Hydro power - the design, use, and function of hydromechanical, hydraulic, and electrical еquipment . pdf

HYDRO PO
The Design, Use, and Function
of Hydromechanical, Hydraulic,
and Electrical Equipment

Professor Dr.-Ing. Joachim Raabe

VDI-cVerlag GmbH
Mrlag desvereins Deulsd~crIrlgenieure - Dlijseldorf


Raal~c,.Joachir~~:
klydro poacr: tllc dcsign. usc. arid ftrnction of hy~lromcch;ln.,Iiydraul., ;111dclcctr. cqttipn~ctlt/
Joacl~iniRaabc. - Diisscldorf: VDI-Vcrlag, 1985.

0 VDI-Verlag GmbH, Diisseldorf 1985
All rights rescrvcd. including the rights of reprinting extracts, partial or cvrnpletc photorne~hanical
reprodvction (photocopying, microfilming) and the translation into foreign languages.
Printed in Germany
Typ~sctting:Dnten- und Lichtsatz-Service, Wiirzburg
.
Printing and binding: Graphischer Betrieb, Konrad Triltsch, Wiirzburg

ISEN 3-18-400616-6

I

I
I

For Bert1

All my thoughts that 1 have.
they are with you . . .
(Old German folk-song)



Prefatory Note
T h e appearance of this new book is doubly welcome, firstly because, beins in English..it
is available to a very large number of readers and, secondly, because i t is nn u p to dale
and largely rewritten account of the subject on which the author has a l r e a d ~macie ;ill
international reputation. Professor Rntrbe's fcur previous books on liydraulic machinery
and installations published by the VDI-Verlag were available to readers of ihs German
language but are now out of print. Althouzh there has also been a translated Russirin
version his valuable account of hydroelectric practice have not therefore been easil!accessible to the vast number of potential readers familiar lvith Enzlish. This has bcen
particularly unfortunate recently because of the world-wide resurgence of the long estnblished hydro power industry. Because of economic problems caused by risinz fuel cosrs
and expendable fossil fuels the interest in hydro power has greatl! increased in most
countries, not only for large schemes but also for mini and micro instilllntions where
power can be used locally for agricultural and industrial use. This new definiri\e ivork b!.
Professor Ratrbe will therefore meet with even ~vidcrrlcclrlin~internat:onall!. than hij
pseviocs publicatio~s.
The author is a distinguished hydraulic expert who has travelled widel!. and lccturcd in
many countries on hydraulic machines and hydro poiver equipment. He hi:> hat1 cxtengive industrial. research and academic experience and is wzll kno11.n c n intrtrnat~or,;ii
technical committees for his valued contributions. This monograpl; rcprzsenis h ~ rtccus
rnulated wisdom over many years together w ~ t haccounts of recent recearchcs ant1 advanccd course lecture material. The result is a valuable trcailse \\~Ii~ch
\\.111 help cnginrers.
teachcrs, advanced students, and many ot heis concerned wi th the creaLlon a n d mallagement of hydroelectric installations.

1 am most grateful for the opportunity to introduce this co~nprel-)ensilenen book and

wish both it and its reciders all success in helping to make the world a better place by the
skilf~ilapplication of hydro power.



Preface
Water is one of nature's gifts. The mere chance of creation has made water vapour lighter
than the surrounding atmosphere. so that sunshine can raise it from the ocean, while
sun-born winds carry it to those regions where it condenses again and then kills down
to the earth, from which gravity makes it flow downhill back towards the ocean, thus
closing its earthly cycle.
Ancient civilizations were fluvial and their members already managed to lift water for
irrigation by machines equipped with pails and driven by water mills of the undershot
t Y Pee
In 1831 when the French engineer B. Fourneyron had already built the first reliable water
turbine, the famous German poet Goethe finished the second part o i his tragedy Fatrsr.
At death's door Faust wins his wager with the devil (to be redeemed if there came a
moment of which he could say, "linger you now you are that fair"), when he has the
following vision of the harnessing of the tidal powers of the ocean.

"A paradise our closed-in land provides,
Though to its margin rage the blustering tides;
When they eat through, in fierce devouring flood,
All swiftly join to make the dammage good.
Ay, in this thought I pledge my faith unswerving.
Here wisdom speaks its final word and true,
None is of freedom or of life deserving,
Unless he daily conquers it anew.
With dangers thus begirt, defying fears,
Childhood, youth, age shall strive through strenuous years.

Such busy, teeming throngs I long to see,
Standing on freedom's soil, a people free.
Then t o the moment could I say:
Linger you now, you are that fair!"
The hard Stachar~ovitehand labour of Goethe's vision of liberty would today be thought
of as an unbelievable slavery in the face of a graceless nature to which men were delivered
up when they had not the powerful tools of today's electrotechnology.
The inventions of engineers in the last century and a half since the death of our famous
Goethe are the main factors which have relieved the average man from laborious slavelike work.
This has been done by harnessing the energy resources offered by nature in the form of
fuel and, last but not least, in the form of hydro power. Even if hydro power covers at
present in West Germany only a modest portion of the electric energy demand, hydroelectricity has made in our country, and especially in its more waterpower blessed
southern part, a decisive contributiorl to the momentum that electrification brought into
our daily economical life during the last century.


2-0 ur~clcl-standthis nianifcstation, a glntlcc .it tlic historicill tlcvclopnicnt of clcctrification
should bc niadc. 7'wo kcy events have stin1ul;lted the consumption and pratll~ctionof
elcctrici ty.

One was the invcti~ionof the self-exciting dynatno (1869) by IV: \*oti Sicittors in Bcrlin and
thc induction motor by h.1. rlo:l Dolivo Dohrol~olskyin IS90 also in Rcrlin. 'Tlic other was
thc inven tiori of the light bulb by the Gertiir~n-AmericanG6hcl 1859 in Ncw York. Erfisotl
made the vital contribution of reinventing this 25 years later and illumitlating a quartcr
of New York by these means with the aid of the first thcrmo-clcctric power plant erccted
1882 in New York.
With the invention of electric illuminatiori a large consumer market was stimulated to
install electricity in homes. These consumers were concentrated in big towns whereas the
usable waterpower was in far remote areas. Therefore power transmission of hydro power
from sites io the consumer became an urgent need.

In 1891 the crucial step forward was made by the Germans 0. votr ,%filler,the promoter,
and 1Vl. yon Dolivo Dobro)lolsky, the construcior, by the transmission of 300 hp over
175 km betv:een Heilbronn and Frankfurt using a 15 000 Volt three phase AC power line.
Aftcr this breakthrough experiment, which was successful, the USA started with the
erection of the first huge power station on the Niagara Falls with 10 5000 hp in 1892.
Anothcr advance for harnessing waterpower was achieved by the German professor Fiitk
in Berlin, who obtained a patent on adjustable wicket gates. I n 1873 the German manufacturer K~itltequipped for the first time a Francis turbine with these gatcs. O ~ i l ythis
combination made the Francis turbine an effective tool for harnessing waterpower.

