608532 - hyperbole - deliverable d2

Deliverable D2.3 Documentation of proposed transposition procedure Project number 608532

Project title HYPERBOLE ‐ HYdropower plants PERformance and flexiBle Operation towards Lean integration of new renewable Energies

Call (part) identifier FP7‐ENERGY‐2013‐1

Funding scheme Collaborative project

Date February 20, 2017

Partner Author P2 – GE Renewable Energy

Name e‐mail

Florian DUPARCHY [email protected]

Deliverable Number Deliverable 2.3

FP7‐ENERGY‐2013‐1 – N° 608532 – HYPERBOLE Deliverable 4.2

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Documentation of proposed

transposition procedure

Contents 1 General data ...................................................................................................................................... 4

1.1 Context and objective ................................................................................................................ 4

1.2 Reference documents ................................................................................................................ 4

2 Proposed transposition procedure .................................................................................................... 4

3 Reduced‐scale physical model test.................................................................................................... 5

3.1 Instrumentation ......................................................................................................................... 5

3.2 Results ....................................................................................................................................... 7

3.2.1 Dynamic strain ................................................................................................................... 7

3.2.2 Frequency signature .......................................................................................................... 8

4 Full‐scale turbine test ...................................................................................................................... 11

4.1 Instrumentation ....................................................................................................................... 11

4.2 Results ..................................................................................................................................... 12

4.2.1 Dynamic strain ................................................................................................................. 12

4.2.2 Frequency signature ........................................................................................................ 13

5 Validation of the transposition procedure ...................................................................................... 16

5.1 Peak‐to‐peak strain divided by net head ................................................................................. 16

5.2 Peak‐to‐peak strain divided by U²/2g ...................................................................................... 17

5.3 Frequency spectra ................................................................................................................... 18

5.3.1 Deep part load ................................................................................................................. 19

5.3.2 Part load........................................................................................................................... 21

5.3.3 Nominal load.................................................................................................................... 23

5.3.4 Full load ........................................................................................................................... 25

6 Summary and discussion ................................................................................................................. 27

6.1 Summary .................................................................................................................................. 27

6.2 Discussion ................................................................................................................................ 30

6.3 Potential impacts of the presented results ............................................................................. 30


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1 General data

1.1 Context and objective

Mechanical measurements using strain gauges directly located on the runner have been performed on

the full‐scale hydropower plant unit of the Francis turbine test case in November 2016. These

measurements give the opportunity to compare the mechanical behaviour of the full‐scale runner to

the reduced‐scale runner previously tested at the Ecole Polytechnique Fédérale de Lausanne (EPFL)

Laboratory for Hydraulic Machines (LMH).

The objective of this document is to propose a procedure to transpose the mechanical strain measured

on the reduced‐scale model to the full‐scale runner.

1.2 Reference documents

[Ref. 1] Hyperbole Deliverable D2.1. Steady state and modal analysis.

[Ref. 2] Hyperbole Deliverable D2.2. Calculation report. Dynamic behaviour of the Francis runner under

full load, part load and deep part load.

[Ref. 3] Hyperbole Deliverable D1.4. Report of Experimental Hydro‐Mechanical test on Model Turbine.

2 Proposed transposition procedure

The main characteristics of both the reduced‐scale physical model and the full‐scale turbine are

summarized in the following table.

Table 1: Main characteristics of the reduced‐scale physical model and of the full‐scale industrial turbine

Parameter Symbol Unit Reduced‐scale model Full scale turbine

Runner outlet diameter

Øs [mm] 350 5400

Net head for the tests

Hn [mWC] 26.8 178.5

Material Young’s modulus

E [MPa] 205000 205000

nED tested nED [‐] 0.268 0.288 0.317 0.277

Nominal QED at given nED

QED,nom [‐] ≈ 0.2 ≈ 0.2 ≈ 0.2 ≈ 0.2

Rotational speed n [rpm] 744 800 880 128.6

Rotational frequency

f0 [Hz] 12.4 13.3 14.7 2.14

Tangential velocity at the low pressure diameter of the runner

U [m/s] 13.63 14.66 16.13 36.36

Grooves for strain gauges

Yes, around 0.28 mm deep No, directly on surface

Gravity g [m/s²] 9.8063 9.8096


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For the transposition of the dynamic strain from the reduced‐scale model to the full‐scale turbine, two

approaches are proposed:

The first one is based on the ratio of the net head, therefore:

. .

with: ε: dynamic strain

Hn: net head E: Young’s modulus

M subscript: reduced‐scale model

P subscript: full‐scale turbine

The second one is based on the ratio of the kinetic energy at runner low pressure diameter of the runner (U²/2g):

.

