performance of turbines
TRANSCRIPT
Performance of Turbines
Lecture slides by
Sachin Kansal
NATIONAL INSTITUTE OF TECHNOLOGY
KURUKSHETRA
2
Introduction A turbine operates most efficiently at its design point, i.e.,
at a particular combination of head, discharge, speed andpower output.
But in actual practice hardly any turbine operates at itsdesigned parameters.
To predict the behavior of the turbine operating at varyingconditions of the head, discharge, speed and poweroutput, the results expressed in terms of quantities thatmay be obtained when the head on the turbine isreduced to unity (1m)
The conditions of the turbine under the unit head aresuch that the overall efficiency of the turbine remainsconstant
A turbine can be compared with the help of the followingcommon characteristic
3
Unit Quantities
Unit Quantities are refer to the turbine parameters which
are obtained when a particular turbine operates under a
unit head at constant efficiency
Unit Quantities make an effort to find other parameters at
the changed head on the assumption that efficiency of
the turbine is not changed
For same efficiency, velocity triangle for actual working
head and for unit head are similar
VfVVr
uVw
Vwu
Vfu
VruVu
uu
Fig (a): Inlet Velocity
triangle for Francis
Turbine, working at
actual head
Fig (b): Inlet Velocity
triangle for Francis
Turbine, working at
unit head
4
Unit Quantities
Unit Speed
Unit Discharge
Unit Power
Unit Force
Unit Torque
5
Unit Speed (Nu)
Speed of a turbine working under a unit head (1m) is
known as unit speed
Let N = Speed of a turbine under a head H,
H = Head under which a turbine is working,
u = Tangential velocity.
or …………..(1)
As triangle (a) is similar to (b) then, or
Put in (1)…… or
or or
g(1)
uV
gH
uV uwu w
H
1.
V
V
u
u
wu
wu
wu
u
w
V
u
V
u
H
1.
u
u
u
u
u
u
H
1
u
uu
H
1
ND 60.
.60ND u
H
1
N
.Nu
H
NuN
u
wu
w
u
u
V
V
huh
6
Unit Discharge (Qu)
Discharge through the turbine working under a unit head
(1m) is known as unit discharge
Let Q = Discharge through the turbine under head H,
H = Head under which a turbine is working,
u = Tangential velocity.
or .....................………..(2)
As triangle (a) is similar to (b) then, or
Put in (2)……
or
f
fuu
V
V
Q
Q
fu
u
f
V
u
V
u
u
u
Q
Q uu
H
1
Q
.Qu
H
QQu
u
u
V
V u
f
fu
fuu
f
DBVkQ
DBVkQ
7
Unit Power (Pu)
Power produced by turbine working under unit head (1m)
is known as unit power
Let P = Power produced by the turbine under head H,
H = Head under which a turbine is working,
or
or
HHH
11.
Q
Q
P
P u u
2/3
u 1
P
.P
H
2/3u
PP
H
0
0
.1)(WQP
(WQH)P
uu
8
Unit Force (Fu)
Tangential force exerted on the runner vanes working
under unit head (1m) is known as unit force
Let F = Force exerted on the runner vanes under head H,
H = Head under which a turbine is working,
or
or
HHu
u
H
u 1.
1.
