 %

-0,242 %

Table 5


K Re

Inlet

Outlet

Difference

Path 1 -45°

0,950

0,943

0,789 %

Path 2 +45°

0,956

0,948

0,833 %

Difference

0,587 %

0,543 %

9


Table 6



7

K Re

Inlet

Outlet

Difference

Path 1 -45°

0,934

0,938

-0,342 %

Path 2 +45°

0,935

0,941

-0,559 %

Difference

0,101 %

0,319 %

MEASUREMENT UNCERTAINTY OF THE TRANSFERABILITY

The transferability of the transducer calibration into the field is quantified as the difference ∆V given by Equ. (6). Following ISO/IEC Guide 98-3:2008 [8], the uncertainty of ∆V is 2 2 2   ∂∆V   ∂∆V   u ( ∆V )  u (VREF )  +  u ( K Re )  =   ∂VREF   ∂K Re 

  ∂∆V   ∂∆V u ( A) +  u ( vl _ DUT )  +   ∂A   ∂vl _ DUT 2

2

.

(12)

This results in the following relative uncertainty:

2 2 2 u ( ∆V ) u (VREF ) u ( K Re )2 u ( A )2 u ( vl _ DUT ) = + + + 2 2 2 VREF VREF K Re A2 vl2_ DUT

The uncertainty of the fluid mechanic calibration factor

(13)

K Re , according to Equ. (11),

is given by: 2 u ( v A _ LDA ) u ( vl _ LDA ) u ( K Re ) = + K Re v 2A _ LDA vl2_ LDA 2

2

(14)

The path velocity vl _ DUT is calculated by the meter under test from the acoustic calibration factor

K a and the measured transit time difference ∆t and transit time t fl in

the fluid according to Equ. (1). The relative uncertainty of the path velocity, therefore, is given by the relative uncertainty of the acoustic calibration factor and the relative uncertainty

ur _ transm of the transit time measurement.

2 u ( vl _ DUT ) u ( Ka ) = + ur2_ transm vl2_ DUT K a2 2

(15)

The cross-sectional area of the pipe is calculated from the outer diameter and the wall thickness as

= A

π 4

( Do − 2w )

2

(16)

10


The relative uncertainty of


A thus is

u ( A)  ∂A 1   ∂A 1  2   −4   =  u ( Do )  +  u ( w) =  u ( Do )  +  u ( w )  (17) 2 A   ∂Do A   ∂w A  Do − w   Do − w  2

2

The assumption

2

2

2

Do  w yields:

u ( A)  u ( Do )   w u ( w )  = 2  + 4  2 A Do   Do w   2

2

2

(18)

The total uncertainty of the measurement of the transferability thus is: 2 2 2 2 u ( ∆V ) u (VREF ) u ( v A _ LDA ) u ( vl _ LDA ) = 2 + + 2 VREF VREF v 2A _ LDA vl2_ LDA

 u ( Do )   w u ( w )  u ( K a ) + 2 + ur2_ transm  + 4  + 2 Do   Do w  Ka  2

2

(19)

2

The numerical evaluation of Equ. (19), for the three test locations, is shown in Table 7 through Table 9. The uncertainty components are listed in the left column. The individual relative standard uncertainties are shown in 6th column. The rightmost column shows the uncertainty contributions. The uncertainty of the reference flow rate is equal to the uncertainty of the test facility. The uncertainties of the pipe dimensions are the uncertainties of mechanical measurements. The uncertainty of the path velocity measurement is calculated following the procedure described in [9]. In order to estimate the uncertainty of the mean velocity v A _ LDA measured by LDA, a factor K LDA was calculated by using the mean velocity

K LDA =

v A _ ref in the LDA chamber, calculated from the reference flow rate:

v A _ LDA

(20)

v A _ ref

Ideally, this factor should be independent of the flow profile, and thus also independent of the Reynolds number. Therefore, the uncertainty of v A _ LDA was quantified by the standard deviation of

K LDA with the Reynolds number. At the 50 mm pipe and

the 300 mm pipe, this uncertainty contribution is about 0.3 %. At the 100 mm pipe, however, it is 1 %, which is much more than expected. The uncertainty of the acoustic calibration factor is equal to the uncertainty of the transducer calibration method, which is

u ( K a ) = 0.15 % [10]. The uncertainty of the

time measurement was calculated according to the recommendations given by ISO 12242:2012 [1].

