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

_

slil?~ing

btlhblc:

.Any

real

bubblc

slips,

wl~cn

it

passcs

a

znnc

with

a

prc-<stl~-c

91.;1dicnt.

.\

slil>pi:~~

bllhl,lc

has

an

addd

liquid

niass

proportional

to

its

volunlc.

This

may

iilcrc;~sc

citn.sidcr;lbly

irs

,lolllcn~~~m-i~~d~~~~d impact

011

a

wall

by

rhc

so-callcd

"rockct

cffccl"

;iftcr

C'lrirrc.l;oll~~

IS.

I

!

31

5.2.1.7.

B~bblc

collapse, impact prcssure

and

rclatcd

cffccts

when a vapour bubble, radius

I(,,

growth rate

R~

=

0,

enters

n

zone whcre the pressure

rises suddenly bp

311

against the critical one.

it

suddenly coil;lpses

by

condcnr.;ltion

lo

;I

with

the vanishingly small radius

R,-

of the re~naini~lg gas. Tlic~i according to

pllYlvigh

(8.461.

the positive

displacement

work done

by

,411:

(413)

rr

(I<:

-

I(:)

.,lp

can

be

found

in the kinetic energy

2

n

Q,

df

R:

(see

8.2-

IS)

of 111c collapsing bulk of liquid.

~~11;lfing both yields the bubble i~nplosion rate

freating the bubble impact pressure

pi

due to the sudde~i destruction

of

R

,.

2s

watcr

hammer

(8.3

-

54),

and imagine

'a'

to be the velocity of sound (ce!erity) of

tl~

liyllid, then

pi

=

@a

Rj.

Contrary to a gro\ving bubblc a collapsing bubble usiially buckles

[S.6],

(Fig.

8.2.3

b).

.4

sl,hcrical

bubble,

collapsing ncar

a

wall, is transformed into

3

toroidal surface. 7'Iicn

:I

liquid

ji.1

penctr;itcs

th:ough

its

inncr orifice.

Whcn

a

bubblc collnpscs close to a solid

wall.

its

st~rf:tcc

may

bucklc

so

a?

to

focus a multiplicity of liquid jets on

il,

where

thcy

impingc

like

droplcts. This

m;tj

he

the

reason.

\vhy

cavitation erosio~: looks as thctigh caused by droplct

impact.

Bccause

of

thc

suddcri

collapse

of a vapourous bubblc

its

gaccous

rernnazit

I\

\trcingl?

compre\r.c,i

~nd

heated. 1'111s creates pressures up

to

some

lo4

bar

lasting

only for

niicio

second5 111:

ICI>I~~I.I-

lure

rise

is

ind~cated

by

luniinesccnce of

the

imploding bubble

[8

61

5.2.1.8.

Cavitatio)i

crosicn, cause,

test

dcviccs,

results

l'he causes of cavitatio~al erosion at cavity collapse are of different na~ure.

3)

Chemical causes: Chemical reactions result as a coj!sequencz of high local

:~iiif

suddc:?

pressure and temperature rise in conncction with the larger oxygen conrent

of

thc cavirich

than that of air. They may be accelerated

by

corrosi\.e qualities of the Irqu~d.

,I

tempora

I

corrosion also originates fronl turbulence and hence a high exchange of matter within tllc

cavitating boulidary layer.

I

he very brief collapse damps the rclati\lcly smiill ove~all

Influence of chernical phenomena, \vhich generally require some timc to react.

b)

Electrolyiic causcs: Galvanic elements arc formed

in

the acid, lme,

or

salt liquid

III

c~nnection with inhomogencities in :he structure of the wall surface

rilld

in connzction

with

local temperature rise due to bubble collapse

[8.1

141.

C)

Mechanical causes:

With

notch-tough material having sufficierlt glidc d~rectio~i\ and

planes, the impact of

a

bubble collapsing on a wall is absorbed easier than

by

n

niate~ial

kith glide capacity reduced (brittle material).

