potential laser doppler

9th ISFFM Arlington, Virginia, April 14 to 17, 2015

Potential of laser-Doppler velocimetry for applications in theflow measurement industry

Denis F. Hinz and Christian Bombis: Kamstrup A/S, Industrivej 28, Stilling,8660 Skanderborg, Denmark

Corresponding author: [email protected]

AbstractLaser Doppler velocimetry (LDV) is commonly used at academic research institutions and national metrol-ogy institutes. Likewise, the method has potential to support the industrial development of commercialflow meters and the associated calibration and verification facilities. In this paper, we assess the potentialof laser-Doppler velocimetry (LDV) for applications in the flow measurement industry. After reviewing thecurrent capabilities and limitations of LDV with emphasis on industrial applications, we present resultsfrom new research initiatives involving experiments with a commercial LDV system (Optolution/ILA) atKamstrup A/S. In the first part, we show how we use LDV for the quantification of flow profiles and perfor-mance indicators for different flow conditions by discussing two illustrative examples. As a first example,we analyze the swirling flow field generated by the standardized flow disturbance generator defined inEN 14154-3:2005 and OIML R 49-2:2013. In the second example, we study stratification effects in hot-water pipe-flow. In the second part of this paper, we present our efforts to quantify the repeatability ofLDV experiments as a measure for the reliability and robustness of the method. Our results show thatthe repeatability of single-point velocity measurements is around 0.5% in the core region of turbulentflow. Further, we find poor repeatability in regions close to the walls. Our results indicate that the devi-ations through repeatability are higher than those estimated through the corresponding standard errorsof the measurements. This suggests that an additional repeatability contribution should be included inuncertainty budgets of LDV systems.

1 Applications of LDV for pipe-flow analysis

Attractive industrial applications of laser-Doppler velocimetry (LDV) include the analysis of flow profilesin undisturbed and disturbed flow conditions as well as the validation of volume flow-rates. The basicconcepts for such experiments have been established throughout several studies at academic researchlaboratories and national metrology institutes. For example, LDV has been used to measure and verifyvolume flow-rates of undisturbed and disturbed flow profiles [1–3]. Similarly, the potential of LDV to providequantitative measurements has been demonstrated within studies of in-situ calibration methods for largeheat and water meters in operation [4–7] and a bilateral project for air-speed comparisons assessed theprospect of LDV to be used as a transfer standard for comparison between different laboratories [8].

Complimentary to measurements with primary focus on quantitative results, LDV has been used forthe qualitative diagnosis of flow conditions on calibration benches [9–11] as well as the diagnosis of in-stallation effects in pipe flow with gas as working fluid [12, 13] and with water as working fluid [14, 15].Apart from analysis and comparison of flow conditions, the potential of LDV to support the development

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Table 1. Summary of advantages and disadvantages of LDV experiments for flow measurement applications.

Advantages Disadvantages

• Flexible (high accuracy over a wide range offlow velocities)

• Time intensive (several hours for the full gridmeasurement of one velocity component)

• Full 3D flow field information accessible • Expensive equipment (significant investmentrequired)

• High accuracy (low uncertainty) • Expert knowledge required• Non-intrusive • Fluid needs to be transparent• Only one calibration constant (the fringe dis-

tance ∆x )• No time-dependent transient flow fields mea-

surable• Straight-forward traceability to primary stan-

dards• Robustness not very well known (accuracy de-

pendent on many factors)• Potential to be used as a primary reference for

volume flow-rates• Flow seeding required (this becomes problem-

atic/expensive in facilities with a large reservoirvolume)

and optimization of commercial flow meters has been demonstrated through a combination of LDV exper-iments and computational fluid dynamics (CFD) simulations investigating flow patterns in an ultrasonicflow meter with the goal of optimizing the geometric design [16, 17].

1.1 Potential and limitations of LDV for flow verification and type testing

In many countries, commercial flow meters are under legal control and have to undergo verification pro-cesses on flow benches, where the meter reading is verified with a reference measurement that is usuallyobtained with a weighing system or a master meter. The robustness of this verification process is keyto achieving a reliable verification and a high production efficiency wherein severe flow disturbances, forexample at the inlet of the measurement section, might compromise the verification robustness and pro-ductivity. Additionally, it is desirable to establish a common reference regarding flow conditions in differentcalibration facilities. Such a common reference can be achieved with a fully developed flow profile. The di-agnosis of fully developed flow profiles can improve the comparability between different flow benches anddifferent laboratories and eliminate uncertainties in comparisons. Hence, analyzing flow conditions hasprospect for improving the productivity and reliability of industrial verification facilities. In such scenarios,LDV can be used as a practical tool to diagnose and optimize flow conditions.

When using LDV for industrial applications, various difficulties should be considered. The advantagesand disadvantages of LDV experiments for industrial flow measurement applications are summarized inTable 1. The overall accuracy and reliability of LDV experiments depends on many factors including op-erating conditions, software and signal processing parameter choices, the amount of flow seeding, themanual adjustment of optics and traversing mechanics, and the installation of the equipment itself. Yet,very little information regarding the robustness of these settings appears to be available. Further, in indus-trial applications, additional time constraints might compromise measurement accuracy and robustness.In particular, an LDV measurement of a full measurement grid of one velocity component requires severalhours and the achievable standard error depends on the number of samples collected at each mea-surement point. Consequently, the accuracy achievable in academic laboratories and national metrologyinstitutes is often not realizable in industrial settings. Such time constraints might represent one of theprincipal challenges for the LDV method in industrial applications.

