THE 4TH ASIAN INTERl(ATIOl(AL
COl(FERENCE ON FLUID MACHIl(ERY
CONSIDERATIOIV OIV EFFECTIVE HEAD IN CROSS-FLOW WATER TURBINE
T. Kitahora,
J. Kulokawa
Yokohama National University, Japan
T. Toyokura
Syounan Industry UniversitY, Japan
It is necessary to supply air into a runner chamber in a cross-flov turbine installed
vith a draft tube, which is different from any other type of vater turbines. Turbine
efficiency changes depending on the supplied air flovrate, and therefore, the efficiency
calculation becolBes more complicated than that of the other water turbines.
As a turbine perfotmance is largely influenced by the behaviour of air volume, it is
still difficult to prcdict overall performance from each component perfornance. Here ve
propose an effective head and recirculation loss by vhich the overall performance of a
cross-flow turbine can be predicted for various operating conditions. And the hydraulic
losses are studied experimentally by changing a nc,zzle installation, a net head and a
runneir dialBeter.
1. Introduction overall efficiency
fro,n each component
performance.
Cross-=flov turbine usually used in In order to determine the method of
the middle head range is inexpensive predicting the overall efficiency of a
and the efficiency decrease in lav cross-flov turbine from the knovn effiflovrates can be prevented by dividing ciency of each component, the experithe axial width of a runner-and-nozzle mental study is performed using se-veral
passage into two parts[l]. conbinations of a runner-and-nozzle and
The authors have studied abol!t a a draft tube.
cross-flov turbine in order to apply it
into lower head range, and the optimum 2. SYmbols ,
H
configuration and the optimum operating
surface of outlet tank )
pressure in runner chamber
efficiency
runner diameter
e*
nozzle installation angle
Q.
vater flovrate
Q.
air flovrate ( at the normalized
condition )
passage vidth
Subscript
of a
p.
n d
head
range[2]. . .
In calculating the efficiency
-
condition vere elucidated very
in a ver low net head ( measured from free
reaction type turbine, the net head
determined by subtracting the velocity
head at the draft tube outl･et from the
total head at the turbine inlet is
usually used. On the other hand, in the
b
case c*f an impulse type turbine, the
total head at a nozzle inlet from the
e
intersection point between the jet
c
center line and the runner pitch circle
is used. These are both based on the
idea that the net head is the receiv-
runneLL exi t
runner center
3. Tes Ap aratus and "ethod
able vater energy.
In calculating the efficiency of
a cross-flov turbine installed with a
draft tube,
the same method as a
Fig. I shovs the experimental apara-
tus of a cross-flov turbine model. In
the turbine A the inlet pipe and the
reaction type can be used. However, the
draft tube efficiency of a 'cross-flov
turbine is lov especially in the high
nozzle are horizontally installed,
vhich is often used for the a,iddle head
head Tange because of the air supply
range. The turbine B is vertically
into a casing for the purpose of avoiding collision of flov against a runner
shaft, and accordingly the overall tur-
installed, vhich is suitable for lov
head range[3]. In the turbine D the
runner-and-nozzle is similar to that of
bine efficiency is largely dependent
on the height and the cfficiency of a
the turbine B･･lbut is reduced to 25134.
The runner-and-nozzles tested vere
draft tube.
confirmed to have good performances
vhen installed in the turbine A, and
Even if the performance of a runner
-and-nozzle is knovn, the combined per-
thcir detailed configurations are shovn
in Fig. 2. As･ the runner diameter of
formance betveen a runner-and-nozzlc
the turbine D is different from the
other two, and the runner vidth b is
and a draft tube･is much different, and
it is still difficult to predict the
367
h'
t,
lllel
Itillt ¥ ,,
tttll
tttttt
C]ttbtf
It tt, ,
l･tltt
,
,)
/
l:
i
( 4¥¥-
IAt f
l
IAi'
lvt t e l
L'b
'L' ,P1
h
/
G･td, ･il,
t,,Iff
ll J
_/;
_l
.
j r,
,,,
l
t
, t
,
i
,,s
'I'
,,,
i,'
t t
,,ft ,,t,
,
I
ii
t
ii
I
ii i
,
Iss
i
,
t
t
I
U]i, Il
B
Turbine
i
ii
, I
t Df," t,,C
i
i
l
i
t ,
. t , l'
Turbine A
s,,
I
tls !