By

hard second phase5 and rcduceJ glidc

planes and directions, the plasticity of the material

is

diminished.

If

the plasticity is exhausted, micro cracks are generated and nil p:lrticles arc

=Parated from the surface which is aidcd by flushing of the turbulent flow. Ncnce

Qvitation pitting is influenced mainly by the structure and the mechan~cal and cheiniciil

Properties

of

the material

[5.65].

d,

Other

causes:

The

sudden growth of

liquid-gas

intcrfaccs and the

shcar

stress

on

them intl~rccd

slip

betwcen

the

pha;cs,

may

release

there

clcctric charges of high potcnti;l!. (Rcmcnibcr,

that

a

!;t:*:trn I)oilcr slipi>ort~tl or1 insirlators, is ht:.onfly clcctric:~llc c:li;~rccci \l!l{lcr

':lit$\\

ti,$\\

n

of

its

s;lfctY

v:~lvc. an 1.ffcct

\\:hicl~,

bv 11:c

\B!;~y,

was

u:;cd

in

11rrns11-(ing's clccrrosi~~lic~ !ii:!l~ \oll;ryc gcllcr;l!,,r,)

e) Further cotiseqilcnccs

oi'

n~ccli;~nic;il tlcs:ruction:

Vapour cavities

in

the bottom nf

thc

crotlcd cratcr

then

collnpsc 1111cIcr

IJI.C!+LI~~

tions.

This

causes water hammer blow focussed on the crntcr bottom. I-atigi~e cr;lcks :1nd

ruptures due to the notch effect tnay origitlatc from this sharp-cdgcd p;lrt. 11fter' IILIs~~~~~

L

of

lcosened particles. the pittings and cr:lcks clue to further frttigl~c cracks

miry

pcnetr;lte

deepzr into thc wall tnaterial, lending finally

to

a spongc-like c~-osiat~

iIS

one of Ihc

typical

features

of

cavitation erosion.

Destruction

of

chemically ncutral n:atcrial, e.g. glass nlay be considcrcd

a:

a

decisive

proof

of

primarily mechznical causes for material erosion.

a

1

%

In

this contcxt

it

rnay bc mcntioncd, that cnly c;lvitics collapsing on or ncar to tllc

\\;III\

may cause

pittings and this is dcemcd to be above

loe5

the part or

:ill

the cavities call,\psing in

;I

cavitating

liquid

18.3;

8.61.

Thc impact of the impinging droplets clue to a collapsing cavity

on

:I

w:;ll

sr~rf:lcc fi~tigucs

the"

filaterial so

as

to show the first pittings after

a

certain incubatio~? time

f,.

'This

may

rcsirlr fro111

the

tirnc needed for !l!c

destruction

of a protective layer, due to oxidizing. rolling, forging. or welding.

After the incubation time the material erosion proceeds faster, following the

law

ot

k'nnpp

[8.6]

which combines the material loss A,~I, the exposure time

t

and the velocity

\rl

relative

to

the wall by

AIII

=

co~lst

t

wn,

(8.2-22)

with

II

ranging from

0

to

6.

Since,

e.g.

the relative velocity on the hub section

ot'a

Knplan

1crbir.e

is

roughly one half that on the runner

tip

scction, durins

n

certain time

t,

the

pitting

by

fillet

cavitation at the hub groove is, at n

-

6,

only 1164th

of

pitting due

to

lip

cl~ilranct. cavitation and hence usually negligible.

Yotc that

my

rc!c\.ant pitting of

a

wall-nttr~ched cavity is ~~1st tlie cavity and hcncc c?tistso~ily

if

t

rcnr of thc czvi~y

is

yct on the wall. Otherwise so-called "super cavitation", which encloses the fa

of

s

body into

a

cavity, does vot harm the body [5.11

51.

Tile erosion pi~s: such

s

wall-attached cavity reaches its maximurn for

a

certain back prcssurc

cavi!ztion index

5

(C3p. 5.3.3).