In this paper, we discuss examples of how we use LDV for industrial applications at Kamstrup A/S. InSection 2, we present the experimental setup. In Section 3, we discuss examples for the diagnosis and

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(a) (b)

Fig. 1. LDV setup at Kamstrup A/S: Window chamber withD = 20.0 mm glass pipe and LDV probe including laser and receivingoptics. (a) Side view. (b) Top view.

θ = 0◦

θ = 18◦

θ = 36◦

θ = 54◦

θ = 72◦θ = 90

◦

θ = 108◦

θ = 126◦

θ = 144◦

θ = 162◦

−→−→ xy

Fig. 2. Measurement grid for the LDV experiments.

analysis of undisturbed and disturbed flow conditions on industrial verification benches. In Section 4, wepresent our approach to quantifying the repeatability of LDV experiments as a measure for the robustnessof the LDV method itself.

2 Material and Methods

We use a commercial LDV system from ILA/Optolution (Figure 1). Following best-practice guidelines, thesettings and parameters of the LDV system are determined based on the characteristic expected velocityof the experiment. In the present experiments, the amount of data acquired at each measurement point isdetermined by the choice of two experimental constraints: (I) the maximal number of single-point samplesnmax and (II) a timeout tmax for each single-point measurement on the measurement grid. For the presentmeasurements we choose

nmax = 103 and tmax = 60 s. (1)

All experiments are performed on a calibration and verification flow bench with an expanded uncertainty of0.30% (coverage factor k = 2.0) for measurements against weight with test-volumes of 3 liter to 100 literand water as working fluid. The flow bench is equipped with three magneto-inductive (MID) master meters,each one controlling a certain flow-rate interval. The volume flow-rate Q, the water temperature T , andthe pressure p are stabilized through PID controlled feedback loops. We verify the stability of Q, T , andp by logging data from the master meters and the corresponding temperature and pressure sensors,

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y0

-55

0x

-5

0.5

1

0

w=w

vol

0

0.2

0.4

0.6

0.8

1

1.2

(a)

x

-5 0 5

y

-6

-4

-2

0

2

4

6

0

0.2

0.4

0.6

0.8

1

1.2

w/w

vol

(b)

Fig. 3. Diagnosis of a fully developed flow profile in cold-water pipe-flow: (a–b) Representative normalized axial velocity profileof LDV measurements at Re = 4.0 · 104 (turbulent) for water temperature T = 20.0 ◦C and D = 15.0 mm.

where QM is the time-averaged master flow-rate and σQM is the associated standard deviation providinga measure for the stability of the flow-rate. We find that σQM/QM ≈ 0.25% and the master meter signalhas the characteristics of random white noise, which confirms that there is no preferred timescale and nolow-frequency disturbances that might bias the long-time accuracy of LDV measurements.

Axial velocity profiles are obtained through a collection of single-point measurements of the local axialmean velocity w over a measurement grid (Figure 2). To determine w , we use the estimator

w =1

n

n∑i=1

wi , (2)

with wi single-point samples of velocities and n the number of samples. The associated turbulence inten-sity is

Tu =σww, (3)

where

σw =

(1

n − 1

n∑i=1

(wi − w)2)1/2

(4)

is the standard deviation of sampleswi . The mean velocity components u in x direction and v in y directionare determined analogously. To obtain all velocity components, three consecutive LDV measurementsare required.

We conduct measurements with T = 20 ◦C and T = 50 ◦C water temperature and different Reynoldsnumbers Re = wvolD/ν, where wvol = Q/A is the average velocity, D is the pipe diameter, Q is thevolume flow-rate, A = πD2/4 is the cross-sectional area of the pipe, and ν is the kinematic viscosity. Thekinematic viscosity of water depends on the temperature, such that ν = 1.004 · 10−6m2/s for T = 20 ◦Cand ν = 0.554 · 10−6m2/s for T = 50 ◦C.

3 Diagnosis of undisturbed and disturbed flow conditions

In this section, we study the flow profiles of undisturbed and disturbed flow conditions on industrial cali-bration and verification benches. In practice, such measurements are used to verify and improve the flowconditions on production flow benches with the goal to increase the robustness of the verification process

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r=R-1 0 1

w=w

vol

0

0.2

0.4

0.6

0.8

1

1.2 3 = 0/

3 = 18/

3 = 36/

3 = 54/

3 = 72/

3 = 90/

3 = 108/

3 = 126/

3 = 144/

3 = 162/

(a)

−→Gersten andHerwig [18, 19]

Fig. 4. Individual velocity profiles in comparison with theoretical reference: Representative normalized axial velocity profiles ofLDV measurements at Re = 4.0 · 104 (turbulent) for water temperature T = 20.0 ◦ C and D = 15.0 mm in comparison withreference profile of Gersten and Herwig [18, 19]. The corresponding measurement grid is shown in Figure 2.

and to obtain test conditions that are fully reproducible across different flow benches and laboratories. Ad-ditionally, such measurements provide detailed information that may be used to optimize the robustnessof commercial flow meters with respect to flow disturbances due to installation effects.

