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eLibrary > PD IEC TS 62882:2020 Hydraulic machines. Francis turbine pressure fluctuation transposition >

PD IEC TS 62882:2020 Hydraulic machines. Francis turbine pressure fluctuation transposition, 2020

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PD IEC TS 62882:2020 Hydraulic machines. Francis turbine pressure fluctuation transposition, 2020

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CONTENTS
FOREWORD
INTRODUCTION
1 Scope
2 Normative references
3 Terms, definitions, symbols and units [Go to Page]
3.1 General terms and definitions
3.2 Units
3.3 Overview of the terms, definitions, symbols and units used in this document [Go to Page]
3.3.1 Subscripts and symbols
3.3.2 Geometric terms and definitions
Figure 1 – Reference diameter of Francis turbine [Go to Page]
3.3.3 Physical quantities and properties terms and definitions
3.3.4 Discharge, velocity and speed terms and definitions
Figures [Go to Page]
[Go to Page]
3.3.5 Pressure terms and definitions
3.3.6 Specific energy terms and definitions
3.3.7 Height and head terms and definitions
Figure 2 – Reference level of the Francis turbine [Go to Page]
3.3.8 Power and torque terms and definitions
Figure 3 – Flux diagram for power and discharge [Go to Page]
3.3.9 Efficiency terms and definitions
3.3.10 General terms and definitions relating to fluctuating quantities
Figure 4 – Illustration of some definitions related to fluctuating quantities [Go to Page]
3.3.11 Fluid dynamic and scaling terms and definitions
3.3.12 Dimensionless terms and definitions
4 Description of pressure fluctuation phenomena [Go to Page]
4.1 General
Tables [Go to Page]
Table 1 – Pressure fluctuation overview matrix
4.2 Pressure fluctuations overview
Figure 5 – Discharge range for the various fluctuation modes
Figure 6 – Efficiency hill chart with pictures of swirling flow
4.3 General description of draft tube flow in Francis turbines
Figure 7 – Example of a waterfall diagram of pressure amplitudes measured in the draft tube cone
Figure 8 – Velocity triangles at inlet and outlet of the runner blade
4.4 Detailed description of pressure fluctuation phenomena [Go to Page]
4.4.1 Mode 1: Pressure fluctuation in high load
Figure 9 – Influence of the discharge on the circumferential component of the absolute velocity [Go to Page]
4.4.2 Mode 2: Pressure fluctuation in best operation range
4.4.3 Mode 3: Pressure fluctuation in upper part load
4.4.4 Mode 4: Pressure fluctuation in part load
Figure 10 – Elliptical vortex rope precessing in the draft tube cone at upper part load
Figure 11 – Decomposition between the synchronous and asynchronous component of part load draft tube pressure fluctuations [Go to Page]
4.4.5 Mode 5: Pressure fluctuation in deep part load
Figure 12 – Example of inter-blade vortex [Go to Page]
4.4.6 Modes 6.a and 6.b: Rotor-stator interaction (RSI) pressure fluctuation
Figure 13 – Modulation process between runner blade flow field and guide vanes flow field
Figure 14 – Diametrical modes shapes representation according to k values
5 Specifications of pressure fluctuation measurement and analysis [Go to Page]
5.1 General [Go to Page]
5.1.1 Overview
5.1.2 Purpose of the measurements
5.1.3 Procedures and parameters to record
5.1.4 Locations of pressure fluctuation test transducers
Figure 15 – Suggested locations of pressure transducers [Go to Page]
5.1.5 Data acquisition for pressure fluctuation measurements
Table 2 – Locations of pressure fluctuations transducers [Go to Page]
5.1.6 Transducers and calibration
5.2 Pressure fluctuation on a model turbine [Go to Page]
5.2.1 General
Figure 16 – Turbine hill-chart with exploration paths [Go to Page]
5.2.2 Homology and limitations
5.2.3 Detailed procedures
Figure 17 – Schematic of the axial aeration device
5.3 Special requirements and information for a prototype turbine [Go to Page]
5.3.1 General
5.3.2 Source of information
5.3.3 Important aspects
5.4 Analysis, presentation and interpretation of results [Go to Page]