1
QV
VQ
F
F
w
wuu u
H
1
F
Fu
H
FFu
wuuu
w
VρQF
ρQVF
9
Unit Torque (Tu)
Torque transmitted to the runner working under unit head
(1m) is known as unit torque
Let T = Torque transmitted to the runner under head H,
H = Head under which a turbine is working,
or
H
1
F
F
T
T u u
H
TTu
R XρQVR XFT
R XρQVR X FT
wu u u
w
10
Use of Unit Quantities
If a turbine is working under different heads, the behavior
of the turbine can be easily known from the values of the
unit quantities
Let,𝐻1 , 𝐻2 = Different heads under which a turbine
works, (both known)
𝑁1 (known), 𝑁2 (unknown) = Corresponding speeds,
𝑄1 (known),𝑄2(unknown )= Corresponding discharge, and
𝑃1(known),𝑃2(unknown)=Corresponding power
F1(known),F2(unknown)=Corresponding force
T1(known),T2(unknown)=Corresponding torque
From the definition of unit quantities, we get
2
2
1
1u
2
2
1
1u
3/22
2
3/21
1u
2
2
1
1u
2
2
1
1u
H
T
H
TT ;
H
F
H
FF ;
H
P
H
PP ;
H
Q
H
QQ ;
H
N
H
NN
11
Use of Unit Quantities
and hence
Hence, if the speed, discharge, and power developed by
a turbine under the head are known, then by using above
relations the speed, discharge and power etc. developed
by the same turbine under a different head can be
obtained easily [Note : Assumption of same efficiency at different head, is not true for fixed
vanes type of turbine]
1
2
21
2
23/2
1
3/22
2
1
22
1
22
H
HT ;
H
HF ;
H
HP ;
H
HQ ;
H
HN
12
Specific Speed
It is defined as the speed of a turbine which is identical in
shape, geometrical dimensions, blade angles, gate
openings, etc. with the actual turbine but of such a size
that it will develop unit power when working under a unit
head.
The specific speed is used in comparing the different
types of turbines as every type of turbine has a different
specific
13
Derivation of Specific Speed (Ns)
The overall efficiency of any turbine is given by,
∴ 𝑃 ∝ 𝑄𝐻 (𝑎𝑠 𝜌 𝑎𝑛𝑑 𝜂𝑜 𝑎𝑟𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡)
As specific turbine is identical to actual turbine in every
respect, its velocity triangle is identical to the actual
turbine under unit head i.e. unit head turbine
1000
1000
PowerWater
PowerShaft 00
gQHP
gQH
P
Parameter Symbol
for unit
head
turbine
Symbol
for
specific
turbine
Diameter of turbine runner 𝐷u Ds
Width of turbine blade Bu = nDu BS= nDs
Power produced by turbine Pu Ps
Flow velocity of water through runner Vfu Vfs
Discharge of water through turbine Qu Qs
Vwu =Vws
Vfu
=Vfs
Vru
=VrsVu =Vs
14
5/4s
3/2u us
us
s
u
2
2
2
s
u
s
u
fs
fu
s
u
uuu ss
us
H
PN N
.H
P N.PN
(1)in Put ,P 1,P As
P
P
)(P
P
)(P
P
V
V.
.1.
.1.
P
P Now,
(1)........................................ N.60
ND
60
ND
uu
0
0
H
N
D
D
D
D
D
D
Ds
D
nDD
D(nD)
BD
DB
A
A
A
A
Q
Q
wQ
wQ
D
DN
s
s
s
ssss
s
u
s
u
s
u
s
u
s
s
So, specific speed increases with decrease in head,
Specific speed of Pelton Turbine is least and Kaplan is
maximum
15
Significance of Specific Speed (Ns)
Specific speed plays an important role in selecting the
type of turbine.
Also, the performance of a turbine can be predicted by
knowing the specific speed of the turbine
The types of turbines for different specific speed are
given in the following table
16
Runaway Speed
It is the maximum speed that a turbine attains under
designed head and gate opening, when the governing
system being disconnected and the load reduces to zero
By experimentation
where N= Normal Speed
Type of Turbine Runaway Speed
Pelton Turbine 1.8-1.9 N
Francis Turbine 2.0-2.3 N
Kaplan Turbine 2.5-2.9 N
17
Characteristics of Turbine
The turbines are generally designed to work at particular
designed conditions
But often the turbines are required to work at different
conditions
Therefore it is essential to determine the exact behaviour
of the turbines under the varying conditions.