Thc way was shcwn for the development of low head river power plants by the patent
of the Germ:~n-Atlstrian 1/: Knplan in 1913 for axial turbines with adjustable runner
vanes. To harness river poivet of the lowest head, the Gernian A. Fischer together with
the Escher Wyss firm have built, since 1936, tubular turbines with rim generators after
Harza's patent from 1919, and the tirst bulb turbine. In the compact design of a rim
generator plant, all the ccimponents have to be adapted to each other with respect to their
purpose and the small space available. In this context the pioneer work of the German
H. FerttzloJ must be mentioned. Pumped storage plants have been developed by the
Slviss firm Sulzer and Escher Wyss and the German firm Voith since the turn of the
century, culminating in 1928 in the Herdecke plant with 4 - 27 M W tandem sets. In 1932
and 1936 Escher Wyss and Voith built the first axial and radial pump turbines in the
German Baldeney plant and the Brazilian Pedreira plant.
G

Recent corner stones in 'the West German development of hydro power are as follows.
Firstly the African plant Cabora Bassa in hqozambiq:ie: There 5 415 h4W \yere installed
for power transmission over 1400 km by 1 million volt DC using dry thyristor technique;
the turbines were manufac:ured by a consortium of the West German firm Voith and the
French firm Neyrpic.
Both firms are now erecting the turbines for the 1 8 . 715 M W Francis turbine sets of
Itaipu in Bra~il,at the moment the hydro power station with the largcst i~lstalled

capacity. In this context it may also be mentioned, that the West German firm Ossberger
has logicaily developed from the Michell type turbine the most reliable and simple small
turbine of the Ossberger type, especially for developing countries.
Crintera., the founder of the author's institute, fonilulated in 1905 the specific speed as the
generally adopted most important criterion to distinguish typcs of hydroturbines. In 1922
my predccessor Tltonrtr introduced the now interfiationally used cavitation index a.


In the past decade I have had the privilege of holdins lecture courses on hydro power for
advanced post-graduate students in the following centres of reccnt water power development: The Indian Institute of Technology Madras, India; The University of Siio Paulo.
Brazil; The Laval University, Quebec and Hydro Quebec, Montreal, Canada: The Central University Caracas, Venezuela; The Polytechnic Institute Timisoara, Rumania; The
Huazhong Institute of Technology, Wuhan, People's Republic of China.
This has stimulated me to publish this book, which can be considered as the outcome of
these lectures, some rewritten chapters of a former book of mine in German, and the
many papers and findings made over the past 15 years in the Teaching Chair and
Laboratory headed by me at The Technical University of Munich, Federal Republic of
Germany.
In this context the names of Dr.-Ing. W Kiihnel, Dr.-Ing. D. Castorph, Dr.-Ing. E. Bar,
Dr.-Ing. M. V-dtter, Dr.-Ing. G. Schlemmer, Dr.-Ing. G. Mollenkoyj; Dr.-Ing. R. Gerich,
Dr.-Ing. M. Lotz (deceased), Dr.-Ing. R. Kirmse, Dr.-Ing. J. Korcian, Dr.-Ing. N. Fttrtner,
Prof. Dr.-Ing. R. Jahn, Dr.-Ing. E. Hartrter, Dip].-Ing. H. Pfoertner, Dr.-Ing. E. Walter.
Dr.-Ing. J. Klein, Prof. Dr.-Ing. F. El Refiie, Professor Dr. Engng Ravinn'rall, a n d Mr.
D. Lauria may be mentioned for their valuable help, their suggestions, and contributions
in connection with scientific papers presented at international or national congresses, or
in connection with work for theses made at the Lehrstuhl und Laborato~iumfur Hydraulische Maschinen und Anlagen der Technischen Hochschule Miinchen.
F o r many neatly drawn figures my thanks are due to Mr. M. Ring. In connection with
the erection of reliable test stands but mainly for his valuable contribution of building
quick response vector probes, the name of Mr. H. Kriegl, head of our lab's workshop
should be mentioned.
Many firms have supported the publication of this book monetarily in a liberal manner.

They are
Allis Chalmers, Milwaukee, Wisconsin, USA
1ng.-Buro Freisl, Garmisch-Partenkirchen, F. R. Germany
Hydroart, Milano, Italy
KaMeWa, Kristineham, Sweden
Kvaerner Brugg, A. S., Oslo, Norway
Neyrpic, Grenoble, France
Ossberger, Weissenburg, F. R. Germany
Sulzer Escher Wyss, Ziirich, Switzerland
Tampella, Tampere, Finland
Vevey-Charmilles Engineering Works, Vevey, Switzerland
Voest Alpine, Linz, Austria
Zahnradfabrik Friedrichshafen, Friedrichshafen, F. R. Germany
The library of the Technical University Munich an organization of the Bavarian State
Ministry of Education and Kultus headed by Dr. Schweigler contributed in a similar
manner.
Moreover thanks should be given to the VDI-Verlag as the publisher, who undertook the
venture of publishing a book directed to all the specialists and students in the world
engaged in the development of hydro power.
The work would not have been succeeded if Mr. T. B. Ferguson, Senior Lecturer at the'
Department of Mechanical Engineering of the University of Sheffield. a well-known
author of a book on turbomachinery, versed in treating technical terms and also versed


in colloqitinl E:~glisl~,
had not revicwed thc wholc manuscript twicc very carcfi~lly.For
[hat I ill11 gre;~llyir~clcbtcdto hirn.
I n this contcsi also two Inclinn hydro turbine speci;tlists Professor Dr. Rlltrrltr Kr.islrtrtr,
head of the t1ydro-turbomachines labor;ltory, 11T Matlras, and l'rofessor Dr.-Ing.
K Vtr.scu~cltrtli,hcad of Dep;irtmcnt at Punjitb Collcgc of Engineering, may bc grc;itfully

mentioned. Thc same holds also for Professor 111Kr11 Alei, Departlnent of IlyJraulic
Engineering at Quinghua University Beijing (Peking), China.
For advice and help in their special fields, I am also indcbted to Prof. Dr. Erhtrrtl
F . Joerrs. Uni\.crsity of Wisconsin, Madison, USA; em.@.Professor. Dr., Dr., Dr., Dr. h.c.,
Dr.-Ing. E.h. E. ,\losotlj.i, University of Karlsruhe, F. R. Gcrniriny, o. Prof. Dr.-Ing.
G. Sclt~l~iclt,
Professor Dr.-Ing. If. Stei~thic~gler,
both at the Technical University Munich,
and Mr. K . !L bl4lli. deputy director of Siemens, El-langcn, F. R. Germany.
Although care has been taken to make the E ~ ~ g l i srendering
h
as clear as possible, it is
hoped that any reader who may detect Faults would kinclly bring them to my attention.
My thanks are also due to Mr. Braitsclr and Mr. Olbricl~fos carefully reading the
manuscript and the proofs7 and for making valuable suggestions.
Last but not least my thanks are due to my secretary .Mrs. A. Fltllr- for having typed parts
of the final copy of the manuscript.
This book may show how scientific work can bridge the frontiers between countries of
different cultures. May Hydro Power, which to date is used only by about ten percent of
its potential, flourish also in future under the motto: vivat, floreat, crescat!
Munich, autumn 1954

Joncllitn Ratrhe


Hints to the reader
In decimal fractions, the decimal point is replaced by a comma, e.g., 5,6 is used instead
of the Anglo American 8 - 6.
In products, multiplication mark ' x ' is replaced by a point e.g., S - 23 is used instead of
the Anglo American 8 x 23. The multiplication mark ' x ' is reserved for vector products

a x b, b) multipliers that extend over one line, c) output of 3 equal sets thus
P = 3 x 30 M W occasionally used.
Abbreviations: Machines types are usually abbreviated as follows: Kaplan turbine = K T
(plural KTs), Francis turbine = FT, Pelton (impulse) turbine = PT, pump-turbine =
PUT, tubular turbine = TT, bulb turbine = BT, pump = P, Straflo turbine = ST.
The vorticity rot c is denoted by curl c.
The inverse functions of sin x, cos x, tan x, cotan x are denoted by arcsin x, arccos .u,
arctan x, arccotan x, instead of sin-'x, cos-' x, tan-' x, cotan-'x.
How to use the references in the text: All references within the text are put in square
brackets and can be found in a reference list at the end of the last chapter. There they are
arranged by chapters and within the chapters in the sequence they are quoted in the
respective chapters. The first number points to the chapter, the second number to the
reference. For example [9.18] quotes reference 18 in chapter 9. More references can be
quoted by [9.18; 9.191, [9.18 t o 9.301 or [8.5; 9.181. References which are not quoted in the
book are found in the second list of reference at the end of the book, arranged in
alphabetical order of the author's names. At its end, the latter is supplemented by same
references, that came out during the production of this book.
Equations are quoted by numbers put in round brackets and' placed behind the number
of the subchapter in which the equation appears, e.g. (10.2-4) refers to equation 4 in
subchapter 10.2.
Hints at subchapters are quoted by cap, and the number of the subchapter behind it, e.g.
cap. 9.3.1 hints at subchaptcr 9.3.1.
The figures are numbered through consecutively, subchapter by subchapter, the number
of which precedes that of the figure, e.g. Fig. 9.2.1 hints at figure 1 in the subchapter 9.2.



