IEC 62882, which is a Technical Specification, provides pressure fluctuation transposition methods for Francis turbines and pump-turbines operating as turbines, including:<\/p>\n
description of pressure fluctuations, the phenomena causing them and the related problems;<\/p>\n<\/li>\n
characterization of the phenomena covered by this document, including but not limited to inter-blade vortices, draft tube vortices rope and rotor-stator interaction;<\/p>\n<\/li>\n
demonstration that both operating conditions and Thoma numbers (cavitation conditions) are primary parameters influencing pressure fluctuations;<\/p>\n<\/li>\n
recommendation of ways to measure and analyse pressure fluctuations;<\/p>\n<\/li>\n
identification of potential resonances in test rigs and prototypes;<\/p>\n<\/li>\n
identification of methods, to transpose the measurement results from model to prototype or provide ways to predict pressure fluctuations in prototypes based on statistics or experience;<\/p>\n<\/li>\n
recommendation of a data acquisition system, including the type and mounting position of model and prototype transducers and to define the similitude condition between model and prototype;<\/p>\n<\/li>\n
presentation of pressure fluctuation measurements comparing the model turbine and the corresponding prototype;<\/p>\n<\/li>\n
discussion of parameters used for the transposition from model to prototype, for example, the peak to peak value at 97 % confidence interval, the RMS value or the standard deviation in the time domain and the relation of main frequency and the rotational frequency in the frequency domain obtained by FFT;<\/p>\n<\/li>\n
discussion of the uncertainty of the pressure fluctuation transposition from model to prototype;<\/p>\n<\/li>\n
discussion of factors which influence the transposition, including those which cannot be simulated on the model test rig such as waterway system and mechanical system;<\/p>\n<\/li>\n
establishment of the transposition methods for different types of pressure fluctuations;<\/p>\n<\/li>\n
suggestion of possible methods for mitigating pressure fluctuation;<\/p>\n<\/li>\n
definition of the limitations of the specification.<\/p>\n<\/li>\n<\/ul>\n
This document is limited to normal operation conditions. Hydraulic stability phenomena related to von Karman vortices, transients, runaway speed and speed no load are excluded from this document.<\/p>\n
This document provides means to identify potential resonances in model test rigs and prototype turbines. Scaling-up resonance conditions are not treated in this document. When resonance exists, the transposition methods identified in this document do not apply. Under these conditions, the relationship between model and prototype pressure fluctuations cannot be determined.<\/p>\n
This document is concerned neither with the structural details of the machines nor the mechanical properties of their components, so long as these characteristics do not affect model pressure fluctuations or the relationship between model and prototype pressure fluctuations.<\/p>\n
| PDF Pages<\/th>\n | PDF Title<\/th>\n<\/tr>\n | ||||||
|---|---|---|---|---|---|---|---|
| 2<\/td>\n | undefined <\/td>\n<\/tr>\n | ||||||
| 4<\/td>\n | CONTENTS <\/td>\n<\/tr>\n | ||||||
| 11<\/td>\n | FOREWORD <\/td>\n<\/tr>\n | ||||||
| 13<\/td>\n | INTRODUCTION <\/td>\n<\/tr>\n | ||||||
| 14<\/td>\n | 1 Scope <\/td>\n<\/tr>\n | ||||||
| 15<\/td>\n | 2 Normative references 3 Terms, definitions, symbols and units 3.1 General terms and definitions 3.2 Units <\/td>\n<\/tr>\n | ||||||
| 16<\/td>\n | 3.3 Overview of the terms, definitions, symbols and units used in this document <\/td>\n<\/tr>\n | ||||||