I tt j
I,tt,,
,Itl',t
t
'b"'
' NIL
Tur b i n-e D
Pig. I Experimcntal Apparatus
elongated to 150mm in order to obtain
6'
the 'same frowrate as the turbine B. Thc
4
height from the free surface of the
outlet tank to the runncr center is
.--. L--*
"(r:f
/
same and 1120mm for all turbines testc,d.
'l
,
The draft tubes of thc turbines A
e'
f "''bc
'l
,aAc
,
' Io :
Cuide
¥ -･-･- ! -
160
t,ttt :
cifclc !
formances at Q./Q-=5%. In this air
of f9aRcf!
supply condition, thc vater level in
the runner chamber is equal- to the
height of thc runner bottom, and this
condition is knovn to have good performance for the case of middlc head
rangc. The shape of the draft tube in
the turbinc D is determined based on
the measured results of the turbine B
in vhich the m*'ximum efficiency was
obtaincd at the ratio of Q./Q_=0.5%.
e
,b,
l
and B are dcsigncd bascd on thc cxperimental resultsC4] to havc optimum per-
,.
,..
e
,rl!.
Ua t t :ataa
Nozzl e
Rt7O
Rlta. a
'L
1･-
cl.
h:
/
"'F
Rl. 6
R.6
The bottom of each draft tubc is
Unit
: at'8
Runncf
inclined so that tfic vater enters into
the draft tube smoothly.
Fig. 2
D e t a i l'e d
Turbines
The guide vane installed in thc
a
v
submerged 100mm decp into thc water,
its horizontal p0Sition is adjustcd to
the optimum one, and chamber valls are
ne
Dimensions of
A, B
nozzle passage., vhich can rotatc and
E'
control the flovrate, is kept full open
f '
i
.d
?
during the present study. Shaft power
is measured from thc strain gauge typc
Q.
torque meter by adding mcchanical loss.
,.
:::
The net head is calculated by adding
Q*
0.6
the static pressure head at the nozzle
entrance, velocity head, and thc hight
I
0,6
o.s
of the pressure tap from thc vatcr
o.s
level of the outlet tank.
0.4
4 Ex erimental Results and Discussions
0.3
(1) Method of performancb calculation
-0.2
.
o.4
of runner-and-nozzle
The performance of the turbine D is
shovn against a rotational spccd in Fig.
3 vhen the draft tubc is not installcd.
0.3
0.2
m 'lltl'
o .o a
o
;O .O 4
In this case, the frec surfacc or the
jet from the nozzle is faced io thc
atmospheric pressure. The curvcs of
Fig. 3
Performancc .of- Turbine D
(runner-and-nozzle)
368
1 0
efficiency η 。 and shaft power P are
the net head 量1。 is defined as the
a runner efficiency． Tぬe flo暫一 rate
seen to de．crease a little 暫ith
aO・−a
thewaterleve1、oftheoutlet tank
isロsuallyロsed’ nthedetermination
SfSn
紅eightof thecenterof the runnerfrom
increaseintherotationalspeed．
RunΩer D
貸
seen to changO parabolaically． Here，
in
In t恥e follo響ings， the cha織ge
cffi−
t轟e performances at the maxim匙2m
OCo重lcI olI”ao『
0。9
●C““冨ol ll“Cl o“1“
OL”‘l ol．n”“
0。8
0．7
0．6
ciency point is describcd by changing
with，
an opcrating condition． To begin
a’clear dctermination of thc ” effective
ΦCedefol璽o“ICO“hl
0
4
8 12 16
H！d
Fiε，．4
tねe
駐ead噌is very important， because
tロrbineefficie醜cy is largely dependent
Kfffciencies
based on several
definitio縮s of the effective ぬead
in
on the difinition as sho響n in Fig．4，
》hich the efficiencis of thc
runner−and
Nozzlo oxi皇 l
CO魯IC‘ 9 『O昌OC『
for
−nozzle in the turbinc D is sho皆n
effcc−
the different definitibns of the
co81cr
i り
tive head。 Four kinds of the effective
head are compared， they arc the heights
i 属
！’一マー”＼、
／。 ！ 、
2 、
at the nozzle exit cehter，the
runner
’ 1 も
りし ロ ロ ほ ロ り ヨ りゆりじ
t翫e
center （ conventional net head ），
冠！ザ ノ
・、∫1 9ノ
runneT exit， and the bottom of
the
、． ．！
rUnner． ”ere， 鱒the nOZZle eXit
center99
Cぬan−
is the center’of the nozzユe exit
the
neユ・ at the runner periphery， and