Contents
Nomenclature

1.

. . . . . .

;

. . . . . . . . . . . . . . . . . . . . . . . .1

The origin of hydro power. its potential and its use in a world wide context

9

1.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2. Water from rivers. its causes and features . . . . . . . . . . . . . . .
1.2.1. The rivers . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 .1. Large sources of water power . . . . . . . . . . . . . . . .
1.1.2. Characteristics and classification of well-known rivers . . . . . .
1.2.1.3. Depth and slope of a river . . . . . . . . . . . . . . . . . .
1.2.1.4. High head and large discharge . . . . . . . . . . . . . . . .
1.2.2. Topography . . . . . . . . . . . . . . . . . . . . . . . .
1.2.2.1. The Elements of the continents . . . . . . . . . . . . . . . .
1.2.2.2. Topography and water circulation . . . . . . . . . . . . . .
1.2.2.3. Topography as the origin of falls and water collection . . . . . .
1.2.3. Climate . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 The potential and its distribution . . . . . . . . . . . . . . . . . . .
1.3.1. Theoretical, harnessable, harnessed, potential . . . . . . . . . .
1.3.2. Distribution of harnessed and harnessable potential . . . . . . .
1.4. Hydroelectricity, its development . . . . . . . . . . . . . . . . . . .
1.4.1. Past and future of hydro power in the context of other power . .
1.4.2. Cost and social problems due to electrification . . . . . . . . .

1.4.3. The Future of hydroelectricity . . . . . . . . . . . . . . . .
1.5. Hydro power, its actual dimensions, development and features . . . . . .
1.5.1. The largest structures found in hydro power at present . . . . .
1.5.2. Survey of historical development . . . . . . . . . . . . . . .
1.5.3. The Features of water power plants . . . . . . . . . . . . . .
1.6. Survey of types of hydro power plants . . . . . . . . . . . . . . . .
1.6.1. Plants of conversion of hydraulic primary energy . . . . . . . .
1.6.1.1. General remarks on conversion of primary energy . . . . . . . .
1.6.1.2. River power plants . . . . . . . . . . . . . . . . . . . . .
1.6.1.3. Depression power plants . . . . . . . . . . . . . . . . . . .
1.6.1.4. Wave energy . . . . . . . . . . . . . . . . . . . . . . . .
1.6.1.5. Tidal power plants . . . . . . . . . . . . . . . . . . . . .
1.6.1.6. Hydro power from gas washers . . .' . . . . . . . . . . . . .
1.6.2. Plants for converserion of secondary energy . . . . . . . . . .
1.6.3. Hydro power in transmission drives (torque converter) . . . . . .
1.6.4. Hydro power plants with respect to their availability . . . . . .
1.6.5. Hydromechanical equipment of outstanding plants . . . . . . .

9

9
9
9
10
11
12
12
12
13
13

14
14
14
17
20
20
21
21
22
22
24
25
25
25
25
26
27
27
29
31
31
36
37
39


. . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1. Introcluct~o~i
2.2. l;.cononiic.~lii\pccts o f hydro y o c c r pi, ~ n t s. . . . . . . . . . . . . . .
2.2.1.

Gc~icriilI . C I I I ; I ~ ;iboilt
~
fc;ihil~ilityo f ii project . . . . . . . . . .
2.2.2. Tlic clcc~ricityrate . . . . . . . . . . . . . . . . . . . . .
2.2.3. l'lic spcci tic invcstr-nent cost pcr inst:~llcctk\I1 . . . . . . . . . .
2.2.4.
Econoniic appruisi~lof the projects . . . . . . . . . . . . . .
2.2.4.1. Tht: present \ri~lucnictl~od . . . . . . . . . . . . . . . . . .
2.2.4.2. i~iternalrate of return ~ncthod . . . . . . . . . . . . . . . .
2.2.4.3. I'lieunni~itymethod . . . . . . . . . . . . . . . . . . . .
. 2.2.4.4. The bcncfit-cost ratio . . . . . . . . . . . . . . . . . . . .
2.2.4.5. P r ~ d u c t i o ncost of energy iinit, electricity raie . . . . . . . . .
2.3. The hydro po~vercicvelopmt.rrt of some Iargc rivers . . . . . . . . . . .
2.3.1. The Tennessee (USA) . . . . . . . . . . . . . . . . . . . .
2.3.2. The Columbia (USA, Carlacia) . . . . . . . . . . . . . . . .
2.3.3. The Far-~ini(Brazil, Paragiiay, Argentine) . . . . . . . . . . .
3 . 4 The Yenissci (USSR, Siberia) . . . . . . . . . . . . . . . .
2.3.5. The Volga (USSR, Eilropean part) . . . . . . . . . . . . . .
2.3.6. I'he Zani besi (Zimbabwe, bloza~nbique,Africa) . . . . . . . . .
2.3.7. TheDanube . . . . . . . . . . . . . . . . . . . . . . . .
2.4. Exceptional sltes . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1.
Churchill 1-alls (Chur-chill River, Labrador, Canada) . . . . . .
. . . . . . . . . . . . . . . . . .
2.4.2. Inga ( Z n i r z , C o ~ g o Africa
)
2.5. Srnal! hydro powcr schemes . . . . . . . . . . . . . . . . . . . . .

3.

Sur\e:i and classificntion of essential de\ices of a hydro powcr plant

42
42
42
42
46
46
47
47
45
49
49
39
49
53
56
59
59
61
64
64
06
67

. . . . 71

. . . . . . . . . . . . . . . . . . . . . .
3.1. Ir;tr3duction ant1 su;vcy
3.2. Dams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2.1. Classification of dams . . . . . . . . . . . . . . . . . . . .
3.2.2. The foundation of a dam and related problems . . . . . . . . .
3.2.7. Gravity dams . . . . . . . . . . . . . . . . . . . . . . .
3.2.4. Arch da11is . . . . . . . . . . . . . . . . . . . . . . . .
3.2.5. Multiple arch dams . . . . . . . . . . . . . . . . . . . . .
3.2.6. Response of present society to social and ecological Impacts of dams
3.2.7.
Environmental conseqilenccs of I;~rgedams . . . . . . . . . . .
3.3. The spillway, sates and shut off devices . . . . . . . . . . . . . . . .
3.3.1. The spili\vay in connection with other members of the plant . . .
3.3.2. The spillway . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2.1. The dutie5 of the spillway . . . . . . . . . . . . . . . . . .
3.3.2.2. Sur\ey of Food discharging devices . . . . . . . . . . . . . .
3.3.2.3. Fiied flood discharging devices . . . . . . . . . . . . . . . .
3.3.2.4. Weir yiite; as an adjustable flood discharging device . . . . . . .
3.3.2.5. Dynamic behaviour of spillways . . . . . . . . . . . . . . .
3.3.3. The stilling basin . . . . . . . . . . . . . . . . . . . . . .
3.3.4. V:~lves . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4. The Po111er housc and its equiprient . . . . . . . . . . . . . . . . .
4 1 . The consti:uen! elernents ot' a power house . . . . . . . . . . .
3.4.1.1. Gencral remarks . . . . . . . . . . . . . . . . . . . . . .
3.4.1.2. The si~pcrstructureof the power house . . . . . . . . . . . .
XVI

41

71
74
74
74

75

77
75
80
81
81
81
85
85
86
56
38

91
92
92
94
34

94
95


3.4.1.3. The substructure of the power house . . . . . . . . . . . . . 129
3.4.2.
Power house design with respect to distance from dam . . . . . . 131

4

.