| 17<\/td>\n | 3.3.1 Subscripts and symbols <\/td>\n<\/tr>\n | ||||||
| 18<\/td>\n | 3.3.2 Geometric terms and definitions Figure 1 \u2013 Reference diameter of Francis turbine <\/td>\n<\/tr>\n | ||||||
| 19<\/td>\n | 3.3.3 Physical quantities and properties terms and definitions 3.3.4 Discharge, velocity and speed terms and definitions Figures <\/td>\n<\/tr>\n | ||||||
| 20<\/td>\n | 3.3.5 Pressure terms and definitions 3.3.6 Specific energy terms and definitions <\/td>\n<\/tr>\n | ||||||
| 21<\/td>\n | 3.3.7 Height and head terms and definitions Figure 2 \u2013 Reference level of the Francis turbine <\/td>\n<\/tr>\n | ||||||
| 22<\/td>\n | 3.3.8 Power and torque terms and definitions Figure 3 \u2013 Flux diagram for power and discharge <\/td>\n<\/tr>\n | ||||||
| 23<\/td>\n | 3.3.9 Efficiency terms and definitions 3.3.10 General terms and definitions relating to fluctuating quantities <\/td>\n<\/tr>\n | ||||||
| 25<\/td>\n | Figure 4 \u2013 Illustration of some definitions related to fluctuating quantities <\/td>\n<\/tr>\n | ||||||
| 26<\/td>\n | 3.3.11 Fluid dynamic and scaling terms and definitions 3.3.12 Dimensionless terms and definitions <\/td>\n<\/tr>\n | ||||||
| 27<\/td>\n | 4 Description of pressure fluctuation phenomena 4.1 General <\/td>\n<\/tr>\n | ||||||
| 29<\/td>\n | Tables Table 1 \u2013 Pressure fluctuation overview matrix <\/td>\n<\/tr>\n | ||||||
| 32<\/td>\n | 4.2 Pressure fluctuations overview Figure 5 \u2013 Discharge range for the various fluctuation modes <\/td>\n<\/tr>\n | ||||||
| 33<\/td>\n | Figure 6 \u2013 Efficiency hill chart with pictures of swirling flow <\/td>\n<\/tr>\n | ||||||
| 34<\/td>\n | 4.3 General description of draft tube flow in Francis turbines Figure 7 \u2013 Example of a waterfall diagram of pressure amplitudes measured in the draft tube cone <\/td>\n<\/tr>\n | ||||||
| 35<\/td>\n | Figure 8 \u2013 Velocity triangles at inlet and outlet of the runner blade <\/td>\n<\/tr>\n | ||||||
| 36<\/td>\n | 4.4 Detailed description of pressure fluctuation phenomena 4.4.1 Mode 1: Pressure fluctuation in high load Figure 9 \u2013 Influence of the discharge on the circumferential component of the absolute velocity <\/td>\n<\/tr>\n | ||||||
| 37<\/td>\n | 4.4.2 Mode 2: Pressure fluctuation in best operation range 4.4.3 Mode 3: Pressure fluctuation in upper part load <\/td>\n<\/tr>\n | ||||||
| 38<\/td>\n | 4.4.4 Mode 4: Pressure fluctuation in part load Figure 10 \u2013 Elliptical vortex rope precessing in the draft tube cone at upper part load <\/td>\n<\/tr>\n | ||||||
| 39<\/td>\n | Figure 11 \u2013 Decomposition between the synchronous and asynchronous component of part load draft tube pressure fluctuations <\/td>\n<\/tr>\n | ||||||
| 40<\/td>\n | 4.4.5 Mode 5: Pressure fluctuation in deep part load Figure 12 \u2013 Example of inter-blade vortex <\/td>\n<\/tr>\n | ||||||
| 41<\/td>\n | 4.4.6 Modes 6.a and 6.b: Rotor-stator interaction (RSI) pressure fluctuation Figure 13 \u2013 Modulation process between runner blade flow field and guide vanes flow field <\/td>\n<\/tr>\n | ||||||
| 42<\/td>\n | Figure 14 \u2013 Diametrical modes shapes representation according to k values <\/td>\n<\/tr>\n | ||||||
| 43<\/td>\n | 5 Specifications of pressure fluctuation measurement and analysis 5.1 General 5.1.1 Overview 5.1.2 Purpose of the measurements <\/td>\n<\/tr>\n | ||||||
| 44<\/td>\n | 5.1.3 Procedures and parameters to record <\/td>\n<\/tr>\n | ||||||
| 45<\/td>\n | 5.1.4 Locations of pressure fluctuation test transducers Figure 15 \u2013 Suggested locations of pressure transducers <\/td>\n<\/tr>\n | ||||||
| 46<\/td>\n | 5.1.5 Data acquisition for pressure fluctuation measurements Table 2 \u2013 Locations of pressure fluctuations transducers <\/td>\n<\/tr>\n | ||||||
