EM39
EM39
EM39
Estimating Reversible
Pump-TurbineCharacteristics
UNtTED STATES DEPARTMENT
OF THE INTERIOR
BUREAU OF RECLAMATlON
MS-230 (l-76)
Bureau of Reclamation
TECHNICAL REiPORT STANDARD TITLE PAG
3. RECIPIENT’S CATALOG NO.
Same
14. SPONSORING AGENCY CODE
5. SUPPLEMENTARY NOTES
6. ABSTRACT
EstimatingReversible Pump-Turbine
Characteristics
BY
R. S. Stelzer
R. N. Walters
SI METRIC
.. .
111
letter Symbols and Quantities
C&Ratio of fluid radial velocity to spouting n=Rotational speed
velocity ns,=Pump best (peak) efficiency specific
D,=Discharge diameter of impeller or en- speed
trance diameter of runner nBt=Turbine best (peak) efficiency specific
Dz=Minimum opening diameter of impeller speed
or runner P,,,=Best efficiency pump power input
Fh=Hydraulic thrust Pd=Turbine full-gate capacity at h,
f =Frequency, Hertz P,=Pump power input
ft=Foot Pt=Turbine capacity
g=Gravitation constant (acceleration) p=Number of poles in generator-motor
gaLGallon Q,,=Pump best efficiency discharge at HBE
I&Head developed (pump) or absorbed Qt=Turbine full-gate discharge at Ha
(turbine) r/min=Revolution per minute
H nzr=Best efficiency head developed (pump) s=Second (time)
H zET=Best efficiency head absorbed (turbine) V=Peripheral velocity of impeller or runner
H,=Atmospheric pressure (head) at D1
Hi=Hydraulic losses in pump suction WEImpeller weight
H,=Static draft head, elevation difference Wpt=Total pump-turbine weight
from D, to minimum tailwater WR2=Product of the weight of revolving parts
H,,=Shutoff head of an impeller or runner and the square of the radius of
H,=Vapor pressure head of water gyration
hd=Turbine design head
hp=Horsepower y=Gamma=Specific weight of water
k=Efficiency factor y=Eta=Hydraulic efficiency
kg=Kilogram ng= Eta,= Generator efficiency
kVA=Kilovolt-ampere capacity of motor- np=Eta,=Pump design efficiency
generator qt=Eta,=Turbine design efficiency
kW=Kilowatt x=pi=3.14159. ..
lb=Pound a=Sigma=Cavitation coefficient
M=Wicket gate height e,,=Sigma begin
MW=Megawatt o,,=Sigma critical
m=Meter +,=Phil=JcnD1/ (60d2gH,,), velocity ratio
NPSH=Pump net positive suction head at D1
iv
Contents
Page
Preface.. .................................................... iii
Letter Symbols and Quantities .................................. iv
Introduction .................................................. 1
UnitSelection ................................................. 3
Speed ....................................................... 3
Effects of Specific Speed on Pump Performance .................... 9
Effects of Wicket Gates on Pump Performance .................... 20
Submergence of Unit .......................................... 20
Sizing the Pump-Turbine ...................................... 22
Performance ................................................. 27
Estimating Turbine Performance ............................... 27
Estimating Runaway Speed .................................... 27
Pump-Turbine Four-Quadrant Diagram .......................... 27
Weight, Inertia, and Hydraulic Downthrust ...................... 34
Hydraulic Similarity .......................................... 34
Bibliography ................................................. 40
vi CONTENTS
FIGURES
Number Page
1 Comparison of pump-turbine impeller and turbine runner
designed for operation at the same head and speed ...... 5
2 Variation of pump-turbine efficiency and turbine output
with speed and head ................................. 7
3 Operating head range vs. specific speed ................... 8
4 Comparison of pump impellers and characteristic
curves with specific speed ............................ 9
Percent pump input vs. specific speed .................... 10
Percent pump head vs. specific speed .................... 11
Percent pump efficiency vs. specific speed ................ 12
Cavitation coefficient (pump sigma) vs. specific speed ...... 13
Critical pump sigma vs. percent of pump best
efficiencyhead ...................................... 14
10 Velocity ratio +1 vs. specific speed ....................... 15
11 Ratio of impeller discharge diameter to throat diameter
vs.specificspeed .................................... 16
12 Ratio of wicket gate height to impeller discharge diameter
vs. specific speed ................................... 1’7
13 Ratio of fluid radial velocity to spouting velocity
vs.specificspeed .................................... 18
14 Ratio of spiral case dimensions to impeller discharge
diameter vs. specific speed ........................... 19
15 Turbine characteristics superimposed on pump
characteristics - n,, = 2,000 .......................... 29
16 Turbine head, discharge, and efficiency superimposed
on pump characteristics - nsp = 2,640 .................. 30
17 Turbine head, discharge, and power superimposed on
pump characteristics - n,, = 2,640 .................... 31
18 Percent reverse runaway speed vs. specific speed .......... 32
19 Pump-turbine four-quadrant diagram ................... 33
20 Impeller weight vs. impeller discharge diameter .......... 35
21 Pump and pump-turbine weight vs. impeller discharge
diameter ........................................... 36
22 Impeller WR2 vs. impeller discharge diameter ............ 37
23 Hydraulic downthrust vs. impeller discharge diameter ..... 38
TABLES
Number
1 Best efficiency pump and turbine specific speeds
for pump-turbines .................................. 4
Permissible operating head range ....................... 5
Operating heads of Bureau of Reclamation pump-turbines ... 6
Comparison of pump and turbine critical sigmas .......... 21
Reversible pump-turbine data ........................... 23
Efficiency factor (k) for the conversion of
velocity head to pressure head ........................ 34
Introduction
Pumped-storage installations provide the used in gas turbine operation. Obviously, gas
most efficient and practical means for storing turbines have advantages-design and construc-
large quantities of energy. Large pump-turbines tion times are considerably less than the 4 to 6
such as the lOO-MW units in the Bureau of years required to design and build a pumped-
Reclamation’s Mt. Elbert Pumped-Storage storage facility, the initial capital investment
Powerplant near Leadville, Colo., can have is small compared to a pumped-storage installa-
overall efficiencies of approximately 75 percent. tion, and gas turbines are not subject to
The overall efficiency includes hydraulic losses geographical site limitations as is a pumped-
and electrical losses associated with the storage facility.