If

both tend to zcro, thc erosion rate clls;~ppcnrs in

consequence

too

strong

a

ventilation of the cavity by diffusion. Thc samc occurs also by thc abscncc of

ca

formation if ille back pressure and cavitation index

G

tend to large values, Thus thc erosion

aitains

a

maximum at

n

certain cavitation index or back pressure. Naturally this 6-value must

n

bc

combined

with

the best performance of the machine.

111

the case

of

material with low cavitational resistance, the erosion rate also somewh

dcpends on

the

chemical composition

of

the liquid

(Fig.

8.2.4

a).

Hence

s;li:y

ocean

wat

erodes a runner

of

low cavitational resistance sumtt\\lhat more ~.hnn fresh water.

T

dikrence vanishes nearly fcr stainless steel and compietcly for alloys \vit!i thc high

cavitational resistance

(Fig.

8.2,3

b)

[8.116].

-

Material propcrries due to cavitation resistance: The erosion rate dccrcases with tlic follo

qualities: Hon~o~cueous structure,

high

resistance against corrosio:l. high rcsilicncc, high n

impact strength, ductility, internal

-

pressure fdue to prcstrcss or thermal

t

rcatnncnt). large

dc

mation potential, c.2. breaking elongation, high tr~~sile strcngth, flat surf:lcc, fine gr:,nular :+ruct

1ar_ge slirfilce hardness, great portion of hard components, rolled structure

[8.3;

5.1

i5].

Thus the cavitation resistance ribes

in

the order of: cast iron. cast stccl. forgcti stecl. bro

alunlirium bronze, chromium nickel steel. Notc: non-metallic coats fail due to thcir

bad

coliduc

of tlie heat from cavity collapse.

275

Fig.

8.2.4.

Cavitation erosion as

a

funclion ofmaterial

and

liquid under stcady

--

and intermit!cnt

-

cavitation. a) h4atcrial loss

111,

vs

timc elapsed

I

of

mild stccl in

3%

NaCl solution,

distilled

water

\sit11

pli

8

value.

b)

Ditto of Inconcl

718.

o

stcady cavitation;

A

intcrniittcnt cnvitation, both in

distilled

\\later:

v

steady cavitation, intermittent cavitation both in

3%

NaCl solution

[8.1

161.

-

Cavitation intensity: After

Thir~r~~engatlurt~

(8.1 171, the cavitation intensity can be

dcfincd

by

the relation

where

I

is the cavitation intensity in W/m2,

11

the mean depth of eroded area,

S,

the

deformation energy of the material linearly extrapolated up to the tensile strength in

bar,

1

the exposure time.

K

depends on the material and has the following value in brackets:

Stcllitc (65

.

lo3), alloyed steel

(35

.

109,

bronze (18

-

lo3), aluminum

(12

-

lo3), cast iron

(9,5

.

lo3), copper (7,5

-

lo3).

Test devices lor cavitation erosion:

a)

Droplet impact apparatus (Fig. 8.2.5a), based on true destruction mechanism and

tlnle-savi~g,

b)

Magneto-strictive apparatus (Fig. 8.2.5

b),

very time saving, fast, but with unrealistic

vibratory cavitati~n.

C)

Cavitation with adjustable nozzles after

Erdmann Jessnitzer

[8.118] and others, very

flexible but not rotating and time consuming (Fig.

8.2.5

c),

Rotating disk (Fig.

8.2.5

d),

tinle saving and realistic for rotor cavitation.

To

reduce exposure time in real fluid machines, radioactive coats have been tried by

Floriar~cic

[8.119].

.

Fie.

8.2.5.

Cavitation erosion dzv

loscope and frequency coulitcr;

2

gate;

6

snap ring;

7

oscillatcr. pox

furnace elcmcnt;

12

high

temperature cavitation vessel (after Knupp,

Ddy,

and Hut~rnlirt

[8.6].