| 47<\/td>\n | 5.1.6 Transducers and calibration 5.2 Pressure fluctuation on a model turbine 5.2.1 General Figure 16 \u2013 Turbine hill-chart with exploration paths <\/td>\n<\/tr>\n | ||||||
| 48<\/td>\n | 5.2.2 Homology and limitations 5.2.3 Detailed procedures <\/td>\n<\/tr>\n | ||||||
| 49<\/td>\n | Figure 17 \u2013 Schematic of the axial aeration device <\/td>\n<\/tr>\n | ||||||
| 50<\/td>\n | 5.3 Special requirements and information for a prototype turbine 5.3.1 General 5.3.2 Source of information 5.3.3 Important aspects <\/td>\n<\/tr>\n | ||||||
| 51<\/td>\n | 5.4 Analysis, presentation and interpretation of results 5.4.1 General 5.4.2 Time-domain analysis Figure 18 \u2013 Schematic arrangement for pressure fluctuation transducers <\/td>\n<\/tr>\n | ||||||
| 52<\/td>\n | 5.4.3 Frequency-domain analysis 5.4.4 Non-dimensional frequency and pressure 5.4.5 Presentation and interpretation of pressure fluctuations <\/td>\n<\/tr>\n | ||||||
| 53<\/td>\n | 6 Identification of potential resonances in test rig and prototype 6.1 General Figure 19 \u2013 Typical plot showing pressure fluctuation coefficient versus relative discharge <\/td>\n<\/tr>\n | ||||||
| 54<\/td>\n | Figure 20 \u2013 Elementary hydroacoustic oscillator <\/td>\n<\/tr>\n | ||||||
| 55<\/td>\n | 6.2 Identify resonance in test rig 6.3 Possible resonance and self-excited pressure fluctuation in prototype 6.3.1 General 6.3.2 Draft tube vortex related resonances and self-excited pressure fluctuation in prototype <\/td>\n<\/tr>\n | ||||||
| 56<\/td>\n | Figure 21 \u2013 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 <\/td>\n<\/tr>\n | ||||||
| 57<\/td>\n | 6.3.3 Rotor-stator interaction (RSI) related resonance 6.3.4 Resonance with fluctuation modes not treated in this document <\/td>\n<\/tr>\n | ||||||
| 58<\/td>\n | 7 Transposition method and procedure 7.1 General 7.2 Parameters influencing transposition 7.2.1 Model test head 7.2.2 Thoma number <\/td>\n<\/tr>\n | ||||||
| 59<\/td>\n | 7.2.3 Froude number 7.3 Relevant quantities for transposition 7.3.1 Fluctuation frequency 7.3.2 Fluctuation amplitude 7.4 Transposable types of fluctuations Figure 22 \u2013 Waterfall diagram of the pressure fluctuations as function of the frequency and Froude number for a given Thoma number <\/td>\n<\/tr>\n | ||||||
| 60<\/td>\n | 7.5 Statistical analysis of model and prototype transposition accuracy Table 3 \u2013 Accuracy for transposition of fluctuation amplitude in draft tube cone Table 4 \u2013 Accuracy for transposition of fluctuation amplitude in vaneless zone <\/td>\n<\/tr>\n | ||||||
| 61<\/td>\n | 8 Mitigations 8.1 Draft tube vortex phenomena 8.1.1 General 8.1.2 Draft tube fins Table 5 \u2013 Accuracy for transposition of fluctuation amplitude in spiral case <\/td>\n<\/tr>\n | ||||||
| 62<\/td>\n | 8.1.3 Draft tube with a central column Figure 23 \u2013 Example of fins in the draft tube and influence on the pressure fluctuations <\/td>\n<\/tr>\n | ||||||
| 63<\/td>\n | 8.1.4 Air admission Figure 24 \u2013 Example of the draft tube with central column extension Figure 25 \u2013 Typical runner cone extensions used for reducing draft tube pressure fluctuations <\/td>\n<\/tr>\n | ||||||
| 64<\/td>\n | 8.1.5 AVR or PSS parameter tuning Figure 26 \u2013 Central and peripheral air admission locations for draft tube pressure fluctuations on a radial flow turbine Figure 27 \u2013 Central air admission <\/td>\n<\/tr>\n | ||||||
| 65<\/td>\n | 8.2 Runner inter-blade vortex 8.3 Blade interaction 8.4 Operation restriction <\/td>\n<\/tr>\n | ||||||