“Characteristic curves of a hydraulic turbine are the
curves, with the help of which the exact behaviour and
performance of the turbine under different working
conditions can be known”
These curves are plotted from the results of the test
performed on the actual turbine or its model under
different working conditions
18
Characteristics of Turbine
The important parameters which are varied during a test
on a turbine are:
• 1. Speed (N)
• 2. Head (H)
• 3. Discharge (Q)
• 4. Power (P)
• 5. overall efficiency (ηo)
• 6. Gate opening (i.e. the percentage of the inlet
passages provided for water to enter the turbine)
Out of these six parameters speed, head and discharge
are independent parameters.
19
Characteristics of Turbine
Different characteristic curves are obtained by keeping
one independent parameter constant and variation of any
parameter with respect to the remaining two independent
parameters.
The following are the important characteristic curves for a
hydraulic turbine:
1. Main Characteristic Curves or Constant Head
Curves
2. Operating Characteristic Curves or Constant Speed
Curves
3. Muschel Curves or Constant Efficiency Curves
20
Main Characteristic Curves or Constant Head Curves
Main characteristic curves are obtained by maintaining aconstant head and a constant gate opening on theturbine
The speed of the turbine is varied by admitting differentrates of flow by adjusting the percentage of the gateopening. The power (P) developed is measuredmechanically.
From each test the unit power Pu, the unit speed Nu, theunit discharge Qu and the overall efficiency ηo aredetermined.
The characteristic curves drawn are:
i. Unit discharge vs unit speed
ii. Unit Torque vs unit speed
iii. Unit power vs unit speed
iv. Overall efficiency vs unit speed
i.Unit discharge vs unit speed
For the Pelton wheel, since Qu depends only on the gate
opening (spear position), So Qu vs Nu plots are horizontal
straight lines.
However, for reaction turbines discharge is the product of
area and velocity of flow. At same gate opening area is
same then Q is directly proportional to Vf. So as speed(N)
increases Vf also increases in order to keep triangle
similar and hence discharge Q. 21
Pelton Turbine
Kaplan Turbine
i.Unit discharge vs unit speedBut in Francis turbines, Qu vs Nu are
drooping curves, thereby indicating
that as the speed increases the
discharge through the turbine
decreases. This is so because in
these turbines a centrifugal head is
developed which retards the flow.
On the other hand for high specific speed Kaplan turbine,
since the flow is axial there is no such centrifugal head
developed which may cause the retardation of flow.
These curves do not passes through 0, as some discharge
is required to overcome the friction to start turbine
22
Francis Turbine
ii.Unit Torque vs unit speed
As F depends upon relative velocity Vr i.e. V-u, So as u
increases F decreases
Force is maximum when when body is stationary i.e u=0
Force is minimum when body is moving with runaway speed, and
hence torque varies
For Pelton turbine, Q is constant for particular gate
opening, So Torque varies linerly with speed, whereas
parabolic in case of reaction turbine 23
Pelton Turbine Reaction Turbine
Tu
Nu Nu
Tu
G=1
G=0.75
G=0.25
G=0.5
G=1
G=0.75
G=0.5
G=0.25
iii. Unit power vs unit speed
As P= Tω
So, P =0, when any of these is zero
P Vs Nu is parabolic with power zero at Nu=0 and at T=0
i.e at runaway speed
24
iv. Overall efficiency vs unit speed
25
constant is H If ,00
Q
P
WQH
P
For Pelton Turbine, Q is constant with speed and for
reaction also, it is almost same, then efficiency vs speed
curves are similar to power vs speed
26
Operating Characteristic Curves or Constant Speed Curves
Operating characteristic curves are plotted when the
speed on the turbine is constant
In the case of turbines, the head is generally constant.