generator-motor and transformer. A pumped-storage installation provides flexi-
Although pumped storage does not increase bility in adapting to power outages. During
power system energy supply (unless there is the pumping cycle the pumping input load is a
natural inflow into the upper reservoir), the large interruptable load that can be readily
large number of pumped-storage systems built removed from the system. When a pump-turbine
worldwide since the 1950’s attests to their value is at speed-no-load (spinning reserve) it can
in power systems for leveling the peaks and assume full output load in 4 to 10 seconds com-
valleys of a typical electrical utility load curve, pared to the half hour required for a steam
and for providing emergency power [l].l plant to achieve maximum output from spin-
Pumped storage combined with thermal gen- ning reserve. Because of its ability to store
erating capacity allows thermal units to operate energy efficiently, pumped storage could ad-
at nearly constant output and best (peak) vance energy development from unconventional
efficiency (BE). sources, such as solar and wind.
A thermal plant using pump-turbines for pro- The Bureau’s Flatiron pump-turbine was the
viding peaking power can have a higher overall first reversible pump-turbine installed in the
system efficiency than a system that uses gas United States. It began operation in 1954.
turbines, another commonly used method for Presently, the Bureau has 23 reversible units
providing peaking power. The pumped-storage installed and 6 more under construction. None
efficiency of 75 percent with a baseload plant of the units is used exclusively for power gen-
thermal efficiency of 40 percent gives an overall eration since all are part of multipurpose water
efficiency of 30 percent as compared to a gas development projects which provide water
turbine efficiency of 20 percent. either for irrigation or municipal and indus-
This higher overall efficiency is obtained trial use.
either with relatively inexpensive nuclear en- Basically, a pump-turbine is a pump that
ergy or coal fuel as opposed to the increasingly operates in the reverse to generate power.
scarce, expensive natural gas or petroleum fuels Figures included compare various characteris-
tics of the three classes of hydraulic machines;
1 Numbers in brackets refer to items in the bibliogra-
i.e., pump, turbine, and pump-turbine.
phy. 1
Unit Selection
Speed 2. The turbine design specific speed (n,,) is
defined by the equation :
Many characteristics of the pump-turbine,
pump, and turbine are plotted as the ordinate
n(Pd)1/2 or
and specific speed as the abscissa. Any hydraulic nst= (2)
machine will have a range of specific speeds (hd 6/4 hd
where :
for a given rotational speed, depending on the
operating point; however, the specific speed at n=rotational speed, r/min,
the best (peak) efficiency operating point is n,,=turbine design specific speed,
customarily used as an index number for de- h,=turbine design head, ft (m), and
scribing the geometrical configurations of the P,=turbine full-gate capacity (at hd) , hp ;
machine and the shape of the characteristic however, for comparing hydraulic ma-
curves. The specific speed at peak efficiency of chines the following will establish tur-
a hydraulic machine does not change with bine output of a pump-turbine as that
changes in rotational speed. All references of obtained at the gate opening and head
pump-turbine specific speed refer to the specific (H& where best (peak) efficiency is
speed at the best efficiency point (BE). attained.
The units of specific speed are noted to re- It can be shown that equations (1) and (2)
mind the reader which parameters express the have correlation upon substitution of discharge
characteristic speed. For brevity, head and (Q) times head (H) for power (P) into equa-
speed are omitted. Comparable formulas are tion (2).
included in the Hydraulic Similarity section. Stepanoff [2], using the same parameters, Q
1. The pump best efficiency specific speed and H, for both machines, expressed the rela-
(n,,) is defined by the equation : tionship between pump and turbine specific
speeds as:
n (&,,I li2 nst=nsp l q (3)
plies the pump specific speed (n,,) formula to pump best efficiency head (H,,, ) for a pump-
all three classes of machines. Of particular in- turbine [4] is:
terest is the comparison of the calculated spe-
H 1
cific speeds for a pump-turbine when analyzed BET= (4)
at best efficiency turbine operation and best effi- H BEP qP’%
ciency pump operation. It is apparent from the where :
nearly equal values of pump and turbine spe- nv=pump hydraulic efficiency, and
cific speeds in table 1 that specific speed does, in qt=turbine hydraulic efficiency.
fact, define similar hydraulic flow parameters.
Comparative specific speed formulas are The value of the ratio of turbine best effi-
shown in the Hydraulic Similarity section. ciency head to pump best efficiency head in-
If an impeller/runner was selected only on creases as specific speed increases. Using the
the basis of turbine performance and the pump- headwater and tailwater surface elevations as
turbine operated in the turbine direction, ex- reference, there is a further divergence of the
pected efficiencies could be equal to or greater turbine best efficiency head from the pump best
than that of a pure turbine [3]. While the tur- efficiency head caused by penstock losses. Ad-
bine best efficiency head is 15 to 30 percent justment of the turbine best efficiency head to
greater than the pump best efficiency head (fig. pump best efficiency head ratio is possible by
IO), in actual practice when pumping perfor- varying the rotational speed (n) , such as by
mance must be considered, there is a sacrifice using a two-speed generator-motor.
of approximately 1 percent of turbine efficiency When either pumping or generating, consid-
for a pump-turbine as opposed to a pure tur- eration must be given to avoiding cavitation
bine. The theoretical minimum value of the damage and vibration that occur at heads
ratio of turbine best efficiency head (HBET) to greatly removed from that of the respective
TABLE l.-Best eficiencg pump and turbine specific speeds for pump-turbines
-
Turbine n,, Pump nsp
Unit U.S.