| 66<\/td>\n | Annexes Annex A (informative) Example of pressure fluctuation records <\/td>\n<\/tr>\n | ||||||
| 68<\/td>\n | Figure A.1 \u2013 Example 1: a case corresponding to mode 1 (a limited high load) <\/td>\n<\/tr>\n | ||||||
| 70<\/td>\n | Figure A.2 \u2013 Example 2: a case corresponding to mode 1 (a large overload) <\/td>\n<\/tr>\n | ||||||
| 72<\/td>\n | Figure A.3 \u2013 Example 3: a case corresponding to mode 2 <\/td>\n<\/tr>\n | ||||||
| 74<\/td>\n | Figure A.4 \u2013 Example 4 : a case corresponding to mode 3 <\/td>\n<\/tr>\n | ||||||
| 76<\/td>\n | Figure A.5 \u2013 Example 5 : a case corresponding to mode 4.a and 4.b <\/td>\n<\/tr>\n | ||||||
| 78<\/td>\n | Figure A.6 \u2013 Example 6: a case corresponding to mode 4.a and 4.b <\/td>\n<\/tr>\n | ||||||
| 80<\/td>\n | Figure A.7 \u2013 Example 7: a case corresponding to mode 4.c <\/td>\n<\/tr>\n | ||||||
| 82<\/td>\n | Figure A.8 \u2013 Example 8: a case corresponding to mode 5.b <\/td>\n<\/tr>\n | ||||||
| 84<\/td>\n | Figure A.9 \u2013 Example 9: a case corresponding to mode 6.a <\/td>\n<\/tr>\n | ||||||
| 85<\/td>\n | Annex B (informative) Typical pressure fluctuation transducers parameters for model test <\/td>\n<\/tr>\n | ||||||
| 86<\/td>\n | Annex C (informative) Pressure transducer dynamic calibration C.1 Fast valve opening method C.2 Rotating valve method Figure C.1 \u2013 Pressure transducer dynamic calibration schematic diagram with fast open valve method <\/td>\n<\/tr>\n | ||||||
| 87<\/td>\n | C.3 Electrical spark method Figure C.2 \u2013 Pressure transducer dynamic calibration with rotating valve method Figure C.3 \u2013 Spark plug used as to generate an impulse excitation in water for pressure transducer dynamic calibration <\/td>\n<\/tr>\n | ||||||
| 88<\/td>\n | Annex D (informative) Proposed remote pressure measurement fluctuation correction D.1 General D.2 Correction method theory <\/td>\n<\/tr>\n | ||||||
| 89<\/td>\n | D.3 Measuring and estimating tube frequency response <\/td>\n<\/tr>\n | ||||||
| 90<\/td>\n | Figure D.1 \u2013 Typical results obtained by shutting off drainage valve Table D.1 \u2013and calculated for p1 to p4 <\/td>\n<\/tr>\n | ||||||
| 91<\/td>\n | D.4 Pressure fluctuation correction Table D.2 \u2013 Estimated frequencies based on tubing mechanical characteristics <\/td>\n<\/tr>\n | ||||||
| 92<\/td>\n | Figure D.2 \u2013 Signal and spectrum of four remote sensors and one local sensor Table D.3 \u2013 Peak-to-peak value on the raw signals Table D.4 \u2013 Wave speed and damping ratio <\/td>\n<\/tr>\n | ||||||
| 93<\/td>\n | Figure D.3 \u2013 Signal and spectrum of four remote sensors (corrected) and one local sensor <\/td>\n<\/tr>\n | ||||||
| 94<\/td>\n | D.5 Limitations Table D.5 \u2013 Peak-to-peak value on the corrected signals <\/td>\n<\/tr>\n | ||||||
| 95<\/td>\n | Annex E (informative) Forced response analysis for Francis turbines operating in part load conditions E.1 General E.2 Systematic methodology based on detailed modelling of hydroelectric power plant E.2.1 Description of the test case <\/td>\n<\/tr>\n | ||||||
| 96<\/td>\n | E.2.2 Modelling of the hydraulic power plant Figure E.1 \u2013 SIMSEN model of the test case Figure E.2 \u2013 Performance hill chart of the Francis turbine for different guide vane openings Table E.1 \u2013 Francis turbine parameters <\/td>\n<\/tr>\n | ||||||
| 98<\/td>\n | Figure E.3 \u2013 Elementary hydraulic pipe of length dx and its equivalent circuit <\/td>\n<\/tr>\n | ||||||
| 99<\/td>\n | E.2.3 Forced response analysis of the test case Figure E.4 \u2013 Forced response for a = 50 m\/s (left) and a = 60 m\/s (right) <\/td>\n<\/tr>\n | ||||||