2

.

2

with: ε: dynamic strain

U: tangential velocity at the low‐pressure diameter of the runner

E: Young’s modulus g: gravity

M subscript: reduced‐scale model

P subscript: full‐scale turbine

3 Reduced‐scale physical model test

3.1 Instrumentation

The runner used for the reduced‐scale physical model tests was equipped with 24 strain gauges

distributed on 3 different blades, namely blades 5, 9 and 13, as shown in Figure 1.

Figure 1: Location of the strain gauges on the reduced‐scale physical model.

In order to reduce the impact on the cavitation and the hydraulic performances, the strain gauges were

not stuck directly on the surface of the blades but at the bottom of grooves. Consequently, the strain at

the surface of the blade was not directly measured. This can have a significant impact on the

transposition of the results between the reduced‐scale model and the full‐scale runner.


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In addition, the geometry of the crown and the band of the reduced‐scale model is different from the

original full‐scale runner, outside of the water passage. These differences are shown in Figure 2. They

can affect the mechanical behaviour of the runner and affect the quality of the transposition.

Figure 2: Differences in term of geometry between the reduced‐scale model runner and the full‐scale prototype runner

According to the conclusions of the deliverable D2.2 [Ref. 2], the strain gauges of the blade 13 are the

most reliable ones. The study is therefore focused on these strain gauges.

The following table summarizes the location of the strain gauges. S is the distance measured between

the trailing edge of the blade and the centre of the strain gauge. W is measured between the fillet radius

and the centre of the strain gauge. The values are given at the prototype scale in order to be compared

to the location of the strain gauge on the full‐scale runner (see § 4).

Table 2: Reduced‐scale runner. Location of the strain gauges (prototype scale)

S (distance to trailing edge)

W (distance to fillet radius)

Strain gauge ‐ model Channel name [mm] [mm]

Crown

B13‐01‐PS‐CR‐TE B13‐SG1 48 120

B13‐03‐PS‐CR‐TE B13‐SG2 131 118

B13‐05‐PS‐CR‐TE B13‐SG3 215 116

B13‐07‐PS‐CR‐TE B13‐SG4 15.9 268

B13‐09‐PS‐CR‐TE B13‐SG5 16.3 422

Band

B13‐11‐PS‐BD‐TE B13‐SG6 76.8 66

B13‐13‐PS‐BD‐TE B13‐SG7 79 200

B13‐15‐PS‐BD‐TE B13‐SG8 154 65.6


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3.2 Results

3.2.1 Dynamic strain As discussed in the Deliverable D2.2 [Ref. 2], the results are post‐processed as follow:

‐ The first five harmonics of the rotational frequency are subtracted since they have been identified to be not generated by hydraulic phenomena;

‐ A 600 Hz low pass filter is applied.

The results for nED = 0.268 and nED = 0.288 in cavitation condition (σ‐plant) are presented because these

nED‐values are the closest to the one tested on the full‐scale‐turbine. These graphs show a significant

strain elevation at full load, around QED/QED, nom=1.3 and another at part load, for 0.3 < QED/QED, nom < 0.7.

Note: a nED‐value closer to the one available during the site test has also been tested on the test rig

during a third measurement campaign. However, during this campaign, most of the sensors have been

lost and all the validation procedure must be repeated before using these measurements, as it has been

done in Deliverable D1.4 [Ref. 3]. Consequently, these results are not used in this report.

Figure 3: Reduced‐scale model. Dynamic strain on blade 13 as a function of the discharge factor. nED = 0.268


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Figure 4: R Reduced‐scale model. Dynamic strain on blade 13. nED = 0.288

3.2.2 Frequency signature In order to identify the dynamic phenomena that solicit the runner, four frequency spectra are plotted

hereinafter, with three different frequency scales, for QED/QED, nom = 0.25, 0.55, 1.00 and 1.32 with nED =

0.288. The spectra are presented for the raw signal without post‐treatment. Therefore, the harmonics

of the rotational frequency are included with the spectra.

Figure 5 is plotted within the range 0‐150*f0, where f0 is the rotational frequency of the runner. It gives

a full overview of the phenomena contained in the spectra without filter and serves as a reference for

the comparison with the prototype measurement. It can be seen that there is no significant phenomena

above 30*f0.