In particular, a new version of the European norm for pattern approval tests of heat meters EN 1434-4:2007 [20] is currently under development (FprEN 1434-4:2015 (480) [21]) and scheduled to be approvedin 2015. Apart from the disturbance tests in EN 1434-4:2007 [20], the new version FprEN 1434-4:2015(480) [21] also requires evidence for fully developed flow profiles in the test lines of calibration facili-ties to be provided. The goal of proving the presence of fully developed flow profiles is to facilitate thefull reproducibility of verification and calibration results across different flow benches and laboratories.The characteristics of the profiles need to be quantified with suitable performance indicators determinedthrough post-processing of measurement data (for example, LDV data). Performance indicators are usedto assess flow conditions with respect to the profile form, asymmetries in the velocity distribution, and theturbulence intensity with respect to theoretical references. Here, we consider the Profile factor Kp, theasymmetry factor Ka, and the turbulence factor KTu. We provide a detailed definition of the performanceindicators in Section A of the Appendix. The admissible values for the performance indicators are basedon a report on laseroptical flow-diagnostics [22]. Presently, the established approximate guidelines foracceptable performance indicators on flow benches are: [3, 23]

Profile factor (10): 0.8 ≤ Kp ≤ 1.3Asymmetry factor (12) : Ka,max = ±1.0%Turbulence factor (14) : KTu,max = 2.0

Swirl angle (15) : φmax = 2.0◦

(5)

Further, the European norm for pattern approval tests of heat meters EN 1434-4:2007 [20] requiresthe testing of new flow sensors in disturbed flow conditions that are generated with a standardized swirldisturbance generator (Figure 5 (a)). Swirl disturbance generators create flow fields that emulate con-ditions in actual installations. For example, a swirl disturbance generator induces a flow field similar tothe flow field encountered after a double bent out-of-plane that is common in actual installations (see,for example, [11, 13, 24, 25]). While flow disturbance tests in principle do not require detailed knowledgeregarding the disturbed flow itself, LDV provides an opportunity to actually measure the flow fields gen-erated by various standardized disturbance generators. Such LDV measurements enable a detailed andsystematic diagnosis of flow patterns in disturbed flow under different operating conditions and, hence,

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(a)

x

-5 0 5

y

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0.05

0.1

0.15

0.2

|wxy|/wvol

(b)

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0x

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0

0.5

1

w=w

vol

0

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1

1.2

w/wvol

(c)

x

-5 0 5

y

-6

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2

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6

-0.2

-0.1

0

0.1

0.2

u/wvol

(d)

x

-5 0 5

y

-6

-4

-2

0

2

4

6

-0.2

-0.1

0

0.1

0.2

v/wvol

(e)

x

-5 0 5

y

-6

-4

-2

0

2

4

6

0

0.2

0.4

0.6

0.8

1

1.2

w/w

vol

(f)

Fig. 5. Diagnosis of swirl in cold-water pipe-flows through full 3-component measurement of normalized x , y , and z velocitycomponents at Re = 4.0·104 (turbulent) for water temperatureT = 20.0 ◦ C andD = 15.0 mm: (a) StandardizedD = 15.0 mm

swirl disturbance generator according to EN 14154-3:2005 [26] and OIML R 49-2:2013 [27]. (b) Normalized in-plane velocityvectors. (c) Normalized axial velocity profile w/wvol. (d–f) Isolines of normalized velocity in x , y , and z direction.

provide a basis for designing optimized flow meters with increased robustness with respect to disturbedflow conditions. In the following sections, we discuss illustrative examples of undisturbed and disturbedflow profiles and the associated performance indicators.

3.1 Example 1: Measurement of fully developed and swirling cold-water pipe-flow

To demonstrate the diagnosis of flow conditions, we start by measuring a fully developed turbulent cold-water flow profile and an artificially generated swirling velocity field at the same Reynolds number. Themeasurement section is located at a distance of 100D downstream from the inlet of the calibration bench.Without installation of additional disturbance objects, an inlet of 100D results in a fully developed flowprofile, as confirmed in Figure 3. The individual profiles associated with the measurement grid (Figure 2)are shown in Figure 4. The fully-developed symmetric axial velocity profile shows close agreement with thetheoretical profile of Gersten and Herwig [18,19] (Figure 4). Apart from a few exceptions, the performanceindicators associated with the fully developed turbulent flow profile are within the established bounds, asshown in Table 2 (a). The observed deviations are related to weak LDV signals at certain measurementpaths due to spurious optical reflections and disturbances.

The swirling velocity field is generated with a standardized D = 15.0mm swirl disturbance generator(Figure 5 (a), EN 14154-3:2005 [26], and OIML R 49-2:2013 [27]). The swirl generator is installed rightin front of the measurement section to ensure that the flow profile upstream from the swirl disturbancegenerator is fully developed, as confirmed through the previous measurement. For the diagnosis of theswirling velocity field, we perform three consecutive measurements to obtain the x , y , and z components

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r=R-1 0 1

w=w

vol

0

0.2

0.4

0.6

0.8

1

1.2 3 = 0/

3 = 18/

3 = 36/

3 = 54/

3 = 72/

3 = 90/

3 = 108/

3 = 126/

3 = 144/

3 = 162/

(a)


r=R-1 0 1

v=w

vol

-0.2

-0.1

0

0.1

0.23 = 0/

3 = 18/

3 = 36/

3 = 54/

3 = 72/

3 = 90/

3 = 108/

3 = 126/

3 = 144/

3 = 162/

(b)

Fig. 6. Individual velocity profiles with swirl at Re = 4.0 ·104 (turbulent) for water temperature T = 20.0 ◦ C andD = 15.0 mm:(a) Normalized axial velocity profiles in comparison with reference profile of Gersten and Herwig [18, 19]. (b) Profiles of thenormalized y component of the velocity. The corresponding measurement grid is shown in Figure 2.