| 100<\/td>\n | Figure E.5 \u2013 Forced response for a = 70 m\/s (left) and a = 80 m\/s (right) Figure E.6 \u2013 Forced response for a = 90 m\/s (left) and a = 100 m\/s (right) Figure E.7 \u2013 Damping and eigenfrequency for a = 50 m\/s (left) and a = 60 m\/s (right) Figure E.8 \u2013 Damping and eigenfrequency for a = 70 m\/s (left) and a = 80 m\/s (right) <\/td>\n<\/tr>\n | ||||||
| 101<\/td>\n | Figure E.9 \u2013 Damping and eigenfrequency for a = 90 m\/s (left) and a = 100 m\/s (right) Figure E.10 \u2013 Eigenmode for a = 50 m\/s and eigenfrequency f = 4,18 Hz Figure E.11 \u2013 Eigenmode for a = 50 m\/s and eigenfrequency f = 3,67 Hz Figure E.12 \u2013 Eigenmode for a = 100 m\/s and eigenfrequency f = 2,61 Hz <\/td>\n<\/tr>\n | ||||||
| 102<\/td>\n | E.3 Simplified approach based on the hydroacoustic properties of the hydraulic system E.3.1 General E.3.2 Cavitating draft tube first natural frequency Figure E.13 \u2013 Draft tube modelled with cavitation compliance and draft tube inductance <\/td>\n<\/tr>\n | ||||||
| 103<\/td>\n | E.3.3 Hydraulic circuit natural frequencies Figure E.14 \u2013 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 <\/td>\n<\/tr>\n | ||||||
| 104<\/td>\n | E.3.4 Example of applications Figure E.15 \u2013 Hydraulic system modelled by an equivalent pipe and corresponding modes shapes for the first and second natural frequencies <\/td>\n<\/tr>\n | ||||||
| 105<\/td>\n | Figure E.16 \u2013 Hydraulic systems 1, 2 and 3 Table E.2 \u2013 Parameters of the hydraulic systems 1, 2 and 3 <\/td>\n<\/tr>\n | ||||||
| 106<\/td>\n | Table E.3 \u2013 Parameters of the equivalent pipe of the hydraulic system 1 <\/td>\n<\/tr>\n | ||||||
| 107<\/td>\n | Table E.4 \u2013 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 \u2013 Parameters of the equivalent pipe of the hydraulic system 2 Table E.6 \u2013 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 <\/td>\n<\/tr>\n | ||||||
| 108<\/td>\n | Table E.7 \u2013 Parameters of the equivalent pipe of the hydraulic system 3 <\/td>\n<\/tr>\n | ||||||
| 109<\/td>\n | E.3.5 Limitations of the methodology Table E.8 \u2013 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 \u2013 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 <\/td>\n<\/tr>\n | ||||||
| 110<\/td>\n | Annex F (informative) Influence of Thoma number on pressure fluctuation Figure F.1 \u2013 Influence of Thoma number on pressure fluctuation <\/td>\n<\/tr>\n | ||||||
| 111<\/td>\n | Figure F.2 \u2013 Example of waterfall diagram of the pressure fluctuations as function of the frequency and Thoma number <\/td>\n<\/tr>\n | ||||||
| 112<\/td>\n | Annex G (informative) Transposition of synchronous pressure fluctuations from model to prototype for Francis turbines operating at off-design conditions G.1 General G.1.1 Overview Figure G.1 \u2013 Peak-to-peak value of pressure fluctuations as a function of the discharge factor measured on the model and the corresponding prototype <\/td>\n<\/tr>\n | ||||||
| 113<\/td>\n | Figure G.2 \u2013 Layout of EPFL test rig PF3 1-D hydroacoustic model Figure G.3 \u2013 Electrical T-shaped representation of the cavitation vortex rope developing in Francis turbine draft tube in part load conditions <\/td>\n<\/tr>\n | ||||||
| 115<\/td>\n | Figure G.4 \u2013 Excitation system and 3D cut-view of the rotating valve <\/td>\n<\/tr>\n | ||||||
| 116<\/td>\n | Figure G.5 \u2013 Strouhal number of the precession frequency as a function of the swirl number computed with Formula (G.6) <\/td>\n<\/tr>\n | ||||||
| 117<\/td>\n | Figure G.6 \u2013 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) <\/td>\n<\/tr>\n | ||||||
| 118<\/td>\n | Figure G.7 \u2013 Predicted values of precession frequency and first eigenfrequency at the prototype scale as a function of the output power of the generating unit <\/td>\n<\/tr>\n | ||||||