The layout of river-run and storage plants with respect to optimized figures sucli
as rated discharge. nnmber of sets and their diameter. storage volume. hydraulic
radius of water way and dimensions of electric transmission line . . . . . . 135

4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2. Optimization of rated discharge of a run-of-river plant . . . . . . . . .
4.2.1.
General remarks and assumptions . . . . . . . . . . . . . .
4.2.2.
Specialization of the problem . . . . . . . . . . . . . . . . .
4.2.2.1. The Case of given runner diameter D and desired i . . . . . . .
4.2.2.2. The Case of given number i of sets and diameter D to be estimated
4.2.3.
Example of the estimation of runner diameter D . . . . . . . .
Reasons for the number of sets relating to the turbines . . . . .
4.2.4.
4.3. The optimum size (D) and number of sets for a river power plant with given

135
137
137
139
139
142
142
143

rated discharge and rated head . . . . . . . . . . . . . . . . . . . . 144

4.3.1.
Introduction to the problem and assumptions . . . . . . . . . 144
The runner diameter as a function of working data . . . . . . . 145
4.3.2.
4.3.2.1. Kaplan turbines (KTs) . . . . . . . . . . . . . . . . . . . 145
4.3.2.2. Francis turbines (FTs) . . . . . . . . . . . . . . . . . . . . 145
The runner diameter as a function of the number of sets . . . . . 146
4.3.3.
The NPSH as function of the working data and type . . . . . . 146
4.3.4.
4.3.5.
The cost of ground excavation, power house and dam . . . . . . 147
4.3.6.
The cost of fabrication and erection of sets . . . . . . . . . . . 148
The cash value of energy loss during useful life . . . . . . . . . 148
4.3.7.
4.3.8.
The resulting cost as a function of number of sets i . . . . . . . 149
4.3.9. Reasons for setting unit size as large as possible . . . . . . . . 149
. . . . . . . . . 150
4.4. The optimum coefficient of peripheral blade speed Ku
4.4.1.
Introduction to the problem . . . . . . . . . . . . . . . . . 150
4.4.2.
Assumptions . . . . . . . . . . . . . . . . . . . . . . . . 151
4.4.3.
Expressing the cost terms as a function of Ktr . . . . . . . . . 152
4.4.4.
The resulting cost of the turbine during its useful life . . . . . . 152
4.5. Problems due to the layout of the reservoir . . . . . . . . . . . . . . 153

.
4.5.1.
Basic considerations concerning a reservoir . . . . . . . . . . . 153
4.5.1.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 153
4.5.1.2. Assumptions for basic relations of layout . . . . . . . . . . . 154
4.5.1.3. The basic relation for the layout and its problems . . . . . . . . 154
4.5.2.
An approach to the layout of a peak load storage plant . . . . . 155
4.5.2.1. Basic relations of reservoir and river feeding it . . . . . . . . . 155
4.5.2.2. Load demand and its balance with energy stored . . . . . . . . 156
4.5.2.3. Storage volume required, also for pumped storage . . . . . . . 156
4.5.2.4. Economical aspects of the layout of a pumped storage plant . . . 157
4.6. The problems of optimizing the cross section of water ways . . . . . . . 158
4.6.1.
General remarks . . . . . . . . . . . . . . . . . . . . . . 158
4.6.2.
The optimization of the channel section . . . . . . . . . . . . 159
4.6.2.1. The rectangular channel section as a model and the resulting loss . 159
4.6.2.2. The cash value of energy loss . . . . . . . . . . . . . . . . 159
4.6.2.3. The investment cost of the channel . . . . . . . . . . . . . . 160
4.6.2.4. The resulting cost and the optimum depth 4, . . . . . . . . . 160

XVII


4.6.3. 'fhe optimization of' the diameter of a prcsst~rizcdduct . . . . . 161
4.6.3.1. The duct wilh cylindric;d cross section as n model . . . . . . . . I61
4.6.3.2. Thc loss, i t s cash value; investment cost . . . . . . . . . . . . 161
4.6.3.3. Thc resulting cost and optitnutn dinrncter . . . . . . . . . . . 161
4.7. Problems of optimization of electric power transmission . . . . . . . . . 163

4.7.1.
Historicalsurvey . . . . . . . . . . . . . . . . . . . . . . 163
4.7.2.
The cost of 1 % loss in relation to that of power transn~ission . . 164
4.7.3.
The optilnization of the conductor . . . . . . . . . . . . . . 164
4.7.4.
The distance of adjacent towers and cable geometry . . . . . . . 166
4.7.5.
The optimum distance of adjacent towers . . . . . . . . . . . 167
4.7.6.
Future developments . . . . . . . . . . . . . . . . . . . . 165
5

.

. . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . .

Survey of basic hydrodynamics. with special reference to hydro power

1'11

5.1. Introduction
171
5.2. The kinematics of an ideal flow . . . . . . . . . . . . . . . . . . . 172
5.2.1.
Mass conserversation (Continuity) . . . . . . . . . . . . . . 172
5.2.2.
Potential flow and the curl (vorticity) . . . . . . . . . . . . . 173

5.2.3. The potential flow in the meridian. stream function . . . . . . . I74
5.2.4. Velocity triangle and relative eddy . . . . . . . . . . . . . . 175
5.2.5. The rate of strain tensor . . . . . . . . . . . . . . . . . . . 177
5.2.6.
The circulation and its relation to curl . . . . . . . . . . . . . 178
5.2.7. Vane circulation and lift . . . . . . . . . . . . . . . . . . . 179
5.3. Dynamics of ideal flow . . . . . . . . . . . . . . . . . . . . . . . 180
180
5.3.1. Equation of motion and energy for a stationary frame of reference
Equation of motion and energy for a rotating frame of reference
5.3.2.
182
5.3.3. The role of unsteadiness for energy transmission . . . . . . . . . 183
5.3.4. The momentum theorems . . . . . . . . . . . . . . . . . . 183
5.3.5.
Problems using the momentum and energy theorems . . . . . . 154
5.3.5.1. Euler's equation . . . . . . . . . . . . . . . . . . . . . . 184
5.3.5.2. The shock loss due to diffusion and deflection . . . . . . . . . 185
5.3.5.3. The shock loss due to the action of turbo machines . . . . . . . 186
5.4. Theory of real fluid flow . . . . . . . . . . . . . . . . . . . . . . 188
5.4.1.
Properties of real liquids . . . . . . . . . . . . . . . . . . . 188
5.4.2. 'The stress tensor . . . . . . . . . . . . . . . . . . . . . . 189
5.4.3. The relation between stress and strain rate . . . . . . . . . . . 190
5.4.4.
The Navier Stokes equation . . . . . . . . . . . . . . . . . 190
5.4.5.
Boundary layer theory . . . . . . . . . . . . . . . . . . . 191
5.4.6.
Flow in straight pipes . . . . . . . . . . . . . . . . . . . . 191

5.4.6.1. General phenomena and laminar flow . . . . . . . . . . . . . 19;
5.4.6.2. Turbulent flow and transition . . . . . . . . . . . . . . . . 193
5.5. Loss mechanism due to real flow in hydro turbomachines . . . . . . . . 195
Some general remarks on loss in hydro turbo machinery . . . . . 195
5.5.1.
5.5.2.
Some loss mechanism of general character . . . . . . . . . . . 195
5.5.3.
Interaction of main flow and boundary layer, stall . . . . . . . 196
5.5.4.
Diffuser (draft tube) flow, rotating stall . . . . . . . . . . . . 196
. 5.5.5.
Secondary flow in curved and rotating ducts . . . . . . . . . . 197
5.5.5.1. Due to turbulence, consequence on energy conversion . . . . . . 197
5.5.5.2. Interaction of b o u ~ ~ d a rlayer
y
and the main flow . . . . . . . . 199
5.5.5.3. Secondary flow in axial turbomachines . . . . . . . . . . . . 201


5.5.5.4.
5.5.6.
5.5.6.1.
5.5.6.2.
5.5.6.3.
5.5.6.4.
5.5.6.5.
5.5.6.6.