Pump-turbine No. ft-gal/min m-m’/ s ft.-hp m-kW ft-gal/min m-ma/s
San Luis 1-8 1,850 36.8 28.5 108 1,950 37.7
Central Valley
Project, California
Flatiron 3 1,960 37.9 30.2 115 1,960 37.7
Colorado-Big
Thompson Project,
Colorado
Mt. Elbert* P/G 1 2,160 41.8 33.2 127 2,240 43.3
Fryingpan-Arkansas
Project, Colorado
Grand Coulee* P/G 7 2,320 44.9 35.7 136 2,640 61.1
Columbia Basin &8
Project, Washington
Senator Wash l-6 4,300 83.2 66.2 252 4,660 89.9
Colorado River
Front Work and
Levee System,
California
* Model data.
UNIT SELECTION
“\
3002
IT!- “w/r-’ _
“P
6 to 9 vanes-
-13 to 21 buckets
P”GoRtion --!$j \ ]
I I
PLAN I
TURBINE RUNNER
I I
~7-~~~~~~~~er
Turbine
rototitinJ+I&
ELEVATION
Notes:
PLAN ’
VT , VP= Peripherol velocity Ot DI
PUMP-TURBINE IMPELLER
Vw= Water velocity
Vwh .&b=Relative velocity of water respect to turbine or pump
0, turbine = 0.7 DI pump
DI =Discharge dia. of impeller or entrance dio. of runner
Dp=Mlnimum opening diometer of impeller or runner D2 turbine = 0.83 DI turbinen0.6 D, pump
D, pump = D, turbine nrp= 2,000 gal/mln (38.7 t’t13/S)
nst=30.8 U.S. hp units (117.3 kW units)
FIGURE L-Comparison of pump-turbine impeller and turbine runner designed for operation at the same head and
speed. IO&Dd56.
best efficiency head. A multispeed generator- creased maintenance when operating at the ex-
motor can be used for a pump-turbine operat- treme. The amount of time that a unit is expect-
ing over a wide head range. In the future, solid- ed to operate at the extreme high or low heads
state variable speed control may be practical. is a factor in determining the permissible oper-
The suggested maximum head range relative to ating head range. Refer to “Submergence of
pump best efficiency head for a single-speed Unit” for operating limitations based on cavi-
pump-turbine is shown in table 2. tation.
High specific speed pumps have relatively
TABLE 2.-Permissible operating head range
steep head-discharge curves as shown on figure
(percent of HBEP)
4; thus, they are more able to operate within a
Maximum Minimum
Pump specific speed, n,, wide head range.
head head
Table 3 shows operating heads of the Bu-
ft-gal/min m-m’ / s percent percent reau’s pump-turbine units. The Flatiron pump-
less than 1,500 less than 29 110 95 turbine operates in the turbine mode at 257
1,500 - 2,000 29 - 38.7 115 90 r/min and in the pump mode at 300 r/min. The
2,000 - 3,500 38.7 - 67.7 125 85
3,500 or greater 67.7 or greater 130 70 San Luis pump-turbines can operate either as a
pump or a turbine at either 120 or 150 r/min,
The limitations in table 2 are based on data whichever effects best efficiency for a given
from existing units and should not be consid- head. Flatiron and San Luis, both with two-
ered absolute. Some existing units exceed these speed generator-motors, are the Bureau’s only
limits and a few units with operating ranges reversible pump-turbine installations where a
that fall within the specified range experience turbine best efficiency head falls within maxi-
considerable noise, rough operation, and in- mum and minimum heads.
6 ESTIMATING REVERSIBLE PUMP-TURBINE CHARACTERISTICS
Turbine Min. Turbine Min. ‘urbine Min Turbine Min. ‘urbine Min.
140 (42.7) 109 (33.2) 27 (8.2) 263 (80.2) 390 (118.9)
Pump Min.
113 (34.4)
Pump BE Turbine Max. Turbine Min. ‘urbine Mar Turbine Max. Turbine Max.
250 (76.2) 260 (79.2) 260 (79.2) 71 (21.6) 352 (107.3) 475 (144.8)
Pump BE
272 (82.9)
Turbine Max. Turbine Max. kmp Max. Pump Max. ‘ump Max.
290 (88.4) 323 (98.5) 74 (22.6) 365 (111.3) 485 (147.8)
Pump Max.
332 (101.2)
Pump Max.
300 (91.4)
Turbine BE ‘urbine BE Turbine BE Turbine BE
340 (103.6) 80 (24.4) 365+ 525 (160.0)
(111.3+)
The allowable variation of operating head is will be in the operating head range for a pump-
narrower for pump-turbines than for real tur- turbine than for a turbine, Selection of pump
bines. Monograph No. 20 indicates the permissi- best efficiency head .or design head near the
ble head range to be between 65 and 125 per- lower end of the operating head range favors
cent of the design head-“. . . the net head at turbine operation at the expense of pump opera-
which peak efficiency is desired.“-for a Francis tion. With the pump design head near the mini-
turbine [5]. Figure 2 shows pump-turbine char- mum head, turbine operation is possible at mini-
acteristics as a function of head and rotational mum head and the turbine best efficiency point
speed for the Bureau’s Mt. Elbert Unit P/G 1. is more likely to occur within the operating
This particular pump-turbine is not capable of head range.
generating power at heads below 67 percent of For multispeed operation, if rotational speed
the pump best efficiency head. varies with the square root of the head, the effi-
Because a pump-turbine has a larger diam- ciency will remain nearly constant regardless
eter (D1) compared to a turbine, the shutoff of change in head, and turbine power output
head is considerably greater for a pump-turbine will be possible as the head decreases toward
rotating in the turbine direction than for a com- zero head. See the four-quadrant diagram on
parable turbine operating at the same speed. figure 19 for a more detailed description of
It is more likely that the turbine shutoff head changes in pump characteristics with changes
UNIT SELECTION
Ratio H/H,,,-%
loo
Turbine Efficiency
versus I
40 60 80 la0
Ratio
li
I20
H/H~E~-%
140 160 I.0 200
220 I-Turbinl
ver
e output
SUS
Head Rqtio
I
Constant Speed
200
---
180
,~
I40
I20
io:
100
FIGURE 2.-Variation of pump-turbine eficiency and turbine output with speed and head. 106-D-357.