Cavitation ~iozzlt: adjustable;

I

observation

window;

2

probe.

d)

Rotating disk in casing;

I

inlet,

p-obe,

3

clearance,

4

rotating disk,

5

outlet.

8.2.2.

Cavitation

with

respect to hydro turbomachinery

8.2.2.1.

Suction

head

required,

cavitation indices

used

Consider

a

hydro turbomachine of the reaction type (Fig.

8.2.6a)

in service.

In

its dr

tube (suction pipe), loss coefficient

i,,

absolute velocity at the outermost point

I

oft

rotor exit,

c,,

n

pressure drop,

+

iDec:/2(+

in pumps), occurs in the flow direction.

further pressure drop in the rotor,

i

Q

\v:/!,

,exists from this exit

I,

to the critical point,

hl~ving the pressure number

E.,

where

w,

IS

the relative velocity in the outermost poin

of the rotor exit.

(In

pumps,

[,

shall also include the loss in

a

longer suction line.)

With the suction head

h,,

as elevation of the critical point, pressure

p,,,

above the

t

water level, on which the pressure

p,

acts, the pressure

p,,

follows from

280

Fig.8.2.6. Cavita:ion index

a

,,,..

or

NPSH

,,:.,

avail;tblc, and c;~vitiltion index

(7

,,,.

or

;VPSlf

,b,.

required:

a) Definition of suc.tio~: I~cad It,, pl.e:jsurc hcad on suctio~i Ic\.cl

p,,

(~cJ).

1

lencc ca:i~;:tion

index

available

no,.

=

[(pA

-

P,,)'(~!I)

-

11,1!

1-1. II

13cing lllc

head.

;IIK~

I),,

being thc cr-itical prcshilre

ofthe plant.

5)

cficicncy

I!

;~nrl

power

I-'

of

;in

;izi:il turbine :is

;I

furlction of

c.

H

fill<:

ca\.itation:

.'jp

tip clcarancc ca\it;ltion,

I.'

surface cavitatio~i

GI]

tl?c suction f,~cv.

if

a

ccrt;ti11

type

U:

CLI\

itation

should bc avoided. then

G,,.

>

a,,,

,

whcrc

cr,,

is duc to this

typc

of c;~vitulion. c) h'et head

1-1

per stage

for reaction turbomechines as

~1

function of the specific speed

ti,

as

;I

collscquence

of

3)

~ind

a

lirnitcd

v;ilue of s11brner9cncc

-

11,.

dur

to cconomic limit;~tions.

c')

NPSH,,

=

a,,H

vs

flotv

Q

(I,,,.,

as

2

fi~nction of c3vit;ltion dcgrce of impellcr in tcrlns of cficiency drop

At/,

or duc

lo

c;~vitation on the

suction Facc

S,

or

thc prus>ure f:rcc

P.

--+-

4t1

=

1

I!/;;

---

Aq

=

5%;

--.u.-

iltl

=

100>;

;;;:

--c-

&?vitation on

P;

--+-

cavitation

(JII

S.

When

pn

is the atmospheric

presyure,

under

an

isothermal change of

state

th

I.OLI~II

t

i~i-"

;irmosphere.

p,

depends

'111

the

data

of

!he

normal

atmosphere

[5.3]

p,,

-

1,013

-

10"'~.

To

=

288,15

K,

and

thc

altitude above

sea

Ievcl

'h'

by the

law

p,

=

p,t,ex~7(

--

IliN,).

\vhere

Iio

=

8435

m. This

reads

approximately

With

the coefficients of relrrtive

and

;~bbolute velocity at station

1.

Kwl

=

\v1;'(2

011)~'~

and

Kc,

-

c,/(2

9~)"'

and thc cavitation index clue to

Tl~onta

[8.120],

hence derived

[hecondition for

a

cavitntion-safe opc~.ation

P,,,~,

2

po

and

(8.2.-

24)

yield the

suction

head

required for the set as

:\.~L'I.c

I1

is

tllc lic:lcl.

