jsme · executive secretary yukio ishiguro (electric power development co., ltd.) ... kiyohito tani...

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Performance Conversion Method for

Hydraulic Turbines and Pump-Turbines

JSME-S008-2018

The Japan Society of Mechanical Engineers

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List of Members on Revising JSME Standard “Performance Conversion Method for

Hydraulic Turbines and Pump-Turbines”

(The Institute of Electrical Engineers of Japan, The Japan Society of Mechanical Engineers)

Chairman Yuji NAKANISHI (Kanagawa University)

Executive Secretary Toshiaki SUZUKI (Toshiba Plant Systems & Services Corporation) Executive Secretary Yukio ISHIGURO (Electric Power Development CO., Ltd.)

Member (The Institute of Electrical Engineers of Japan) Mitsuo UNO (Kyushu Kyoritsu University)

Toshiaki KANEMOTO (Kyushu Institute of Technology)

Takaya KITAHORA (Shonan Institute of Technology)

Hiroshi TSUKAMOTO (National Institute of Technology,

Kitakyushu College)

Akinori FURUKAWA (National Institute of Technology,

Oita College)

Masatake MAEKAWA (Hitachi Mitsubishi Hydro

Corporation)

Kiyohito TANI (Hitachi Mitsubishi Hydro Corporation)

Ryoji SUZUKI (Voith Fuji Hydro K. K.)

Makoto EZAKI (Tokyo Electric Power Company Holdings,

Inc.)

Eiji NISHIHATA (Chubu Electric Power Co., Inc.)

Kiyoshi IKENO (The Kansai Electric Power Co., Inc.)

Kaneo SUGISHITA (Toshiba Corporation)

Member (The Japan Society of Mechanical Engineers) Jun MATSUI (Yokohama National University)

Michitsugu MORI (Hokkaido University)

Toshiharu KAGAWA (Tokyo Institute of Technology)

(En Route Resigned Executive Secretary) Hideaki SAGARA (Electric Power Development CO., Ltd.) Satoshi SUZUKI (Electric Power Development CO., Ltd.)

(En Route Resigned Assistant Secretary)Tsuyoshi YAMAZAKI (Electric Power Development CO.,

Ltd.)

Hirohito YAMASHIRO (Electric Power Development CO.,

Ltd.)

Akihiko MATSUI (Electric Power Development CO., Ltd.)

Takeshi SASAKAWA (Electric Power Development

CO., Ltd.)

(En Route Resigned Member The Institute of Electrical Engineers of Japan)Kazuyoshi MIYAGAWA (Mitsubishi Heavy Industries,

Ltd.) Takayuki SHIOZAKI (Tokyo Electric Power CO.,

Inc.)Hirotaka WATANABE (Tokyo Electric Power CO.,Inc.)Toshimitsu SEKIZAWA ( Tokyo Electric Power CO.,Inc.)

Shiroh KIKUCHI (Tokyo Electric Power CO., Inc.) Yoshiaki TSUKIYAMA (Chubu Electric Power CO., Inc.) Kiyoshi KOMURA (Chubu Electric Power CO., Inc.) Shigenori ITO (Chubu Electric Power CO., Inc.) Haruki OGIWARA (The Kansai Electric Power Co., Inc.) Takuya IDEHARA (The Kansai Electric Power Co., Inc.)

(En Route Resigned Member The Japan Society of Mechanical Engineers)Koji KIKUYAMA (Nagoya Sangyo University) Tadashi NARABAYASHI (Hokkaido University)

(Note) Name of the affiliation of each member was based on the name at the time, when he first attended this committee.

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PREFACE TO THE REVISION

Nineteen years have passed since the revised edition of JSME Standard, JSME-S008-1999, “Performance Conversion Method for Hydraulic Turbines and Pump-Turbines” for converting the measured performances of model turbines and model pump-turbines to those of their prototypes was published. At this period, the corresponding international code IEC 62097 was published in 2009. In this code, the general idea for the conversion and the relevant data needed for the conversion follow JSME-S008-1999, and more exact conversions are realized by the calculation of each flow passage component instead of a whole machine.

On the other hand, within Japan, JSME-S008-1999 and JIS-B8103-1989 have been widely used for commercial transactions. Especially the latter has been needed to update because it includes the conversion method prescribed in the first edition of S008, JSME-S008-1989.

Under the circumstances, the revising work of JSME-S008-1999 began in 2010 to lay the groundwork for future standardization of the conversion method. The Japan Society of Mechanical Engineers and the Institute of Electrical Engineers of Japan decided to work together to make the draft of a new edition of JSME-S008. The Committee for the Revision of “Performance Conversion Method for Hydraulic Turbines and Pump-Turbines” was set up in the Institute of Electrical Engineers of Japan, and made up of members from universities, manufacturers and users.

This standard was revised while maintaining the physical appropriateness in loss calculation as a standard ofacademic society. To convert the performances more exactly, component-wise conversion was employed following IEC 62097 instead of the conversion of a whole machine. This allows us to convert the performances with high accuracy and to apply to the refurbishment and replacement of aged components. As for axial flow turbines, relative scalable losswas added in a practical range of specific speed. Not only can this revision convert performances at each flow passage component with relative scalable loss taken over from JSME-S008-1999, but this revision gives various relevant data for the conversion, standardized as functions of specific speed by considering flow phenomena in machines, which are consistent with the existing machines. These contribute to enhancement of the usability of this conversion method.Furthermore, the relationship between arithmetic mean roughness and equivalent sand roughness was reconsidered, and roughness distribution of flow passage surfaces in prototype machines was also considered.

This revision was accomplished by long-term devoted work of the committee members. I would like to express my deepest gratitude and sincere appreciation to all the members involved in the work on the revision.

Prof. Yuji Nakanishi, Chairman Committee for the Revision of “Performance Conversion Method for Hydraulic Turbines and Pump-Turbines”

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SUBSTANCE OF REVISION

Through the prototypes and models of hydraulic turbines and pump-turbines are made geometrically similar to each other, the efficiency of the prototype is usually higher than that of the model. This is caused by the difference in the rate of wall friction loss to the total hydraulic energy, as the Reynolds number is largely different between the prototype and the model as well as the surface roughness. This deviation from the fundamental similarity law is called “scale effect”.

Wall friction causes not only the dissipation of specific hydraulic energy E of the main flow but also the disk friction power loss at the back surface of a runner. Then the difference in wall friction between model and prototype results in the difference of specific energy efficiency and power efficiency, and further of discharge efficiency. In the previous edition of JSME-S008-1999, in order to express the changes of these three component efficiencies by this scale effect, it had been defined the scale factors as the ratio of each component efficiency of the prototype to the model, and had standardized them first in the world. However, although this surface roughness varies depending on each component passage (spiral case, stay vane, guide vane, runner and draft tube) in hydraulic turbines and pump-turbines, the relationship of the roughness ratio between model and prototype of each component passage had been simplified by introducing the roughness ratio dependency coefficient β in the previous edition.

This standard should be a fundamental one relating to the performance conversion of hydraulic turbines and pump-turbines, so it should avoid above mentioned simplification and should be based on the physical phenomenon as much as possible.

Substance of the present revision is summarized hereinafter.

1. Specific Energy Efficiency Scale Factor 1) Evaluation of the relative scalable loss divided into each flow passage component in the hydraulic turbines and pump-turbines

In order to obtain a more exact performance conversion method, the conversion based on divided components passages similar to IEC 62097-2009 instead of the conversion based on the whole flow passage used by the previous edition was adopted. Five divided component passages (spiral case, stay vanes, guide vanes, runner and draft tube) were used for Francis turbines and Francis type pump-turbines and six divided component passages (spiral case , stay vanes, guide vanes, flow passage from guide vane outlet to runner inlet, runner and draft tube) were used for diagonal flow and axial flow turbine. Then the relative scalable loss ECO and the friction coefficient ratio CO of each component passage were obtained, and from these, the specific energy efficiency scale factor EF of the whole flow passage in hydraulic turbine and pump-turbine can be calculated. As a result, the roughness ratio dependence coefficient β was not used and the conversion becomes more exact, and can be applied for the case that the surface roughness ratio differs greatly for each flow passage between the model and the prototype such as the partial renovation of the existing hydraulic turbines and pump-turbines as well. 2) Standardization of relative scalable loss E by the polynomial approximation based on physical phenomenon

In the previous edition, the relative scalable loss data obtained from the flow analysis had been expressed simply as a first order approximation to the specific speed. In this edition, model turbines and pump-turbines over a wide specific speed range were virtually designed, and a reference dimension factor DdhCO ， DlCO and a reference velocity factor uCOv for each of them were calculated. Then each relative scalable loss ECO was standardized by the approximation polynomial formula against the specific speed based on the one dimensional theory. As a result, more suitable approximation of the relative scalable loss expressing the physical phenomenon was given than the previous edition. 3) Recalculation of relative scalable loss of axial flow turbines

In case of the previous edition, the number of data on the relative scalable loss of the axial flow turbines (Kaplan turbines and bulb turbines) had been small, and for the Kaplan turbines, the relative scalable loss of the flow passage

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from the guide vane outlet to the runner inlet had not been included. In this edition, the flow analysis was newly carried out to obtain the relative scalable loss ECO for each flow passage component, and the evaluation accuracy was improved. 2. Discharge Efficiency Scale Factor 1) Standardization of more exact formula on discharge efficiency scale factor

In case of the previous edition, the discharge efficiency scale factor had been set to a constant value for Francis turbines and pump-turbines, however, the conversion formula taking the size and Reynolds number into consideration was standardized in order to become more exact in this edition. 3. Power Efficiency Scale Factor 1) Standardization of more exact formula on power efficiency scale factor

In case of the previous edition, the power efficiency scale factor had been defined by a formula determined only by the specific speed, however, the conversion formula taking Reynolds number and surface roughness in flow passage into consideration was standardized in order to become more exact in this edition. 4. Coordination Of Terms And Symbols with IEC Standards

In order to internationalize this standard, the terms and symbols were coordinated with IEC standards.

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Content

1. GENERAL･･･････････････････････････････････････････････････････････････････････････1

1・1 Object 1・2 General Remarks

2. CONDITIONS FOR APPLICATION ･･･････････････････････････････････････････････････2

2・1 Types of Hydraulic Machines2・2 Requirements on Geometrical Similarity and Model Test 2・3 Reynolds Number at Model Test 2・4 Corresponding International Standards

3. LIST OF TERMS, DEFINITIONS, SYMBOLS AND UNITS･･････････････････････････････3

3・1 Terms 3・1・1 Related to geometry 3・1・2 Related to physical quantity and property 3・1・3 Related to discharge 3・1・4 Related to rotational speed and peripheral speed3・1・5 Related to specific energy 3・1・6 Related to power 3・1・7 Related to efficiency 3・1・8 Related to scaling 3・1・9 Related to dimensional performance

3・2 Subscript

4. CONVERSION METHOD OF TURBINE PERFORMANCE OF HYDRAULIC TURBINESAND PUMP-TURBINES･･････････････････････････････････････････････････････････････11

4・1 Fundamental Formulae for Performance Conversion 4・2 Calculation of Specific Energy Efficiency Scale Factor EF

4・2・1 Specific speed QEN

4・2・2 Standard speed factor EDstdn , standard discharge factor EDstdQ

4・2・3 Reference dimensional factor DdhCO , DlCO

4・2・4 Reference velocity factor uCOv

4・2・5 Standard relative scalable (friction) loss ECOstd4・2・6 Friction coefficient of model component passage MCO , MfCOC

4・2・7 Relative scalable (friction) loss ECO for each tested point

4・2・8 Friction coefficient of prototype component passage PCO , PfCOC

4・2・9 Friction coefficient ratio CO4・3 Calculation for Discharge Efficiency Scale Factor QF

4・3・1 Discharge efficiency scale factor QF for Francis turbines and Francis type pump-turbines (turbine operation) 4・3・2 Discharge efficiency scale factor QF for diagonal /axial flow turbines

4・4 Calculation for Power Efficiency Scale Factor TF4・4・1 Power efficiency scale factor TF for Francis turbines and Francis type pump-turbines (turbine operation) 4・4・2 Power efficiency scale factor TF for diagonal/axial flow turbines

4・5 Surface Roughness of Component Passage MCORa , PCORa

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5. CONVERSION METHOD OF PUMP PERFORMANCE OF PUMP-TURBINES ･････････26

5・1 Fundamental Formulae for Performance Conversion 5・2 Calculation of Specific Energy Efficiency Scale Factor EF





5・2・5 Standard relative scalable (friction) loss ECOstd

5・2・6 Friction coefficient of model component passage MCO , MfCOC



5・2・9 Friction coefficient ratio CO

5・3 Calculation for Discharge Efficiency Scale Factor QF 5・3・1 Discharge efficiency scale factor QF for Francis type pump-turbines (pump operation) 5・3・2 Discharge efficiency scale factor QF for diagonal/axial flow pump-turbines (pump operation)