11


Table 7


Uncertainty of the measurement of the transferability, pipe nominal diameter 50 mm

Uncertainty component

Symbol Distribution

u(x i )

Xi u

Reference flow rate Pipe outer diameter

u u

Path velocity of the LDA

u

V.REF

0,010%

1

0,00000001

D.o_MUT

normal

0,1

[mm]

0,166%

2

1,09644E-05

0,331%

w

normal

0,05

[mm]

1,852%

0,18

1,09644E-05

0,331%

v.A_LDA

normal

-

0,378%

1,0

1,4287E-05

0,378%

v.l_LDA

normal

-

0,236%

-1,0

5,59268E-06

0,236%

K. α

normal

-

0,150%

1

0,00000225

0,150%

r_transm

normal

-

0,300%

1

0,000009

0,300% 0,728% 1,457%

u

Acoustic calibration factor

Time measurement Combined uncertainty Expanded uncertainty (k=2)

u

u (x i )/x i

rel. Variance Uncertainty sensitivity contribution factors ci ci² * u(x i )²/x i 2 ci * u (x i )/x i

-

u

Mean velocity of the LDA

rel. standard uncertainty

normal

Pipe thickness

Table 8

Standard Unit uncertainty

U

ΔV

0,010%



Symbol Distribution Standard Unit uncertainty

u (x i )/x i

u(x i )

Xi u

Reference flow rate Pipe outer diameter

u

rel. standard uncertainty


V.REF

normal

-

0,010%

1

0,00000001

D.o_MUT

normal

0,1

[mm]

0,088%

2

3,0671E-06

0,175%

w

normal

0,05

[mm]

1,449%

0,12

3,0671E-06

0,175%

u

Pipe thickness

0,010%


u

v.A_LDA

normal

-

1,008%

1,0

0,000101516

1,008%


u

v.l_LDA

normal

-

0,195%

-1,0

3,78446E-06

0,195%

u



Table 9

u

K. α

normal

0,150%

1

0,00000225

0,150%

r_transm

normal

0,300%

1

0,000009

0,300% 1,108% 2,215%

U

ΔV



Symbol Distribution

u u


u


u


V.REF

-

0,010%

1

0,00000001

0,010%

D.o_MUT

normal

0,1

[mm]

0,031%

2

3,80569E-07

0,062%

w

normal

0,05

[mm]

1,316%

0,05

3,80569E-07

0,062%

v.A_LDA

normal

-

0,289%

1,0

8,35152E-06

0,289%

v.l_LDA

normal

-

0,119%

0,119%

-1,0

1,42571E-06

K. α

normal

0,150%

1

0,00000225

0,150%

r_transm

normal

0,300%

1

0,000009

0,300% 0,467% 0,934%

u


u


normal

u

Pipe thickness

rel. standard uncertainty u (x i )/x i

u(x i )

Xi Reference flow rate Pipe outer diameter

Standard Unit uncertainty

U

ΔV

8

RESULTS

8.1

Reproducibility with Varying Transducer Specimen Under the Same Application Conditions

20 sets of transducers type FSQ (4 MHz) where installed at the 100 mm pipe. The transducers were taken from two different lots. Two transducers were tested simultaneously at the measurement planes +45° and -45°, respectively. 12


Figure 9


Distribution of the acoustical calibration factor over measurement error

Figure 9 shows the acoustic calibration factor found by the in-house calibration plotted over the flow error found at the test location. The average over the whole set of transducers was subtracted in both numbers. The differences between the two lots are clearly visible. The effect of the transducer calibration can be seen when comparing the difference between the two lots with the difference of the error between the two lots. As shown in Table 10, the average difference between the two lots is 1.06 %. The difference between the average measurement errors of the two lots is only -0.18 %. The standard deviation of the acoustical calibration factor is 0.56 %. The standard deviation of the measurement error is only 0.22 %. Table 10

Reproducibility with varying transducer specimen

Average difference between the two lots Standard deviation

8.2

Acoustic calibration factor 1,062% 0,56%

Error -0,18% 0,22%

Reproducibility with Varying Application Conditions

The reproducibility is quantified according to Equ. (6), as the difference between the reference volumetric flow and the flow calculated from the path velocity of the ultrasonic meter by multiplying it with the fluid mechanical calibration factor as determined from the LDA measurement and the cross sectional area of the measuring pipe. The average errors for all Reynolds numbers are shown in Figure 10 through Figure 12. The figures show the error at the two path orientations +45° and -45° as shown in Figure 6 for different temperatures. For the 50 mm pipe and the 100 mm pipe the errors are below the uncertainty estimates shown in Table 7 and in Table 8. The maximum error at the 300 mm pipe shown in Figure 12 is 1.2 %, which is above the uncertainty estimate of 0,9 % shown in Table 9. This can be explained by the 13



non-ideal inflow conditions at this pipe. The LDA chambers at this location were about 5 % smaller than the pipe diameter of the measurement section. Therefore, the flow profile at the location of the ultrasonic transducers could differ from the profile within the LDA chambers. The reduction inside the chambers caused a flattening of the profile. This would lead to an increase in the fluid mechanic calibration factor which explains the errors to be negative.