8 ESTIMATING REVERSIBLE PUMP-TURBINE CHARACTERISTICS
600
500
400
400
I-
Loo
L
, _ >Grdnd Coulee P/G 78 8
s
I Flatiron
200
50
40
loo
30
80
70
20
60
I!5
in speed or size as established by pumpturbine tion of water flow at the outer periphery is
similarity laws. more radial for a turbine runner than for a
Figure 1 shows a turbine runner compared pump-turbine impeller. The throat diameter
to a pump-turbine impeller having the same (Dz) will be nearly equal for either a turbine
specific speed and selected to operate at the runner or pump-turbine impeller operating at
same head and rotational speed. The pump- the same head and speed. As indicated on figure
turbine impeller diameter (D1) is 30 percent 11, the throat diameter (D2) of a pump-turbine
greater than that of a turbine runner. Because is approximately 10 percent greater than that
the passages are shorter in a turbine runner, of a comparable centrifugal pump for the same
deceleration of water, when the runner is used specific speed. The dimensional expressions of
as a pump, is too abrupt for efficient diffusion diameters shown on figure 1 were derived from
within the runner. Conversely, water is accel- figures 10 through 13.
erated in the turbine direction ; however, hy-
draulic acceleration is inherently more efficient
than deceleration. The acceleration process does Effects of Specific Speed on Pump
not cause a significant loss in the efficiency of Performance
the turbine runner.
A turbine runner has two to three times more Figure 3 shows the range for operating head
blades than a pump-turbine impeller. The direc- versus pump specific speed of many worldwide
Note: DI expressions are based on the same He~p=O.l8 HsEP, radial HeEP= 0.04 H,,,,rodiol
capocltles and rotational speeds
Efficiency
FIGURE a.-Comparison of pump impellers and characteristic qurves with specific speed. 106-D-859.
10 ESTIMATING REVERSIBLE PUMP-TURBINE CHARACTERISTICS
/ I , . I
u+off/heod I
-
-
Shutoff head
0
Grand Coulee P/G 7a8
T
(Mt. Elbert P/G I
-
Pumps
rl
20
--mm-
30
Pump- turbines with wicket gates
-..I
40 50 60
, I, , ,
70 80 90 loo
I
T150 i
IO - I I
IO00 2ooo 3ooo 4ooo 5000 7000 g,ol/min
Ei 8 8 Ei 3 $8 8 E B
ESTIMATING REVERSIBLE PUMP-TURBINE CHARACTERISTICS
.-------Pump -
I.&-
1.4--
1.2.-
1.0
0.9.-
0.8.-
0.5..
0.4--
0.2 ,
0.18 -- Mt. Elbert P/G I
40
I. 50 60 70 80 90 ioo 150 ma//s
I I
I’
I I I I
1000 2000 3000 5000 7000 gal /min
PUMP SPECIFIC SPEED - nrp
FIGURE 8.-Cavitation coeficient (pump sigma) vs. specific speed. 106-0363.
\ I CRITICAL PUMP S&IA-PEFICEINT OF PU~~PBEST EF~CIENCY HEAD
I I
P=Pump
P-T = P/G = Pump-turbine
Metric specific speed ( m3/s units:
indicated by parentheses
I
l-
Z 0.6
Grand Coulee PI -P6,nsp=
i 850 ( 35.8)
TY 1
1 .
LDos Amigos, Centrifugal P, n,,=
I 3050 (59)
-b-
z 0.4
0 Cnn I .,ic D-T IznI-nm \ tf /
.
1 ,M t. El bert P/G I-n,,=
I/ 2240 (43.3j - -’ 3Y
I
I/ Grand
7 I3 8. n,,.= 2640 (50
FIGURE 9.-Critical pump sigma vs. percent of pump beet e&iency head. 106-D-86.4.
UNIT SELECTION
qsom Jo~ouaS -
uo+s!mai --
_---
I
I
0 1
- I--_
w
w
- %- DMO6!JOlUO ____ _ __--
.---\
i
gd - Id aalno3 PUDJ~)~-- - -
*I
lasnolyuou-
t
- -0 ’
I
I
!bDJO+D&DyO- a
I 0
ynos umDk--’
I -*
-- -1-d OJ!qC
DJDddDUJnN- \
1
16 ESTIMATING REVERSIBLE PUMP-TURBINE CHARACTERISTICS
I
P-H MD-l
I N yaaJ3 ayDuS-”
.---
*
1 I I
+DM JO+DUaS-----
.-- --- uo+s!mal
I
- SO6!lu~ soa
all!1 ,J ,; ----------.
I
9/d aalnog PUDJS---j/
.-----
---
UdJ!,DIj
---9d-Id
.--
‘8 sin’
aalno3
JOhD3
PUDJ~
Ualg
1
!’
-----JaAODH
UNIT SELECTION
l 0 +
--+-
8 I
4SOM AO(DUaS -- - ,
-- ------A30~1 -43
sq ws3Aio~lj - -- -
0.0396 0 (U.S.)
cr = r 0, M (H1”2
1 0.0718 0 (metric)
DI
-
hr au w Jo W 70 0” Jv I”” mrs
:
I 1 I1 I 2
1000 2000 3000
. 4ooo 5000 gol/min
FIGURE 13.-Ratio of fluid radial velocity to spouting velocity vs. specific speed. 106-D-368.