Secondary flow due to relative whirl in an axial turbomachine

The predicition of component loss in fluid machines . . . . .
The rotor vane loss by means of aerodynamics . . . . . . .
The draft tube (diffuser) loss . . . . . . . . . . . . . . .
Disk friction loss . . . . . . . . . . . . . . . . . . . .
The leakage (volumetric) loss . . . . . . . . . . . . . . .
The windage loss of an impulse turbine . . . . . . . . . .
The loss due to cross flow on a bucket of a PT . . . . . . .

. . 201
. . 202
. . 202
. . 203
. . 204
. . 205
. . 207
. . 208

6. Prediction of internal flow in cascades and rotor . . . . . . . . . . . . . 209
6.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
6.2. The straight cascade as a model for axial fluid machines . . . . . . . . . 209
6.2.1.
Prediction of flow (indirect problem) by means of singularities . . 209
6.2.1.1. Introduction. description and theory of problem . . . . . . . . 209
6.2.1.2. Practical solution of the indirect problem . . . . . . . . . . . 213
6.2.1.3. Simplified method after Ackermann and Birnbaum . . . . . . . 213
6.3. Some problems of steady flow through cascades . . . . . . . . . . . . 219
6.3.1.
The circular cascade with axisyminetric stream surfaces . . . . . 219
The direct problem of a cascade in potential flow . . . . . . . . . 220
6.3.2.

6.3.3. The indirect problem of the flow through a mixed flow rotor on
axisymmetric stream faces of constant depth . . . . . . . . . . 221
Cascade in an axisymmetric flow lamina of variable depth . . . . 223
6.3.4.
6.4. The unsteady flow through straight cascades in tandem arrangement, moving
relative to each other . . . . . . . . . . . . . . . . . . . . . . . . 226
6.4.1.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . 226
6.4.2.
Model of cascade and assumptions . . . . . . . . . . . . . . 226
6.4.3.
Basic idea of the procedure . . . . . . . . . . . . . . . . . 227
6.4.4.
Realization of the procedure . . . . . . . . . . . . . . . . . 228
6.4.5.
List of used symbols . . . . . . . . . . . . . . . . . . . . 229
6.4.6.
Derivation of governing linear integral equation . . . . . . . . 229
6.4.7.
Solution of integral equation by polynomials following M. Lotz . . 230
6.4.8.
Lift and moment on the passive cascade . . . . . . . . . . . . 231
6.4.9.
Discussions of evaluated results . . . . . . . . . . . . . . . . 231
6.4.10. Conclusion of practical results, effect of wakes . . . . . . . . . 232
6.5. Distribution of meridional velocity normal to stream face . . . . . . . . 234
6.5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 234
6.5.2. Special assumptions . . . . . . . . . . . . . . . . . . . . . 235
6.5.3.
Equation of motion, Euler's relation, loss formulation . . . . . . 235

6.5.4.
c i as a function of moment of momentum c, r . . . . . . . . . 236
6.5.5.
Linear differential equation for the c, distribution . . . . . . . 237
6.5.6. Step by step solution for the design task . . . . . . . . . . . . 237
Calculating c, (n) or y ( x ) for a runner of given geometry under a
6.5.7.
given flow rate Q . . . . . . . . . . . . . . . . . . . . . . 237
6.5.8.
Computation of fl as function of vane geometry . . . . . . . . 238
6.6. The slip effect in the flow past a rotor . . . . . . . . . . . . . . . . 238
6.6.1.
Irltroduction . . . . . . . . . . . . . . . . . . . . . . . . 238
6.6.2. Slip p;t, in coilsequence of the relative eddy . . . . . . . . . . . 240
6.6.3.
Slip p: in consequence of wakes . . . . . . . . . . . . . . . 240
XIX


6.6.4.
6.6.5.
7.

Slip/).;ninconsctlucnccofcasc.rclcHow . . . . . . . . . . . . 341
c
of thc rotor . . . . 24;
Slip pz as ;i consequence of varying ~ h breath

Losscs tluc ro vorticity nntl boundary layers . . . . . . . . . . . . . . . 345

7.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2. I3robletns cluc to kinematics of vortices in fluid machines . . . . . . . .
7.2.1. Fund~in~cntals
of vortices . . . . . . . . . . . . . . . . . .
7.2.2.
Energy loss due to lengthening of vortcx tube . . . . . . . . .
7.2.2.1. Lengthening of a vortex tube prirnllc! to the n ~ r ~ itlow
n
. . . . .
7.2.2.2. Dislocation and Icnzthening of a vortcx within 2 bend . . . . . .
7.2.2.3. Tllc lcngtl~cningof a vortex tubc within a rotor . . . . . . . . .
7.2.2.4. Generation of secondary flow past a cascade . . . . . . . . . .
7.2.2.5. The s~reamwisevorticity pasi i~ radial flow impellcr . . . . . . .
7.3. The boundarv layer and its dissipation at the rotor wall . . . . . . . . .
7.3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . .
7.3.2.
Assumptions . . . . . . . . . . . . . . . . . . . . . . . .
d vane
7.3.3. The momentum theorem of a boundr~rylayer on a c ~ ~ r v erotor
7.3.4.
Differential equation for the growth of the boundary layer . . . .
7.3.5.
Con~putationof the wake past a rotor vane . . . . . . . . . .
7.3.6. The energy theorem of the boundary layer and ioss predictions . .
7.3.7.
I'he flow about the inlet edge . . . . . . . . . . . . . . . .

8.

245

245
245
246
246
247
248
2.19
250
251

251
251
255
257
260
263
267

Cavitation and water hammer as detriniental effects . . . . . . . . . . . 270

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
8.1. Introd~~crion
8.2. Caviiatioii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
8.2.1. Survey of fundamentals of cavitation and res~~lting
erosion . . . . 271
8.2.1.1. In!roduction to the \larious phenomena and aspects . . . . . . . 271
8.2.1.3. Piuclci as origin . . . . . . . . . . . . . . . . . . . . . . 272
8.2.1.3. Ilquatior? of motion of a bubble restings in the lluid . . . . . . . 274
8.2.1.3. Some estimates on cavitation scale effects at onset . . . . . . . 275
8.2.1.5. Transfer ot' energy under cavitation . . . . . . . . . . . . . . 276

5.2.1 6 . Gas diffusion u ~ d c rcavitation . . . . . . . . . . . . . . . . 276
8.2.i.7. Uubb!e collapse, impact pressure and related ctTects . . . . . . . 277
S . S . C;tvitation erosion, cause, devices, results . . . . . . . . . . . 277
8.2.2. Ca~.itationwith respect to hydro turbomachinery . . . . . . . . 280
8.2.2.1. Suction head required, cavitation indices used . . . . . . . . . 280
8.2.2.2. The meaning of cavitatiorl index . . . . . . . . . . . . . . . 253
8.2.2.3. Theoretical cavitation index, scale effects . . . . . . . . . . . 284
8.2.2.4. Influence of air content and its control . . . . . . . . . . . . 254
8.2.2.5. The influence of roughness on cavitation . . . . . . . . . . . . 285
5.2.2.6. Differences in cavitation of turbines and pumps . . . . . . . . 287
5.2.2.7. Cavitation in pumps or pump-turbines when pumping . . . . . . 355
5.2.2.5. Cavitation in turbines . . . . . . . . . . . . . . . . . . . . 290
5.3.2.9 Protective measures against cavitation . . . . . . . . . . . . . 293
An approach for the prediction of pressure number at the ciritical
8.2.3.
point in the rotor . . . . . : . . . . . . . . . . . . . . . . 295
8.2.3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 295
5.2.3.2. Assumptions . . . . . . . . . . . . . . . . . . . . . . . . 296
8.2.3.3. Mised flow rnacllines . . . . . . . . . . . . . . . . . . . . 236