5・4 Calculation for Power Efficiency Scale Factor TF 5・4・1 Power efficiency scale factor TF for Francis type pump-turbine (pump operation) 5・4・2 Power efficiency scale factor TF for diagonal/axial flow pump-turbines (pump operation)


APPENDIX-A DERIVATION OF SCALE EFFECT FORMULAE FOR PERFORMANCE OF HYDRAULIC TURBINES AND PUMP-TURBINES IN TURBINE OPERATION

A1. FUNDAMENTAL EQUATIONS on TURBINE PERFORMANCE and APPLICATION CONDITIONS for CONVERSION FORMULAE･･････････････････････････････････････････40

A1・1 Specific Hydraulic Energy A1・2 Fundamental Equations on Turbine Performance A1・3 Application Conditions for Performance Conversion Formulae

A2. DERIVATION of FORMULAE for PERFORMANCE CONVERSION････････････････････････43

A3. DERIVATION of CONVERSION FORMULAE of SPECIFIC ENERGY EFFICIENCY ･････････44

APPENDIX-B DERIVATION OF SCALE EFFECT FORMULAE FOR PERFORMANCE OF PUMP-TURBINES IN PUMP OPERATION

B1. FUNDAMENTAL EQUATIONS on PUMP PERFORMANCE and APPLICATION CONDITIONS for CONVERSION FORMULAE････････････････････････････････････････････････････････46

B1・1 Specific Hydraulic Energy B1・2 Fundamental Equations on Pump Performance B1・3 Application Conditions for Performance Conversion Formulae

B2. DERIVATION of FORMULAE for PERFORMANCE CONVERSION････････････････････････48

B3. DERIVATION of CONVERSION FORMULAE of SPECIFIC ENERGY EFFICIENCY ･････････49

APPENDIX-C RELATIVE SCALABLE LOSS

C1. CALCULATION METHOD and RESULT of RELATIVE SCALABLE LOSS by ANALYTICAL METHOD･･･････････････････････････････････････････････････････････････････････････52

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C1・1 Definition and Derivation of Relative Scalable Loss C1・2 Calculation Result of Relative Scalable Loss C1・3 Calculation Methods of Friction Loss

C1・3・1 Approximation to equivalent pipe flow C1・3・2 Approximation to flow along a flat plate C1・3・3 Boundary layer analysis

C2. METHOD to CALCULATE RELATIVE SCALABLE LOSS in CONSIDERATION of TURBINE TYPE, SPECIFIC SPEED and OPERATING RANGE･･････････････････････････････････････61

C2・1 General Equation to Calculated Relative Scalable Loss C2・1・1 Spiral case, draft tube C1・1・2 Stay vanes, guide vanes C1・1・3 Runner

C2・2 Change of Relative Scalable Loss due to Types of Turbines and Specific Speed of the Best Efficiency Point

C2・2・1 Best efficiency points of models of Francis turbines, diagonal/axial flow turbines and pump-turbines C2・2・2 Dimensions of flow passages of Francis turbines, diagonal/axial flow turbines and pump-turbines C2・2・3 Pump-turbines other than Francis type pump-turbines C2・2・4 Calculation results

C2・3 Relative Scalable Loss under Operating Conditions off the Optimum Point C2・3・1 Relative scalable loss under operating conditions off the optimum point for Francis turbines or Francis

type pump-turbines C2・3・2 Relative scalable loss under operating conditions off the optimum point for diagonal/axial flow turbines C2・3・3 Relative scalable loss under operating conditions off the optimum point for Francis type pump-turbines

in pump operation C2・3・4 Relative scalable loss under operating conditions off the optimum point for diagonal/axial flow

pump-turbines in pump operation

APPENDIX-D FRICTION COEFFICIENT RATIO

D1. FORMER TREATMENT and PROBLEMS on SURFACE ROUGHNESS and FRICTION COEFFICIENT･･･････････････････････････････････････････････････････････････････････92

D1・1 Reynolds Number and Friction Characteristics D1・2 Admissible Equivalent Sand Roughness D1・3 Correlation between Arithmetic Mean Roughness Ra and Equivalent Sand Roughness ksD1・4 Treatment of Raadm in the Present Standard

D2. FORMULAE for FRICTION COEFFICIENT RATIO･･･････････････････････････････････････97

D2・1 Friction Coefficient Ratio in the Former S008 D2・2 Formulae for Friction Coefficient Ratio Adopted in This Standard

D2・2・1 Spiral case and draft Tube D2・2・2 Stay vanes, guide vanes and runner

D3. SURFACE ROUGHNESS and FRICTION COEFFICIENT in PROTOTYPE･･････････････････101

D3・1 Influence of Variation in Velocity and Surface Roughness in a Component D3・2 Discussion on Surface Roughness Recommended by IEC 62097 D3・3 Prototype Roughness Recommended in Various Standards

APPENDIX-E LEAKAGE LOSS AND DISCHARGE EFFICIENCY

E1. CALCULATION of LEAKAGE FLOW･････････････････････････････････････････････････109

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E2. DISCHARGE EFFICIENCY of TURBINES and PUMP-TURBINES･････････････････････････111

E2・1 In the Case of Seal Clearance within the Specified Tolerance E2・2 In the Case of Seal Clearance out of the Specified Tolerance

E3. CONVERSION FORMULAE of DISCHARGE EFFICIENCY and SCALE FACTOR･･･････････112

E3・1 Derivation of Discharge Efficiency E3・2 Derivation of Discharge Efficiency Scale Factor

APPENDIX-F DISK FRICTION AND POWER EFFICIENCY

F1. CALCULATION of DISK FRICTION LOSS･････････････････････････････････････････････120

F2. POWER EFFICIENCY in TURBINES and PUMP-TURBINES･･････････････････････････････122

F3. CONVERSION FORMULA of POWER EFFICIENCY and POWER EFFICIENCY SCALE FACTOR･･･････････････････････････････････････････････････････････････････････････123

F3・1 Derivation of Conversion Formula and Scale Factor F3・2 Ratio of Disk Friction Torque Coefficient TF3・3 Determination of Scale Factor TF of Power Efficiency

APPENDIX-G COMPARISON WITH THE EXISTING CONVERSION METHOD

G1. SPECIFIC ENERGY EFFICIENCY SCALE FACTOR･････････････････････････････････････135

G2. DISCHARGE EFFICIENCY SCALE FACTOR･･･････････････････････････････････････････138

G3. POWER EFFICIENCY SCALE FACTOR ･･･････････････････････････････････････････････140

G4 EXAMPLES of CALCULATION RESULTS of EFFICIENCY SCALE FACTOR･･･････････････143

G5 COMPARISON with the CONVERSION RESULTS of the PREVIOUS METHOD･････････････148

APPENDIX-H PERFORMANCE CONVERSION FOR PELTON TURBINES

H1. INTRODUCTION･･･････････････････････････････････････････････････････････････････151

H2. GREIN’S FORMULA to CONVERT HYDRAULIC EFFICIENCY CONSIDERING SCALE EFFECT･･･････････････････････････････････････････････････････････････････････････151

H2・1 Efficiency Conversion Formula Dependent on Fr, Re & We Numbers H2・2 Future Issues for Grein’s Formula

H3. SIMILARITY LAW for PERFORMANCE CONVERSION of PELTON TURBINES････････････152

H3・1 Similarity Law to Convert Runner Performance H3・2 Similarity Law to Convert Specific Hydraulic Energy Coefficient EnD H3・3 Similarity Law to Convert Discharge Coefficient QnD

H3・4 Similarity Law to Convert Power Coefficient PnD

H4. INTERNAL FLOW of PELTON TURBINES and PERFORMANCE SCALE FACTORS････････156

H4・1 Flow Similarity at Runner Inlet H4・2 Flow Similarity at Runner Outlet H4・3 Outflow from Cutout of BucketsH4・4 Steady Conduit Flow and Energy Scale Factor EcF

H4・5 Unsteady Free Flow and Energy Scale Factor EFFH4・6 Free Jet at Nozzle Outlet and Discharge Scale Factor QF

H5. JET INTERFERENCE and SCALE EFFECT of MULTI NOZZLE PELTON TURBINES･･････160

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APPENDIX-I PHYSICAL PROPERTIES OF WATER AND ACCELERATION DUE TO GRAVITY

I1. DENSITY of WATER ････････････････････････････････････････････････････････････････164

I2. KINEMATIC VISCOSITY of WATER ･･････････････････････････････････････････････････168

I3. ACCELERATION due to GRAVITY････････････････････････････････････････････････････169

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PERFORMANCE CONVERSION METHOD FOR HYDRAULIC TURBINES AND PUMP-TURBINES

1. GENERAL

1・1 Object

This standard prescribes “Performance conversion method for acceptance test” to convert the hydraulic performance of a model turbine, pump-turbine or storage pump tested accurately under non-cavitating condition to that of a prototype hydraulic machine with due consideration on the scale effect. The conversion method compensates for the effects on hydraulic performance due to the difference in Reynolds number and surface roughness between the model and the prototype, using the relative scalable (friction) loss of the model E and the friction coefficient ratiobetween the prototype and the model . Difference in the type of hydraulic machine, specific speed and operating conditions are also considered. It also provides accurate conversion methods for discharge, head and power characteristics as well as for efficiency characteristics.

[Explanation 1・1] Surface roughness of a prototype hydraulic machine is in many cases hydraulically rough. Its effect on the hydraulic performance conversion is not negligible. So the roughness effect was taken into account in this standard. Also surface roughness of the model and the prototype differ in each component flow passage (a spiral case, stay vanes, guide vanes, a runner and a draft tube) so the surface roughness was defined for each component flow passage to carry out more accurate conversion. Furthermore, to correct the influence due to Reynolds number difference between the model and the prototype, the relative scalable (friction) loss E was determined by considering the dependence on the specific speed and the operating condition (not only for optimum operating point but also non-optimum operation) as well as the difference in the type of the hydraulic machine.

1・2 General Remarks

The values of the relative scalable (friction) loss E of the model, which is a standard reference parameter used inthe performance conversion method set out in this standard, were determined by friction loss analysis based on manymodel test results. Also more accurate conversion method than the one given in the former standard JSME S008-1999 was established by using each component passage conversion based on each relative scalable (friction) loss ( ESP ,

ESV , EGV , ERU , E and EDT ) defined for each component passage (a spiral case, stay vanes, guide vanes, a runner and a draft tube).

There are some opinions that the accuracy of performance conversion methods should be verified by the comparison of converted performance with field efficiency test results. However, it is very difficult technically and practically to carry out field efficiency tests with the accuracy sufficient for such evaluation. In most cases, the uncertainty of the field test results is comparable to the step-up difference of the efficiency due to scale effect and it is actually impossible to verify the accuracy of a performance conversion method by field efficiency tests. Hence the conversion method presented in this standard is established by separating the scalable loss using the results of the latest theoretical research work on the internal loss analysis of hydraulic machines, which have been verified experimentally by many model tests.

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2. CONDITIONS FOR APPLICATION

2・1 Types of Hydraulic Machines This standard is applicable to the machines which are used as main units of hydropower stations. The types of the

machines covered by this standard are set out below. Hydraulic turbines: Francis turbines, diagonal flow turbines (Deriaz turbine), axial flow turbines (Kaplan turbines,

bulb turbines, propeller turbines, S-type tubular turbines) Pump-turbines: Francis type pump-turbines, diagonal flow pump-turbines (Deriaz pump-turbine), axial flow

pump-turbines (Tubular pump-turbine), storage pumps for hydropower station

[Explanation 2・1]

See Appendix H for the performance conversion method of Pelton turbines.

2・2 Requirements on Geometrical Similarity and Model Test It is required for the application of this standard that the geometrical similarity between the model and the

prototype is maintained within the tolerance stipulated in JEC/IEC/JIS code of equivalent. The angle of guide vanes (also the angle of runner vanes for turbines with adjustable runner blades) of both the model and the prototype shall be identical. Surface roughness of the model and the prototype shall also conform to the requirement of the relevant code.

The conversion method set out in this standard shall be applied to the performance conversion from the model performance characteristics, which is obtained by model tests conducted in accordance with JIS/IEC code or equivalent, to the geometrically homologous prototype performance characteristics.

[Applicable code for geometrical similarity between model and prototype] JIS B 8103 (1989) : Methods for Model Tests of Hydraulic Turbines and Reversible Pump-Turbine. JEC-4003 (2001) : Dimensional Inspection of Hydraulic Turbines and Pump-Turbines. IEC 60193 (1999) : Hydraulic Turbines, Storage Pumps and Pump-Turbines － Model Acceptance Tests. [Applicable code for model test] JIS B 8103 (1989) : Methods for Model Tests of Hydraulic Turbines and Reversible Pump-Turbine. IEC 60193 (1999) : Hydraulic Turbines, Storage Pumps and Pump-Turbines － Model Acceptance Tests.