In Figure 6 (zoom in the range 0‐30*f0), a peak at 20*f0 can be seen in the 4 spectra, which corresponds

to the guide vane passing frequency. In

Figure 7, which is focused on the low frequencies range (zoom in the range 0‐5*f0), the following

observations can be made:

‐ There is no distinctive phenomenon at QED, nom and QED/QED, nom=0.25; ‐ A peak at 0.65*f0 is observed at QED/QED, nom=0.55, which corresponds to the frequency signature

of the convective term of the part load helical vortex rope seen from the rotating frame. A second harmonic is also observed;

‐ A peak at 0.23*f0 with several harmonics is observed at QED/QED, nom=1.32. It corresponds to the effect of the pressure surge observed in presence of the axial vortex rope;

‐ Several peaks at f0 and higher multiples of the rotation frequency are observed. They are induced by the measurement system (electromagnetic noise in the signals of the strain gauges) and is probably not related to hydraulic loadings of the turbine.


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Similar observations can be done on a strain gauge close to the band (Figure 8).

Figure 5: Reduced‐scale model. nED = 0.288. Frequency spectra 0‐150*f0. Crown. B13‐SG1 (B13‐01‐PS‐CR‐TE).


QED/QED, nom 0.25 1.32 1.00 0.55

QED/QED, nom 0.25 1.32 1.00 0.55


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Figure 8: Reduced‐scale model. nED = 0.288. Frequency spectra 0‐30*f0. Band. B13‐SG6 (B13‐11‐PS‐BD‐TE).

QED/QED, nom 0.25 1.32 1.00 0.55

QED/QED, nom 0.25 1.32 1.00 0.55


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4 Full‐scale turbine test

4.1 Instrumentation

The full‐scale runner was equipped with 24 strain gauges distributed on 2 blades angularly spaced by

180°, namely blades 7 and 15. For both blades, the strain gauges are located at the same position.

Figure 9: Full‐scale runner. Location of the strain gauges

Table 3: Full‐scale runner. Location of the strain gauges on Blade 7. Pressure side.

S (distance to trailing edge) W (distance to fillet radius)

Strain gauge ‐ prototype mm mm

Crown

B7‐01‐PS‐CR 35 90

B7‐03‐PS‐CR 65 90

B7‐05‐PS‐CR 35 170

B7‐07‐PS‐CR 65 170

Band B7‐09‐PS‐BD 35 35

B7‐11‐PS‐BD 65 35

Table 4: Full‐scale runner. Location of the strain gauges on Blade 7. Suction side.

S (distance to trailing edge) W (distance to fillet radius)

Strain gauge ‐ prototype mm mm

Crown

B7‐02‐SS‐CR 35 90

B7‐04‐SS‐CR 65 90

B7‐06‐SS‐CR 35 170

B7‐08‐SS‐CR 65 170

Band B7‐10‐SS‐BD 35 35

B7‐12‐SS‐BD 65 35

By comparison with Table 2, it can be seen that the location of the strain gauges is different between

the reduced‐scale model and the full‐scale runner (also see Table 15).


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4.2 Results

4.2.1 Dynamic strain The results in terms of dynamic strain are shown in the following graphs. The nED‐value during the

prototype tests is equal to 0.277. The first analysis has been done on the raw time series without post‐

treatment. These graphs show a significant strain elevation at full load, around QED/QED, nom = 1.3 and

another at part load, for 0.3 < QED/QED, nom < 0.6 as it has been observed on the reduced‐scale model (see

Section 3.2.1). However, for 0.6 < QED/QED, nom < 1.0, an additional strain elevation is observed on the

prototype.

Figure 10: Full‐scale runner. Dynamic strain on blades 7 & 15. Pressure side, crown. nED = 0.277

Figure 11: Full‐scale runner. Dynamic strain on blades 7 & 15. Suction side, crown. nED = 0.277


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Figure 12: Full‐scale runner. Dynamic strain on blades 7 & 15. Pressure side, band. nED = 0.277

Figure 13: Full‐scale runner. Dynamic strain on blades 7 & 15. Pressure side, band. nED = 0.277

4.2.2 Frequency signature

The frequency spectra for QED/QED, nom = 0.25, 0.5, 0.9 and 1.27 are plotted for a large frequency band,

from zero to 150*f0, with f0=2.15 Hz.