Figure 10

DN 50: Average error over all Reynolds numbers for transducer types FSQ and FSP at path orientations +-45°

Figure 11

DN 100. Average error over all Reynolds numbers for transducer types FSQ and FSP at path orientations +-45°

14


Figure 12

9


DN 300. Average error over all Reynolds numbers for transducer types FSP and FSM at path orientations +-45°

SUMMARY

This paper has presented a new method for calibrating transducers for Clamp-on ultrasonic flow meters that allows calibrating the transducers independently of the transmitter and without the need for a flow calibration facility. Therefore, the uncertainties caused by non-ideal flow profile conditions and by the pipe geometry of the calibration facility, are excluded from the calibration of the transducers. Another advantage of the independent transducer calibration is the possibility to exchange or recalibrate transducers after the installation of the flow meter in the field without invalidating the calibration of the flow transmitter. The transferability of the transducer calibration to the field was investigated in research cooperation with the PTB at the hydrodynamic test field (HTF) in Braunschweig, which represents the German national standard of liquid flow measurands. The investigations were conducted on three pipes with 50 mm, 100 mm and 300 mm nominal pipe diameter. The errors found at the two smaller pipes where within the uncertainty estimate of the test setup. At the 300 mm pipe the error was 1.3 % while the estimated expanded uncertainty of the test setup was 0.93 %. The reason for this error was that the inflow conditions were not quite ideal. The repeatability of the calibration method with varying transducer specimen was verified at 20 specimens of transducers of the same type and taken from two different lots. It had been shown that the calibration reduced the difference between the two lots significantly. The calibration showed a difference of 1.06 % between the two lots. After the calibration, the difference between the errors of the two lots shown in the flow tests, was reduced to 0.18 %.

15


10


NOTATION

DN HTF LDA PTB A [m²] ALDA [m²]

D, d [m] K Re [-]

K a [-] L, l [m] R, r [m] Re [-] t [s] T [°C] ∆t [s] t fl [s] u [%] U [%] v [m/s] v A [m/s] vl [m/s] V [m³/h] V [m³/h] REF

∆x [m]

Nominal pipe diameter Hydrodynamic Test Field (PTB’s high-accuracy water flow standard facility) Laser Doppler Anemometry Physikalisch-Technische Bundesanstalt Cross sectional area of the pipe Cross sectional area of the LDA glass pipe Diameter Fluid mechanic calibration factor Acoustic calibration factor Length Radius Reynolds number time Temperature Time difference Fluid transit time Uncertainty Expanded uncertainty flow velocity Mean flow velocity Average path velocity Flow rate Reference flow rate Local displacement

11

REFERENCES

[1]

ISO 12242:2012, Measurement of fluid flow in closed conduits — Ultrasonic transit-time meters for liquid

[2]

Büker, O.: Untersuchung zur Darstellung und Weitergabe der Skala „Volumen von Wasser“ mithilfe laseroptischer und konventioneller Messverfahren. Dissertation, Berlin 2010

[3]

Lederer, T.; Wendt, G.; Mathies , N.; Többen, H.; Müller, U.; Dues, M.: Verfahren zur Messung von Geschwindigkeitensverteilungen eines durch einen Rohrquerschnitt strömenden Fluides und Messanordnung zur Durchführung des Verfahrens. Deutsches Patent- und Markenamt, DE 10 2006 039 489 B3, 31. Januar 2008.

[4]

Müller, U.; Adunka, F.; Dues, M.; Guntermann, P.; Rose, J.; Lederer, Th.: Möglichkeiten zur Vor-Ort-Überprüfung von großen Durchflusssensoren. In EuroHeat&Power Jg. 40 (2011), H.6, S. 48-52.

16



[5]

Müller, U.; Dues, M.; Baumann, H.: Vollflächige Erfassung von ungestörten und gestörten Geschwindigkeitensverteilungen in Rohrleitungen mittels der Laser-Doppler-Anemometrie. In Technischs Messen 74 (2007), H.6, S.

[6]

Müller, U.: Richtlinie zur strömungstechnischen Validierung von KalibrierPrüfständen im Rahmen der EN 1434. Hrsg. von AG Laseroptische Strömungsmesstechnik, Berlin 2009.

[7]

Müller, U.; Dues, M.; Baumann, H.: Vollflächige Erfassung von ungestörten und gestörten Geschwindigkeitensverteilungen in Rohrleitungen mittels der Laser-Doppler-Anemometrie. In Technischs Messen 74 (2007), H.6, S. 343.

[8]

ISO/IEC Guide 98-3:2008, Uncertainty of measurement — Part 3: Guide to the expression of uncertainty in measurement (GUM:1995)

[9]

Müller, U.: Messunsicherheitsbudget für LDV-Pfadmessung im ZIM-Projekt Flexim GmbH – PTB Braunschweig. Optolution Messtechnik GmbH, Reinach 2012

[10]

Calibration Certificate for the Reference of the Aperture Calibration System, Flexim GmbH, Technical information.

17

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