Hence the variation of discharge, power, efficiency are
calculated and plotted as
i. Efficiency vs Load
ii. Power vs Discharge
iii. Efficiency vs Discharge
i. Efficiency vs Load
From obsevation, Pelton and Kaplan turbine have high
efficiency for larger variation of loads as compared to
Francis and Propeller turbine as shock loses are
prodominant in these due to fixed blades
Curve passes through zero as power produced is zero at
no load
27
ii. Power vs Discharge
The power curve for turbines shall not pass through the
origin because a certain amount of discharge is needed to
produce power to overcome initial friction.
iii. Efficiciency vs Discharge
Also originate from same point as that of power
It is not linear because variable types of losses like
hydraulic, volumetric, mechanical etc. are there28
QP
QT
TP
TP
But
So,
constant is speed,constant At
So, power increases linearly
from zero, when gate is closed
to maximum at full gate opening
Muschel Curves/ Constant Efficiency Curves/ Universal
curve/ Iso- efficiency curve
These curves are obtained from the speed vs. efficiency and
speed vs. discharge curves (main characteristic curves) for
different gate openings
• For a given efficiency there are
two values of speeds and two
values of discharge for a given
gate opening, these can be
plotted
• The procedure is repeated for
different gate openings and the
curves Q vs. N are plotted
29
Muschel Curves/ Constant Efficiency Curves/ Universal
curve/ Iso- efficiency curve
• The curves having the same
efficiencies are joined. The
curves having the same efficiency
are called iso-efficiency curves
• These curves are helpful in
determining the zone of constant
efficiency and for predicting the
performance of the turbine at
various efficiencies
30
31
Cavitation in Turbine In hydraulic turbine when, water while passing, comes in
region where the pressure of the liquid falls below itsvapour pressure( usually at outlet of turbine and inlet ofpump, bend of pipe, convex surface of curve vane), itstarts boiling and vapour bubbles are formed
These vapour bubbles when reach the region of higherpressure suddenly collapse to create a cavity in thatplace
The liquid near the bubble goes into that cavity orvacuum, which create a very high local pressure
The metallic surfaces, above which these vapour bubblescollapse, is subjected to these high pressures, whichcause pitting action on the surface.
Thus cavities are formed on the metallic surface and alsoconsiderable noise and vibrations are produced
32
This phenomena is called as cavitation
Effects of Cavitation
1) The metallic surfaces are damaged and cavities are
formed on the surfaces.
2) Due to sudden collapse of vapour bubble, considerable
noise and vibrations are produced.
3) The efficiency of a turbine decreases due to cavitation.
4) Due to pitting action, the surface of the turbine blades
becomes rough and the force exerted by water on the
turbine blade decreases. Hence the work done by water or
output horse power becomes less and thus efficiency
decreases.
Cavitation is the phenomena of formation, growth and
collapsing of vapour bubbles in the flowing liquid
33
In turbines, only reaction turbines are subjected to cavitation.
In reaction turbines, the cavitation may occur at the outlet
of the runner or at the inlet of the draft tube, where the
pressure is considerably reduced (i.e. , which may be
below the vapour pressure of the liquid flowing through
the turbine).
Due to cavitation, the metal of the runner vanes and draft
tube is gradually eaten away, which results in lowering
the efficiency of the turbine.
Hence the cavitation in a reaction turbine can be noted
by a sudden drop in efficiency.
In order to determine whether cavitation will occur in any
portion of a reaction turbine, the critical value of Thoma’s
cavitation factor (𝜎) is calculated
34
Thomsa’s Cavitation No.
where, H= Net head available
Ha= Atmospheric pressure head
Hv= Vapour pressure head of liquid
h= height of the turbine above the tail race
Cavitation factor/no. is useful for proper selection of
turbines and to decide the turbine with respect to tail race
Experimentally, it depends upon specific speed of turbine
For particular value of specific speed, it can be very much
reduced without effecting efficiency
But if it reduced beyond a certain value i.e. critical
cavitation factor ( )there is decline in efficiency
H
HhH va
c
2)445
(625.0Ns
c
35
Detection of Cavitaion
1) By photography in the interior of turbine
2) By measuring noise and vibration level
3) By studying the hydraulic performance of turbine
Methods to prevent Cavitation
1) The pressure of the flowing liquid in any part of the
hydraulic system should not be allowed to fall below its
vapour pressure.