Table 2. Performance indicators of the velocity profiles determined from the LDV measurements for Re = 4.0 · 104. (a)Fully developed turbulent pipe-flow shown in Figure 3 and Figure 4. (b) Swirling pipe-flow shown in Figure 5 and Figure 6 (a).Performance indicators that do not fulfill the admissible limits (5) are marked in red.

(a) fully de-veloped

T = 20 ◦C

Re = 4.0 · 104

Q = 1.7045 m3/h

θ Kp Ka KTu[deg] [−] [%] [−]

0 ◦ 1.770 0.05 1.45

18 ◦ 1.133 −0.13 1.48

36 ◦ 1.163 −0.25 1.52

54 ◦ 1.568 −1.79 1.43

72 ◦ 1.252 −0.67 1.44

90 ◦ 1.188 −0.24 1.48

108 ◦ 1.168 −0.36 1.46

126 ◦ 1.188 −0.12 1.43

144 ◦ 1.161 0.02 1.47

162 ◦ 1.147 0.09 1.57

(b) swirlT = 20 ◦C

Re = 4.0 · 104

Q = 1.7045 m3/h

θ Kp Ka KTu[deg] [−] [%] [−]

0 ◦ 0.993 −0.28 2.05

18 ◦ 0.434 −1.68 2.23

36 ◦ 0.465 −1.81 2.06

54 ◦ 0.472 −1.56 2.05

72 ◦ 0.489 −1.13 2.05

90 ◦ 0.463 −0.37 2.05

108 ◦ 0.423 0.33 2.05

126 ◦ 0.340 0.41 2.05

144 ◦ 0.315 0.83 2.05

162 ◦ 0.304 1.35 2.05

of the velocity vector.The in-plane velocity vectors associated with the secondary flow are shown in Figure 5 (b), where

the spots with missing velocity vectors correspond to points where the LDV signal is weak due to opticalreflections and disturbances. The associated axial velocity profile is shown in Figure 5 (b) and contourplots of the velocity components are displayed in Figure 5 (d–f). The comparison of the individual axialvelocity profiles with the theoretical reference profile of Gersten and Herwig [18, 19] shows that the axialvelocity profile is not fully developed (Figure 6 (a)). In particular, the velocity profiles are flat in the coreregion and do not exhibit the characteristic peak of a fully developed profile. Hence, the secondary flowalso impacts the axial velocity components, resulting in performance indicators that do not fulfill the re-quirements (5), as displayed in Table 2 (b). Apart from the performance indicators associated with theaxial velocity profiles, we determine a swirl angle (15) of φ = 10.6 ◦, which also exceeds the admissiblemaximum value indicated in (5)4.

Our results show that secondary flow impacts the axial velocity components, resulting in performance

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10

y0

-1010

0x

0

1

1.5

0.5

-10

w=w

vol

0

0.5

1

1.5(a)

x

-10 -5 0 5 10

y

-10

-5

0

5

10

0

0.5

1

1.5

w/w

vol

(b)

10

y0

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0x

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vol

0

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1.5

2

(c)

x

-10 -5 0 5 10y

-10

-5

0

5

10

0

0.5

1

1.5

2

w/w

vol

(d)

Fig. 7. Diagnosis of stratification effects in hot water pipe-flows: Representative normalized axial velocity profiles of LDV mea-surements at Re = 4.0 · 104 (turbulent) and Re = 1.0 · 103 (laminar) for water temperature T = 50.0 ◦C and D = 20.0 mm.(a–b) Normalized axial velocity profile w/wvol for Re = 4.0 · 104 (turbulent). (c–d) Normalized axial velocity profile w/wvol forRe = 1.0 · 103 (laminar).

indicators that do not fulfill the established criteria. The diagnosis of secondary flow has considerablepotential to improve the flow conditions on verification benches and to achieve meaningful interpretationof performance test results. Additionally, the full repeatability of test results across different test facilitiescan only be guaranteed with identical flow conditions. On the other side, water, heat,and cooling metersmight be exposed to similar disturbances in realistic installations and swirl disturbance generators providea realistic simulation of commonly encountered installation effects. Consequently, achieving robustnesswith respect to disturbed flow conditions is a desirable design objective that can only be achieved withdetailed flow diagnosis using spatially resolved flow measurements. Our results show that such diagnosiscan be achieved with LDV measurements.

3.2 Example 2: Stratification effects in hot-water flow

As an example for the diagnosis of symmetric and non-symmetric flow profiles, we perform LDV mea-surements of turbulent and laminar hot-water flows in horizontal pipes without insulation. The inlet watertemperature is T = 50 ◦C and we measure cases with Reynolds numbers Re = 4.0 · 104 (turbulent flow)and Re = 1.0 · 103 (laminar flow). The measurement section for the LDV experiments is located at 100Ddownstream from the inlet of the calibration bench. The flow profiles and contour plots for both Reynoldsnumbers are shown in Figure 7.