In the high frequency range, a strain elevation is clearly visible for frequencies around 60*f0 (130 Hz),

especially for QED/QED, nom = 0.9. This elevation is suspected to be related with a natural frequency of the

runner, which is not directly a transposable characteristic between the reduced‐scale runner and the

full‐scale runner. Several natural frequencies around 130 Hz have been calculated in Deliverable 2.1

[Ref. 1.]. Therefore, for the validation of the transposition procedure, the signal of the prototype should

be low‐pass filtered at 25*f0.


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In Figure 15, which is focused on the range 0‐30*f0, the following observations can be done:

‐ An emergence at the guide vane passing frequency (20*f0) is visible on all the spectra; ‐ There is no significant phenomenon at QED/QED, nom = 0.9 and QED/QED, nom = 0.25

In Figure 16, which is focused on the frequency range 0‐5*f0, the following observations can be done:

‐ The harmonics of the rotational frequency, i.e. f0, 2*f0 and 3*f0 are present and their amplitudes increase with the discharge;

‐ A peak at 0.61*f0 is observed at QED/QED, nom = 0.5, which corresponds to the frequency signature of the convective term of the part load helical vortex rope seen from the rotating frame. A second harmonic is also observed;

‐ A peak at 0.35*f0 is observed at QED/QED, nom = 1.27. Two harmonics are also visible; ‐ There is no distinctive phenomenon at QED/QED, nom=0.9.

Figure 14: Full‐scale runner. Frequency spectra 0‐150*f0. B7‐01‐PS‐CR.

QED/QED, nom 0.25 1.27 0.9 0.5


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QED/QED, nom 0.25 1.27 0.9 0.5

QED/QED, nom 0.25 1.27 0.9 0.5


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5 Validation of the transposition procedure First, the peak‐to‐peak values are compared. For this purpose and based on the previous observations,

the first five harmonics of the rotational frequency are subtracted and a 25*f0 low pass filter is applied

to the reduced‐scale model time signals. To be consistent, the same post‐treatment is applied to the

prototype time signals.

The measurements at nED = 0.288 and nED = 0.268 on the reduced‐scale model are compared to the

prototype measurements (nED=0.277). The strain gauges selected for the comparison are given in Table

5.

Table 5: Strain gauges used for the validation of the transposition procedure

Strain gauge Reduced‐scale model Full scale turbine

Runner crown B13‐01‐PS‐CR‐TE B7‐01‐PS‐CR

Runner band B13‐06‐PS‐BD‐TE B7‐10‐SS‐BD

The frequency spectra are finally compared, as well the magnitude of the main phenomena.

5.1 Peak‐to‐peak strain divided by net head

Figure 17: Dynamic strain/Hn. Comparison between model and prototype. Crown.


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Figure 18: Dynamic strain/Hn. Comparison between model and prototype. Band.

5.2 Peak‐to‐peak strain divided by U²/2g

Figure 19: Dynamic strain/(U²/2g). Comparison between model and prototype. Crown.


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Figure 20: Dynamic strain/(U²/2g). Comparison between model and prototype. Band.

5.3 Frequency spectra

The frequency spectra at the operating points given in Table 6 are compared between model and

prototype. The points are selected to have the same QED/QED, nom value on both model and prototype,

except at full load. On each of them, the amplitude of the main phenomena is extracted. At full load,

the instability is studied, even if it does not appear at the same QED/QED, nom value for the three tested

conditions, i.e. nED = 0.268 & 0.288 on the model and nED = 0.277 on the prototype.

Table 6: Selected points for the frequency spectra comparison

Reduced‐scale model Full scale turbine

QED/QED,nom nED =0.268 nED=0.288 nED =0.277

Deep part load 0.25 0.25 0.25

Part load 0.60 0.60 0.60

Nominal load 1.00 1.00 1.02

Full load 1.27 1.32 1.27

The following frequency spectra are presented without post‐treatment. Therefore, the harmonics of the

rotational frequency are included in the spectra.


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5.3.1 Deep part load At deep part load, there is no significant phenomena, except the guide vane passing frequency at 20*f0.

The amplitude of this phenomenon is compared. In the range 0‐30*f0, the frequency spectra of the

model and the prototype have globally the same shape but their level is different.

Figure 21: Frequency spectra comparison model‐prototype. Deep part load. Crown.

Table 7: Model‐prototype comparison. Amplitude at 20*f0. Deep part load. Crown.