II ’ I I I
I.7
w RATIO SPIRAL CASE DIMENSIONS TO DIAMETER
1.s I ,A++ A . B &etc.-Denote ooints for
2 Grand Coulee PI-P6,PumpT 1 I
I.6 m
3 1.4 j I!& 1 I_---- -f&~++y+-
I.5 ?
turuines witnout
c I.3 :I ! 2
irl wicket gates 1.4
I.2 k
::
Okutotoragi - - I.3 z
s I.1 . . 0
I etc.-Denote points
pump-turbines
with wicket gates 1.4 4
E
I.3
a
I.2
!!i
ith wicket gates -
I.1
I i
a I I
z I.3
I II
pJ I.2 I 0,
I I
I t-
u) I.1 Without
wicket e-4
,J 1 ’ I I
--
g I.0
3i gotes ‘10 I d/ I
+z
= 0.9
p 8 I
r 0.6 t I
0 I ' Longitudinol t ‘I -
I.1 I I
I 4 I
ii I
3 l.O- I
I 1 I ’
~ 0.9
s Q6
iL For units with
u) 0.7
and without
g 0.6 --
wicket gates
.- F= Constant 20.5
0 0.5 --------0 with and without
wicket gates
I 1
20 30 40 so 60 70 60 90 loo IS0 ma/s
I I 1 I I I
I
1000 2000 3000 4000 SO00 6000 gal/min
FIGURE 14.-Ratio of spiral case dimensima to impelk dticharge diameter 218. specific speed. 106-D-369.
20 ESTIMATING REVERSIBLE PUMP-TURBINE CHARACTERISTICS
pump-turbine units. On figure 3, the term occur near the shutoff head. The lower the spe-
-
ns,dH plots as a straight line of a constant cific speed, the less becomes the slope of the
value. Pump-turbine manufacturers consider head versus discharge curve from best efficiency
this term a basic design parameter, in addition head to shutoff head. The maximum power input
to head and size. There is not a theoretical limit to the pump usually will occur just below best
to this parameter. The curves show that the efficiency head and will decrease with increasing
pump-turbine manufacturers’ present experi- head.
ence limit is : Generally, the higher the specific speed of the
pump, the smaller the physical dimensions for
n,,,H1/*=70,000 ft-gal/min (U.S. units) (5) a given capacity and head, Pumps that have the
n,,H1/*=750 m-m3/s (metric units) highest attained efficiency are those with spe-
cific speeds approximating 2,500 gal/min (48
When deep submergence is prohibitively ex- m3/s). To prevent cavitation at a given head,
pensive, the limiting factor will be a lower the submergence required for a pump will in-
value of the experience limit, n,,dR. crease as specific speed increases.
Figure 4 compares impeller geometry and
characteristic curves of three different pumps
with different specific speeds and having like Effects of Wicket Gates on Pump Performance
rotational speeds and capacities. The general
category of centrifugal pumps is: Although wicket gates are provided on pump-
turbines primarily for controlling turbine load,
1. Centrifugal pumps (radial-flow) with the plot of pump characteristics for pump-
radial discharge having low values of spe- turbines versus wicket gates (represented by
cific speed-less than 4,000 gal/min (77 dashed lines on figs. 5, 6, and 7), also shows
m3/s). The hydraulic passages in centrifu- that wicket gates are beneficial for pump opera-
gal pump impellers are relatively long and tion. During pump operation, the position of
the cross sections relatively small. As the the wicket gates is usually set at the point
specific speed decreases, the passages be- where the best efficiency can be obtained-at
come longer. the given head-with decreasing gate opening
2. Diagonal flow (mixed-flow) pumps correction for an increasing head. Under cer-
having specific speeds in the range of 4,000 tain conditions, such as pumping at low head,
to 8,000 gal/min (77 to 155 m3/s). They the gate position is adjusted to decrease the
have axial and radial components of veloc- power input or to reduce capacity for prevent-
ity at the impeller discharge. ing undue cavitation.
3. Propeller pumps (axial-flow) with When operating at heads other than best effi-
axial discharge having specific speeds ciency head, the decrease in pump efficiency for
greater than 8,000 gal/min (155 m3/s). The pump-turbines with wicket gates is less than
hydraulic passages through the impeller the decrease in efficiency of pumps without
are relatively short and larger in cross wicket gates. Also, at shutoff head the conver-
section. sion of velocity head to pressure head is more
Upon comparison of low specific speed pumps efficient for a pump-turbine with wicket gates;
with high specific speed pumps, figure 4 shows thus resulting in a higher shutoff head (gates
that for a high specific speed pump, the best closed) and a reduced power input than for a
efficiency point occurs near zero head and maxi- comparable pump without wicket gates.
mum discharge. The slope of the head versus
discharge curve for a high specific speed pump
will rise relatively steep from the best efficiency Submergence of Unit
point to shutoff head, and the power input will
increase with increasing head. For a low spe- To prevent excessive cavitation in pump-
cific speed pump, the best efficiency point will turbines, submergence requirements are more
UNIT SELECTION 21
demanding for pump operation than for turbine Although critical sigma increases with increas-
operation. The term customarily used for de- ing specific speed, cavitation can be tolerated at
scribing the effects of cavitation on unit per- the lower heads which are usually associated
formance or similarity of cavitation conditions with high specific speed pumps. The destructive
between machines having similar geometry and effects of cavitation increase with the cube of
hydraulic characteristics is defined as the the head [‘7].