| 119<\/td>\n | Figure G.8 \u2013 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) <\/td>\n<\/tr>\n | ||||||
| 120<\/td>\n | Figure G.9 \u2013 Hill chart comparing the measured and the predicted resonance conditions assuming a constant pressure value in the draft tube cone of the prototype <\/td>\n<\/tr>\n | ||||||
| 121<\/td>\n | Annex H (informative) Statistical analysis of pressure fluctuation data H.1 Normalizing step for the comparison of data <\/td>\n<\/tr>\n | ||||||
| 122<\/td>\n | Figure H.1 \u2013 Pressure fluctuations versus discharge factor Figure H.2 \u2013 Normalized discharge of pressure fluctuations Figure H.3 \u2013 Normalized pressure amplitude of pressure fluctuations Figure H.4 \u2013 Comparison of pressure fluctuations of model and prototype <\/td>\n<\/tr>\n | ||||||
| 123<\/td>\n | H.2 Collected data H.3 Draft tube zone phenomena Figure H.5 \u2013 Set of pressure fluctuation of models and prototypes for draft tube analysis Table H.1 \u2013 World hydropower plant references <\/td>\n<\/tr>\n | ||||||
| 124<\/td>\n | Figure H.6 \u2013 Difference between pressure fluctuations between the model and the prototype Figure H.7 \u2013 Standard deviation of difference of pressure fluctuation <\/td>\n<\/tr>\n | ||||||
| 125<\/td>\n | Figure H.8 \u2013 Transposition accuracy for draft tube cone <\/td>\n<\/tr>\n | ||||||
| 128<\/td>\n | H.4 Vaneless zone phenomena Figure H.9 \u2013 Transposition of each power plant test case for the draft tube cone <\/td>\n<\/tr>\n | ||||||
| 129<\/td>\n | Figure H.10 \u2013 Set of pressure fluctuation of models and prototypes for vaneless zone analysis Figure H.11 \u2013 Difference between pressure fluctuations between the model and the prototype <\/td>\n<\/tr>\n | ||||||
| 130<\/td>\n | Figure H.12 \u2013 Standard deviation of difference of pressure fluctuation Figure H.13 \u2013 Transposition accuracy for vaneless zone <\/td>\n<\/tr>\n | ||||||
| 131<\/td>\n | Figure H.14 \u2013 Transposition of each power plant test case for vaneless zone <\/td>\n<\/tr>\n | ||||||
| 132<\/td>\n | H.5 Spiral case phenomena Figure H.15 \u2013 Set of pressure fluctuation of models and prototypes for spiral case analysis <\/td>\n<\/tr>\n | ||||||
| 133<\/td>\n | Figure H.16 \u2013 Difference between pressure fluctuations between the model and the prototype Figure H.17 \u2013 Standard deviation of difference of pressure fluctuation <\/td>\n<\/tr>\n | ||||||
| 134<\/td>\n | Figure H.18 \u2013 Transposition accuracy for spiral case <\/td>\n<\/tr>\n | ||||||
| 135<\/td>\n | Figure H.19 \u2013 Transposition of each power plant test cases for spiral case <\/td>\n<\/tr>\n | ||||||
| 136<\/td>\n | Annex J (informative) Gathering worldwide pressure fluctuation data J.1 Chinese test cases <\/td>\n<\/tr>\n | ||||||
| 137<\/td>\n | J.2 France test case Figure J.1 \u2013 Comparison of pressure fluctuations on the draft tube for 10 Chinese model and prototype references <\/td>\n<\/tr>\n | ||||||
| 138<\/td>\n | Figure J.2 \u2013 Comparison of pressure fluctuations on the draft tube for one France model and prototype reference Figure J.3 \u2013 Comparison of pressure fluctuations on the spiral case for one France model and prototype reference <\/td>\n<\/tr>\n | ||||||
| 139<\/td>\n | J.3 Norway test case Figure J.4 \u2013 Comparison of pressure fluctuations on the draft tube for one Norway model and prototype reference <\/td>\n<\/tr>\n | ||||||
| 140<\/td>\n | Bibliography <\/td>\n<\/tr>\n<\/table>\n","protected":false},"excerpt":{"rendered":" Hydraulic machines. Francis turbine pressure fluctuation transposition<\/b><\/p>\n |