Amplitude at 20*f0 Amplitude at 20*f0 /Hn Amplitude at 20*f0 /(U²/2g)

[µm/m RMS] [(µm/m)/mWC RMS] [(µm/m)/m RMS]

Reduced‐scale model

nED =0.268 0.374 0.014 0.039

nED=0.288 0.414 0.015 0.038

Full scale turbine

nED =0.277 3.950 0.022 0.059

Proto

nED=0.277

Model

nED=0.268

Model

nED=0.288


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Figure 22: Frequency spectra comparison model‐prototype. Deep part load. Band.

Table 8: Model‐prototype comparison. Amplitude at 20*f0. Deep part load. Band.




nED =0.268 0.267 0.010 0.028

nED=0.288 0.239 0.009 0.022

Full scale turbine

nED =0.277 2.720 0.015 0.040

Proto

nED=0.277

Model

nED=0.268

Model

Ned=0.288


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5.3.2 Part load At part load, the frequency of the convective component of the part load vortex rope is the main

phenomenon. Its value made dimensionless by the runner frequency is the same on both the model and

the prototype. However, the amplitude depends on the nED‐value on the model. After transposition, the

amplitude measured on the model is significantly lower than the amplitude measured on the prototype.

Figure 23: Frequency spectra comparison model‐prototype. Part load. Crown.

Table 9: Model‐prototype comparison. Amplitude at 0.67*f0. Part load. Crown.

Amplitude at

0.67*f0 Amplitude at 0.67*f0

/Hn Amplitude at 0.67*f0 /(U²/2g)



nED =0.268 0.359 0.013 0.038

nED=0.288 0.586 0.022 0.053

Full scale turbine

nED =0.277 8.680 0.048 0.129

Proto

nED=0.277

Model

nED=0.268

Model

nED=0.288


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Figure 24: Frequency spectra comparison model‐prototype. Part load. Band.

Table 10: Model‐prototype comparison. Amplitude at 0.67*f0. Part load. Band.

Amplitude at

0.67*f0 Amplitude at 0.67*f0

/Hn Amplitude at 0.67*f0 /(U²/2g)



nED =0.268 0.101 0.004 0.011

nED=0.288 0.139 0.005 0.013

Full scale turbine

nED =0.277 2.580 0.014 0.038

Proto

nED=0.277

Model

nED=0.268

Model

nED=0.288


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5.3.3 Nominal load At nominal discharge, there is no significant phenomena. However, an emergence at 1.25*f0 is observed

in the frequency spectra for the full‐scale runner but no for the reduced‐scale model. Moreover, this

emergence is not visible for other discharge values on the full‐scale runner.

The amplitude of the peaks at the guide vane passing frequency are compared in the following.

Figure 25: Frequency spectra comparison model‐prototype. Nominal load. Crown.

Table 11: Model‐prototype comparison. Amplitude at 20*f0. Nominal load. Crown.




nED =0.268 0.685 0.026 0.072

nED=0.288 0.418 0.016 0.038

Full scale turbine

nED =0.277 7.770 0.044 0.115

Proto

nED=0.277

Model

nED=0.268

Model

nED=0.288


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Figure 26: Frequency spectra comparison model‐prototype. Nominal load. Band.

Table 12: Model‐prototype comparison. Amplitude at 20*f0. Nominal load. Band.




nED =0.268 0.483 0.018 0.051

nED=0.288 0.264 0.010 0.024

Full scale turbine

nED =0.277 4.480 0.025 0.066

Proto

Ned=0.277

Model

Ned=0.268

Model

Ned=0.288


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5.3.4 Full load At full load, in presence of the instability, the frequency spectra of the prototype measurements are

very different from those measured on the model. Moreover, the frequency of the phenomena is

different. On the model, its first harmonic is at 0.18*f0 and 0.23*f0 for nED = 0.268 and nED = 0.288,

respectively. On the prototype, its frequency is at 0.36*f0. After transposition, the amplitudes measured

on the reduced scale model are slightly higher than the amplitudes on the prototype.

Figure 27: Frequency spectra comparison model‐prototype. Full load. Crown.

Table 13: Model‐prototype comparison. Amplitude of the first harmonic of the instability. Full load. Crown.