The turbulent flow exhibits a fully-developed symmetric axial velocity profile (Figure 7 (a–b)) that showsclose agreement with the theoretical profile of Gersten and Herwig [18, 19] (Figure 8 (a)). Apart from oneexception, the performance indicators associated with the turbulent flow profile are within the establishedbounds, as shown in Table 3 (a). The profile at 0 ◦ exceeds the established limit of the asymmetry fac-

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r=R-1 0 1

w=w

vol

0

0.5

1

1.53 = 0/

3 = 18/

3 = 36/

3 = 54/

3 = 72/

3 = 90/

3 = 108/

3 = 126/

3 = 144/

3 = 162/

(a)


r=R-1 0 1

w=w

vol

0

0.5

1

1.5

23 = 0/

3 = 18/

3 = 36/

3 = 54/

3 = 72/

3 = 90/

3 = 108/

3 = 126/

3 = 144/

3 = 162/

(b)

−→Poiseuillle

Fig. 8. Individual velocity profiles in comparison with theoretical references: Representative normalized axial velocity profilesof LDV measurements at Re = 4.0 · 104 (turbulent) and Re = 1.0 · 103 (laminar) for water temperature T = 50.0 ◦ C andD = 20.0 mm. (a) Re = 4.0 · 104 (turbulent) in comparison with the reference profile of Gersten and Herwig [18, 19]. (b)Re = 1.0 · 103 (laminar) in comparison with the Poiseuille reference profile. The corresponding measurement grid is shown inFigure 2.

tor (5)2. However, this deviation is related to weak LDV signals in the 0 ◦ measurement path due tospurious optical reflections and disturbances.

In contrast to the turbulent profile, the laminar profile exhibits a strong displacement of the peak ve-locity towards the top of the cross-section of the pipe (Figure 7 (c–d)). Visual inspection of the individ-ual axial velocity profiles (Figure 8 (b)) confirms a notable deviation from the ideal Poiseuille profile forlaminar flow. The associated performance indicators are outside the established bounds, as shown inTable 3 (b). The physical mechanism for this stratification is a combination of buoyancy effects and thetemperature dependency of the viscosity of water. The heat loss of the uninsulated pipes results in anon-symmetric temperature distribution, where water with higher temperatures accumulates at the top ofthe pipe, resulting in a local reduction in water viscosity. The driving pressure gradient along the pipeaxis is approximately constant over the pipe cross-section, such that the regions with lower viscosity mustdevelop larger gradients in the velocity profile to achieve equilibrium conditions. The combination of thesemechanisms results in the displacement of the peak velocity towards the top of the pipe. This mecha-nism only works under laminar flow conditions, since turbulent flows induce instabilities that break up thelaminar stratification, ultimately resulting in turbulent mixing and symmetric velocity profiles.

Both laminar and turbulent flow conditions are commonly encountered in the verification and calibra-tion of heat meters, where the laminar case corresponds to the low flow-rate verification point and theturbulent case corresponds to the intermediate and high flow rate verification point. Hence, to be able toreach meaningful conclusions from verification and calibration tests, it is important to know under whichconditions such stratification effects may emerge in the corresponding verification facilities.

In operating installations, pipes are usually insulated, which makes the stratification effect less pro-nounced. However, in the low flow-rate limit, it is reasonable to expect such stratification effects for heatmeters in operation. Consequently, assuring robustness of heat meters with respect to such effects is animportant design objective and LDV experiments similar to the ones demonstrated here have significantpotential to assist the meter design process.

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Table 3. Performance indicators of the velocity profiles determined from the LDV measurements for Re = 1.0 · 103 andRe = 4.0 · 104 shown in Figure 8. Performance indicators that do not fulfill the admissible limits (5) are marked in red.

(a) turbulentT = 50 ◦C

Re = 4.0 · 104

Q = 1.2530 m3/h

θ Kp Ka KTu[deg] [−] [%] [−]

0 ◦ 1.274 1.23 1.18

18 ◦ 1.117 0.32 1.29

36 ◦ 1.163 0.28 1.20

54 ◦ 1.168 0.10 1.22

72 ◦ 1.169 −0.09 1.21

90 ◦ 1.189 −0.14 1.18

108 ◦ 1.194 −0.32 1.18

126 ◦ 1.182 −0.43 1.16

144 ◦ 1.179 −0.54 1.19

162 ◦ 1.151 −0.39 1.19

(b) laminarT = 50 ◦C

Re = 1.0 · 103

Q = 0.0313 m3/h

θ Kp Ka KTu[deg] [−] [%] [−]

0 ◦ 0.571 0.99 N/A

18 ◦ 0.526 4.26 N/A

36 ◦ 0.649 7.08 N/A

54 ◦ 0.490 10.10 N/A

72 ◦ 0.760 4.68 N/A

90 ◦ 0.406 10.66 N/A

108 ◦ 0.544 13.34 N/A

126 ◦ 0.583 10.31 N/A

144 ◦ 0.635 7.85 N/A

162 ◦ 0.556 3.14 N/A

4 Establishing the repeatability of LDV experiments

Whereas the previous examples demonstrated the potential of LDV to be used for applied flow diagnostics,this example of LDV studies at Kamstrup A/S is targeted at achieving a more detailed knowledge on themethod and the measurement procedure itself.

The combined uncertainty of single-point LDV measurements as well as an estimated volume flow-rate Qm has been established through detailed uncertainty budgets that account for various systematicand random uncertainty contributions [1, 3, 4, 10, 28]. These uncertainty analyses are commonly basedon the GUM (Guide to the Expression of Uncertainty in Measurement [29]) approach, also referred toas “bottom-up” approach, that amounts to estimating the combined uncertainty from variances associ-ated with the input parameters of the underlying mathematical model. Complementary to the “bottom-up”approach, experimental uncertainty evaluation amounts to conducting “top-down” uncertainty estimatesthrough repeatability and reproducibility studies (cf., e.g., ISO 21748 [30]). However, such “top-down”repeatability studies of LDV experiments appear to be unavailable and uncertainty budgets of LDV sys-tems [1, 3, 4, 10, 28] do not explicitly account for the notion of repeatability relating to the entire measure-ment process rather than the uncertainty of an individual result. Yet, the overall repeatability as a measureof the consistency of LDV systems to achieve identical results across repeated experiments are key toachieve a reliable interpretation of experimental data. This is particularly important for the mentionedmetrology applications, where qualitative and quantitative information is sought.