8.2.3.4. Axial machines . . . . . . . . . . . . . . . . . . . . . . . . 299
8.2.4.
Fundamentals of pitting rate as function of velocity . . . . . . . 302
8.2.4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 302
8.2.4.2. Assumptions about wall-attached cavity and its erosion . . . . . 303
8.2.4.3. Realization of the approach . . . . . . . . . . . . . . . . . 303
8.2.4.4. Erosion rate as a function of the velocity w, . . . . . . . . . . 305
8.3. Water hammer . . . . . . . . . . . . . . . . . . . . . . . . . . . 306
8.3.1.

Celerity, fundamentals of method of characteristics in the
c, p.plane . . . . . . . . . . . . . . . . . . . . . . . . . 306
8.3.2.
Fundamentals of method of characteristics in the s t-plane . . . 308
8.3.3.
Application of method of characteristics in x, 2-plane . . . . . . 310
8.3.4.
The celerity a in two phase mixture . . . . . . . . . . . . . . 310
8.3.5.
Influence of evaporation and diffusion . . . . . . . . . . . . . 312
8.3.6.
Boundary conditions in the p, c-plane, loss influence . . . . . . . 313
Examples of the method of characteristics in the c, p-plane . . . . 315
8.3.7.
8.3.8.
Characteristics method in the c, o-plane . . . . . . . . . . . . 319
8.3.9.
Remedies against water hammer . . . . . . . . . . . . . . . 320

.

9.

Similarity laws. characteristics. research

. . . . . . . . . . . . . . . . 322

9.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322
9.2. Similarity laws and characteristice of machines . . . . . . . . . . . . . 323
9.2.1.

Criteria of similarity. numbers of Froude. Euler. Reynolds . . . . 323
9.2.2.
The unit values of speed. flow. power . . . . . . . . . . . . . 324
9.2:3.
The type number (specific speed) . . . . . . . . . . . . . . . 325
9.2.4.
The efficiency hill diagram . . . . . . . . . . . . . . . . . . 330
9.2.5.
The cam curves of double regulated turbines . . . . . . . . . . 333
9.3. Head and efficiency measurement by the thermodynamic method . . . . . 334
9.3.1.
Specific head. enthalpy. component measurement . . . . . . . . 334
9.3.2.
Fundamentals of thermodynamic head measurement . . . . . . 336
9.3.3.
Thermodynamic measurement of internal efficiency . . . . . . . 338
9.3.4.
Conventional measurement of internal efficiency . . . . . . . . 339
9.3.5.
The scale effect of internal efficiency . . . . . . . . . . . . . 341
9.3.6.
Several efficiences and their measurement . . . . . . . . . . . 344
9.4. Experimental techniques . . . . . . . . . . . . . . . . . . . . . . 345
9.4.1.
Instrumentation for steady flow . . . . . . . . . . . . . . . 345
9.4.1.1. Manometers . . . . . . . . . . . . . . . . . . . . . . . . 345
9.4.1.2. The measurement of velocity by piezometry . . . . . . . . . . 347
9.4.1.3. Pressure measurement by air injection . . . . . . . . . . . . . 351
9.4.2.
Calibration of probes for arbitrary flow . . . . . . . . . . . . 352

9.4.3.
Methods for dynamical measurements of unsteady flow . . . . . 352
9.4.3.1. General remarks on unsteady flow . . . . . . . . . . . . . . 352
9.4.3.2. Velocity measurement . . . . . . . . . . . . . . . . . . . . 353
9.4.3.3. Measurement of pressure . . . . . . . . . . . . . . . . . . 354
9.4.4.
Problems arising with rotating probes . . . . . . . . . . . . . 355
9.4.4.1. General remarks about rotating probes . . . . . . . . . . . . 355
9.4.4.2. Transmission of values measured from rotor to stationary indicator 356
9.4.4.3. Scanning valve for connection of rotating tappings with stationary
manometers . . . . . . . . . . . . . . . . . . . . . . . . 356
9.4.5.
Measurement of the torque . . . . . . . . . . . . . . . . . 357

XXI
t


9.5.

.
9.6.

9.7.

9.3.

9.9.

9.4.6. The visualization of flov~ . . . . . . . . . . . . . . . . . . 359

9.4.7.
Fluids to be used in tests . . . . . . . . . . : . . . . . . . 360
Measurcmcnt of unstcatly relative imd nhsolute llow in a Kaplnn turbine
by a vectorial probe of quick response frcm D . C~lsforpli . . . . . . . . 350
9.5.1.
Introduction . . . . . . . . . . . . . . . . . . . . . . . 360
9.5.2. blci~surementof the absolute velocity ficltl of the runner . . . . 361
9.5.2.1. Instiurnentation . . . . . . . . . . . . . . . . . . . . . . 361
9.5.2.2. Measuring planes, results upstream and downstream of the rotor 362
9.5.3. Measurement of unsteady relative flow . . . . . . . . . . . . 365
9.5.3.1. Instrumentation . . . . . . . . . . . . . . . . . . . . . . 365
9.5.3.2. Experimental results from the rotating probe . . . . . . . . . 365
Influence of runner vane number on relative and absolute flow in axial
366
turbines according to air tests arid comparative-predictons by tK Kiillnel
9.6.1. Formulation of the problem . . . . . . . . . . . . . . . . . 366
9.6.2. Test devices and instrumentation used . . . . . . . . . . . . 367
9.6.2.1. Air test rig . . . . . . . . . . . . . . . . . . . . . . . . 367
9.6.2.2. Layout of the runner . . . . . . . . . . . . . . . . . . . . 370
9.6.2.3. Instru~rlentsand probes used . . . . . . . . . . . . . . . . 370
9.6.3.
bleasurement of flow, discussion of results . . . . . . . . . . 371
9.6.3.1. I~lvestigatiot~s
of the absolute flow . . . . . . . . . . . . . . 371
9.6.3.2. Investigation of the relative flow . . . . . . . . . . . . . . . 372
9.6.3.3. Discussions of the measuring results . . . . . . . . . . . . . 374
9.6.4. Theoretical computation of relative flow field and coinparison
between this and experiments . . . . . . . . . . . . . . . . 350
9.6.4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . 380
9.6.4.2. The spatial singularity method . . . . . . . . . . . . . . . . 380

9.6.4.3. Comparison of computed results with measured . . . . . . . . 384
Dynamic ~neasurementsof unsteady flow near and within the boundary
layer of r11nner vanes by N . F:crtrrer . . . . . . : . . . . . . . . . . 386
3.7.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . 386
9.7.2. Experiments on a Kaplan water turbine model . . . . . . . . 386
9.7.3. Experiments on a Francis water turbine runner . . . . . . . . 390
.
Investi_gation on unsteady flow in a Fraccis turbine by R . Gericlt and
G . 1l.f ollejlkopj' . . . . . . . . . . . . . . . . . . . . . . . . . . 391
9.8.1. . Introduction . . . . . . . . . . . . . . . . . . . . . . . 391
9.3.2. Unsteady flow and turbulence level at runner exit . . . . . . . 391
9.8.3. Fluctuations of tota! pressure at runner exit . . . . . . . . . . 395
9.5.4. Unsteady absolute flow between gate and runner . . . . . . . . 395
9.8.5. Unsteady flow in the draft tube of the turbine . . . . . . . . . 397
9.8.6. Rerriedies against draft tube surge and power swing . . . . . . 397
Laser Dopplcr anemometer for Reynolds stress measurements by E. Hortner . 398
9.9.1. I~ltroduction . . . . . . . . . . . . . . . . . . . . . . . 398
9.9.2. Example of a flow measurement, carried out by means of a two
dirne~isionalLDA with tracking processors . . . . . . . . . . 400

10. The turbomachine. its design and construction
10.1. Introduction . . . . . . . . . . . . . .
10.2. Project and construction of axial turbines .
10.2.1. General survey of types . . . . . .
10.2.2. The true Kaplan turbine (KT) . . .