5.4.1 General
5.4.2 Time-domain analysis
Figure 18 – Schematic arrangement for pressure fluctuation transducers [Go to Page]
5.4.3 Frequency-domain analysis
5.4.4 Non-dimensional frequency and pressure
5.4.5 Presentation and interpretation of pressure fluctuations
6 Identification of potential resonances in test rig and prototype [Go to Page]
6.1 General
Figure 19 – Typical plot showing pressure fluctuation coefficient versus relative discharge
Figure 20 – Elementary hydroacoustic oscillator
6.2 Identify resonance in test rig
6.3 Possible resonance and self-excited pressure fluctuation in prototype [Go to Page]
6.3.1 General
6.3.2 Draft tube vortex related resonances and self-excited pressure fluctuation in prototype
Figure 21 – Part load vortex rope in the draft tube and its fluctuation frequency range and corresponding risk of resonance with the generator local mode of oscillation valid for both Fgrid = 50 Hz and Fgrid = 60 Hz [Go to Page]
6.3.3 Rotor-stator interaction (RSI) related resonance
6.3.4 Resonance with fluctuation modes not treated in this document
7 Transposition method and procedure [Go to Page]
7.1 General
7.2 Parameters influencing transposition [Go to Page]
7.2.1 Model test head
7.2.2 Thoma number
7.2.3 Froude number
7.3 Relevant quantities for transposition [Go to Page]
7.3.1 Fluctuation frequency
7.3.2 Fluctuation amplitude
7.4 Transposable types of fluctuations
Figure 22 – Waterfall diagram of the pressure fluctuations as function of the frequency and Froude number for a given Thoma number
7.5 Statistical analysis of model and prototype transposition accuracy
Table 3 – Accuracy for transposition of fluctuation amplitude in draft tube cone
Table 4 – Accuracy for transposition of fluctuation amplitude in vaneless zone
8 Mitigations [Go to Page]
8.1 Draft tube vortex phenomena [Go to Page]
8.1.1 General
8.1.2 Draft tube fins
Table 5 – Accuracy for transposition of fluctuation amplitude in spiral case [Go to Page]
8.1.3 Draft tube with a central column
Figure 23 – Example of fins in the draft tube and influence on the pressure fluctuations [Go to Page]
8.1.4 Air admission
Figure 24 – Example of the draft tube with central column extension
Figure 25 – Typical runner cone extensions used for reducing draft tube pressure fluctuations [Go to Page]
8.1.5 AVR or PSS parameter tuning
Figure 26 – Central and peripheral air admission locations for draft tube pressure fluctuations on a radial flow turbine
Figure 27 – Central air admission
8.2 Runner inter-blade vortex
8.3 Blade interaction
8.4 Operation restriction
Annexes [Go to Page]
Annex A (informative) Example of pressure fluctuation records
Figure A.1 – Example 1: a case corresponding to mode 1 (a limited high load)
Figure A.2 – Example 2: a case corresponding to mode 1 (a large overload)
Figure A.3 – Example 3: a case corresponding to mode 2
Figure A.4 – Example 4 : a case corresponding to mode 3
Figure A.5 – Example 5 : a case corresponding to mode 4.a and 4.b
Figure A.6 – Example 6: a case corresponding to mode 4.a and 4.b
Figure A.7 – Example 7: a case corresponding to mode 4.c
Figure A.8 – Example 8: a case corresponding to mode 5.b
Figure A.9 – Example 9: a case corresponding to mode 6.a
Annex B (informative) Typical pressure fluctuation transducers parameters for model test
Annex C (informative) Pressure transducer dynamic calibration [Go to Page]
C.1 Fast valve opening method
C.2 Rotating valve method
Figure C.1 – Pressure transducer dynamic calibration schematic diagram with fast open valve method [Go to Page]
C.3 Electrical spark method
Figure C.2 – Pressure transducer dynamic calibration with rotating valve method
Figure C.3 – Spark plug used as to generate an impulse excitation in water for pressure transducer dynamic calibration
Annex D (informative) Proposed remote pressure measurement fluctuation correction [Go to Page]
D.1 General
D.2 Correction method theory
D.3 Measuring and estimating tube frequency response