、→・一響
2
Slr￠amHacl
i『墾旦脅o『 oxi竃
simply
鱒runnerexit薩 is determined by
line
aSSum三ng a representatiVe stream
passing through the nozzle center
as
Fig．
！腎
of
sho■n in Fig．5under theassu叩tion
aa infinite number of runner vanes，
no
5 Definitionof『effective head
0
line
slip condition and straight stream
Rロ踊Cf
A
Φc8盈le『ll川：1‘“山1
i“side the r““ner〔5〕．
0。9
From Fig．5it isclearly recognized
that the efficiency based on the
effec−
tive head of the ”runner exit”
change s
1ittユe over the 耀hole net・head
range．
0C“1“ol”IB屡
●Cg““lll““1“““
OLa1“oll”“1
0．8
the
器o胃ever， the effic三ency based on
”r纏nner center” or the ”nozzle
exit
0。7
head
center” changes largely in the loΨ
gives
range． This isbecauseFtheflo響
0．6
in
energy to the runner vanes notonly
exit
the entrance half but also in the
the
half，and tわe effec・tiveぬeightof
Fig．・6
runner eXit iS taken into
account
onlyinthecaseof”r観n臓erexit齢．。
0
4
8 12
H／d
Efficieacies based on several
defi！1itions of the effective head
resロユts，
From t為e above−mentioned
be
the 齢runaer exit”・height shoロ1d
ef−
adopted for the definition of the
fective head instead of tbe conveηtion−
Wnぬo讐l d r a f l l u b c
of
ごhe installation condition（轟eight
Wi星』 d r a臼 1讐b c
TUfbioc B 丁懸rblocD
on
ヤal net head， asitdependslittle
the 額et head）ワ
Theaboveadopted definition of the
to
effective head is further examined
Table 1
ef一
confir皿 the validity and the
ficie“cies are co耐pared三nFig．6 響hen
the
the nozzle instanationangleand
67．1
61．1
74 5
70．2
Comparison of efficiencies
calculated fro皿 effective head
difinition of tbe ”runner exit陶 is used．
is
runner diameter are cbanged． As
sho響nin Fig。・6，theefficiencyis also
seen to be almost cohstant for the
the
variation of the net head 響hen
effective head based on thc ” runner
This might becausedby thechangein
free s“rface configuration inside．the
runner chamber， as the Froude Ωumber
cぬangesd腿etoaverylo冒．velocity．
6
exit貿 is used、Here。inFigs．5and
．theefficiency curve changesa 1ittle
（2） lnflu●nco of 『unn6『
di．am●t●r on亀h●
●fficioncy
t新c
inavery lo冒 headrangc，evenif
The efficiency of
369
a 。runner。and一
nozzle is illustrated in Tablc l, in
vhich that of the turbinc B is 67. IX
O. l
for the case of II./d=5.8. This value is
Runncr B
:3
:s
O
7.4X Iover than that or the turbine D
･hich has a smaller runner diamctcr.
This is mainly .caused by a leakage loss
The aspect ratio of the runner in the
turbine B is smaller than that in the
turbine D, and therefore the loss per
unit flovrate becomes larger. According
O
-O.
O.s
0.1
O
side vall and the casing, as the clearance in both sides is 1..5mm and 1.0alm
in the turbine B, vhile in the turbine
D it is 0.75mm and 0.25mm, respectively'.
l
o 0= 1 80'
e e=230'
1
at the - clearance betveen the runner
x/b
Ruonef D
:a
:
O
to StepanoffC6], the efficiency di ffer-
ence betveen both turbines amounts to
-O
To clarify the cause of the efficiency difference, the transverse veloc-
ity distributions vere measured by a
Pitot probe inserted at O. 03d dofnstream of the runner exit. The energy
'O
Q. S
.O
x/b
Energy distribution at the runner
outlet
F'ig. 7
distribution are compered for' the turbines B and D in Fig.7, in vhich Ma, is
l.
o
the product of angular moment u and
angular veiocity a, ,
1
o 6= 1 8 O'
e 0=230'
1
about 3X.
and x is the
distance from the side vall. It is
recognized that the flov leaves th_e
1'
O.
o
¥,,
1
runner vith higher energy in thc runncr
B than in the runner D, and the visualized flov shoved that the turbulence of
'
O.