111

the

;lh~;vc

11,

;lrli!

rr

;\I.(.

;lr

i~':.l;\lll

~l~?~,!.:~lilly

~>oi~ll

:11111

:,l:lliO,l,

cri~icill

ivitl~

rcspcct to L.;I\~I!:III~I~. Accordi112 to 11:c

,

I

I;(

'

L.o\!c.

,111~i

11

;I

:,;II>I;;

I~~;,~~,,~~,,

there (tcfi~~cd. tllc criti~.;~I prcssi~re

I),,

;11111

11ic co~.~.c:~l>o~!~li~ 12

i;\\-11;1

I

ion

I~IIIIII>~~-

;lrL'

defined

so

as

to opcr;~tc tlic

sct

above

a

cliiic:~i c;lvit;~tion il~dc.\

rr,,.

carlsing 1!111I~'~i~;~bl~

effccts, lilic clrop of

head

or

efficiency

(Fig.

8.2.6

b).

T3.

(8.11

20)

~11~11

;I

'6'

is

ii11k;~~i

lo

certain

operating

data Kw,,

Kc,,

i,

and

i,,

of

a

certain

i~~;~cllinc ;111d

IICIICL'

clc~iot~d

b

a,,,

~neaning

"o

required"

for this and a certaill

'11.

Q

and

(1):

Y

On

the other hanti, the cavitation index follows also from the data

of

thc plt111t's

sur-

roundings

by

(8.2--27),

(taken with

=

sign) as

f

Leaving aside the dependence of

p,,

on the flow, as expressed

Ijy

(5.2

-

4)

or

on

the critical

'

size of the nuclei, ns expressed by

(8.2-

3),

and replacins

!?,,

ill

(5.2

23)

by

111~

;1n1bient-

related vapour pressurep,, so as to have now

ri

as a function of tht. rlmb~cnt-rclarcd

values

It,,

H,

Q,

p,

,

p,

(directions for thc: planner), hence denoted

13)

fit],

.

meaning o-a

L

:~il:lble,

the

last relati011 reads

A

cavitation-safe operation of

a

set requires that (Fig.

5.2.6

b):

a,,.

<

a,,

.

7

he problem

arising is

t11;lt

strictly speaking

11,

and

H,

c.g.

in a run-of rikcr plant nla\i dcpcnd on

t

tajdrograpli and on the backwater effect. The 1;~ticr depends lirst

on

tfic topozraphy

the valley, thc flow-off of the river, the storing capacity of 11ie plant. and the licncc derive

necessity of spillage operation but to a

sm:~ilt.r extent illso

on

the working prosram

of the plant. Hence

a,,

is also defined

a$

o

,,,,,,.

It

may be rcalizeJ from this, that the proper setting of

a

p1;11lt's s~icti011 he:ld by mea

of

(8.2-37)

has to be liandlcd very carefully with

due

cotl~lctcl.;~tion of tllc conclitio

rs,,

<

a,,

and

with respect to the plant-conditioned a11d riles-cc~lid~rio~~c~l o~cil1,tbions

o

h;a;i-arid tail-water level and the herice following var-~at~o~ls

ot

the

suction

Ilc;~il

h,.

Not

that

any cavitation area has its own suction head!

-

The

dependence

of

a,,

(denoted here by

a)

on the specific

speed,

:iscJ

~1s

i)rc num

11,:

For simp!icity this relation is established now for the bcp

iv1t11

vanisll~ng \vhirl at

rator's throat.

c,,

=

0.

But, on the base of a remark in

Cap

4.2.2.1..

it

can be cxpan

also to

a

rated point with an arbitrary gate opening and

(.,,,

=+

0.

For the bep

K

=

Klr;

+

Kc,',,.

Hence

o

=

k'ri:[i.