2・3 Reynolds Number at Model Test

The test Reynolds number shall be the one stipulated in the applicable codes shown in Section 2・2.

2・4 Corresponding International Standards

IEC 62097 (2009) Hydraulic machines, radial and axial - Performance conversion method from model to prototype

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3. LIST OF TERMS, DEFINITIONS, SYMBOLS AND UNITS

3・1 Terms

3・1・1 Related to geometry

No. Term Definition Symbol Unit

1.1 Reference diameter Reference diameter of the hydraulic machine as expressed by the runner outlet/impeller inlet or throat ring diameter.

D m

1.2 Arithmetic mean roughness Arithmetic mean roughness of flow surface * Ra μm

1.3 Equivalent sand roughness Equivalent sand roughness of flow surface** ks μm

1.4 Admissible equivalent sand roughness

Maximum equivalent sand roughness regarding as hydraulically smooth.

admks μm

1.5 Roughness correlation factor Ratio of equivalent sand roughness ks to arithmetic mean roughness Ra : RaksCk

kC －

1.6 Reference dimension of a flow passage

Diameter of a pipe based on the equivalent pipe flow approximation (=4m，m ; Hydraulic radius)

hd m

1.7 Reference dimension of a flow passage

Length of a flat plate based on the equivalent flat plate flow approximation

l m

* Refer to JIS B 0601**Refer to Nikuradse, J., Gesetzmӓβigkeit der turbulenten Strӧmung in glatten Roheren, Forsh. Arb. Ing-Wes, Nu. 356,(1932)

3・1・2 Related to physical quantity and property


2.1 Acceleration due to gravity Local value of gravitational acceleration as a function of altitude and latitude, refer to Appendix I3.

g m s-2

2.2 Density of water Mass of water per unit volume, refer to Appendix I1. kg m-3

2.3 Kinematic viscosity of water Ratio of dynamic viscosity to density of water , refer to Appendix I2.

m2 s-1

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3・1・3 Related to discharge


3.1 Discharge

Volume of water per unit time passing through any section on the system.

Q m3 s-1

3.2 Mass flowrate

Mass of water flowing through any section in the system. )( Q kg s-1

3.3 Discharge at reference section

Volume of water per unit time flowing through the reference section 1 or 2.

1Q ， 2Q m3 s-1

3.4 Leakage flowrate

Leakage flowrate through the runner/impeller seals. q m3 s-1

3.5 Active flowrate through runner/impeller

Volume of water per unit time flowing through runner/impeller. a) Turbine operation : qQQm 1 b) Pump operation : qQQm 1

mQ m3 s-1

3・1・4 Related to rotational speed and peripheral speed


4.1 Rotational speed

Number of revolutions per unit time.

n s-1

4.2 Peripheral speed

Peripheral speed at the reference diameter : Dnu u m s-1

4.3 Velocity

Velocity in the flow passage v m s-1

3・1・5 Related to specific energy


5.1 Specific hydraulic energy of machine

Specific energy of water available between the high and low pressure reference section 1 and 2 of the machine.

E J kg-1

5.2 Turbine head or pump head

Energy per local unit weight of water available between the high and low pressure reference sections of the turbine/pump : gEH

H m

5.3 Specific hydraulic energy loss

Specific hydraulic energy dissipated between any two sections.

LE J kg-1

5.4 Scalable (friction) specific hydraulic energy loss of machine

Specific hydraulic energy loss caused by the hydraulic friction on the surface of flow passages.

LfE J kg-1

5.5 Non-scalable specific hydraulic energy loss of machine

Specific hydraulic energy loss caused by the hydraulic phenomena other than the hydraulic friction, such as turbulence, separation of flow, abrupt change of flow passages, etc.

LkE J kg-1

5.6 Specific hydraulic energy of runner/impeller

Specific energy available for the runner or imparted to the water by the impeller： a) Turbine operation : Lm EEE b) Pump operation : Lm EEE

mE J kg-1

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3・1・6 Related to power


6.1 Hydraulic power

Hydraulic power available for turbine or imparted to the pump water : 11QEPh

hP W

6.2 Hydraulic power of runner/impeller

Hydraulic power available for the runner or imparted by the impeller to the water : mmr QEP 1

rP W

6.3 Mechanical power of runner/impeller

Mechanical power transmitted through the coupling of the runner/impeller and the shaft: a) Turbine operation : Ldrm PPP b) Pump operation : Ldrm PPP

mP W

6.4 Mechanical power of machine

Mechanical power delivered by the turbine shaft or to the pump shaft. a) Turbine operation : Lmm PPP b) Pump operation : Lmm PPP

P W

6.5 Disk friction power loss

Hydraulic power dissipated in the chambers between the outer surfaces of the runner/impeller and the corresponding stationary walls due to the friction loss.

LdP W

6.6 Mechanical power loss

Mechanical power dissipated in guide bearings, thrust bearings and shaft seals of the machine.

LmP W

3・1・7 Related to efficiency


7.1 Specific energy efficiency of runner/impeller

a) Turbine operation : EEmE b) Pump operation : mE EE

E －

7.2 Discharge efficiency of runner/impeller

a) Turbine operation : 1QQmQ b) Pump operation : mQ QQ1

Q －

7.3 Power efficiency of runner/impeller

a) Turbine operation : rmT PP b) Pump operation : mrT PP

T －

7.4 Hydraulic efficiency

a) Turbine operation : TQEhmh PP b) Pump operation : TQEmhh PP

h －

7.5 Mechanical efficiency

a) Turbine operation : mm PP b) Pump operation : PPmm

m －

7.6 Efficiency

a) Turbine operation : mhhPP

b) Pump operation : mhh PP －

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3・1・8 Related to scaling


8.1 Reynolds number

Ratio of inertia forces to viscous forces : DuRe Re －

8.2 Difference of hydraulic efficiencies

Difference between hydraulic efficiency at two hydraulically similar operating points : MP hhh

h －

8.3 Specific energy efficiency scale factor

Ratio of prototype specific energy efficiency to model specific energy efficiency : MP EEEF

EF －

8.4 Discharge efficiency scale factor

Ratio of prototype discharge efficiency to model discharge efficiency : MP QQQF

QF －

8.5 Power efficiency scale factor

Ratio of prototype power efficiency to model power efficiency : MP TTTF

TF －

8.6 Relative scalable (friction) loss of machine

Ratio of the scalable (friction) specific hydraulic energy loss of the machine to the specific hydraulic energy of it : EELfE

E －

8.7 Relative non-scalable loss of machine

Ratio of the non-scalable specific hydraulic energy loss of the machine to the specific hydraulic energy of it : EELkns

ns －

8.8 Friction coefficient for a pipe

Friction coefficient of the flow passage based on the equivalent pipe flow approximation

－

8.9 Friction coefficient for a plate

Friction coefficient of the flow passage based on the equivalent flat plate flow approximation

fC －

8.10 Friction coefficient ratio Ratio of the prototype friction coefficient fC to the model one for stay vanes, guide vanes and a runner : MP ff CC

Ratio of the prototype friction coefficient to the model one for a spiral case, a flow passage from guide vane outlet to runner inlet and a draft tube : MP

－

3・1・9 Related to dimensional performance


9.1 Speed factor

Rotational speed nondimensionalized by the specific hydraulic energy and reference diameter : 21EnDnED

EDn －

9.2 Discharge factor

Discharge nondimensionalized by the specific hydraulic energy and reference diameter : )( 212EDQQED

EDQ －

9.3 Power factor

Mechanical power of the runner/impeller nodimensionalized by the specific energy and reference diameter : )( 232

1 EDPP mED

EDP －

9.4 Energy coefficient Specific hydraulic energy of the machine nondimensionalized by the rotational speed and reference diameter : )( 22DnEEnD

nDE －

9.5 Discharge coefficient

Discharge nondimensionalized by the rotational speed and reference diameter : )( 3

1 nDQQnD nDQ －

9.6 Power coefficient

Mechanical power of the runner/impeller nondimensionalized by the rotational speed and reference diameter : )( 53

1 DnPP mnD

nDP －

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3・1・9 Continue

9.7 Specific speed

43212143211 nDnDEDEDQE EQQnEnQN

432160 HnQnsQ (Definition having been used)

QEN

sQn － min-1, m3 s-1, m

3・2 Subscript

Subscript Definition

1 The high pressure reference section of the hydraulic machine where the performance guarantees refer

2 The low pressure reference section of the hydraulic machine where the performance guarantees refer

E Denoting values related to the specific hydraulic energy

h Denoting values related to the hydrodynamic condition

L Denoting values related to the losses

f Denoting values dependent of Re (scalable)

ns Denoting values independent of Re (non-scalable)

Ld Denoting values related to the power (disk friction loss) dissipated in the chambers between the outer surface of the runner/impeller and the corresponding stationary walls due to the hydraulic loss

Q Denoting values related to the discharge

T Denoting values related to the outer surface of runner/impeller, T or TF

M Denoting values related to the model

P Denoting values related to the prototype

ref Denoting values related to the specified reference condition

opt Denoting values related to the best efficiency point

std Denoting values related to the standard condition

CO Denoting values related to each component passage of the hydraulic machine

SP Denoting values related to the spiral case or the casing of the bulb turbine

SV Denoting values related to the stay vanes

GV Denoting values related to the guide vanes

GR Denoting values related to the flow passage from guide vane outlet to runner inlet

RU Denoting values related to the runner

DT Denoting values related to the draft tube

TR Denoting values related to the rotating part

TS Denoting values related to the stationary part.

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(a) Flux diagram of specific hydraulic energy, discharge, power and efficiency for turbine

Remarks: Respective symbol is explained on page 10.

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(b) Flux diagram of specific hydraulic energy, discharge, power and efficiency for pump

Remarks: Respective symbol is explained on page 10.

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No. Term Turbine Pump

1 Discharge Q1 Q1

2 Leakage flowrate q = q’＋q’’ q =q’＋q’’

3 Active flowrate through runner/impeller Qm= Q1－q Qm= Q1 + q

4 Specific hydraulic energy of machine E E

5 Specific hydraulic energy loss of machine EL EL

6 Specific hydraulic energy of runner/impeller

Em = E－EL Em = E＋EL

7 Hydraulic power Ph = E(ρQ)1 Ph = E(ρQ)1

8 Hydraulic power of runner/impeller Pr = Em(ρQ)m Pr = Em(ρQ)m

9 Disk friction power loss PLd = P’Ld + P’’Ld PLd = P’Ld + P’’Ld

10 Mechanical power of runner/impeller Pm = Pr－PLd Pm = Pr + PLd

11 Mechanical power loss PLm PLm

12 Mechanical power of machine P = Pm－PLm P = Pm＋PLm

13 Specific energy efficiency of runner/impeller

ηE = Em / E ηE = E / Em

14 Discharge efficiency of runner/impeller ηQ = Qm / Q1 ηQ = Q1 / Qm

15 Power efficiency of runner/impeller ηT = Pm / Pr ηT = Pr / Pm

16 Hydraulic efficiency ηh = Pm / Ph =ηEηQηT ηh = Ph / Pm =ηEηQηT

17 Mechanical efficiency ηm = P / Pm ηm = Pm / P

18 Efficiency η= P / Ph =ηhηm η= Ph / P =ηhηm

Fig. 3.1 Flux diagram of specific hydraulic energy, discharge, power and efficiency for turbine and pump

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4. CONVERSION METHOD OF TURBINE PERFORMANCE OF HYDRAULICTURBINES AND PUMP-TURBINES

4・1 Fundamental Formulae for Performance Conversion

The performance conversion from the model to the prototype shall be done on the premise of the application conditions stipulated in Clause 2・2.

In the performance conversion, the prototype hydraulic efficiency Ph can be derived directory from the model hydraulic efficiency Mh by using the specific energy efficiency scale factor EF , the discharge efficiency scale factor

QF and the power efficiency scale factor TF without giving the specific energy efficiency, discharge efficiency and the power efficiency separately. Definitions of the specific energy efficiency scale factor EF , the discharge efficiency scale factor QF and the power efficiency scale factor TF are as below. (Refer to Appendix-A)

M

P

E

EEF

(4・1)

M

P

Q

QQF

(4・2)

M

P

T

TTF

(4・3)

Procedures to calculate these efficiency scale factors are shown in following clauses. Flow chart to show the procedure to calculate these efficiency scale factors from the specific speed QEN at the best efficiency point of the model is shown in Fig. 4・1. Calculation results for actual examples are shown in Appendix-G4.

Specific energy efficiency scale factor EF Clause 4・2 Discharge efficiency scale factor QF Clause 4・3 Power efficiency scale factor TF Clause 4・4

The prototype turbine performance is calculated using these efficiency scale factors as shown below.