C
O.
vater is larger in the runner B. This
S
uight be because the influence of
e
¥
85F
O.
secondary flov near ･the vall betomes
relatively larger in the turbine B due
4
e.
Sjx
-
to a small aspect ratio, and because
e=
3
the runner vane thickness is not simil
1'
4
O.
ar.
2
(3) Overall performance of turbine with
draft tube
¥,
2
O.
l
Overall pcrfora,ances of turbines
vith runner-and-nozele and draft tubes
are compared vith.each cou]ponent performance in this section.
e
e
a
a
Perfor,Dance curves are shovn in Fig.
8, in vhich the net head l, is taken as
the height from the free surface of the
:¥
Is8
¥O. 2
O.
1
I
O. 8 ¥
c
supplied air flovrate is controlled so
O
,
outlet tank as is usually used. The
te 20
that the runner chamber pressurc is
kept constant(-12kPa). The vater level
in the runner chaa:]ber measured from the
Fig. 8
bottom of the runner is also shovn in
30
10 oSO
Ce
d/ll f p" ' d"
'l'
Overall performance curve
the
figure.
' efficiThe difference
of maximum
Oi
ency in both turbines is about 9X.
Air
dH
Vatef lllef
!
Considering that the air pressure in-
,
side the runner is nearly equal to ･that
/ * '-.
i '¥
i
,
!
! e':
.¥.
in the .runner chamber, the effective
net head H. can be calculated by the
folloving equation.
¥
t.
c
.-.- ･ -
Effective net head: H.=11.-p./p g '(1)
The efficiencies recalculated using the
above equat'ioh become necessarily vorse
than that using the net head, and are
coatpared in T8ble l. The efficiency of
.l
t
i
¥¥ i ../
. *.,
the turbine installed vith a draft "tube
Pig. 9
37 O
F l'o v
¥
inside runner
is seen to bc lover than that vithout a
draft tube. The reason in consi'dered as
follovs.
¥.
About a half part of the runner is
filled vith air, but near the tip
region of vanes betveen the air and the
vater the vater is involved and forms a
tater layer as shovn･ in the. figure,
B
1'o.04
The vater flovs into a runner from
a nozzle and leaves out of the runner
at the runner exit, as shovn in Fig. 9.
Turbine
o.Q3
o.Q2
Tufbinc D
O. O]
because the pressure in the runner
H=2. 97m
o
chamber is a little higher than that in
the air region inside the runner. Nov
putting the thickness of vater layer as
-llO -'o -70 -SO-30 e-lO
d e g.
c, as shovn in Fig. g, the folloving
yater layer Thickness as a
Fig. lO
equation of momentum balance is deduced
function of O
considering the pressure, the centrifugal force,' and the vane vork, and
assuming that c((d:
2 _ Ap
a cu
ua)
d6?i
c2
2(_ tan,e
-d )cde
r
a,
(2)
',f:r
¥ ･ F!=1:'
"
I "
''
p
llerc. O : angle mcasured from thc upper
edge of thc runncr. Ap : prcssure
l'
differcnce betwcen thc watcr layer and
the air,
u : peripheral velocity. P :
- ' !"!L"';:._:1(;.'
5
Je.
vanc outlct anglc.
The vater layer thickness c is cal-
.
t),
culated for thc turbines B and D, and
is plotted in Fig. 10 as a function of
e . Vith an increase in the depth from
"'
¥."
"* ':
the water surfacc thc vatcr entcrs
dceper into thc runncr, which increascs
the vater layer thickncss c. Undcr the
sao]e net head condition the rotational
'
b
".
, !;:f.-.
!
:(',:lyt
' '1:: .:;- i
.
;
h¥
..
a "t. .,e. '
,
_ ,
it
' '
･ !･( :db:..'.""':-..'. '. . '
. " ' - /1 i..., .".
.
L ; ' ..' 't(
speed is smaller, and the thickness
becomes largcr in thc turbipe B than in
the turbinc D, and hcnce the re-enterd
vater volumc is larger in thc turbine D.
'{!r;:#;c"/:/,L.._
,.. .
a.$ _ i:c t;
(
l
: "
*
The runner gives the angular mo-
. .::1J
,,+.,
IBentum to the re-enterd watcr. Assuming
that the angular momentum givcn to the
rig, I I Photograph of flov around
runner
re-enterd water layer becomes torque
loss, the lost head ( we call this as
the 'recirculation loss') can be pre-_
dicted. The efficiency decrease thus
calculated amounts to 2. 3 % in the
turbine B and 1.7 in the turbine D.