As a step towards a thorough experimental uncertainty analysis, we focus on quantifying the repeata-bility of LDV experiments. To this end, we conduct a series of LDV experiments for pipe-flow analysis inindustrial applications. As a field test with realistic conditions, we choose the representative example ofmeasurements for the diagnosis of flow conditions in flow benches used for the calibration and verificationof water, heat, and cooling meters. Using this experimental setup, we quantify the overall repeatability ofLDV measurements through various consecutive measurements under repeatability conditions [29, 30].Following the GUM [29], we define repeatability as the “closeness of the agreement between the resultsof successive measurements of the same measurand carried out under the same conditions of measure-ment”. We quantify repeatability in terms of the dispersion characteristics of the results obtained fromLDV experiments under repeatability conditions. In the following, measurand is used interchangeably

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with quantity.We note that experiments under reproducibility conditions are likely to provide additional experimental

evidence for a thorough “top-down” uncertainty analysis, but are beyond the scope of this paper. However,performing reproducibility experiments in addition to this repeatability study might well be worth the effortin future investigations.

We determine the repeatability of local quantities and global quantities. For the local quantities, wefocus on single-point measurements of the local axial mean velocity (2). Conversely, global quantitiesare inferred from the local quantities of the LDV experiments through additional post-processing steps.For example, an integration of the individual point measurements w on a measurement grid in polarcoordinates yields the volume flow-rate

Qm =

2π∫0

R∫0

wr drdϕ. (6)

Our choice of measurement grid contains Nθ = 10 individual (2D) profiles through radial paths. Thecounterpart of (6) for one measurement path is

Qi = 2π

R∫0

wr dr . (7)

In view of (7), the overall volume flow-rate (6) can be estimated through

Qm =1

Nθ

∑Qi , (8)

where the integral in (7) needs to be approximated with a suitable numerical integration scheme. Here,we use a second-order Simpson scheme and no additional wall approximation or profile reconstruction.

All repeatabilities are quantified as standard deviations of consecutive experiments. In particular, σr ,wdenotes the repeatability standard deviations of single point measurements of w and σr ,Qm denotes therepeatability standard deviation of the volume flow-rate (8). Notice that all standard deviations are definedanalogously to (4) and no coverage factors are applied to the presented standard deviation.

4.1 Repeatability of local single-point measurements

In Figure 9, we show the single-point repeatability standard deviations of experiments with pipe diameterD = 20mm and Reynolds number Re = 4.0 · 104. Panel (a) shows repeated measurements of arepresentative velocity profile (θ = 72◦). The associated repeatability standard deviation of this profile isindicated through the shaded area. Panel (b) show the repeatability standard deviations for all profiles,where the different markers correspond to different profiles in the measurement cross-section. Notice thatincreasing repeatability standard deviations in panel (b) correspond to deceasing repeatability.

The local repeatability standard deviations are approximately constant within the core region −0.8 ≤r/R ≤ 0.8, where we find σr ,w ≈ 0.5% (Figure 9 (b)). However, the repeatability deteriorates towards theouter regions, and measurements close to the wall are de-facto unrepeatable with repeatability standarddeviations around 10–100% for σr ,w (not shown due to the axis ranges of Figure 9 (c)).

11


r/R-1 -0.5 0 0.5 1

w/w

vol

0

0.5

1

1.5

exp. 01

exp. 02

exp. 03

exp. 04

exp. 05

exp. 06

exp. 07

exp. 08

exp. 09

(a)

r=R-1 -0.5 0 0.5 1

w=w

vol

0

0.5

1

1.5

Gersten & Herwigwavg=wvol

wavg=wvol ' <r;w

optical disturbances →

r/R-1 -0.5 0 0.5 1

σr,w/w

avg[%

]

0

0.5

1

1.5

2

2.5

3θ = 0◦

θ = 18◦

θ = 36◦

θ = 54◦

θ = 72◦

θ = 90◦

θ = 108◦

θ = 126◦

θ = 144◦

θ = 162◦

(b)

Fig. 9. Local repeatability of LDV experiments: (a) Normalized velocity w/wvol for a representative profile (θ = 72◦), (b)repeatability standard deviation σr ,w (in percentage of w/wvol) for all profiles. In panel (a), the markers correspond to n = 9

repeated measurements of the same profile, the red line is the average of repeated measurements, and the shaded area indicatesthe repeatability standard deviation. In panel (b), the markers correspond to repeatability standard deviations of different profiles.

Table 4. Repeatability of Qm.

Re Q Qm,avg σr ,Qm/Qm,avg

[−] [m3/h] [m3/h] [%]

4.0 · 104 2.2728 2.2476 0.59 %

4.2 Repeatability of the volume flow-rate

In Table 4, we show the overall volume flow flow-rate (8), where Qm,avg is the average of repeated ex-periments. We find a repeatability standard deviation of Qm around 0.59%. In conclusion, the globalrepeatability of Qm is of similar magnitude as the repeatability of individual point measurements. Thisindicates that individual points with poor repeatabilities appear to have no significant impact on the re-peatability of the volume flow-rate.