MP hTQEh FFF (4・4) 12

P2

P2

MP EED FDnnE (4・5)

12121P

2PMP1

QEED FFEDQQ (4・6)

TEEDm FFEDPP 23P

23P

2PMP (4・7)

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Calculation of specific speed QEN at the best efficiency point of the turbine operation of the model (Sub-clause 4・2・1)

Friction coefficient ratio for each tested point of the model test CO (Sub-clause 4・2・9)

Relative scalable (friction) loss for each tested point of the model test ECO (Sub-clause 4・2・7)

Reference velocity factor of each component passage uCOv (Sub-clause 4・2・4)

Reference dimensional factor for each component passage Dd hCO , DlCO (Sub-clause 4・2・3)

Standard speed factor EDstdn and standard discharge factor EDstdQ (Sub-clause 4・2・2)

<Calculation of standard values for the specific speed QEN >

Reynolds number MRe , component Reynolds number

MCORe and component friction coefficient MCO , MfCOC for each tested point of the model test (Sub-clause 4・2・6)

Component Reynolds number of each prototype component passage PCORe and component friction coefficient PCO ， PfCOC (Sub-clause 4・2・8)

<Calculation for performance value of the prototype>

<Calculation for each tested point of the model test>

Power efficiency scale factor for each tested point of the model test TF (Clause 4・4) ）

Fig. 4.1 Flow chart of performance conversion for a turbine and a pump-turbine (turbine operation)

Standard relative scalable (friction) loss of each component passage ECOstd ( Sub-clause 4・2・5)

<Result> The prototype performance converted from each model tested point Eq. (4・4) through Eq. (4・7)

Discharge efficiency scale factor QF

(Clause 4・3)

<Input> Conditions of the prototype - Reynolds number PRe

- Surface roughness CORa

- etc.

Specific energy efficiency scale factor for each tested point of the model test EF Eq. (4・8) or Eq. (4・8)’

<Input> Best efficiency point of the model EDoptn , EDoptQ

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4・2 Calculation of Specific Energy Efficiency Scale Factor EF Specific energy efficiency scale factor for a turbine (including turbine operation of a pump-turbine) is given by

following equations. (Refer to Eq. (A3・6) in Appendix-A3)

M

P

E

EEF

(Francis turbine and Francis type pump-turbine)

DTEDTRUERUGVEGVSVESVSPESP

111111

1 (4・8)

(Diagonal /axial flow turbine)

DTEDTRUERUGREGRGVEGVSVESVSPESP

1111111

1 (4・8)’

where.

ESP ；Relative scalable(friction) loss of a model spiral case under model test condition

ESV ；Relative scalable(friction) loss of model stay vanes under model test condition

EGV ；Relative scalable(friction) loss of model guide vanes under model test condition

EGR ；Relative scalable(friction) loss of a model flow passage from guide vane outlet to runner inlet

ERU ；Relative scalable(friction) loss of a model runner under model test condition

EDT ；Relative scalable(friction) loss of a draft tube under model test condition

SP ；Friction coefficient ratio of model to prototype for a spiral case MP SPSP

SV ；Friction coefficient ratio of model to prototype for stay vanes MP fSVfSV CC

GV ；Friction coefficient ratio of model to prototype for guide vanes MP fGVfGV CC

GR ；Friction coefficient ratio of model to prototype for a flow passage from outlet of guide vane to inlet of a

runner MP GRGR

RU ；Friction coefficient ratio of model to prototype for a runner MP fRUfRU CC

DT ；Friction coefficient ratio of model to prototype for a draft tube MP DTDT Subscripts SP，SV，GV，GR，RU，DT shown above mean a spiral case, stay vanes, guide vanes, a flow passage from

outlet of guide vane to inlet of a runner, a runner and a drat tube. Subscript CO represents a general term for them. Namely, subscript CO means SP for a spiral case, SV for stay vanes, GV for guide vanes, GR for a flow passage from outlet of guide vane and inlet of a runner, RU for a runner and DT for a draft tube. And subscripts M and P indicate model and prototype respectively.

Calculation procedures for relative scalable (friction) loss ECO and friction coefficient ratio CO listed above are shown in the later Sub-clause 4・2・1 through 4・2・9.


Specific speed QEN for turbine operation shall be calculated according to the equation shown below using speed

factor EDoptn and discharge factor EDoptQ at the best efficiency point of the model (including turbine operation of a pump-turbine).

EDoptEDoptQE QnN (4・9)

Furthermore, calculation procedures mentioned in the later section can be used on condition that QEN calculated above is within the range specified in Table 4.1. If QEN is outside of the range specified in Table 4.1, following calculations shall be carried out according to the procedure shown in Appendix-C depending on each case.

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Table 4.1 Applicable range of QEN

Type of turbine Applicable range of QEN

Francis turbine 0.3007.0 ～ Diagonal flow turbine 0.3015.0 ～ Axial flow turbine (Kaplan, Bulb) 0.9025.0 ～ Francis type pump-turbine (turbine operation) 0.1807.0 ～ Diagonal flow pump-turbine (turbine operation) 0.3015.0 ～ Axial flow (Tubular) pump-turbine (turbine operation) 0.9025.0 ～


Standard speed factor EDstdn and standard discharge factor EDstdQ shall be calculated according to the equation

shown in Table 4.2 as a function of specific speed QEN for turbine operation. And, as for turbine operation of diagonal flow pump-turbines or axial flow (tubular) pump-turbines, calculation

results for diagonal flow turbines or axial flow turbines shown in Table 4.2 may be used respectively, if the specific speeds NQE for turbine operation of those pump-turbines are within the range shown in Table 4.1.

Table 4.2 Calculation formulas for EDstdn and EDstdQ

EDstdn EDstdQ Remark

Francis turbine 3231QEnQEDstd Nkn 3232

QEnQEDstd NkQ 7.0nQk

Diagonal/axial flow turbine 95185QEnQEDstd Nkn 9895

QEnQEDstd NkQ 7.0nQk

Francis type pump-turbine (turbine operation)

0502.083.1 QEEDstd Nn 2

2

0564.005.2

26.1

QE

QEEDstd

N

NQ


Model reference dimensional factor MM DdhCO , MM DlCO of each component passage shall be calculated

according to Eq. (4・10), (4・11) and (4・12) shown below as a function of specific speed QEN for turbine operation. Furthermore, if the prototype is geometrically similar to the model, the reference dimensional factor of the prototype must be equal to the one of the model. So, subscript M and P may be omitted in case that strict distinction between the model and the prototype is not required. Values for the coefficients 1a , 2a , 3a , 4a in Eq. (4・12) are shown in Table 4.3.

And, as for turbine operation of diagonal flow pump-turbines or axial flow (tubular) pump-turbines, calculation results for diagonal flow turbines or axial flow turbines shown in Table 4.3 may be used respectively, on condition that the specific speeds NQE for turbine operation of those pump-turbines are within the range shown in Table 4.1.

Furthermore, if the reference dimensional factor based on the actual dimensions is remarkably different from the one given from Table 4.3 due to the different design concept from the standard design concept, the one based on the actual dimensions may be used. Also for the turbine with different structure, such as the turbine without guide vanes or the turbine with fixed guide vanes, the reference dimensional factors derived from the actual structure considering the actual flow condition may be used.

(Spiral case, flow passage from guide vanes outlet to runner inlet and draft tube)

DdDdDd hCOhCOhCO PPMM (4・10)

(Stay vanes, guide vanes and runner) DlDlDl COCOCO PPMM (4・11)

QEQEQECOhCO NaaNaNaDlDd 4322

1, (4・12)

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Table 4.3 Coefficients of the polynomial for Dd hCO ， DlCO

1a 2a 3a 4a

Francis turbine

Spiral case ( DdhSP ) 0.0 1.0 0.890 0.0 Stay vane ( DlSV ) 1.498 -0.7348 0.215 0.005127 Guide vane ( DlGV ) 2.093 -1.026 0.301 0.007167 Runner ( DlRU ) -0.2848 0.5736 -0.192 0.07980 Draft tube ( Dd hDT ) 0.0 0.0 1.17 0.0

Diagonal/axial flow turbine

Spiral case ( Dd hSP ) Diagonal 0.0 0.0 1.20 0.0 Spiral case ( Dd hSP ) Full-spiral

Kaplan 0.0 0.0 1.20 0.0

Spiral case ( Dd hSP ) Semi-spiral

Kaplan 0.0 0.0 1.41 0.0

Casing ( Dd hSP ) Bulb 0.0 0.0 1.41 0.0 Stay vane ( DlSV ) All except Bulb 0.0 0.0 0.148 0.0 Stay vane ( DlSV ) Bulb Guide vane ( DlGV ) -0.1122 0.2169 0.0735 0.02614 Guide vane to runner ( Dd hGR ) 0.0 0.0 0.937 0.0 Runner ( DlRU ) 0.0 -0.06081 0.113 0.1737 Draft tube ( Dd hDT ) 0.0 0.0 1.17 0.0


Spiral case ( Dd hSP ) 0.0 -0.289 1.12 -0.006747 Stay vane ( DlSV ) 12.231 -5.386 0.84 0.0 Guide vane ( DlGV ) 10.87 -4.788 0.747 0.0 Runner ( DlRU ) 0.6511 5.573 -2.53 0.3979 Draft tube ( Dd hDT ) 0.0 0.0 1.17 0.0

(Note) Reference dimensional factor of a flow passage from guide vane outlet to runner inlet for a Francis turbine and a Francis type pump-turbine, differing from a diagonal/axial flow turbine, is not necessary to be considered, because its influence was included in guide vanes and a runner. Also, reference dimensional factor of stay vanes for a bulb turbine is not necessary to be considered, because its frictional loss was included in a casing as shown in Table 4・5.


Model reference velocity factor MM uCOv of each component passage shall be calculated according to Eq. (4・13),

(4・14), (4・15) and (4・16) shown below using specific speed QEN for turbine operation, EDstdEDopt nn and

EDstdEDopt QQ . Furthermore, if the operating condition of the prototype turbine is kinematical similar to the one of the model, reference velocity factor for the prototype must be equal to the one for the model. So, subscript M and P may be omitted in case that strict distinction between the model and the prototype is not required. Values for the coefficients 1a , 2a , 3a , 4a in Eq. (4・16) are shown in Table 4.4.

And, as for turbine operation of diagonal flow pump-turbines or axial flow (tubular) pump-turbines, calculation results for diagonal flow turbines or axial flow turbines shown in Table 4.4 may be used respectively, on condition that the specific speeds NQE for turbine operation of those pump-turbines are within the range shown in Table 4.1.

Furthermore, if the reference velocity factor based on the actual flow condition is remarkably different from the one given from Table 4.4 due to the different design concept from the standard design concept, the one based on the actual flow condition may be used. Also the reference velocity factors for the turbine with different structure, such as the turbine without guide vanes or the turbine with fixed guide vanes, may be determined according to the actual flow condition.

uuu COCOCO vvv PPMM (4・13)

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(Except runner)

EDstd

EDopt

EDstd

EDoptCOstdCO

n

n

Q

Quu vv (4・14)

(Runner) 212

2

212

2

16

2

116

2

1

EDstd

EDstd

EDopt

EDoptCOstdCO

n

Q

n

Quu

vv (4・15)

QEQEQECOstd NaaNaNau 4322

1 v (4・16)

Table 4.4 Coefficients of the polynomial for uCOstdv

1a 2a 3a 4a

Francis turbine

Spiral case ( uSPstdv ) 0.6378 -0.6995 0.353 0.0

Stay vane ( uSVstdv ) -0.8936 -0.1619 0.208 0.05752

Guide vane ( uGVstdv ) -1.122 -0.3691 0.345 0.07751

Runner ( uRUstdv ) 0.0 0.0 0.762 0.0

Draft tube ( uDTstdv ) 0.0 0.0 0.207 0.0


Spiral case ( uSPstdv ) Diagonal -0.08446 0.2044 0.085 0.0

Spiral case ( uSPstdv ) Full-spiral Kaplan -0.08446 0.2044 0.085 0.0

Spiral case ( uSPstdv ) Semi-spiral

Kaplan -0.04745 0.1305 0.066 0.0

Casing ( uSPstdv ) Bulb -0.04745 0.1305 0.066 0.0

Stay vane ( uSVstdv ) All except Bulb -0.1086 0.3101 -0.142 0.07943

Stay vane ( uSVstdv ) Bulb

Guide vane ( uGVstdv ) 0.1467 -0.1269 0.141 0.05062

Guide vane to runner ( uGRstdv ) -0.1081 0.2974 0.150 0.0

Runner ( uRUstdv ) 0.0 0.0519 0.719 0.0

Draft tube ( uDTstdv ) -0.08877 0.2149 0.089 0.0



Stay vane ( uSVstdv ) 0.0 -0.07147 0.111 0.05274


Runner ( uRUstdv ) 0.0 -0.3945 0.816 0.0

Draft tube ( uDTstdv ) 0.0 -0.7484 0.308 0.0

(Note) Reference velocity factor of a flow passage from guide vane outlet to runner inlet for a Francis turbine and a Francis type pump-turbine, differing from a diagonal/axial flow turbine, is not necessary to be considered, because its influence was included in guide vanes and a runner. Also, reference velocity factor of stay vanes for a bulb turbine is not necessary to be considered, because its frictional loss was included in a casing as shown in Table 4・5.