Thoma sigma (a) : Figure 9 shows how critical sigma varies with
Q=- NPSH (6)
head for several large pumps and pump-
H turbines. The relationship of critical sigma with
where : specific speed shown by the expressions on fig-
H=head developed (pump) or absorbed ure 8 can be considered a general law, but the
(turbine), ft (m), design of an impeller for a particular specific
NPSH=net positive suction head at some speed can be varied to some extent by varying
location, ft (m) , and the throat diameter and the impeller vane en-
o,,=critical sigma value at which there trance angle to obtain the desired suction per-
is an abrupt decrease in perfor- formance. This variation in design of suction
mance of the hydraulic machine. performance is the reason sigma curves cross
NPSH (net positive suction head) of the each other, as shown on figure 9, for impellers
pump is defined as: of different specific speeds. The interrelations,
nevertheless, can be approximated by the gen-
NPSH=H,+H,-H,--HI (7) eral law of critical sigma versus specific speed.
where : Suction performance can be improved by sacri-
H,=static draft head with reference to tail- ficing pump efficiency [ 161.
water surface above impeller/runner Localized cavitation usually occurs at sigma
centerline, ft (m) , values higher than the critical sigma values. Al-
H,=atmospheric pressure head for altitude though localized cavitation is too limited to
at pump suction supply, ft (m), have an appreciable eff,ect on the pump effi-
H,=vapor pressure head of water for highest ciency, it is of concern since sufficient material
expected temperature, ft (m), and can erode from an impeller to affect the struc-
H,=head loss in the pump suction line and tural integrity of the impeller. The Bureau de-
impeller approach, ft (m) . fines excessive cavitation as the removal of
Table 4 compares critical sigmas at the same 0.00004 pounds of metal per operating hour
head for both pump and turbine operation for per square foot of impeller/runner throat area
three of the Bureau’s reversible units. The (at D2) or:
values were obtained from manufacturers’ Pounds= 4.0 lo-” (hours)
l (area, ft2) (8)
model tests. Kilograms=19.5 10m5(hours)
l (area, m2)
TABLE I.-Comparison of pump and turbine critical The above formula is for aluminum bronze
sigmas and stainless steel. For carbon steel the allow-
Pump BE head able rate of metal removal is four times greater.
Pump-turbine ft Turbine gcr Pump ver
m The conditions at which cavitation is first ob-
Flatiron 250 76.2 0.05 0.10 served in pump model tests, using a transparent
Grand Coulee 287 87.5 .07 .13 suction tube, are defined as sigma begin (ub).
Mt. Elbert 440 134.1 .08 .17 The dashed line on figure 8 represents the
sigma begin values obtained by a hydraulic
The table reveals that substantially more sub- equipment manufacturer [16].
mergence is required for pump operation than As a compromise between the deep setting
for turbine operation. required of pumps for eliminating cavitation
Figure 8 shows critical sigma as a function of and the likelihood of attendant excavation and
specific speed at best efficiency pumping head. structural costs, units under heads of 400 ft
22 ESTIMATING REVER’SIBLE PUMP-TURBINE CHARACTERISTICS
Grand Coulee P/G7k61267 (67) (1900 (53.6) (200 12640 (51) 81.6 1 67,:
Mt.Elbert P/G I IWO (1310 13200 (90.7) II60 12240 (‘43.3) 1
Yidono 1240 (73) 12700 (76.6) 1 I50 13GOO
Omoriaa*a 1360 (110) 1390 (II) IWO II960 (37.9) 1 89 16, loo (l3.5)1 ‘J-(z.c
Ludinaton 1305Yin (93) III.IW (314) 1112.5 1366CUax (66.9)1 27.5 (8.575)
I I I I I I I
most efficient, this value is assumed for the The rotational (synchronous) speeds close to
first trial. 636 are 600 and 720 r/min. Because ndH value
In the example, limitations of size, speed, of 80,000 gal/min (852 m3/s) (see fig. 3) is
or submergence are not placed on the unit beyond the current experience limit at a specific
selection. speed of 2,500 gal/min (48.4 m3/s), a rotational
The turbine discharge (QJ at full gate is speed of 600 r/min is selected. Also, the num-
calculated from : ber of poles which gives 600 r/min is divisible
by four. To maintain best efficiency head and
P=“W=( QtHyrlt550 (U.S.)
1,341) (11) discharge for the design conditions, pump spe-
cific speed (the required parameter) should be
QtHynt (metric) adjusted by the ratio of rotational speeds:
MW=102 (1,000)
Qt= MW (1,341) 100 (1,341)
0.1134 hd nt = 0.1134 (1,000) 0.89 n,,=2,500 g =2,358 gal/min (45.6 m3/s)
=1,329 ft?/s ( )
MW 100 If a specific speed value of 2,500 gal/min is
= 9.804 - lo3 hd qt = 9.804 * 10-3 (305) 0.89 used at 600 r/min, either pump best efficiency
=37.6 m3/s head or discharge and power will change. On
Referring again to table 5, an assumed ratio figure 10, +l equals 1.04 at a pump specific
of unity is used for turbine output to pump in- speed of 2,358 gal/min.
put at design head. This power ratio (Pt/PBEr) The impeller/runner diameter ( D1) calcula-
can be adjusted, within limits, by the pump- tion is:
turbine design or wicket gate position to obtain
a balance between motor input and generator $1 W)“2 1.04 ww 1’2 -8 3g4 ft
output over the operating range. D1=6.53 lo-3 n =6.53 * lo3 (600)- ’
l
is the same for both customary and metric cal- With reference to figure 14, spiral case dimen-
culations : sions are calculated :
nsp<HBE>S/4 2,500 (1,000)3’4 A~1.3 (8.394) z10.912 ft (3.326 m) radius
n= (&,,I 1/Z =(60 . 7.48 . 1,088) l,~=~~~ r/min B~1.2 (8.394)=10.073 ft (3.070 m) radius
C=l.l (8.394) = 9.233 ft (2.814 m) radius
nspWBE) 2/4 48.4 (305) 314 E=l.O (8.394) = 8.394 ft (2.558 m) radius
=636 r/mm
= (&,,)I/2 = (30.8)“2 G=0.6 (8.394) = 5.036 ft (1.535 m) dia
UNIT SELECTION 25
hence :
A+C=20.145 ft (6.140 m) dia
B+E=18.467 ft (5.628 m) dia
Therefore, longitudinal and transverse dimen-
sions of the spiral case will be 20 by 18.5 ft (6.1
by 5.7 m) , respectively.