Figure D.1 – Typical results obtained by shutting off drainage valve
Table D.1 –and calculated for p1 to p4 [Go to Page]
D.4 Pressure fluctuation correction
Table D.2 – Estimated frequencies based on tubing mechanical characteristics
Figure D.2 – Signal and spectrum of four remote sensors and one local sensor
Table D.3 – Peak-to-peak value on the raw signals
Table D.4 – Wave speed and damping ratio
Figure D.3 – Signal and spectrum of four remote sensors (corrected) and one local sensor [Go to Page]
D.5 Limitations
Table D.5 – Peak-to-peak value on the corrected signals
Annex E (informative) Forced response analysis for Francis turbines operating in part load conditions [Go to Page]
E.1 General
E.2 Systematic methodology based on detailed modelling of hydroelectric power plant [Go to Page]
E.2.1 Description of the test case
E.2.2 Modelling of the hydraulic power plant
Figure E.1 – SIMSEN model of the test case
Figure E.2 – Performance hill chart of the Francis turbine for different guide vane openings
Table E.1 – Francis turbine parameters
Figure E.3 – Elementary hydraulic pipe of length dx and its equivalent circuit [Go to Page]
[Go to Page]
E.2.3 Forced response analysis of the test case
Figure E.4 – Forced response for a = 50 m/s (left) and a = 60 m/s (right)
Figure E.5 – Forced response for a = 70 m/s (left) and a = 80 m/s (right)
Figure E.6 – Forced response for a = 90 m/s (left) and a = 100 m/s (right)
Figure E.7 – Damping and eigenfrequency for a = 50 m/s (left) and a = 60 m/s (right)
Figure E.8 – Damping and eigenfrequency for a = 70 m/s (left) and a = 80 m/s (right)
Figure E.9 – Damping and eigenfrequency for a = 90 m/s (left) and a = 100 m/s (right)
Figure E.10 – Eigenmode for a = 50 m/s and eigenfrequency f = 4,18 Hz
Figure E.11 – Eigenmode for a = 50 m/s and eigenfrequency f = 3,67 Hz
Figure E.12 – Eigenmode for a = 100 m/s and eigenfrequency f = 2,61 Hz [Go to Page]
E.3 Simplified approach based on the hydroacoustic properties of the hydraulic system [Go to Page]
E.3.1 General
E.3.2 Cavitating draft tube first natural frequency
Figure E.13 – Draft tube modelled with cavitation compliance and draft tube inductance [Go to Page]
[Go to Page]
E.3.3 Hydraulic circuit natural frequencies
Figure E.14 – Simplified model of a cavitation draft tube connected to a tailrace pipe composed by cavitation compliance of the draft tube and downstream inductance of the tailrace pipe [Go to Page]
[Go to Page]
E.3.4 Example of applications
Figure E.15 – Hydraulic system modelled by an equivalent pipe and corresponding modes shapes for the first and second natural frequencies
Figure E.16 – Hydraulic systems 1, 2 and 3
Table E.2 – Parameters of the hydraulic systems 1, 2 and 3
Table E.3 – Parameters of the equivalent pipe of the hydraulic system 1
Table E.4 – Estimation of the natural frequencies f0 to f6 of the hydraulic system 1 based on Formulae (E.9) and (E.11) and comparison with results obtained with eigenvalue calculation and corresponding errors
Table E.5 – Parameters of the equivalent pipe of the hydraulic system 2
Table E.6 – Estimation of the natural frequencies f0 to f6 of the hydraulic system 2 based on Formulae (E.10) and (E.11) and comparison with results obtained with eigenvalue calculation and corresponding errors
Table E.7 – Parameters of the equivalent pipe of the hydraulic system 3 [Go to Page]
[Go to Page]
E.3.5 Limitations of the methodology
Table E.8 – Estimation of the natural frequencies f0 to f6 of the hydraulic system 3 based on Formulae (E.10) and (E.11) and comparison with results obtained with eigenvalue calculation and corresponding errors
Table E.9 – Pressure mode shape obtained by eigenvalue and eigenvector calculation for the three first natural frequencies f1, f2 and f3 of the hydraulic systems 1 and 2
Annex F (informative) Influence of Thoma number on pressure fluctuation
Figure F.1 – Influence of Thoma number on pressure fluctuation
Figure F.2 – Example of waterfall diagram of the pressure fluctuations as function of the frequency and Thoma number