5 Summary and conclusions

In the first part, we studied the potential of LDV to provide practical diagnosis of flow conditions in cali-bration and verification benches. We discussed examples of disturbed and undisturbed flow conditionsand the associated performance indicators. Our results confirm that artificially generated swirling velocityfields provide performance indicators that are outside the established guidelines. Similarly, temperaturestratification effects also lead to strongly disturbed flow profiles that do not pass the established guidelinesfor admissible values of pipe-flow performance indicators. We discussed the potential use of such LDVmeasurements for the optimization of flow benches and for supporting the optimization of commercialwater, heat, and cooling meters.

In the second part, we studied the repeatability of LDV experiments for the diagnosis of flow condi-tions in calibration benches. Our results show that the repeatability standard deviations of single-pointmeasurements of the mean velocity w is around 0.5% in the core region. Further, we find poor repeata-bility in regions close to the walls. The volume flow-rate Qm is found to exhibit a repeatability standarddeviation of 0.59%. Hence, the repeatability standard deviations of Qm and w are of similar magnitude,suggesting that individual points with poor repeatabilities in w (for example points close to the wall) donot significantly impact the overall repeatability of the volume flow-rate.

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The determined repeatabilities provide experimental evidence and practical guidelines for the inter-pretation of LDV experiments. As discussed in ISO 21748 [30], different notions of how to account forrepeatability and reproducibility in uncertainty budgets exist. For example, the GUM approach allowsfor a separate repeatability and reproducibility contribution to the combined uncertainty, whereas ISO21748 [30] suggests that experimentally observed repeatability and reproducibility variance is a directestimate of the same overall uncertainty. Alternatively, experimental uncertainty evaluation through re-peatability and reproducibility studies may be used to verify the underlying mathematical models anddetect incomplete or unknown effects.

LDV uncertainty budgets [1, 3, 4, 10, 28] estimated with the GUM approach suggest that one of thelargest contributions to the combined uncertainty is the standard error

σw =Tu√nw (9)

associated with the turbulence intensity and the number of single-point samples. Since this contributionis stochastic, it is reasonable to assume that repeatability is most influenced by the combination of ex-perimental constraints (1) and flow conditions (i.e. turbulence intensity). Our results indicate that therepeatability standard deviations are higher than those expected through estimating the correspondingstandard errors (9). This suggests that an additional repeatability contribution should be included in un-certainty budgets of LDV experiments.

A Appendix

A.1 Profile factor

Following Yeh and Mattingly [14], the dimensionless profile factor Kp is defined as

Kp =Kp,mKp,s

, (10)

with

Kp,m =1

wvolD

R∫0

(wm − w) dr and Kp,s =1

wvolD

R∫0

(wm,s − ws) dr , (11)

where wm = w(r = 0) is the velocity at the pipe center, wm,s is the velocity of the norm profile atthe pipe center, and ws is the velocity of the norm profile. The profile factor is a measure for peakness(Kp > 1) or flatness (Kp < 1) of measured velocity profiles with respect to standard profiles such asHagen–Pouiseuille for laminar flow or Gersten and Herwig [18, 19] for turbulent flow.

A.2 Asymmetry factor

Following Yeh and Mattingly [14], the asymmetry factor

Ka =1

D

R∫0

rw dr

R∫0

w dr

(12)

quantifies the relative radial displacement of the center of gravity of the area under the flow profile withrespect to the pipe center.

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A.3 Turbulence factor

Each LDV point measurement is a collection of a large number of bursts resulting in a histogram (orprobability density function) for the axial velocity component. The level of dispersion (i.e. the standarddeviation) of this histogram quantifies the turbulence intensity (3). As discussed by Durst et al. [31] andgeneralized by Pashtrapanska [32], the turbulence intensity (3) in the core region −0.2 ≤ r/R ≤ 0.2 canbe estimated as

Tus = 0.13

(Rewm,swvol

)−1/8(13)

for Rewm,swvol≥ 4500. The turbulence factor KTu is defined as

KTu =TumaxTus

, (14)

where Tumax is the maximum of (3) in the core region −0.2 ≤ r/R ≤ 0.2.

A.4 Swirl angle

Following Yeh and Mattingly [15], the level of swirl can be measured quantitatively quantitative throughthe maximal swirl angle

φ = arctan

(|v |maxwvol

), (15)

where |v |max is the magnitude of the maximal tangential mean velocity. Geometrically, the swirl angle (15)is the angle between the ideal velocity vector and the actual velocity vector with swirl.

References[1] D. Bublitz, S. Frank, and H. E. Siekmann, “Einsatz eines Laser-Doppler-Velozimeters als Volumenstrom-Messgerat hoher

Genauigkeit,” EuroHeat&Power, vol. 25, pp. 588–598, 1996.[2] S. Frank, C. Heilmann, and H. E. Siekmann, “Point-velocity methods for flow-rate measurements in asymmetric pipe flow,”

Flow Measurement and Instrumentation, vol. 7, pp. 201–209, 1996.[3] O. Buker, Untersuchungen zur Darstellung und Weitergabe der Skala ,Volumen von Wasser‘ mithilfe laseroptischer und

konventioneller Messverfahren. PhD thesis, 2010.[4] A. Drysdale, J. Frederiksen, and M. A. Rasmussen, “New on-site calibration technique for large flow meters using laser

doppler velocimetry,” in Flowmeko 2005, no. June, pp. 1–12, 2005.[5] P. Guntermann, J. Rose, T. Lederer, M. Dues, U. Muller, and A. Duckwe, “Vorort-Untersuchung von Warmemengenzahlern

im Betrieb,” EuroHeat&Power, vol. 39, pp. 44–47, 2010.[6] U. Muller, F. Adunka, M. Dues, P. Guntermann, J. Rose, and T. Lederer, “Moglichkeiten zur Vor-Ort-Uberprufung von großen