Model standard relative scalable (friction) loss ECOstd (under reference Reynolds number refRe , standard speed

factor EDstdn , standard discharge factor EDstdQ and hydraulically smooth surface) shall be calculated according to the equation shown below depending on type of the turbine and specific speed QEN . Values for the coefficients 1a , 2a ,

3a , 4a in Eq. (4・17) are shown in Table 4.5. And, as for turbine operation of diagonal flow pump-turbines or an axial flow (tubular) pump-turbines, calculation

procedure for diagonal flow turbines or axial flow turbines shown in Table 4.5 may be used respectively, on condition that the specific speeds NQE for turbine operation of those pump-turbines are within the range shown in Table 4.1.

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Furthermore, if the reference dimensional factors MM DdhCO , MM DlCO and/or the reference velocity factors MM uCOv are determined based on the actual dimensions and/or the actual flow condition due to the different design

concept from the standard one, the standard relative scalable (friction) loss ECOstd shall be the relative scalable (friction) loss calculated at the best efficiency point assuming EDoptEDstd nn and EDoptEDstd QQ according to the procedure shown in Appendix-C.

100)( 4322

1 QEQEQEECOstd NaaNaNa (4・17)

EDTstdERUstdEGRstdEGVstdESVstdESPstdECOstdEstd (4・18)

, Table 4.5 Coefficients of the polynomial for ECOstd

1a 2a 3a 4a

Francis turbine

Spiral case ( ESPstd ) -3.953 2.298 0.23 0.0 Stay vane ( ESVstd ) -3.830 1.679 -0.16 0.05425 Guide vane ( EGVstd ) -22.48 9.983 -0.73 0.1568 Runner ( ERUstd ) 0.0 4.2 0.65 0.0 Draft tube ( EDTstd ) 0.0 0.9069 -0.03 0.0 Total ( Estd ) -30.26 19.07 -0.04 0.2111

Diagonal flow turbine

Spiral case ( ESPstd ) 2.389 0.6573 -0.02 0.0 Stay vane ( ESVstd ) 0.04326 0.2297 -0.18 0.07688 Guide vane ( EGVstd ) -4.199 1.047 0.69 0.0 Guide vane to Runner ( EGRstd ) 0.0 0.0 0.23 0.0 Runner ( ERUstd ) -0.8288 2.312 2.13 0.003298 Draft tube ( EDTstd ) 0.9865 0.3593 -0.03 0.0 Total ( Estd ) -1.609 4.605 2.82 0.08018

Axial flow turbine (Kaplan)

Spiral case ( ESPstd )-Full-spiral 2.389 0.6573 -0.02 0.0 Spiral case ( ESPstd ) -Semi-spiral 0.7153 0.2268 -0.01 0.0 Stay vane ( ESVstd ) 0.04326 0.2297 -0.18 0.07688 Guide vane ( EGVstd ) 1.022 -0.8254 0.34 0.1273 Guide vane to Runner ( EGRstd ) 0.0 0.0 0.68 0.0 Runner ( ERUstd ) -0.8288 2.312 2.13 0.003298 Draft tube ( EDTstd ) 0.9865 0.3593 -0.03 0.0 Total ( Estd ) -Full-spiral 3.612 2.733 2.92 0.2075 Total ( Estd ) -Semi-spiral 1.938 2.302 2.93 0.2075

Bulb turbine Casing ( ESPstd ) 0.3167 0.1158 -0.01 0.0 Stay vane ( ESVstd ) 0.0 0.0 0.0 0.0 Guide vane ( EGVstd ) 1.022 -0.8254 0.34 0.1273 Guide vane to Runner ( EGRstd ) 0.0 0.0 0.40 0.0 Runner ( ERUstd ) -0.8288 2.312 2.13 0.003298 Draft tube ( EDTstd ) 0.9865 0.3593 -0.03 0.0 Total ( Estd ) 1.496 1.962 2.83 0.1306


Spiral case ( ESPstd ) 0.0 0.2958 0.49 0.0 Stay vane ( ESVstd ) -20.00 8.433 -0.91 0.07970 Guide vane ( EGVstd ) -59.01 25.35 -2.54 0.1838 Guide vane to Runner ( EGRstd ) 0.0 0.0 0.0 0.0 Runner ( ERUstd ) 11.95 2.295 1.44 0.0 Draft tube ( EDTstd ) 0.0 0.5153 0.01 0.0 Total ( Estd ) -67.06 36.89 -1.51 0.2635

(Note) Friction loss of a flow passage from guide vane outlet to runner inlet for a Francis turbine and a Francis type

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pump-turbine is not necessary to be considered, because it was included in guide vanes and a runner. Also, loss of stay vanes of a bulb turbine is equal to 0, because it was included in a casing.


Friction coefficient MCO and MfCOC of each model component passage based on Reynolds number MRe at each model tested point and friction coefficient refCO M and reffCOC M of each component passage under reference Reynolds number refRe shall be calculated as shown below. 1) Reference component Reynolds number refCORe M under reference Reynolds number refRe ( 6107 ) shall be

calculated using reference dimensional factor DdhCO , DlCO shown in Sub-clause 4・2・3 and standard reference velocity factor uCOstdv shown in Sub-clause 4・2・4 as shown below.

(Spiral case, Guide vanes outlet to runner inlet, Draft tube) refCOstdhCO

refCO ReuD

dRe

vM (4・19)

(Stay vanes, Guide vanes, Runner) refCOstdCO

refCO ReuD

lRe

vM (4・20)

2) Each component Reynolds number MCORe under tested Reynolds number MRe shall be calculated as shown below.

M

MMMM

νnDD

Re

(4・21)

(Spiral case, Guide vanes outlet to runner inlet, Draft tube) MM ReuD

dRe COhCO

COv

(4・22)

(Stay vanes, Guide vanes, Runner) MM ReuD

lRe COCO

COv

(4・23)

Next, friction coefficient refCO M and reffCOC M of each model component passage under the reference condition

(Surface of the model component passage shall be hydraulically smooth and under reference Reynolds number6107refRe ) shall be calculated. Friction coefficient MCO and MfCOC shall be calculated both for smooth surface

and rough surface, then final value shall be determined. Subscript s means smooth surface and Subscript r means rough surface.

3) Friction coefficient of a spiral case, a flow passage from guide vanes outlet to runner inlet and a draft tube (Subscript

CO represents a general term, which means SP for a spiral case, GR for guide vane outlet to runner inlet and DT for a draft tube.) Reference condition (Smooth surface, reference Reynolds number 6107refRe )

8.0log21

MM10

M

refCOrefCO

refCO

Re

(4・24)

Smooth surface

8.0log21

MM10

M

sCOCO

sCO

Re

(4・25)

Equations (4・24), (4・25) is an implicit function of refCOM , sCOM . So, the equations shown below instead of

them may be used to calculate easily.

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26.0

10774.000854.0

2.0

M

6

MrefCO

refCORe

(4・26)

26.0

10774.000854.0

2.0

M

6

MCO

sCORe

(4・26)’

Rough surface

2

6M

M10M 74.1

104

2log2

CO

hCOrCO

Ra

d (4・27)

where, MhCOd can be calculated as DdD hCOM using reference dimensional factor DdhCO shown in

Sub-clause 4・2・3. MCORa means arithmetic mean roughness for each model component passage as shown in Clause 4・5. (Refer to Appendix-D)

Finally, friction coefficient MCO of model component passage under the test condition of each tested point of the model test shall be sCOM or rCOM , whichever larger. For hydraulically smooth surface, sCOM ＞ rCOM .

),(max MMM rCOsCOCO (4・28)

4) Friction coefficient of stay vanes, guide vanes and a runner (Subscript CO represents a general term, which means

SV for stay vanes, GV for guide vanes and RU for a runner.) Reference condition (Smooth surface, reference Reynolds number 6107refRe )

(4・29)

Smooth surface

(4・30)

Rough surface

5.2M

6M10M )]102(log62.189.1[1 COCOrfCO lRaC (4・31)

where, MCOl can be calculated as DlD COM using reference dimensional factor DlCO shown in Sub-clause

4・2・3. MCORa means arithmetic mean roughness for each model component passage as shown in Clause 4・5. (Refer to Appendix-D)

Finally, friction coefficient MfCOC of model component passage under the test condition of each tested point of the model test shall be sfCOC M or rfCOC M , whichever larger. For hydraulically smooth surface, sfCOC M ＞

rfCOC M .

),(max MMM rfCOsfCOfCO CCC (4・32)

582Mref10M )](log[455.0 .

COreffCO ReC

58.2M10M )](log[455.0 COsfCO ReC

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Standard relative scalable (friction) loss ECOstd of each component passage given in Sub-clause 4・2・5 is the value under standard speed factor EDstdn and standard discharge factor EDstdQ given in Sub-clause 4・2・2, and at the best efficiency point under the reference condition (Smooth surface, reference Reynolds number 6107refRe ). So, relative scalable (friction) loss ECO of each tested point of the model test shall be calculated according to equations shown below, considering influence of test Reynolds number MRe and discharge ratio to best efficiency discharge

EDoptED QQ . Furthermore, following points should be noted that MCO and MfCOC are friction coefficient of a component passage given in Sub-clause 4・2・6 and FEK is ratio of the relative scalable (friction) loss of each tested point to the one of the best efficiency point. (Definitions for inlet and outlet are based on flow direction of turbine operation.) (Spiral case, Guide vanes outlet to runner inlet, Draft tube)

2MM EDstdEDoptECOstdrefCOCOFEECO QQK (4・33)

(Stay vanes, Guide vanes)

2MrefM EDstdEDoptECOstdfCOfCOFEECO QQCCK (4・34)

(Runner)

2

2

22

2

2

22

MM8

2

8

2EDstdEDstdEDoptEDoptERUstdreffRUfRUFEERU QnQnCCK

(4・35)

Furthermore, the ratio of friction coefficients may be calculated approximately on condition that the surface of the

model component passage is hydraulically smooth. (Spiral case, Guide vanes outlet to runner inlet, Draft tube)

218.0MM EDstdEDoptECOstdrefCOCOFEECO QQReReK (4・36)



(Runner)

2

2

22

2

2

22

18.0MM

8

2

8

2EDstdEDstdEDoptEDoptERUstdrefRURUFEERU QnQnReReK

(4・38)

where, ratio of the relative scalable (friction) loss of each tested point to the one of the best efficiency point FEK shall be calculated according to following equations. (Refer to Appendix-C2・3) Francis turbine, Francis type pump-turbine (turbine operation)

EDoptED QQ ≦ :0.1 0.1FEK (4・39)

:0.1EDoptED QQ 2]7.0)[(91.0 EDoptEDFE QQK (4・40)

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5.02EDoptEDEDoptEDFE QQnnK (4・41)


Friction coefficient PCO , PfCOC of each prototype component passage shall be calculated as shown below.

1) Prototype Reynolds number PRe shall be calculated as shown below.

P

PPPP

nDD

Re (4・42)

2) Each prototype component Reynolds number PCORe shall be calculated using reference dimensional factor DdhCO ,

DlCO and reference velocity factor uCOv given in Sub-clause 4・2・3 and 4・2・4.

(Spiral case, Guide vanes outlet to runner inlet, Draft tube) PP ReuD

dRe COhCO

COv

(4・43)

(Stay vanes, Guide vanes, Runner) PP ReuD

lRe COCO

COv

(4・44)

Next, friction coefficient PCO and PfCOC of each prototype component passage shall be calculated considering each

component Reynolds number PCORe and surface roughness PCORa . Friction coefficient PCO and PfCOC shall be calculated both for smooth surface and rough surface, then final value shall be determined. Subscript s means smooth surface and Subscript r means rough surface.

3) Friction coefficient of a spiral case, a flow passage from guide vanes outlet to runner inlet and a draft tube (Subscript CO represents a general term, which means SP for a spiral case, GR for guide vane outlet to runner inlet and DT for a draft tube.)

Smooth surface

8.0log21

PsP10

P

COCO

sCO

Re

(4・45)

Equation (4・45) is an implicate function of sCOP . So, the equation shown below instead of it may be used to

calculate easily.