XXII

. . . . . . . . . . . . . 403
. . . . . . . . . . . . . 403

. . . . . . . . . . . . .
. . . . . . . . . . . . .
. . . . . . . . . . . . .

405
405
406


The tubular turbine (TT) . . . . . . . . . . . . . . . . . 406
Gencral linlitations and reasons for' Kaplan turbines . . . . . 418
The design of an axial turbine . . . . . . . . . . . . . . 423
The optimization of runner diameter D . . . . . . . . . . 423
The "best possible" type number (specific speed) . . . . . . 430
The velocity triangles . . . . . . . . . . . . . . . . . . 431
Design features of axial turbines . . . . . . . . . . . . . 431
Rapids turbines for using kinetic energy only . . . . . . . . 431
Fundamentals, design, head, discharge . . . . . . . . . . . 431
The optimum diameter . . . . . . . . . . . . . . . . . . 433
The installed power . . . . . . . . . . . . . . . . . . . 433
Some remarks about runner chamber and distributor . . . . 434
Flow prediction in the vaneless space and distributor . . . . . 434
Tidal power turbines, layout . . . . . . . . . . . . . . . 437
Runner design, simple procedure . . . . . . . . . . . . . 443
10.3. The project and construction of Francis turbines (FT) with hints at Pelton
turbines (PT) . . . . . . . . . . . . . . . . . . . . . . . . . . . 447
General remarks . . . . . . . . . . . . . . . . . . . . 447
10.3.1.
Comparison of Francis (FT) and Pelton (PT) turbines . . . . 449
10.3.2.

The limits of a F T in the lower head range . . . . . . . . . 466
10.3.3.
Efficiency of a FT as a function of specific speed . . . . . . 467
10.3.4.
10.3.5.
The design of a Francis turbine . . . . . . . . . . . . . . 467
Design of runner vane, simplified method . . . . . . . . . 473
10.3.6.
10.3.7.
Simple stress calculation of a runner vane . . . . . . . . . 478
Simple stress calculation of the hub . . . . . . . . . . . . 479
10.3.8.
10.3.9.
Derivation of the relation (10.3-23) . . . . . . . . . . . . 480
10.4. Optimization of pump-turbines in terms of efficiency and cavitation also
applicable to impeller pumps . . . . . . . . . . . . . . . . . . . . . 481
10.4.1.
Introduction . . . . . . . . . . . . . . . . . . . . . . 481
Optimum outside diameter of impeller on pump-turbines in terms
10.4.2.
of efficiency . . . . . . . . . . . . . . . . . . . . . . 488
New formula for the type number of a semi-axial centrifugal
10.4.3.
pump impeller . . . . . . . . . . . . . . . . . . . . . 494
Optimum diameter of the impeller with respect to internal losses 494
10.4.3.1.
10.4.3.1 .1. Impeller loss . . . . . . . . . . . . . . . . . . . . . . 494
10.4.3.1.2. Diffuser loss . . . . . . . . . . . . . . . . . . . . . . 496
10.4.3.1.3. Optimum diameter of the impeller eye in respect to inernal loss 496
497

Optimum diameter of the impeller eye with respect to cavitation
10.4.3.2.
Optimum type number with respect to efficiency and cavitation 497
10.4.3.3.
The discharge ratio as a function of the speed ratio . . . . . 498
. 10.4.4.
Example for the con~putingoptimum values of impeller diameter,
10.4.5.
type number and discharge ratio iis compared with corresponding quantities of an actual pump-turbine . . . . . . . . . . 499
10.4.5.1.
Data . . . . . . . . . . . . . . . . . . . . . . . . . 499
10.4.5.2.
Results . . . . . . . . . . . . . . . . . . . . . . . . 500
10.4.6.
Special operational features of pump-turbines . . . . . . . . 500
10.4.7.
Sources of troubles and remedies . . . . . . . . . . . . . 502
. 10.4.7.1.
Normal pumping . . . . . . . . . . . . . . . . . . . . 502
10.4.7.2.
Abnormal operating conditions . . . . . . . . . . . . . . 503
10.4.7.3.
Beginning of pumping . . . . . . . . . . . . . . . . . . 504
10.2.3.
10.2.4.
10.2.5.
10.2.5.1.
10.2.5.2.
10.2.5.3.
10.2.5.4.

10.2.6.
10.2.6.1.
10.2.6.2.
10.2.6.6.
10.2.7.
10.2.8.
10.2.9.
10.2.10.

XXIII


10.4.8.
Expcrin~cntalrrsearch of Fi-~~ncis
p l ~ m p - t ~ ~ r l ~byi ~%l c. si\lc~i . .
10.5. Shaft . bc~~rings.
accessories 01' hydro po\\lcr scts . . . . . . . . . . . .
10.5.1.
Lilyout of the shaft . . . . . . . . . . . . . . . . . . .
10.5.1.1. Gcnerr~lremarks . . . . . . . . . . . . . . . . . . . .
10.5.1.3. Flexural vibrations . . . . . . . . . . . . . . . . . . .
10.5.1.3. Torsional vibrations . . . . . . . . . . . . . . . . . . . .
10.5.1.4. Excitation of shaft vibrations by runner Xi11 . . . . . . . .
10.5.2.
Intluence of bearings 011 shaft vibration . . . . . . . . . .
10.5.2.1. General remarks . . . . . . . . . . . . . . . . . . . .
10.5.2.2. Thc spring rate of the film of lubricant . . . . . . . . . . .
10.5.2.3. The damping coefficient of the lubricant's lilm . . . . . . .
10.5.2.4. Control of bearings . . . . . . . . . . . . . . . . . . .
10.5.3.

Bearing design and arrangement . . . . . . . . . . . . .
10.5.3.1. General remarks . ; . . . . . . . . . . . . . . . . . .
10.5.3.2. Guidc bearings . . . . . . . . . . . . . . . . . . . . .
10.5.3.3. Thrust bearing design, brake . . . . . . . . . . . . . . .
10.5.4.
Lubricants and their cooling . . . . . . . . . . . . . . .
10.5.5.
Runaway and its problems . . . . . . . . . . . . . . . .
20.5.5.1.
General remarks . . . . . . . . . . . . . . . . . . . .
10.5.5.2. Protection of the set against runaway . . . . . . . . . . .
10.6 The coi~putationof flow in a Francis runner . . . . . . . . . . . . .
10.6.1.
Flow predicition for given runner and working data . . . . .
10.6.1.1. Introduction . . . . . . . . . . . . . . . . . . . . . .
10.6.1.2. Assuinptions . . . . . . . . . . . . . . . . . . . . . .
List of symbols used: (Fig. 10.6.4 to 6) . . . . . . . . . . .
10.6.2.
10.6.3.
Computation or relative velocity distribution . . . . . . . .
13.6.3.1. In the peripheral 9-direction . . . . . . . . . . . . . . .
10.6.3.2. In the shroud to hub (= cr) direction . . . . . . . . . . . .
. . . . . . .
10.6.3.3. Method of solution with exact ~ v ( n distribution
)
.
. . . . . . .
10.6.3.4. Relations needed for the coefficients A and B
10.6.4.
Simplified relation for shroud to hub distribution . . . . . .