Amplitude of the first harmonic of the instability

Amplitude of the first harmonic of the instability /Hn


/(U²/2g)



nED =0.268 1.540 0.058 0.162

nED=0.288 2.090 0.078 0.191

Full scale turbine

nED =0.277 11.460 0.065 0.170

Proto

nED=0.277

Model

nED=0.268

Model

nED=0.288


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Figure 28: Frequency spectra comparison model‐prototype. Full load. Band.

Table 14: Model‐prototype comparison. Amplitude of the first harmonic of the instability. Full load. Band.


Amplitude of the first harmonic of the instability /Hn


/(U²/2g)



nED =0.268 0.876 0.033 0.092

nED=0.288 1.380 0.052 0.126

Full scale turbine

nED =0.277 3.070 0.017 0.046

Proto

nED=0.277

Model

nED=0.268

Model

nED=0.288


6 Summary and discussion

6.1 Summary

First, several major differences must be highlighted between the reduced‐scale model runner and the

full‐scale runner. These differences have a major impact on the validation of the transposition

procedure.

‐ The strain gauges are embedded in grooves in the reduced‐scale model runner whereas they are located at the surface of the blades in the full‐scale runner. By considering that a part of the solicitation of the blades is bending, the strain measured at the bottom of the grooves ‐ i.e. closer to the neutral axis ‐ is very different from the strain measured at the surface of the blades. The difference is accentuated where the thickness of the blade is low as this is the case close the trailing edge;

Figure 29: Illustration of the stress gradient in the section of a beam in bending

‐ The location of the strain gauges is different between model and prototype. This has a significant impact, particularly where the stress gradients are high, i.e. close to the hotspot;

‐ The geometry of the runner crown and band are also different between model and prototype. They have been simplified on the reduced‐scale model and the crown is significantly thicker, due to instrumentation constraints. This affects the stiffness of the blade‐to‐crown and blade‐to‐band junctions and, potentially, the stress distribution close to these areas.

Figure 30: Illustration of the dynamic stress gradient (Von Mises) on the reduced‐scale model runner at part load


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Table 15: Location of the strain gauges on model and prototype runners. Pressure side. Prototype scale. S: distance to trailing edge, W: distance to fillet radius

Reduced‐scale model runner Full scale runner

S W S W

Strain gauge ‐ model [mm] [mm] Strain gauge ‐ prototype [mm] [mm]

Crown

B13‐01‐PS‐CR‐TE 48 120 B7‐01‐PS‐CR 35 90

B13‐03‐PS‐CR‐TE 131 118 B7‐03‐PS‐CR 65 90

B13‐05‐PS‐CR‐TE 215 116 B7‐05‐PS‐CR 35 170

B13‐07‐PS‐CR‐TE 15.9 268 B7‐07‐PS‐CR 65 170

B13‐09‐PS‐CR‐TE 16.3 422

Band

B13‐11‐PS‐BD‐TE 76.8 66 B7‐09‐PS‐BD 35 35

B13‐13‐PS‐BD‐TE 79 200 B7‐11‐PS‐BD 65 35

B13‐15‐PS‐BD‐TE 154 65.6

Figure 31: Differences in term of geometry between reduced‐scale model runner and full‐scale prototype runner

‐ Finally, the nED‐values tested on the reduced scale model during the second measurement campaign do not correspond to the net head available on the prototype turbine during on‐site tests. A change in the nED‐value can affect the occurrence and the intensity of the phenomena. Note: a nED‐value closer to the one available during the on‐site tests has also been tested on EPFL test rig during a third measurement campaign but the measurements have not been validated and post‐treated yet.

Therefore, the measurements between the reduced‐scale model runner and the full‐scale runner

cannot be compared directly. Despite these differences, two transposition procedures have been

proposed. The first one is based on the ratio of the net heads. This transposition is based on the

hypothesis that the amplitude of the phenomena does not depend directly on the nED‐value. On the

contrary, the second transposition procedure takes into account the ratio of U²/2g, which depends on

the nED‐value for a fixed head on the reduced‐scale model.

To validate the transposition procedure, the non‐transposable phenomena have been identified and

removed from the signals, i.e. natural frequencies of the runner and harmonics of the rotational


02.20.2017 page 29/31

frequency. It can be noted that a wide‐frequency band phenomenon, which is suspected to be related

to a natural frequency of the runner, has been identified on the full‐scale runner. This phenomenon

generates a significant dynamic strain increase for 0.6 < QED/QED, nom < 1.0, which has not been observed

on the reduced scale model.