26.0

10774.000854.0

2.0

P

6

PCO

sCORe

(4・46)

Rough surface

2

6P

P10P 74.1

104

2log2

CO

hCOrCO

Ra

d (4・47)

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where, PhCOd can be calculated as DdD hCOP using reference dimensional factor DdhCO shown in Sub-clause 4・2・3. PCORa means arithmetic mean roughness for each prototype component passage as shown in Clause 4・5. (Refer to Appendix-D)

Finally, friction coefficient PCO of prototype component passage under tested condition shall be sCOP or rCOP , whichever larger.

),(max PPP rCOsCOCO (4・48)


SV for stay vanes, GV for guide vanes and RU for a runner.)

Smooth surface

58.2P10P log455.0 COsfCO ReC (4・49)

Rough surface

52

P6

P10P ][ )102(log62.189.11.

COCOrfCO lRaC (4・50)

where, PCOl can be calculated as DlD COP using reference dimensional factor DlCO shown in Sub-clause

4・2・3. PCORa means arithmetic mean roughness for each model component passage as shown in Clause 4・5. (Refer to Appendix-D)

Finally, friction coefficient PfCOC of prototype component passage shall be sfCOC P or rfCOC P , whichever larger.

),(max PPP rfCOsfCOfCO CCC (4・51)


Friction coefficient ratio CO shall be calculated using the friction coefficient of model component passage MCO ,

MfCOC and the one of prototype component passage PCO , PfCOC mentioned above.

MP COCOCO ,or MP fCOfCOCO CC (4・52)

4・3 Calculation for Discharge Efficiency Scale Factor QF 4・3・1 Discharge efficiency scale factor QF for Francis turbines and Francis type pump-turbines (turbine

operation) Discharge efficiency scale factor QF for Francis turbines and Francis type pump-turbines (turbine operation) seems

to be equal to the one at the best efficiency point QoptF . Then they shall be calculated as shown below. (Refer to Appendix- E)

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optQQoptQoptQ

optQQoptQ FF

MMM

P

1

1

(4・53)

where, optQM and optQP mean model and prototype discharge efficiency at the best efficiency point and Q means friction coefficient ratio to be calculated as below. optReM means Reynolds number at the best efficiency point in the model test.

2M 0000361.0993.0 QEoptQ N (4・54)

21

41PM2132

21

21322

1

)()(

)()(

ReRebNbaNaNa

bNbaNaNa

optQEQEQE

QEQEQEQ (4・55)

For Francis turbines and Francis type pump-turbines with the normal design, coefficients a1, a2, a3, b1, b2 shall be as shown Table 4.6.

Table 4.6 Coefficients of the polynomial for Q a1 a2 a3 b1 b2 Francis turbine 0.03581 0.9368 1.44 0.9515 0.73 Francis type pump-turbine -1.789 -7.659 9.00 -1.654 3.26

4・3・2 Discharge efficiency scale factor QF for diagonal/axial flow turbines

Discharge efficiency of diagonal flow turbines and axial flow turbines other than Francis turbines and Francis type pump-turbines is equal to 1 ( 0.1M Q ). So discharge efficiency scale factor QF shall be as bellow.

0.1 QoptQ FF (4・56)

4・4 Calculation for Power Efficiency Scale Factor TF

4・4・1 Power efficiency scale factor TF for Francis turbines and Francis type pump-turbines (turbine

operation) Power efficiency scale factor TF for Francis turbines and Francis type pump-turbines (turbine operation) shall be

calculated as shown below. (Refer to Appendix-F)

TT

T

T

TT Λ

ΛF

MM

P 1

(4・57)

where, MT means power efficiency for each tested point of the model test and T means friction coefficient ratio. Those shall be calculated as below.

EDEDoptEDoptED

optTT PPnn 3

MM 1

111

(4・58)

where, EDoptn and EDn mean the speed factor at the best efficiency point and the speed factor at each tested point respectively. Also EDoptP and EDP mean the power factor at the best efficiency point and the power factor at each tested point respectively. Furthermore, optTM means the power efficiency at the best efficiency point and shall be

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calculated as shown below, when the surface of the model runner is hydraulically smooth. (Refer to Appendix-F)

stdToptrefoptrefoptT ReReReRe M2.0

M2.0

MM 1 (4・59)

where, optReM means the tested Reynolds number at the best efficiency point. stdTM means the best power efficiency under the reference Reynolds refRe and shall be calculated as shown below.

(Francis turbine) 2M 0000451.0995.0 QEstdT N (4・60)

(Francis type pump-turbine, turbine operation) 2M 000144.0989.0 QEstdT N (4・61)

The friction coefficient ratio T means ( MP LdLd CC ), the ratio of the friction coefficient LdC for runner outer surface and shall be calculated as shown below.

2P102

M10MP loglog SSLdLdT KKCC (4・62)

Furthermore, MSK and PSK means relative roughness for the model and the prototype. They are the relative

roughness for smooth surface sSK M , sSK P (indicated by the subscript s) defined as below or the relative roughness of rough surface rSK M , rSK P (indicated by the subscript r) defined as below, whichever larger. optReM means the tested Reynolds number at the best efficiency point and PRe means the Reynolds number of the prototype turbine.

rSsSS KKK MMM ,max , rSsSS KKK PPP ,max (4・63)

Smooth surface

2M

M200

DSopt

sSRe

K

, 2

P

P200

DS

sSRe

K

(4・64)

Rough surface

DSrS

D

RaK

M

6M

M102

, DS

SPrD

RaK

P

6P 102

(4・65)

where, DS means the ratio of the runner maximum diameter ( MSD or PSD ) to the runner reference diameter ( MD or

PD ) and shall be calculated based on the specific speed as shown below

PPMM DDDD SSDS (4・66)

(Francis turbine) 33

21 )( aaNa QEDS ( QEN ≦ 228.0 ， 7.531 a ， 3.02 a ， 98.03 a ) (4・67)

00.1DS ( QEN 228.0 ) (4・68)

(Francis type pump-turbine) 3

221 )903.0( aaNa QEDS ( QEN ≦ 220.0 ， 7.421 a ， 244.02 a ， 06.13 a ) (4・69)

06.1DS ( 220.0QEN ) (4・70)

Furthermore, MRa and PRa shown in Eq. (4・65) mean the surface roughness of the model and the prototype

corresponding to the respective roughness of the runner outer surface. The respective roughness is weighted average

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of the arithmetic mean roughness RRaT measured at runner outer surface (crown and band) and the SRaT measured at the stationary surface facing to the measured surface of the runner. (Where, subscript T can be replaced by M for the model and P for the prototype. Refer to Appendix-F)

32 TTT SR RaRaRa (4・71)

4・4・2 Power efficiency scale factor TF for diagonal/axial flow turbines

Power efficiency of diagonal flow turbines and axial flow turbines other than Francis turbines and Francis type pump-turbines is equal to 1 ( 0.1M TT ). So power efficiency scale factor TF shall be as bellow.

0.1 ToptT FF (4・72)


Definitions for the surface roughness of each component passage of the model and the prototype, MCORa and

PCORa , referred in Sub-clause 4・2・5 and Sub-clause 4・2・8 are as shown below. Those definitions are same for both the model and the prototype. (Refer to Appendix-D)

Spiral case; Average values measured around inlet of a spiral case ( Ra ) Stay vanes; Average values measured on guide vanes side surface of stay vanes ( Ra ) Guide vanes; Average values measured on runner side surface of guide vanes ( Ra ) Flow passage from guide vanes outlet to runner inlet; Average value of tip side and hub side of upstream of runner vanes of a diagonal flow turbine and an axial flow turbine ( Ra ) Runner; Average values on suction side surface near outlet (lower pressure side) ( Ra ) Draft tube; Average values measured at upper draft tube area ( Ra )

Furthermore, Ra mentioned above means arithmetic mean roughness and relation to the equivalent sand roughness ks was shown in Appendix-D1・3.

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5. CONVERSION METHOD OF PUMP PERFORMANCE OF PUMP-TURBINES

5・1 Fundamental Formulae for Performance Conversion The performance conversion from the model to the prototype shall be done on the premise of the application

conditions stipulated in Clause 2・2. In the performance conversion, the prototype hydraulic efficiency Ph can be derived directory from the model

hydraulic efficiency Mh by using the specific energy efficiency scale factor EF , the discharge efficiency scale factor

QF and the power efficiency scale factor TF without giving the specific energy efficiency, discharge efficiency and the power efficiency separately. Definitions of the specific energy efficiency scale factor EF , the discharge efficiency scale factor QF and the power efficiency scale factor TF are as below. (Refer to Appendix-B)

M

P

E

EEF

(5・1)

M

P

Q

QQF

(5・2)

M

P

T

TTF

(5・3)

Procedures to calculate these efficiency scale factors are shown in following clauses. Flow chart to show the

procedure to calculate these efficiency scale factors from the specific speed QEN at the best efficiency point of the model is shown in Fig. 5・1. Calculation results for actual examples are shown in Appendix-G4.

Specific energy efficiency scale factor EF Clause 5・2 Discharge efficiency scale factor QF Clause 5・3 Power efficiency scale factor TF Clause 5・4 The prototype pump performance is calculated using these efficiency scale factors as shown below.

MP hTQEh FFF (5・4)

EED FDnnE 2P

2P

2MP (5・5)

QEED FFEDQQ 2121P

2PMP1

(5・6) 123

P23

P2

PM TEEDm FFEDPP P (5・7)

And formulas shown below shall be used when energy coefficient nDE , discharge coefficient nDQ and power

coefficient nDP are used.

EnD FDnEE 2P

2PMP (5・5)’

QnD FDnQQ 3PPMP1 (5・6)’

15P

3PPMP

TnDm FDnPP (5・7)’

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Calculation of specific speed QEN at the best efficiency point of the pump operation of the model (Sub-clause 5・2・1)

Friction coefficient ratio for each tested point of the model test CO (Sub-clause 5・2・9)

Relative scalable (friction) loss for each tested point of the model test ECO (Sub-clause 5・2・7)

Reference velocity factor of each component passage uCOv (Sub-clause 5・2・4)

Reference dimensional factor for each component passage Dd hCO , DlCO (Sub-clause 5・2・3)

Standard speed factor EDstdn and standard discharge factor EDstdQ (Sub-clause 5・2・2)

<Calculation of standard values for the specific speed QEN >

Reynolds number MRe , component Reynolds number

MCORe and component friction coefficient MCO , MfCOC for each tested point of the model test (Sub-clause 5・2・6)

Component Reynolds number of each prototype component passage PCORe and component friction coefficient PCO ， PfCOC (Sub-clause 5・2・8)

<Calculation for performance value of the prototype>

<Calculation for each tested point of the model test>

Power efficiency scale factor for each tested point of the model test TF (Clause 5・4) ）

Fig. 5.1 Flow chart of performance conversion for a pump-turbine (pump operation)

Standard relative scalable (friction) loss of each component passage ECOstd ( Sub-clause 5・2・5)

<Result> The prototype performance converted from each model tested point Eq. (5・4) through Eq. (5・7)

Discharge efficiency scale factor QF

(Clause 5・3)

<Input> Conditions of the prototype - Reynolds number PRe - Surface roughness CORa - etc.

Specific energy efficiency scale factor for each tested point of the model test EF Eq. (5・8) or Eq. (5・8)’

<Input> Best efficiency point of the model EDoptn , EDoptQ

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5・2 Calculation of Specific Energy Efficiency Scale Factor EF Specific energy efficiency scale factor for pump operation of a pump-turbine is given by following equations.

(Refer to Eq. (B3・5) in Appendix-B3)

M

P

E

EEF

(Francis type pump-turbine) DTEDTRUERUGVEGVSVESVSPESP 111111 (5・8)

(Diagonal /axial flow pump-turbine) DTEDTRUERUGREGRGVEGVSVESVSPESP 1111111 (5・8)’

where.

ESP ；Relative scalable(friction) loss of a model spiral case under model test condition

ESV ；Relative scalable(friction) loss of model stay vanes under model test condition

EGV ；Relative scalable(friction) loss of model guide vanes under model test condition

EGR ；Relative scalable(friction) loss of a model flow passage from guide vane outlet to runner inlet

ERU ；Relative scalable(friction) loss of a model runner under model test condition

EDT ；Relative scalable(friction) loss of a draft tube under model test condition

SP ；Friction coefficient ratio of model to prototype for a spiral case MP SPSP

SV ；Friction coefficient ratio of model to prototype for stay vanes MP fSVfSV CC

GV ；Friction coefficient ratio of model to prototype for guide vanes MP fGVfGV CC

GR ；Friction coefficient ratio of model to prototype for a flow passage from outlet of guide vane to inlet of a

runner MP GRGR

RU ；Friction coefficient ratio of model to prototype for a runner MP fRUfRU CC

DT ；Friction coefficient ratio of model to prototype for a draft tube MP DTDT Subscripts SP，SV，GV，GR，RU，DT shown above mean a spiral case, stay vanes, guide vanes, a flow passage from outlet of guide vane to inlet of a runner, a runner and a drat tube. Subscript CO represents a general term for them. Namely, subscript CO means SP for a spiral case, SV for stay vanes, GV for guide vanes, GR for a flow passage from outlet of guide vane and inlet of a runner, RU for a runner and DT for a draft tube. And subscripts M and P indicate model and prototype respectively. Furthermore, definitions for inlet and outlet are the same as the one for turbine operation, so the inlet means high pressure side of a component passage and the outlet means its low pressure side.