Annex G (informative) Transposition of synchronous pressure fluctuations from model to prototype for Francis turbines operating at off-design conditions [Go to Page]
G.1 General [Go to Page]
G.1.1 Overview
Figure G.1 – Peak-to-peak value of pressure fluctuations as a function of the discharge factor measured on the model and the corresponding prototype
Figure G.2 – Layout of EPFL test rig PF3 1-D hydroacoustic model
Figure G.3 – Electrical T-shaped representation of the cavitation vortex rope developing in Francis turbine draft tube in part load conditions
Figure G.4 – Excitation system and 3D cut-view of the rotating valve
Figure G.5 – Strouhal number of the precession frequency as a function of the swirl number computed with Formula (G.6)
Figure G.6 – Strouhal number of the first eigen frequency of the test rig as a function of swirl number (a), the wave speed in the draft tube determined in the 1-D model (b)
Figure G.7 – Predicted values of precession frequency and first eigenfrequency at the prototype scale as a function of the output power of the generating unit
Figure G.8 – Comparison between observed and predicted values of the precession frequency frope and the first eigenfrequency f0 of a 444 MW hydropower unit (HYPERBOLE project test case)
Figure G.9 – Hill chart comparing the measured and the predicted resonance conditions assuming a constant pressure value in the draft tube cone of the prototype
Annex H (informative) Statistical analysis of pressure fluctuation data [Go to Page]
H.1 Normalizing step for the comparison of data
Figure H.1 – Pressure fluctuations versus discharge factor
Figure H.2 – Normalized discharge of pressure fluctuations
Figure H.3 – Normalized pressure amplitude of pressure fluctuations
Figure H.4 – Comparison of pressure fluctuations of model and prototype [Go to Page]
H.2 Collected data
H.3 Draft tube zone phenomena
Figure H.5 – Set of pressure fluctuation of models and prototypes for draft tube analysis
Table H.1 – World hydropower plant references
Figure H.6 – Difference between pressure fluctuations between the model and the prototype
Figure H.7 – Standard deviation of difference of pressure fluctuation
Figure H.8 – Transposition accuracy for draft tube cone [Go to Page]
H.4 Vaneless zone phenomena
Figure H.9 – Transposition of each power plant test case for the draft tube cone
Figure H.10 – Set of pressure fluctuation of models and prototypes for vaneless zone analysis
Figure H.11 – Difference between pressure fluctuations between the model and the prototype
Figure H.12 – Standard deviation of difference of pressure fluctuation
Figure H.13 – Transposition accuracy for vaneless zone
Figure H.14 – Transposition of each power plant test case for vaneless zone [Go to Page]
H.5 Spiral case phenomena
Figure H.15 – Set of pressure fluctuation of models and prototypes for spiral case analysis
Figure H.16 – Difference between pressure fluctuations between the model and the prototype
Figure H.17 – Standard deviation of difference of pressure fluctuation
Figure H.18 – Transposition accuracy for spiral case
Figure H.19 – Transposition of each power plant test cases for spiral case
Annex J (informative) Gathering worldwide pressure fluctuation data [Go to Page]
J.1 Chinese test cases
J.2 France test case
Figure J.1 – Comparison of pressure fluctuations on the draft tube for 10 Chinese model and prototype references
Figure J.2 – Comparison of pressure fluctuations on the draft tube for one France model and prototype reference
Figure J.3 – Comparison of pressure fluctuations on the spiral case for one France model and prototype reference [Go to Page]
J.3 Norway test case
Figure J.4 – Comparison of pressure fluctuations on the draft tube for one Norway model and prototype reference
Bibliography [Go to Page]

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PD IEC TS 62882:2020 Hydraulic machines. Francis turbine pressure fluctuation transposition, 2020

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