A homogeneous post‐treatment of the data has been applied: the first five harmonics of the rotational

frequency have been removed and a 25*f0 low pass filter has been applied on both model and prototype

data.

Figure 32: Hill chart. Comparison of the nED‐values used on reduced scale model and prototype

The evolution of the peak‐to‐peak values with the discharge has been then compared for two strain

gauge locations on the pressure side of the blade, close to the crown and close to the band. The curves

show several similarities. A significant strain elevation is found at full load in presence of the self‐excited

instability. A second strain elevation is observed at part load in presence of the part load vortex rope for

0.3 < QED/QED, nom < 0.7.

To compare the measurements more in detail, the frequency spectra at four operating points ‐ deep

part load, part load, nominal load and full load – have been compared. The signature of the phenomena

and the shape of the spectra are globally the same between the model and the prototype, except at full

load. For instance, the frequency of the part load vortex rope is very close. However, some differences

should be mentioned: an emergence at a frequency of 1.25*f0 in nominal conditions is observed only on

the prototype. In addition, the frequency of the instability at full load is very different. For this case, the

differences in term of hydraulic circuit have certainly an important impact. The magnitude of the

phenomena is also compared and transposed but no conclusion can be done due to the differences

mentioned previously.

Proto

nED=0.277

Model

nED=0.288

Model

nED=0.268


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6.2 Discussion

Due to the differences between the reduced‐scale model runner and the full‐scale runner, it is not

possible to validate the transposition procedures proposed in this report. To overpass these differences,

mechanical calculations of the full‐scale runner could help to evaluate their impact.

Three mechanical calculations – at deep part load, part load and full load – have been performed on the

reduced‐scale model runner and have shown a good consistency with the measurements (see

Deliverable D2.2 [ref. 2]). By applying the same pressure fields on a mechanical model of the full‐scale

runner and by comparing the results with the on‐site measurements, it would be possible to have a

better idea of the validity of the proposed transposition procedures.

In addition, it has been observed that the maximum dynamic strain intensity caused by the part load

vortex rope has probably not been reached during the model test. On the full‐scale runner, it occurs at

QED/QED, nom = 0.5 whereas there is no operating point recorded for 0.35 < QED/QED, nom < 0.55 on the

reduced scale model.

6.3 Potential impacts of the presented results

In the framework of Work Package 2 (WP2), a methodology for the calculation of the dynamic

mechanical behaviour for conventional and reversible storage hydropower plants in various operation

modes (full load, part load, deep part load and transients) has been validated. For Francis turbines and

reversible pump‐turbines, the validation was done by comparison of numerical results with

experimental measurements on both the model‐scale and full‐scale turbines.

In addition, the structural response of the turbine runner loaded by dynamic pressure fields has been

analysed and the damage associated to each operation modes has been defined. It was assumed that

the runner is one of the main impacted component when operating in off‐design conditions. However,

the dynamic pressure loadings applied on other turbine components (penstock, distributor, head cover

and bottom ring, draft tube etc.) have also been characterized in the Work Package 1 (WP1) and could

allow future analyses of the damage generated on such components.

Finally, relevant parameters for the transposition of the structural dynamic behaviour from model to

prototype have been identified by comparison between model tests and on‐site tests. A corresponding

procedure is proposed in this report and further validation will allow improving it.

Potential impacts of the results obtained in the framework of WP2 can be identified as follows:

For the equipment manufacturers, the unsteady stress simulation will allow designing more

robust hydraulic turbines with an extended operating range;

For existing power plants, mastering dynamic phenomena in off‐design conditions will allow the

utilities to take a balanced strategy to optimize components life‐time and productivity gains;

Finally, for the fast mode change of reversible pump‐turbines, the knowledge of the turbine

behaviour during transients will allow optimizing the control strategy and increasing the lifetime

of the components.

More generally, the procedures developed in the framework of WP2 represent a decisive step toward

the complete assessment of the mechanical behaviour of both conventional Francis turbines and

reversible pump‐turbines operating in off‐design and transient conditions. This will enable the extension

of the operating range of the machine, a longer lifetime of the mechanical components of the machine

and finally a reduction of the maintenance costs inherent to the damages caused by flow instabilities.


02.20.2017 page 31/31

“This project has received funding from the European Union’s Seventh Programme for research, technological development and demonstration under grant agreement No ERC/FP7‐ ENERGY‐2013‐1‐Grant 608532”.

608532 - hyperbole - deliverable d2

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