Calculation procedures for relative scalable (friction) loss ECO and friction coefficient ratio CO listed above are shown in the later Sub-clause 5・2・1 through 5・2・9.


Specific speed QEN for pump operation of a pump-turbine shall be calculated according to the equation shown

below using speed factor EDoptn and discharge factor EDoptQ at the best efficiency point of the model.

EDoptEDoptQE QnN (5・9)

Furthermore, calculation procedures mentioned in the later sections can be used on condition that QEN calculated above is within the range specified in Table 5.1. If QEN is outside of the range specified in Table 5.1, following calculations shall be carried out according to the procedure shown in Appendix-C depending on each case. Furthermore, descriptions for Francis type pump-turbines can be used for storage pumps for a hydraulic power plant.

As for a diagonal flow pump-turbine and an axial flow (tubular) pump-turbine, its specific speed for turbine

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operation shall be located within the range shown in Table 4.1 in Sub-clause 4・2・1.

Table 5.1 Applicable range of QEN

Type of turbine Applicable range of QEN

Francis type pump-turbine (pump operation) 0.2008.0 ～ Diagonal flow pump-turbine (pump operation) )(TQEN for Table 4.1

Axial flow (Tubular) pump-turbine (pump operation) )(TQEN for Table 4.1


Standard speed factor EDstdn and standard discharge factor EDstdQ of Francis type pump-turbines shall be calculated

according to the equation shown in Table 5.2 as a function of specific speed QEN for pump operation. And, as for pump operation of diagonal flow pump-turbines or axial flow (tubular) pump-turbines, calculation

results for diagonal flow turbines or axial flow turbines shown in Table 4.2 in Sub-clause 4・2・2 may be used respectively, if the specific speeds NQE for turbine operation of those pump-turbines are within the range shown in Table 4.1 in Sub-clause 4・2・1.

Table 5.2 Calculation formulas for EDstdn and EDstdQ

EDstdn EDstdQ

Francis type pump-turbine (pump operation)

0564.085.1 QEEDstd Nn 2

2

0564.085.1

QE

QEEDstd

N

NQ


Model reference dimensional factor MM DdhCO , MM DlCO of each component passage shall be calculated

according to Eq. (5・10), (5・11) and (5・12) shown below as a function of specific speed )(TQEN for turbine operation. Furthermore, if the prototype is geometrically similar to the model, reference dimensional factor of the prototype must be equal to the one of the model. So, subscript M and P may be omitted in case that strict distinction between the model and the prototype is not required. Values for the coefficients 1a , 2a , 3a , 4a in Eq. (5・12) are shown in Table 5.3.

And, as for pump operation of diagonal flow pump-turbines or axial flow (tubular) pump-turbines, calculation results for diagonal flow turbines or axial flow turbines shown in Table 4.3 in Sub-clause 4・2・3 may be used respectively, on condition that the specific speeds )(TQEN for turbine operation of those pump-turbines are within the range shown in Table 4.1 in Sub-clause 4・2・1.

Furthermore, if the reference dimensional factor based on the actual dimensions is remarkably different from the one given from Table 5.3 due to the different design concept from the standard design concept, the one based on the actual dimensions may be used. Also for the pump-turbine with different structure, such as the storage pump without guide vanes, the reference dimensional factors derived from the actual structure considering the actual flow condition may be used.

(Spiral case, flow passage from guide vanes outlet to runner inlet and draft tube)

DdDdDd hCOhCOhCO PPMM (5・10)

(Stay vanes, guide vanes and runner) DlDlDl COCOCO PPMM (5・11)

TQETQETQECOhCO NaaNaNaDlDd 4322

1, (5・12)

Furthermore, if the specific speed for turbine operation )(TQEN shown in Eq. (5・12) is not known, it shall be

calculated from the specific speed for pump operation )(PQEN according to the procedure shown in [Explanation 5・1].

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Table 5.3 Coefficients of the polynomial for Dd hCO ， DlCO

1a 2a 3a 4a Francis type pump-turbine (pump operation)

Spiral case ( Dd hSP ) 0.0 -0.289 1.12 -0.006747 Stay vane ( DlSV ) 12.231 -5.386 0.84 0.0 Guide vane ( DlGV ) 10.87 -4.788 0.747 0.0 Runner ( DlRU ) 0.6511 5.573 -2.53 0.3979 Draft tube ( Dd hDT ) 0.0 0.0 1.17 0.0

(Note) Reference dimensional factor of a flow passage from guide vane outlet to runner inlet for a Francis type pump- turbine is not necessary to be considered, because its influence was included in guide vanes and a runner. (Furthermore definitions for inlet and outlet are based on flow direction of turbine operation.)

[Explanation 5・1]

To avoid different reference dimension factors are given for turbine operation and pump operation of the same pump-turbine

model, it was determined that the reference dimension factors to be calculated based on the specific speed QE(T)N for the best

efficiency point of the turbine operation. Furthermore if the specific speed QE(T)N for the turbine operation is not known in

case of the storage pump, it shall be calculated using the specific speed QE(P)N of the best efficiency point of the pump

operation. (Refer to Eq. (C2・28) in Appendix-C)

QE(P)QE(T) NN 903.0


Model reference velocity factor MM uCOv of each component passage shall be calculated according to Eq. (5・13),

(5・14), (5・15) and (5・16) shown below using specific speed QEN for pump operation, EDstdEDopt nn and

EDstdEDopt QQ . Furthermore, if the operating condition of the prototype turbine is kinematical similar to the one of the model, reference velocity factor for the prototype must be equal to the one for the model. So, subscript M and P may be omitted in case that strict distinction between the model and the prototype is not required. Values for the coefficients 1a , 2a , 3a , 4a in Eq. (5・16) are shown in Table 5.4.

And, as for pump operation of diagonal flow pump-turbines or axial flow (tubular) pump-turbines, calculation results for diagonal flow turbines or axial flow turbines shown in Table 4.4 in Sub-clause 4・2・4 may be used respectively, on condition that the specific speeds QE(T)N for turbine operation of those pump-turbines are within the range shown in Table 4.1 in Sub-clause 4・2・1.

Furthermore, if the reference velocity factor based on the actual flow condition is remarkably different from the one given from Table 5.4 due to the different design concept from the standard design concept, the one based on the actual flow condition may be used. Also the reference velocity factors for the pump-turbine with different structure, such as the storage pump without guide vanes for a hydraulic power plant, may be determined according to the actual flow condition.

uuu COCOCO vvv PPMM (5・13)

(Except runner)

EDstd

EDopt

EDstd

EDoptCOstdCO

n

n

Q

Quu vv (5・14)

(Runner) 212

2

212

2

16

2

116

2

1

EDstd

EDstd

EDopt

EDoptCOstdCO

n

Q

n

Quu

vv (5・15)

QEQEQECOstd NaaNaNau 4322

1 v (5・16)

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Table 5.4 Coefficients of the polynomial for uCOstdv



Stay vane ( uSVstdv ) 0.0 -0.09824 0.109 0.04985


Runner ( uRUstdv ) 0.0 -0.2739 0.790 0.0

Draft tube ( uDTstdv ) 0.0 -0.5886 0.268 0.0

(Note) Reference velocity factor of a flow passage from guide vane outlet to runner inlet for a Francis type pump-turbine is not necessary to be considered, because its influence was included in guide vanes and a runner. (Furthermore definitions for inlet and outlet are based on flow direction of turbine operation.)


Model standard relative scalable (friction) loss ECOstd (under reference Reynolds number refRe , standard speed

factor EDstdn , standard discharge factor EDstdQ and hydraulically smooth surface) shall be calculated according to the equation shown below depending on specific speed QEN . Values for the coefficients 1a , 2a , 3a , 4a in Eq. (5・17) are shown in Table 5.5.

And, as for pump operation of diagonal flow pump-turbines or axial flow (tubular) pump-turbines, calculation procedure for diagonal flow turbines or axial flow turbines shown in Table 4.5 in Sub-clause 4・2・5 may be used respectively, on condition that the specific speeds QE(T)N for turbine operation of those pump-turbines are within the range shown in Table 4.1 in Sub-clause 4・2・1.

Furthermore, if the reference dimensional factors MM DdhCO , MM DlCO and/or the reference velocity factors MM uCOv are determined based on the actual dimensions and/or the actual flow condition due to the different design

concept from the standard one, the standard relative scalable (friction) loss ECOstd shall be a relative scalable (friction) loss calculated at the best efficiency point assuming EDoptEDstd nn and EDoptEDstd QQ according to the procedure shown in Appendix-C.

100)( 4322

1 QEQEQEECOstd NaaNaNa (5・17)

EDTstdERUstdEGRstdEGVstdESVstdESPstdECOstdEstd (5・18)

Table 5.5 Coefficients of the polynomial for ECOstd


Spiral case ( ESPstd ) 0.0 0.2974 0.47 0.0 Stay vane ( ESVstd ) 0.3772 0.8052 -0.03 0.05073 Guide vane ( EGVstd ) -0.3419 3.357 0.01 0.09890 Runner ( ERUstd ) 41.22 -7.718 3.34 -0.05963 Draft tube ( EDTstd ) 0.0 0.4488 0.01 0.0 Total ( Estd ) 41.26 -2.810 3.80 0.0900

(Note) Friction loss of a flow passage from guide vane outlet to runner inlet for a Francis type pump-turbine is not necessary to be considered, because it was included in guide vanes and a runner. (Furthermore definitions for inlet and outlet are based on flow direction of turbine operation.)


Friction coefficient MCO and MfCOC of each model component passage based on Reynolds number MRe at each model tested point and friction coefficient refCO M and reffCOC M of each component passage under reference Reynolds number refRe shall be calculated as shown below. Furthermore, the calculation procedure in this section is identical

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with the one shown in Sub-clause 4・2・6 for turbine operation. (Furthermore definitions for inlet and outlet are based on flow direction of turbine operation.) 1) Reference component Reynolds number refCORe M under reference Reynolds number refRe ( 6107 ) shall be

calculated using reference dimensional factor DdhCO , DlCO shown in Sub-clause 5・2・3 and standard reference velocity factor uCOstdv shown in Sub-clause 5・2・4 as shown below.

(Spiral case, Guide vanes outlet to runner inlet, Draft tube) refCOstdhCO

refCO ReuD

dRe

vM (5・19)

(Stay vanes, Guide vanes, Runner) refCOstdCO

refCO ReuD

lRe

vM (5・20)

2) Each component Reynolds number MCORe under tested Reynolds number MRe shall be calculated as shown below.

M

MMMM

νnDD

Re

(5・21)

(Spiral case, Guide vanes outlet to runner inlet, Draft tube) MM ReuD

dRe COhCO

COv

(5・22)

(Stay vanes, Guide vanes, Runner) MM ReuD

lRe COCO

COv

(5・23)

Next, friction coefficient refCOM and reffCOC M of each model component passage under the reference condition

(Surface of the model component passage shall be hydraulically smooth and under reference Reynolds number6107refRe ) shall be calculated. Friction coefficient MCO and MfCOC shall be calculated both for smooth surface

and rough surface, then final value shall be determined. Subscript s means smooth surface and Subscript r means rough surface.

3) Friction coefficient of a spiral case, a flow passage from guide vanes outlet to runner inlet and a draft tube (Subscript

CO represents a general term, which means SP for a spiral case, GR for guide vane outlet to runner inlet and DT for a draft tube.) Reference condition (Smooth surface, reference Reynolds number 6107refRe )

8.0log21

MM10

M

refCOrefCO

refCO

Re

(5・24)

Smooth surface

8.0log21

MM10

M

sCOCO

sCO

Re

(5・25)

Equations (5・24), (5・25) is an implicit function of refCOM , sCOM . So, the equations shown below instead of

them may be used to calculate easily.

26.0

10774.000854.0

2.0

M

6

MrefCO

refCORe

(5・26)

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26.0

10774.000854.0

2.0

M

6

MCO

sCORe

(5・26)’

Rough surface

2

6M

M10M 74.1

104

2log2

CO

hCOrCO

Ra

d (5・27)

where, MhCOd can be calculated as DdD hCOM using reference dimensional factor DdhCO shown in

Sub-clause 5・2・3. MCORa means arithmetic mean roughness for each model component passage as shown in Sub-clause 5・5. (Refer to Appendix-D)

Finally, friction coefficient MCO of model component passage under the test condition of each tested point of the model test shall be sCOM or rCOM , whichever larger. For hydraulically smooth surface, sCOM ＞ rCOM .