+

(I,

+

1

<D)cp:],

where

cp,

=

Kc,,,,

jK

11,

=

tan

13,

is

a design parameter, ug~!ally resulting

frcm

the

op

"

..

nliziilg

of

the rotor's cavitn:ional suscegtibility. Hence: Set ring

cp,

,

GD,

/.

p\es

o

-

K

u

Tile simil:trity l;iws (Cap. 9.2) indicate that the specific specd

n,

in ternis of Ktr

eroportion,ll to KH;" or then K11,

-

11:'~

and

K

1,;

-

11:

!

lTlius

n

-

n,

a

=

colist

11'

'.

With tl-te latter relation and

=

sign.

(8.2-27)

reads:

h,

=

(I,,

-

p,,)i(~O

const

if

11:

'!

With the tendency of increasing

11,.

especially under highcr he.ld

If

becomes nsgati~e (so-c;~lled submergence). The11 the excaviltion cost rises

with

-

k,,

submergence.

Fro111 the 1,lst relation follows: const

H

n613

=

-

j),,)

(g

c))

--

/I,, The v:rlue

/I,

-

tugether with

I,,,

=

I),

and

y,

from (8.2-25) vttlies ollly sli_c!~tly. There

may

be

;I

tcnde

252

;,dnlit higher submel-fence

-

/I, whcn thc Ilcnd

H

increases. Pi~tting this iisidc. ;issum-

i,lgp,-c

-

I),,

=

constant, ;111d also

-

11,

=

co:ist;int for reasons of economy. and introduc-

ing

NI'SII

(net positivc coction head)

ArPSH

=

all,

then the 3b0\~ and (8.2-27) rcsult in NYSH

=

corlst and

Fig. 8.2.6 c delnonstrates such a linkage between the head

H

and the specific spced

n,

for

tile

case of reaction turbines.

-

Other cavitation indices used: Preferably in pumps instcad of a, the parilmeter

,vpSl-I

=

a

H

is used. Anglo Saxon countries also use the suction specific speed

S.

3

non

dinlensi01lal specific spced formed with

IVPSH

instead of

If

:

S

=

11'

Q'

'/(y

NPSH)~".

~ependence of cavitation parameters on working data: After Pjleiderci.

(6.411

at bep.

;.,;,

and operating data of the set given,

or,

(S.2-2S),

then expressed in terms of kncwn

data

like

t:,,,

(at bep) can be made

a

minimum:

113

413

a,,i,

=

(312)

{[2

n

i./(l

-

N *)]

(1

_t

CD

+

I-))

nqop.

(8.2-

34)

]{elice the mini~num ArPSfl:

and

the optinlum suction specific speed S:

So,

=

(2/3)"4 {(2

n

1./(1

-

N ')]

(1

_f

C,

+

L)]

-

'I4,

(8.2-

36)

where N is the hub to tip ratio in the rot01 throat.

Whereas a,,,,,

varies greatly with the type number

t~,,,,

the econon~ic reasons, ~vhich yield

(8.2-33), make NPSN,,,, more or iess independent of the type number.

The

same holds

also for

Sop, but for physical reasons. (Small variation of-).,

[,

at bep.)

At

the moment, the machine operates away from the bep, the pressure number

i

of its

critical point,

due to

the

then growing angle of incidence and the corresponding

a

and

IVPSH

increases rapidly with the distance of point from the bep

(Fig.

8.2.6d). (ri,,,,, follows from inserting

Krl,

-

Cap. 9.2) in (8.2--26).j

8.2.2.2.

The

meaning

of

cavitation

index

With

(I

S.2-

29)

and

(I

8.2--

32):

a

=

NPSHIH

=

(P,

-

Q

g

A,

-

p,,)/e

gH-

(8.2

-

37)

Imagine the fluid to pass, instead of :he rotor, a horizontal test tunnel around the critical

pint. Downslream of the critical point the pressure may recover to pA

-

Q

g

h,.

Since the

cavity has the pressure

p,,,

it collapses under the differential pressure

p,

-

Q

g

11,

-

p,,,

corresponding

essentially to NPSH and found

ill

the nu~nerator of

a

in (8.2-37). The

denominator of a,

Q~H

consists of the pressure, which induces the cavity by the high

velocity in the critical section.