Figure 8 and equations (6) and (7) are used
to calculate the required minimum submergence
(distributor centerline to minimum tailwater at
best efficiency head) :
0~~7.2 l 10-O (n,) 4/3=7.2 1O-G(2,358) 4/3=0.23
l
relation between discharge, head, speed, and Stepanoff [2] expressed the theoretical shut-
gate opening in four quadrants or modes of off head (H,,) of an impeller as a function of
pump-turbine operation. The diagram includes the diameter and rotational speed, and is inde-
all combinations of variables which a pump- pendent of the specific speed. Shutoff head can
turbine is likely to encounter. Head-discharge be calculated by the following formula:
trends may be more readily interpreted from
figures 16 and 17, as both coordinates of the (14)
four-quadrant diagram (fig.19) are shown as where :
a ratio of two variables.
g=gravitational constant (acceleration),
The quadrants are numbered in the sequence ft/s2 (m/s2),
as direction of flow and sense of rotation en- H,,=shutoff head, ft (m),
countered by the pump or pump-turbine after a V=peripheral velocity of the impeller at D1,
pump power failure. The quadrants do not ft/s (m/s), and
necessarily have to be followed in sequence to k=an efficiency for the conversion of veloc-
arrive at a particular state, as the head and ity head to pressure head (about 0.58
magnitude and sense of rotational speed define for pumps without wicket gates).
the state of the system. The quadrants and con-
ditions are described as follows: For pump-turbines with wicket gates, the
shutoff heads are higher than values calculated
I. Normal Pumping with the above 0.58 efficiency. Presumably, this
A. Flow in pump direction higher shutoff head occurs because the wicket
B. Rotation in pump sense gates restrict the volume in which the water
II. Energy Dissipation circulates, resulting in a higher velocity to
A. Flow in turbine direction pressure conversion efficiency. Furthermore,
B. Rotation in pump sense the assumption of constant conversion efficiency
III. Turbine regardless of specific speed does not seem strict-
A. Flow in turbine direction ly to apply to pump-turbines with wicket gates.
B. Rotation in turbine sense The short, broad impeller passages of high spe-
cific speed pump-turbines probably allows more
IV. Reverse Pumping
fluid circulation within the impeller passages at
A. Flow in pump direction
shutoff than do low specific speed pump-tur-
B. Rotation in turbine’sense
bines.
A pump or pump-turbine will not go into the The lower velocity to pressure conversion effi-
fourth quadrant after a power failure because ciency for high specific speed pump-turbines
the region above the zero torque (runaway) line (compared to low specific speed pump-tur-
requires a power input; however, if a vertical bines), when rotating in the turbine direction,
gate characteristic curve occurs in the zero serves as an advantage for turbine operation
torque zero flow regime, the machine is unstable because it permits turbine operation at a lower
and can operate in either the normal turbine head for a given single speed.
(III) or reverse pumping (IV) quadrants for a In addition to a turbine efficiency improve-
given head and speed. A pump-turbine with a ment resulting from decreased turbine rota-
vertical gate characteristic curve will be un- tional speed as described in the speed section,
stable for the turbine speed-no-load gate condi- figure 19 shows there is an increase in turbine
tion. Since the unit is connected across the line, power output in certain head ranges with a
it can go into reverse pumping while drawing lower turbine speed. See figure 2, which is
power from the system [lo]. The situation based on the same pump-turbine unit as the
probably occurs when the pump shutoff head four-quadrant diagram (fig. 19).
(at small gate openings), with rotation in the The k values for the Bureau’s two pump-
turbine direction, exceeds the static hydraulic turbine installations with wicket gates are
head. shown in table 6.
PERFORMANCE 29
150 I
Pump characteristics with turbine characteristics
6 superimposed for a single speed pump-turbine
140 (San Luis) without wicket gates.
a nsp=2,000 gal/min (38.7 m3/s units)
I I 1 I
I
\
I
- IOO-
l
v
z 80 -
W
0
- 70.
Ia.
IL
W
I /l I
FIGURE 16.-Turbine head, discharge, and eficiency superimposed on pump characteristics - n,, = 2,640.106-0371.
HEAD ‘and POWER RATIOS -‘OISCHARGE RATIO
140
Pump characteristics with turbine c aracteristics PgEP= Pump input at best efficiency head
20 -
superimposed for Grand Coulee P/G 7 a 8 - --- = Turbine output to pump input (at the same heads)-
with wicket gates. -.-.T- p+‘pp
IO
-nsp /
gol/min , I m3&
(51. , ,
) units
0
0 IO 20 30 40 50 60 70 xl 90 100 IlO I20 Is0 140 150 160 170 160
FIGURE 17.-Turbine head, discharge, and power superimposed on pump characteristics - nsP = 2,640.106-D-372.
32 ESTIMATING REVERSIBLE PUMP-TURBINE CHARACTERISTICS
--*
Pumping
Unit P/G I
nip= 2240 gal/min units
=43.3 m/s units
a,, = 33.2 U.S. hp units
= 127 kW units
/I1
I00 Best efflcl---..
/
I. Normal Pumping
\v @i,”
\\ \\ 452
\\
\ \\
J\,,
loo m
Max. output n.Gz Rotation in pumping
c-7
=. -K&F Rotation in “EP direction
’ nEEP turbine
direction
Shaft Torque-%0
PUMP-TURBINE
FOUR-QUADRANT DIAGRAM
llI.Generoting
TABLE 6.-Eflciency factor (k) for the conversion of on the fluid in these chambers.
welocitg head to pressure head
The hydraulic thrust curve shows the maxi-
Mt. Elbert Grand Coulee mum net hydraulic downthrust, but for some
n,,=2,240 ft- n,,=2,240 ft- conditions a net upthrust can occur. This net
gal/min ‘rgal/min
Condition (43.3 m-m*/s) (51.1 m-m8/s) upthrust can be of the same magnitude as the
net downthrust values shown on the curve. De-
Normal pump rota-
tion-zero gate 0.68 0.66
signers attempt to minimize the net upthrust,
Normal pump rota- since the net upthrust can exceed the weight of
tion-100 percent the rotating parts and lift the rotating parts
gate .62 .51 off the thrust bearing [lo].