),(max MMM rCOsCOCO (5・28)


SV for stay vanes, GV for guide vanes and RU for a runner.) Reference condition (Smooth surface, reference Reynolds number 6107refRe )

(5・29)

Smooth surface

(5・30)

Rough surface

5.2M

6M10M )]102(log62.189.1[1 COCOrfCO lRaC (5・31)

where, MCOl can be calculated as DlD COM using reference dimensional factor DlCO shown in Sub-clause

5・2・3. MCORa means arithmetic mean roughness for each model component passage as shown in Clause 5・5. (Refer to Appendix-D)

Finally, friction coefficient MfCOC of model component passage under the test condition of each tested point of the model test shall be sfCOC M or rfCOC M , whichever larger. For hydraulically smooth surface, sfCOC M ＞

rfCOC M .

),(max MMM rfCOsfCOfCO CCC (5・32)


Standard relative scalable (friction) loss ECOstd of each component passage given in Sub-clause 5・2・5 is the value under standard speed factor EDstdn and standard discharge factor EDstdQ given in Sub-clause 5・2・2, and at the best efficiency point under the reference condition (Smooth surface, reference Reynolds number 6107refRe ). So,

582Mref10M )](log[455.0 .

COreffCO ReC

58.2M10M )](log[455.0 COsfCO ReC

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relative scalable (friction) loss ECO of each tested point of the model test shall be calculated according to equations shown below, considering influence of test Reynolds number MRe and discharge ratio to best efficiency discharge

EDoptED QQ . Furthermore, following points should be noted that MCO and MfCOC are friction coefficient of a component passage given in Sub-clause 5・2・6 and FEK is ratio of the relative scalable (friction) loss of each tested point to the one of the best efficiency point. (Definitions for inlet and outlet are based on flow direction of turbine operation.) (Spiral case, Guide vanes outlet to runner inlet, Draft tube)

2MM EDstdEDoptECOstdrefCOCOFEECO QQK (5・33)


2MrefM EDstdEDoptECOstdfCOfCOFEECO QQCCK (5・34)

(Runner)

2

2

22

2

2

22

MM8

2

8

2EDstdEDstdEDoptEDoptERUstdreffRUfRUFEERU QnQnCCK

(5・35)

Furthermore, the ratio of friction coefficients may be calculated approximately on condition that the surface of the

model component passage is hydraulically smooth. (Spiral case, Guide vanes outlet to runner inlet, Draft tube)




(Runner)

2

2

22

2

2

22

18.0MM

8

2

8

2EDstdEDstdEDoptEDoptERUstdrefRURUFEERU QnQnReReK

(5・38)

where, ratio of the relative scalable (friction) loss of each tested point to the one of the best efficiency point FEK shall be calculated according to following equations. (Refer to Appendix-C2・3) Francis type pump-turbine (pump operation)

696.06.09.1 2 EDoptEDFE QQK (5・39)

Diagonal/axial flow pump-turbine (pump operation)

5.02EDoptEDEDoptEDFE QQnnK (5・40)

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Friction coefficient PCO , PfCOC of each prototype component passage shall be calculated as shown below. Furthermore, the calculation procedure in this section is identical with the one shown in Sub-clause 4・2・8 for turbine operation. (Furthermore definitions for inlet and outlet are based on flow direction of turbine operation.)

1) Prototype Reynolds number PRe shall be calculated as shown below.

P

PPPP

nDD

Re (5・41)

2) Each prototype component Reynolds number PCORe shall be calculated using reference dimensional factor DdhCO ,

DlCO and reference velocity factor uCOv given in Sub-clause 5・2・3 and 5・2・4.

(Spiral case, Guide vanes outlet to runner inlet, Draft tube) PP ReuD

dRe COhCO

COv

(5・42)

(Stay vanes, Guide vanes, Runner) PP ReuD

lRe COCO

COv

(5・43)

Next, friction coefficient PCO and PfCOC of each prototype component passage shall be calculated considering each

component Reynolds number PCORe and surface roughness PCORa . Friction coefficient PCO and PfCOC shall be calculated both for smooth surface and rough surface, then final value shall be determined. Subscript s means smooth surface and Subscript r means rough surface.

3) Friction coefficient of a spiral case, a flow passage from guide vanes outlet to runner inlet and a draft tube (Subscript CO represents a general term, which means SP for a spiral case, GR for guide vane outlet to runner inlet and DT for a draft tube.)

Smooth surface

8.0log21

PsP10

P

COCO

sCO

Re

(5・44)

Equation (5・44) is an implicate function of sCOP . So, the equation shown below instead of it may be used to

calculate easily.

26.0

10774.000854.0

2.0

P

6

PCO

sCORe

(5・45)

Rough surface

2

6P

P10P 74.1

104

2log2

CO

hCOrCO

Ra

d (5・46)

where, PhCOd can be calculated as DdD hCOP using reference dimensional factor DdhCO shown in

Sub-clause 5・2・3. PCORa means arithmetic mean roughness for each prototype component passage as shown in Clause 5・5. (Refer to Appendix-D)

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Finally, friction coefficient PCO of prototype component passage under tested condition shall be sCOP or rCOP , whichever larger.

),(max PPP rCOsCOCO (5・47)


SV for stay vanes, GV for guide vanes and RU for a runner.)

Smooth surface

58.2P10P log455.0 COsfCO ReC (5・48)

Rough surface

52

P6

P10P ][ )102(log62.189.11.

COCOrfCO lRaC (5・49)

where, PCOl can be calculated as DlD COP using reference dimensional factor DlCO shown in Sub-clause

5・2・3. PCORa means arithmetic mean roughness for each model component passage as shown in Clause 5・5. (Refer to Appendix-D)

Finally, friction coefficient PfCOC of prototype component passage shall be sfCOC P or rfCOC P , whichever larger.

),(max PPP rfCOsfCOfCO CCC (5・50)


Friction coefficient ratio CO shall be calculated using the friction coefficient of model component passage MCO ,

MfCOC and the one of prototype component passage PCO , PfCOC mentioned above. Furthermore, the calculation procedure in this section is identical with the one shown in Sub-clause 4・2・9 for turbine operation.

MP COCOCO ,or MP fCOfCOCO CC (5・51)

5・3 Calculation for Discharge Efficiency Scale Factor QF

5・3・1 Discharge efficiency scale factor QF for Francis type pump-turbines (pump operation)

Discharge efficiency scale factor QF for Francis type pump-turbines (pump operation) seems to be equal to the one

at the best efficiency point QoptF . Then they shall be calculated as shown below. (Refer to Appendix- E)

QQ

Q

Q

optQQoptQ Λ

ΛFF

MoptMopt

P )1(

(5・52)

where, optQM and optQP mean model and prototype discharge efficiency at the best efficiency point and Q means friction coefficient ratio to be calculated as below. optReM means Reynolds number at the best efficiency point in the model test.

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2M 0000361.0993.0 QEoptQ N (5・53)

21

41PM2)(13)(2

2)(1

2)(13)(22

)(1

)()(

)()(

optoptTQETQETQE

TQETQETQEQ

ReRebNbaNaNa

bNbaNaNa (5・54)

The specific speed )(TQEN in Eq. (5・54) shall be the one for turbine operation. For the Francis type pump-turbines with the normal design, coefficients a1, a2, a3, b1, b2 shall be as shown Table 5.6. Furthermore, if the specific speed for turbine operation )(TQEN is not known, it shall be calculated from the specific speed for pump operation )(PQEN according to the procedure shown in [Explanation 5・1].

Table 5.6 Coefficients of the polynomial for Q a1 a2 a3 b1 b2 Francis type pump-turbine -1.789 -7.659 9.00 -1.654 3.26

5・3・2 Discharge efficiency scale factor QF for diagonal/axial flow pump-turbines (pump operation)

Discharge efficiency for pump operation of diagonal flow pump-turbines and axial flow (tubular) pump-turbines other than Francis turbines and Francis type pump-turbines is equal to 1 ( 0.1M Q ). So discharge efficiency scale factor QF shall be as bellow.

0.1 QoptQ FF (5・55)

5・4 Calculation for Power Efficiency Scale Factor TF

5・4・1 Power efficiency scale factor TF for Francis type pump-turbine (pump operation)

Power efficiency scale factor TF for Francis type pump-turbines (pump operation) shall be calculated as shown

below. (Refer to Appendix-F)

TTTT

TT

ΛΛF

MM

P

1

1

(5・56)

where, MT means power efficiency for each tested point of the model test and T means friction coefficient ratio. Those shall be calculated as below.

EDEDoptEDoptED

optTT PPnn 3

MM 1

111

(5・57)

where, EDoptn and EDn mean the speed factor at the best efficiency point and the speed factor at each tested point respectively. Also EDoptP and EDP mean the power factor at the best efficiency point and the power factor at each tested point respectively. Furthermore, optTM means the power efficiency at the best efficiency point and shall be calculated as shown below, when the surface of the model runner is hydraulically smooth. (Refer to Appendix-F)

][ M2.0

M2.0

MM 11 stdToptrefoptrefoptT ReReReRe (5・58)

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where, optReM means the tested Reynolds number at the best efficiency point. stdTM means the best power efficiency under the standard Reynolds refRe and shall be calculated as shown below.

(Francis type pump-turbine, pump operation) 2

M 000189.0986.0 QEstdT N (5・59)

The friction coefficient ratio T means ( MP LdLd CC ), the ratio of the friction coefficient LdC for runner outer surface and shall be calculated as shown below.

2P102

M10MP loglog SSLdLdT KKCC (5・60)

Furthermore, MSK and PSK means relative roughness for the model and the prototype. They are the relative

roughness for smooth surface sSK M , sSK P (indicated by the subscript s) defined as below or the relative roughness of rough surface rSK M , rSK P (indicated by the subscript r) defined as below, whichever larger. optReM means the tested Reynolds number at the best efficiency point and PRe means the Reynolds number of the prototype turbine.

rSsSS KKK MMM ,max , rSsSS KKK PPP ,max (5・61)

Smooth surface

2M

M200

DSopt

sSRe

K

, 2P

P200

DS

sSRe

K

(5・62)

Rough surface

DSrS

D

RaK

M

6M

M102

, DS

rSD

RaK

P

6P

P102

(5・63)

where, DS means the ratio of the runner maximum diameter ( MSD or PSD ) to the runner reference diameter ( MD or

PD ) and shall be calculated based on the specific speed for turbine operation TQEN as shown below. Furthermore, if the specific speed for turbine operation )(TQEN is not known, it shall be calculated from the specific speed for pump operation )(PQEN according to the procedure shown in [Explanation 5・1].

PPMM DDDD SSDS (5・64)

(Francis type pump-turbine) 3

221 )903.0( aaNa TQEDS ( QEN ≦ 220.0 ， 7.421 a ， 244.02 a ， 06.13 a ) (5・65)

06.1DS ( 220.0TQEN ) (5・66)

Furthermore, MRa and PRa shown in Eq. (5・63) mean the surface roughness of the model and the prototype

corresponding to the respective roughness of the runner outer surface. The respective roughness is weighted average of the arithmetic mean roughness RRaT measured at runner outer surface (crown and band) and the SRaT measured at the stationary surface facing to the measured surface of the runner. (Where, subscript T can be replaced by M for the model and P for the prototype. Refer to Appendix-F)

32 TTT SR RaRaRa (5・67)

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5・4・2 Power efficiency scale factor TF for diagonal/axial flow pump-turbines (pump operation)

Power efficiency for pump operation of diagonal flow pump-turbines and axial flow (tubular) pump-turbines than Francis type pump-turbines is equal to 1 ( 0.1M TT ). So power efficiency scale factor TF shall be as bellow.

0.1 ToptT FF (5・68)


Definitions for the surface roughness of each component passage of the model and the prototype, MCORa and

PCORa , referred in Sub-clause 5・2・5 and Sub-clause 5・2・8 are as shown below. Those definitions are same for both the model and the prototype. (Refer to Appendix-D) (Furthermore definitions for inlet and outlet are based on flow direction of turbine operation.)

Spiral case; Average values measured around inlet of a spiral case ( Ra ) Stay vanes; Average values measured on guide vanes side surface of stay vanes ( Ra ) Guide vanes; Average values measured on runner side surface of guide vanes ( Ra ) Flow passage from guide vanes outlet to runner inlet; Average value of tip side and hub side of upstream of runner vanes of a diagonal flow pump-turbine and an axial flow (tubular) pump-turbine ( Ra ) Runner; Average values on suction side surface near outlet (lower pressure side) ( Ra ) Draft tube; Average values measured at upper draft tube area ( Ra )

Furthermore, Ra mentioned above means arithmetic mean roughness and relation to the equivalent sand roughness ks was shown in Appendix-D1・3.

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