In

the

usual

horizontal cavitation tul~nel the ]lead produces the velocity head

p

w32

and

a

pressure

before

the

lest swtion.

Here

the numerator

of

o

contains

p,

-

p_.

For convenience the total

h~d

in the denominator is replaced

by the

veloclty

head,

see

also

R.

Knapp.

J.

Daily

and

I:.

!;.

Ilt~~~r~trirr

(iS.6).

1'11~

prcssiirc

I),.,

rrt

thc critical point can bc Jrlincd by :I prcssurc numbcc

l\'itli thc abo~e tlic convcntion:~l caviti~tion indcx rcacls

0.z-

K

prr

-=

2

(PO

-

P~)/'(Q

bv:).

(8-2

-

39)

8.2.2.3.

l'hcorctical cnvittltio:~ index,

scale effects

Accounting for the cncrgy thcorcm of ideiil

flow,

the Iaht rclntion rcack ns

ai,,

=

(~,,,/l.~',)~

-

1,

with

,t.,,,

the

velocity

at the ~ninimum prcssuro point. Obviously for

,I

ccrtnin ste,tdy poicntinl

now

around

a

body, the ratio

\v,,,j,\~,

depends only on

thc

geometry of thc body and ncithcr on its

flow

bclocity nor its si/c, so-called scalc effects.

I

Bec;iusc of the bcalc cffccts the rcal cavitation indcx

rri

at onset is sma!!cr than

rr,

,,,

(Fig.

8.2.3

a).

One

reasol: for this sccms to bc thc boundary laycr.

It

diminishes

iv,,,,

by viscosity :ind by the

then

diminishcrl curvature of the main flow.

1,

Ara.keri

and

.lt.ostu

[8.

j6] found the re-attachment of laminar scpar:ltion region iind

-

in case

of

desincnt cacitation

-

the transition into turbulent boundary laycr

io

influence

a,,

when

they occur

in thc critical region. Surcly the then longer pcriod of dwell of nuclei. thc high tiirbulence there,

and

strong prcbsure pulbations which faci1it:ltc the pressure to fall short of its critical valut., may favou

the sudden growth of nuclei cspccially by

rectified

diffusion [8.121].

f,

Othcr re:-\son.;

a,

structuie

and

!cvcl of turbulencc, and surfacs roughness

werc

mentioned by

Am&

(8.5

11

and

13il!c,r

(8.481.

In

thc

case of devclopcd cavitation, thc

'B

factor' after .Steponofl[S.l22]

thermnci.nan~~c cffccts rneniioncd by

Bonnit~

[8.58] and

Raabe

[8.36; 8.611 may influence the sc

eflect.

An

attempt

-,vns i~l\o made by

(8.2-

17) to explain scale effects.

5.2.2.4.

Jllfl~~encc

of

air content

and

its control

On

the

011~:

liand the free air content is

a

prerequisite for the onset of cavitation. On

t

other

hand the air content influences the cavitation index

u

as

3

function of flow.

Therefore any cavitation test stand

(Fig.

8.2.7j

requires the control of air content. Usual

tbc

tot21

air content is corltrolled by means of a ran

Slykr

apparatus

[8.123].

Fig.

5.2.8

reveals

that

this parameter is not as significant for the onset of cavita!ior, as the free

content

(Fig.

8.2.8

a).

The

usual closed test

rig.

(Fig.

8.2.7)

has a device, which deflects the undissolved free

into

il

dome before the fluid enters the test section. Otherwise the preparedr~ess of

li

there to cavitilte would increase

by

too large nl~clei entrained.

On

the other

hand

by

dsaeration the natural air content of the liquid is lowered and hence also

a

measure

the critical

polnt.