Hovever, this value is much smaller
e' Q
60
-lO
20
S
E"
o.
coa,pared ･ith the measured efficiency
difference shovn in Table l.
This might be due to the under-
:
.
estimation of the vater laycr thickness
c because of the assumption of infinite
vane number. To measure the real thickness of the vater laybr is very difri-
l"
O ..8
,
cult, and the photograph of the flov
betveen vanes is illustrated in Fig. Il
0.7
0.6
for the case of the turbine D. The
･,
R
o
vater betveen vanes are seen to be gasliquid multi-phase floll, and from the
photo the maximum vater layer thickness
:::
oO. 1
O .7 5
J'g
'
8
O
O
ratio 2c/d can be roughly measured to
be about O. l, vhich is about 2,5 t.imes
the calculated value in Fig. 10.
12
In order to establish the ovcrall
efficiency of a cross flow turbinc from
Pig. 12
371
H/d 1 6
Comparison of performance
O
the efficiency of a runher-and-nozzle,.
the measured overall efficiency is coo]-
loss proposed here. It is recom,nended
to adopt an effective net head instead
of the conventioned net head in
pared vith the predicted efficiency in
Fig. 12 from the runner-and.-nozzle efficiency. The runner chamber pressure
predicting the overall turbine perfQrm-
turbine D.
Acknovledgement
ance.
is also compared for the case of the
'
n the figure, the efficiency(shovn
by e) obtained by using the net head
The Authors vould vish to acknovledge T. Xubota (Kana ava Univ.) for his
helpful advice, and vish to acknovledge
Fuji Electric company for a]anufacturing
experioental apparatus.
from the free surface of outlet tank is
compared vith the one (shovn by O )
using the effective head given by Eq,
(1). The efficiency based on the free
surface of the outlet tank is almost
constant against the net head H. Hov-
RefGrendes
ever, the efficiency based on the
tl] Kubota.T.. Vater Turbine for Lov
effective net head Hn decreases vith.an
decrease in H. Considering that the
recirculation loss increases largely
Head, Journal of JSXE,83-735,B(1980),p.
1509
vith a decrease in the net head due to
[2] Toyokura,T., et al. Study on'Crossflov Turbine, Trans. of JSUB, 51-461. B
turbine should decrease vith a decrease
in the net head, though the runner-and-
C3] Toyokura,T., et al, Study on Cross-
the decrease of rotating speed, the
overall eff-iciency of a cross flov
( 1985-1), p. 143
flov Turbine ( Further Report. Appli-
nozzle efficiency is kept constant.
Accdrdingly the efficiency curve de'
cation for Lov Head. Trans. of JSXE,5349 l. B( 1987-7), p. 2078
neted by O is considered to given real
efficiency of cross flov turbine.
The predicted efficiincy curvc is
also plotted by the dotted line in Fig.
12, in vhich the vater layer thick.ness
[4] Toyokura,T.,et al,Vertical Diffuser
Performance vith Gas-liquid Tvo-phase
Flov,Tran. of JSME,51-470.B(1985-lO),p.
3376
[5] Kitahora,T., Toyokura,T.. Proc. of
The 23th Symp.of 'Turbomachinery Society
c is treated as 2.5 times the.calculated value as mentioned before. The
predicted curve agrees very vell vith
the one using the effective net head
of Japah, (1989), p. l
[6] A.J.Stepanoff.Centrifugal and Axial
Pump, (John Viley & Sons, 1948)
over the vhole range.
5. Conclusion
The cross-flov tu rbine is exper imentally studied, and the main 'res.ults
are summerized as follovs.
(1) The efficielacy of a runner-and-
nozzle becomes cqnstant in a vide range
of the net head by using the effective
head proposed here, vhile the efficiency using a convential net head
changes largely in the lov head range.
The effective head is defined as the
head based on the height of the runner
exit.･- center, and the efficiency u.sing
this becomes almost constant in the
range that a similarity lav is consist-
ent.
(2) The comparison of tvo similar
runner-and-nozzles vith the ･different
aspectratio has revealed that the effi-
ciency of the smaller aspect ratio
runner has 7. 4X I over at the same
flovrate, because the flov is largely
influenced by the secondary flov near
the vall and the outlet flow has larger
turbulence.
(3) The overall efficiency of a cross-
flov turbine can be vell predicted
using an effective net head from the
runner-and-nozzle performance, runner
chamber pressure and the recirculation
372
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