2) The special materials or coatings such as aluminum-
bronze and stainless steel, which are cavitation resistant
materials, should be used
3) Avoid sharp corners or curvature to avoid vorticies,
eddies etc.
4) Install the turbine at lesser height than given by safe
value of suction height
36
5) Velocity at outlet of the turbine should be as small as
possible, since velocity increases the suction pressure
6) Temperature of the liquid should be low as pressure
rises with increase in temperature
7) Proper machining of the parts should be done, since
high finish leads to low chance of cavitation
37
Governing in Turbine
The governing of a turbine is defined as the operation by
which the speed of the turbine is kept constant under all
working conditions (irrespective of the load variations)”
The governing of a turbine is necessary as, a turbine is
directly coupled to an electric generator, which is
required to run at a constant speed under all fluctuating
loads conditions.
It is done automatically by means of a governor, which
regulates the rate of flow through the turbines according
to the changing load conditions on the turbine
The governor used in hydraulic turbines should be very
strong as it has to deal with the water coming at a very
large force and huge quantity
38
All type of turbines use oil pressure governor, whichconsists of the following parts:
Oil pump (Gear pump), which is driven by the powerobtained from the turbine. It supplies oil at high pressure
The servo motor, also known as a relay cylinder, whichconsists of a cylinder in which piston reciprocates underthe action of oil pressure. It is connected at both endswith the distributor valve through the pipelines
The distributor valve or control valve or relay valve, whichslides whenever load changes and thereby allows the oilto go to either side of the servomotor.
The centrifugal governor or actuator, which is connectedto the turbine main shaft through a belt or gears
39
Governing of Pelton Wheel
In Pelton wheel turbine, the quantity of water supplied by
the nozzle can be regulated by Spear Regulation method
Spear Regulation
It consists of a nozzle in which spear moves to and fro by
the action of the servomotor piston and controls the
quantity of water at changing demands.
This movement is useful when the fluctuations in load are
small. But when the load changes suddenly, a sudden
change in the nozzle area causes a water hammer in the
penstock. Therefore a simple regulation system is not
used in modern turbines where fluctuations in the load
are sudden.
41
Working
When the load on the generator decreases, the speed of
the generator increases. Hence the speed of the turbine
also increases beyond the normal speed
The centrifugal governor which is connected to the
turbine's main shaft will be rotating at an increased speed
and hence centrifugal force on the fly ball increases and
it moves upward. The sleeve of the governor will also
move upward. As the sleeve moves upward, a horizontal
lever turns about the fulcrum and the piston rod of the
control valve moves downward. This closes the valve V1
and opens the valve V2 as shown in Fig.
The oil pumped from the oil pump to the control valve
under pressure will flow through the valve V 2 to the
servomotor and will exert force on the face A of the piston
of the relay cylinder
42
Working
Piston along with piston rod and spear will move towards
the right. This will decrease the area of flow of water at
the outlet of the nozzle and it will reduce the rate of flow
to the turbine which consequently reduces the speed of
the turbine
Meanwhile, the bell crank lever moves downward, the jet
deflector will operate and divert whole or part of the jet
away from the buckets
As soon as speed becomes normal, the fly balls, sleeves,
lever and piston rod come to its normal position.
43
Governing of Francis Turbine
The guide blades of the Francis turbine are pivoted and
connected by levers and links to the regulating ring.
The regulating ring is attached with two regulating rods
connected to the regulating lever
44
When the load on the turbine decreases, the speed tendsto increase, which moves fly balls upwards and thusraises sleeves
The main lever on the other side of the fulcrum pushesdown the control valve rod and opens port V1
Oil under pressure enters the servomotor from left andpushes the piston to moves towards the right
When the piston of the servomotor moves towards theright, the regulating ring is rotated to decrease thepassage between the guide vanes by changing guidevane angles
Thus the quantity of water reaching the runner bladesreduces and speed decreases to the normal speed
Sudden reduction in a passage between the guide bladesmay cause a water hammer which can be prevented byproviding a relief valve near the turbine which diverts thewater directly to the tailrace