The best guarantee for a natural air content

may

be an open test rig. For

a

turbine sta

the upper reservoir must have

a

free level. This limits the erection of such a stand

b

topogri~phy of its surroundings. Some laboratories in the

USA

and Canada

[8.124]

closed

test rigs use

big

resorber vessels for recuperation of

the

natural free air

con

(

Fig.

8.2.9).

A

stand should have

a

device for the cpntrol of the free air content with respec

spectrum and density of nuclei elltrained in the test section. This may operate

acoustic

babis after :\:Ic).e~.

nnd

Sk~rJozyc

[8.125],

by means of Laser after

Keller.

[S.

b!

visualization of the cavitation susceptibility through

a

transparent Venturi

t

by-passing the test section after Oldertziel

[8.27].

284

Fig.

8.2.7.

Scction of

universal

closetl test rig for air and water, for cflicicncp and cavitation tests on

low

head reaction turbincs (hcrc bulb turbines). With minor changcs. the lest section can be

ad;ip~cd

also to a vcrtical sct with spiral casing.

I

head water tank;

2

intake;

3

turbi~ic block i\.ith bulb turbine

4,

power take-off via bevel gcar.

To

clirnin;~te bearing friction, the bearins box is col~nectcd to thc

swinging stator of an air-cushioned clcctric torquc reaction

dynamometer;

6

tailwater tank;

7

;iir

separator;

8

circulation pump;

9

cooling circuit;

10

bypass;

1

I

flow ~nensuring scction:

12

Vcnturi

nozzle;

13

cooler, heater respectivcly for change of viscosity also changing Reynolds-nu~nber.

A

similar stand with a vertical Francis turbine

in

the test section is in thc iiuthor's Inboratory at the

Technical

Univcrsity Munich. (Drawing courtesy Sulzer

Escl~cr

Wyss)

Bcfore a flow lamina enters the critical zone a portion of its nuclei is screened away from

the

body's face. This originates from the concave curvature of the flow around the

Stagnation point. The convex curvature of the body's facc near the critical point

htls

the

opposite effect. This raises thc question, whether the nuclei measured upstream

of

the

critical point are representative for those entrained into the area of cavitation

[S.6;

8.751.

8.2.2.5.

The

influence of roughness on cavitation

Obviously a wall roughness causes an increase of velocity along

a

convex curved \~;i11.

This enlarges the cavitation index. As

a

model

11011

[8.49]

has assumed a roughness

formed

by

a rectangular equilateral triangle facing the flow with its small side and

located

on

the point of minimum pressure of

a

prolile with its pressure number

=

2

(p,

-

p,i,,)/(~

~2).

For incipient cavitation the cavitation index of this rough-

ness on a flat plate reads

q,,,

=

2(pmin

-

prr)/(e wiin), where wmi, is the local velocity at

'

6

9

12

75

m/s

7x00

cl

a=

17-1Zg/m3

5

l3

t

15

20 min 25

bl

'

7*m

Fig.

8.2.8.

Ci~vit~~tion phcnornena as

a

tion of gas contcnt. a) Cavitation incc

index vs velocity

MI,,

ns

a

function of

contcnt.

?'ists on ogival body

1,511

b)

Ditto with rcspcct to varying total

contcnt. cj 1;rcc

i~ii

contcnt of

n

closed test

as

a

function of pressure

nnd

tirnc. After

J

l(i/~pki,;l.

.I.

,I/.

Kil(w1:

Gils bilbbl~s, their

m

surument

and

iuflucncc

in

cavitation testj

Proc. It4

tl

R

Synip. Scntlai

1962,

p.

37.

Fig.

5.2.9.

Closed tcs! rig with cavitation

and resorber of Californian Institute of

nology. Pasadena.

I

resorber;

2

upward flow

3

downward flow pipe; 4 section

A

-

A;

wards

flow

chamber;

6

downwards flow cham

7

separation wall of resorber;

8

circulation

9

260

kW

motor;

10

diffuser;

11

working

12

probe;

13

nozzle;

14

rectifier. After

K

Doily,

Hotnn~ir

'[5.6].

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

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