The twist of the stream face in the runner channel . . . . . .
10.6.5.
The state of knowledge in predicting the relative flow . . . .
10.6.6.
10.7. Computer aided desigil of hydro turbines . . . . . . . . . . . . . . .
10.7.1.
Introduction . . . . . . . . . . . . . . . . . . . . . . .
10.7.2.
General goals . . . . . . . . . . . . . . . . . . . . . .
10.7.3.
Hardware for a CAD system . . . . . . . . . . . . . . .
10.7.4.
Software for the CAD system . . . . . . . . . . . . . . .
ProliIe of a comercial computer aided design program for Francis
10.7.5.
turbines . . . . . . . . . . . . . . . . . . . . . . . .
10.7.6.
Conclusions . . . . . . . . . . . . . . . . . . . . . .

.

505

510
510
510
511
513
514
515

515
515
515
516
516
516
517
517
521
522
522
523
524
524
524
524
526
526
526
528
529
530
531
532
534
537
537
537
537
537

538
539

. . . . . . . . . . . . . 540
11.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 540
11.2 . Regulation of hydro power sets. governors. accessories . . . . . . . . . 542
11

Regr~lationof hydro power sets. the generator

11.2.1.
11.2.1.1.
11.2.1.2.

The governor. its purposes. its design . . . . . . . . . . . 542
Survey of control . different kinds. why speed control . . . . . 542
Control loop. governor. controlled system . . . . . . . . . 543


11.2.1.3.
11.2.1.4.
11.2.2.
112 2 . 1 .
11.2.2.2.
11.2.3.
11.2.3.1.
11.2.3.2.
11.2.3.3.
11.2.3.4.

11.2.4.
11.2.5.

Working together of turbine and grid. self control . . . . . .
The tasks of speed control . . . ; . . . . . . . . . . . .
Design of speed and acceleration metering members . . . . .
Mechanical and hydromechanical members . . . . . . . . .
Electronic governor . . . . . . . . . . . . . . . . . . .
Simple treatment of the dynamic behaviour of governors . . .
Nomenclature and assumptions . . . . . . . . . . . . . .
Proportional governor, servomotor with stiff feedback (speed
governor) . . . . . . . . . . . . . . . . . . . . . . .
Proportional-integral governor with acceleration feedback (acceleration governor, PD governor) . . . . . . . . . . . . .
Proportional integral governor, servomotor with elastic retarding
feedback (PI governor) . . . . . . . . . . . . . . . . . .
Other time parameters, tuning . . . . . . . . . . . . . .
Special regulating devices . . . . . . . . . . . . . . . .

543
545
548
548
548
558
558
558
560
560
560
562

11.3. Stability of control with respect to water hammer. autoregulation of grid. and

.

11.3.1.
11.3.2.
11.3.3.
11.3.4.
11.3.4.1.
11.3.4.2.
11.3.4.3.
11.3.4.4.
11.3.4.5.
11.3.5.
11.3.6.
11.3.7.
11.3.8.

turbine characteristics . . . . . . . . . . . . . . .
Introduction to the problem . . . . . . . . . . . .
Assumptions . . . . . . . . . . . . . . . . . . .
Dynamically equivalent types of governors . . . . . .
The controlled system (turbine, grid, penstock) . . . .
General remarks on the electric grid . . . . . . . . .
Linkage of turbine characteristic and grid . . . . . .
Intervention of penstock . . . . . . . . . . . . . .
Boundary conditions of water hammer in a simple pipe
Relation for the controlled system . . . . . . . . . .
Relation for closed control loop, stability parameters .

Special h (q) relations at the lower penstock end . . . .
Example . . . . . . . . . . . . . . . . . . . . .
Theory of motion and resonance in the pipe system . .

11.4. The electric machine (generator. alternator. motor) . . . .
11.4.1.
Survey . . . . . . . . . . . . . . . . . . .
11.4.1 .1. General remarks . . . . . . . . . . . . . .
11.4.1.2.
Output as a function of speed . . . . . . . . .
11.4.1.3.
Water cooling . . . . . . . . . . . . . . .
11.4.1.4.
Pumped storage motor-generators . . . . . . .
11.4.1.5.
Special machines for low head . . . . . . . .
11.4.1.6.
Operating regimes . . . . . . . . . . . . . .
11.4.1.7.
Computerized design . . . . . . . . . . . .
11.4.2.
Alternator, electric feztures . . . . . . . . . .
11.4.3.
Design features with respect to critical speed . .
11.4.4.
Dimensioning the alternator rotor . . . . . . .
11.4.5.
Alternator output as a function of working data .
11.4.6.
Cooling in practice . . . . . . . . . . . . .

11.4.7.
Rotor construction . . . . . . . . . . . . .
11.4.8.
Stator construction . . . . . . . . . . . . .

.

12

List of References

. . . 562
. . . 562
. . . 563
. . . 563
. . . 564
. . . 564
. . . 564
. . . 565
. . . 565
.
.
.
.

.
.
.
.

.
.
.
.

566
566
568
568
. . . 569

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

. . .

. . .
. . .
. . .
. . .

.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.

.
.
.
.
.
.
.

.

. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .

. . . . . .
. . . . . .

572
572
572
573
573
574
575
575
575
575
577
578
579
581
584
589

. . . . . . . . . . . . . . . . . . . . . . . . .

593

. . . . . .

xxv


.

. . . . . . . 639
13.1. Suyplctncnt of ti~rtlic
r. Literature in alp11;lbctic order of the authors . . . 635

13

List of further Litcrnturc in olpl~abcticortlcr'of the auil~ors

14.

Subject index

. . . . . . . . . . . . . . . . . . . . . . . . . . .

641

.

Author indcx

. . . . . . . . . . . . . . . . . . . . . . . . . .

675

15


Nomenclature
a ) Romnn letters
celerity ( = velocity of sound); thermal diffusivity; distance, distance between
adjacent towers; direction from shroud t o h u b along the rotor vane. a n d along
lines of approximately constant moment of momentum.
projection of the a-line in the meridian
revenue factor.
capital recovery factor = l / a .
constant, e.g., due to the bound vortex distribution y,.,
surface area, cross' sectional area.
real wetted cross sectional area of channel.
cross sectional area of a rotor vane's intersection with an axisymmetric floiir
plane.
projection of A, onto a plane normal to the rotor axis.
alternating current.
cost term due to dam section (4.3 - 16).
b
width (i.e. of river valley); span (width) of a blade (vane); depth of flow layer
o r elementary turbine; minimum distance of conductor from p o u n d ; acceleration; rotor breadth.
Ab
axial thickness of shroud and crown (hub) a t external diameter.

length of power house normal to flow direction.
b~
width of excavated ground volume per set.
b,
B
barometric head [IA-critical head h,, (due t o cavitation);
constant, i.e. due to the bound vortex distribution y,.
c
absolute velocity; specific heat.
C,
meridional component of c.
Cu
whirl component of c.
Ca
axial component of c.
C
constant, due to the bound vortex distribution ;,; gas concentration of solved
gas (kg/m3), iron utilization factor of alternator (Esson number).
d
damping coefficient; diameter of pipe; diameter of conductor
diameter.
do
jet diameter (impulse turbine).
depth of excavated ground volume.
d,
original depth of river bed below minimum tailwater level.
4
D
Nominal rotor diameter (reaction machines: outmost diameter of rotor
passage; i~npulseturbines: jet circle diameter); mass diffusivity; diameter of

vortex tube.
optimum
diameter D with respect to efficiency of axial turbine.
Do~q
DopNpsH o p t i m u n ~diameter D with respect t o NPSH of axial turbine.