Durchflusssensoren,” EuroHeat&Power, vol. 40, pp. 52–55, 2011.[7] U. Muller, F. Adunka, M. Dues, P. Guntermann, J. Rose, and T. Lederer, “Notwendigkeiten der Vor-Ort-Uberprufung von

großen Durchfluss-Sensoren,” EuroHeat&Power, vol. 40, pp. 48–52, 2011.[8] H. Muller, “EURAMET Project No . 827 LDA-based intercomparison of anemometers,” tech. rep., 2012.[9] U. Muller, M. Dues, and H. Baumann, “Vollflachige Erfassung von ungestorten und gestorten Geschwindigkeitsverteilungen

in Rohrleitungen mittels der Laser-Doppler-Velocimetrie,” Technisches Messen, vol. 74, pp. 342–352, Jan. 2007.[10] T. Eichler and K. Tawackolian, “Sromungsanalyse mit zwei Messtechniken und Simulationen,” EuroHeat&Power, vol. 39,

pp. 38–44, 2010.[11] B. Mickan, G. Wendt, R. Kramer, and D. Dopheide, “Systematic investigation of pipe flows and installation effects using

laser Doppler anemometry—Part II. The effect of disturbed flow profiles on turbine gas meters—a describing empiricalmodel,” Flow Measurement and Instrumentation, vol. 7, pp. 151–160, 1996.

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[12] B. Mickan, G. Wendt, R. Kramer, and D. Dopheide, “Systematic investigation of flow profiles in pipes and their effects ongas meter behaviour,” Measurement, vol. 22, pp. 1–14, 1997.

[13] C. Wendt, B. Mickan, R. Kramer, and D. Dopheide, “Systematic investigation of pipe flows and installation effects usinglaser Doppler anemometry—Part I. Profile measurements downstream of several pipe configurations and flow conditioners,”Flow Measurement and Instrumentation, vol. 7, pp. 141–149, 1996.

[14] T. T. Yeh and G. E. Mattingly, “Pipeflow downstream of a reducer and its effects on flowmeters,” Flow Measurement andInstrumentation, vol. 5, no. 3, pp. 181–187, 1994.

[15] T. T. Yeh and G. E. Mattingly, “Laser Doppler velcimeter studies of the pipeflow produced by a generic header,” NISTTechnical Note 1409, 1995.

[16] N. C. Temperley, M. Behnia, and A. F. Collings, “Flow patterns in an ultrasonic liquid flow meter,” Flow Measurement andInstrumentation, vol. 11, pp. 11–18, Mar. 2000.

[17] N. C. Temperley, M. Behnia, and A. F. Collings, “Application of computational fluid dynamics and laser Doppler velocimetryto liquid ultrasonic flow meter design,” Flow Measurement and Instrumentation, vol. 15, pp. 155–165, June 2004.

[18] K. Gersten and H. Herwig, Stromungsmechanik. 1992.

[19] K. Gersten, “Fully developed turbulent pipe flow,” in Fluid Mechanics of Flow Metering (W. Menzenkirch, ed.), pp. 1–22,Springer, second ed., 2005.

[20] EN 1434-4:2007 Heat meters – Part 4: Pattern approval tests. 2007.

[21] FprEN 1434-4:2015 Heat Meters – Part 4: Pattern approval tests. 2015.

[22] Guidelines for the fluid mechanical validation of calibration test-benches in the framework of EN 1434. 2009.

[23] U. Muller and M. Dues, “Measurements of flow profiles and characteristic numbers for flow conditions on test benches,” inMeeting of WEL MEC WG 11 - Sub working group water and heat, 2007.

[24] A. Hilgenstock and R. Ernst, “Analysis of installation effects by means of computational fluid dynamics—CFD vs experi-ments?,” Flow Measurement and Instrumentation, vol. 7, no. 314, pp. 161–171, 1996.

[25] K. Tawackolian, Fluiddynamische Auswirkungen auf die Messabweichung von Ultraschall-Durchflussmessgeraten. PhDthesis, 2013.

[26] EN 1415-3:2005+A2:2011: Water meters – Part 3: Test methods and equipment. 3rd ed., 2011.

[27] International Recommendation OIML R 49-2:2013. 2013.

[28] S. Frank and H. E. Siekmann, “Flow-rate measurements in asymmetric waterflows by means of laser-Doppler-velocimetry,”in Proceedings of FLOMEKO ’96, Beijing, China, 1996, 1996.

[29] JGCM 100:2008 Evaluation of measurement data — Guide to the expression of uncertainty in measurement. first ed.,2008.

[30] ISO 21748: Guidance for the use of repeatability, reproducibility and trueness estimates in measurement uncertainty esti-mation. 2010.

[31] F. Durst, M. Fischer, J. Jovanovic, and H. Kikura, “Methods to set up and investigate low Reynolds number, fully developedturbulent plane channel flows,” Journal of Fluids Engineering, vol. 120, pp. 496–503, 1998.

[32] M. N. Pashtrapanska, Experimentelle Untersuchung der turbulenten Rohrstromungen mit abklingender Drallkomponente.PhD thesis, Erlangen-Nurnberg, 2004.

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potential laser doppler

Documents

pipe flow

applications of ldv

potential of ldv

different flow conditions

disturbed flow conditions

comparison of flow conditions

limitations of ldv

disturbed flow profiles