Turbine rotation- It may be oversimplification to relate these
zero gate .45 .37
characteristics to a single function, D1, but this
Turbine rotation-
100 percent gate .32 .20 term gives as good a correlation as other more
complicated functions which take into account
criteria such as head and specific speed.
Weight, Inertia, and Hydraulic Downthrust
The scatter of points on the figures is prob-
Figures 20 through 23 show impeller weight ably because each manufacturer’s particular
( W) , pump-turbine weight ( W,,) , impeller design and fabrication techniques have as great
moment of inertia (WR2) , and hydraulic thrust an effect on the variables considered as do the
(Fh) as a function of impeller diameter (D1). basic design parameters-head, speed, dis-
All pumps and pump-turbines plotted on the charge, or specific speed. For instance, the de-
curves have spiral cases, with the exception of cision whether to cast or fabricate an impeller
the Snake Creek Unit. The Snake Creek Unit is can make a substantial difference in the final
a vertical column pump having a bowl-type weight.
diffuser.
The values obtained from the respective
Hydraulic Similarity
curves are only rough estimates, but it is de-
sirable to have these figures available in the For geometrically and hydraulically similar
early stages of planning. The generator-motor machines (i.e., equal specific speeds), certain
moment of inertia, in addition to the impeller performance data obtained for a unit of a given
complement, is used in the calculations to de- size and speed can be used to determine the
termine transient pressures during pump power performance for other size units and different
failure or turbine load rejection. The impeller rotational speeds. The following laws give the
and pump-turbine weights are used to obtain relationship of a point on a characteristic curve
cost estimates. The hydraulic thrust affects the for a given rotational speed and diameter with
generator-motor design with respect to the respect to an equivalent point on another curve
thrust bearing and bearing support. with a different rotational speed and/or diam-
The hydraulic thrust shown on figure 23 eter.
depends largely on factors other than the basic
hydraulics. The clearances at the periphery of 1. The affinity laws used for pump-turbine
the impeller and at the wearing rings, the sur- scaling are :
face configuration in the annular chambers be- V2 n2 Dt
tween the head cover and impeller crown and Tq= n, l K
KILOGRAMS YDS
s-4
VERSUS
.-2 IMPELLER DIAMETER
. * Pumps
l Pump- turbines
--IO' Oroville
--9
-8
-7 +Mt. Elbert P/G I
-6
,-5
.-4 ~
1 Grand +$e PI-P6
.-5
w Grand Coulee P/G 7 8 C
3 -2
I
k
3
w
3
-lo*
.-9
E W= 129(DlILA LB.
--5
.-4
--3
.-2
--IO'
--5
I I I I I I I ,I111 I I I I
0.5 I 1.5 2 3 4 5 6 7890 I5 METRES
IMPELLER DIAMETER-D!
;r
KILOGRAMS POI UNOS
I
I! !Ill
PUMP AND PUMP-TURBINE WEIGHT- I
i VERSUS /
IMPELLER DIAMETER I V
/
* Pumps
I I I IIII /I
1 104.
9
i 8
7.
6
-San Luis
5 1
'2 I/ **Grand Coulee PI- P6 1 1
4
3,
DOSjiws~~ I I +
lo'
9 2
#t=-Snake Creek
e
7
6
5
IOJI I 1
.-sC Welton Mohawk .I
4
8 No. I2- /
without wicket gates
7-
3 I
0'
,
2 3 4 5 6 78910 20 30 40 50 FEET
I 1 I I I I I I,,,, I I I ,
0.5 I I.5 2 3 4 5 6 76910 I5 METRES
IMPELLER DIAMETER-D,
FIGURE 21.-Pump and pump-turbine weight vs. impeller discharge diameter. 106-D-676.
PERFORMANCE
KG*M’ LB l f‘T’
c IO’
9
a
3 7
6
WR’-IMPELLER DIAMETER 1 / LMt: Elb;?rt i&i 1
5
2
- * Pumps
l Pump - turbines
105
I
9
2 _-
6
Grand Coulee’ PI 1 P$ ’
7
Grond Coulee P/G 7 a 8
6
5
IO6 -
4 9 -
6 -.
3 7
Sna 7- !ek
6 -
- *H -Tro&
5 -I-
2
-
I
- I t WR2= [
i3(D,)45 (U.S.)
115(DI)4s (metric)
3ti ron
IO’ r-t--
9
9
IO’
4
9
6
3 7
3- I
IO’ !
I
9
2t
9
Welton Mohawk No. I--r
1 I I I I I I Illll I I I 1
0.1 I I.5 2 3 4 !5 6 7 6 9 IO I5 METRES
IMPELLER DIAMETER-D,
.-5
--4
.-3
s ----___
.-2 I
4
.-2 F
4
-IO4
2
.-9
,-6
--7
.-6 I ienotor Wash, ( I/) ) 1 )
.-s I VI YIIII
10
,-4 9
6
r-
.-3
6
5
.-2
4
Welton Mohawk No. I
3
II
--Chandler
--IO8
2.
‘CM ti?e
,--- Glendive
.-I
’ 10
i JLC ** II I I I> I,,
2 3 4 5 6 7 0910 IS 20 30 40 50 FEET
1 I I t , I
a5 I I I , I I I 1 (
1.5 2 3 45 7 IO I5 METRES
IMPELLER DIAMETER-D,
2. The turbine homologous equations are cus- I horsepower (metric) =1.014 horsepower
tomarily written : (U.S.)
1 horsepower (U.S.) =550 foot-pounds per
For constant diameter : For constant head : second
~0.7457 kilowatt
1 gallon (U.S.) ~0.003 785 cubic meter
1 pound (mass) ~2.204 622 kilogram
1 foot=O.3048 meter
n (&,,I li2
%= (J3#4
nst=n(Pd)1'2
(hd 6'4
power factor
1 horsepower (metric) =75 meter-kilograms
per second
1 kilowattrl01.971 meter-kilo-
grams per second
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40