BBaassiicc aanndd AApppplliieedd ... Data/Thermodynamics/Study/Chapter 13- Steam... · 1878, a...
Transcript of BBaassiicc aanndd AApppplliieedd ... Data/Thermodynamics/Study/Chapter 13- Steam... · 1878, a...
For more information log on www.brijrbedu.org
Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)
Copyright by Brij Bhooshan @ 2013 Page 1
BBaassiicc aanndd AApppplliieedd TThheerrmmooddyynnaammiiccss
CChhaapptteerr--1133 SStteeaamm TTuurrbbiinneess
PPrreeppaarreedd BByy
BBrriijj BBhhoooosshhaann
AAsssstt.. PPrrooffeessssoorr
BB.. SS.. AA.. CCoolllleeggee ooff EEnngggg.. AAnndd TTeecchhnnoollooggyy
MMaatthhuurraa,, UUttttaarr PPrraaddeesshh,, ((IInnddiiaa))
SSuuppppoorrtteedd BByy::
PPuurrvvii BBhhoooosshhaann
In This Chapter We Cover the Following Topics
Art. Content Page
13.1 Steam Turbine 3
13.2 Impulse Turbines
The Single-Stage Impulse Turbine
Velocity Diagram and Calculations for Impulse Turbine
Optimization of Turbine Stage
6
6
7
10
13.3 Methods of Reducing Wheel or Rotar Speed
Compounding in Impulse Turbine
The Velocity - Compounding of the Impulse Turbine
Pressure Compounding or Rateau Staging
Pressure- Velocity Compounding
11
11
12
13
14
13.4 Reaction Turbine 14
13.5 Stage Efficiency and Reheat Factor 16
References:
1. M. J. Moran and H. N. Shapiro, Fundamentals of Engineering Thermodynamics, 6e,
John Wiley & Sons, Inc., New York, 2008.
2. G. J. Van Wylen, R. E. Sonntag, C. Borgnakke, Fundamentals of Thermodynamics,
John Wiley & Sons, Inc., New York, 1994.
3. J. P. Holman, Thermodynamics, 4e, McGraw-Hill, New York, 1988.
4. F. W. Sears, G. L. Salinger, Thermodynamics, Kinetic theory, and Statistical
Thermodynamics, 3e, Narosa Publishing House, New Delhi, 1998.
5. Y. A. Cengel and M. A. Boles, Thermodynamics: An Engineering Approach, 2e,
McGraw-Hill, New York, 1994.
6. E. Rathakrishnan, Fundamentals of Engineering Thermodynamics, 2e, PHI Learning
Private Limited, New Delhi, 2008.
7. P. K. Nag, Basic and Applied Thermodynamics, 1e, McGraw-Hill, New Delhi, 2010.
For more information log on www.brijrbedu.org
Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)
Copyright by Brij Bhooshan @ 2013 Page 2
2 Chapter 13: Steam Turbines
8. V Ganesan, Gas Turbine, 2e, Tata McGraw-Hill, New Delhi, 2003.
9. Y. V. C. Rao, An Introduction to Thermodynamics, 1e, New Age International (P)
Limited, Publishers, New Delhi, 1998.
10. Onkar Singh, Applied Thermodynamics, 2e, New Age International (P) Limited,
Publishers, New Delhi, 2006.
Please welcome for any correction or misprint in the entire manuscript and your
valuable suggestions kindly mail us [email protected].
For more information log on www.brijrbedu.org
Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)
Copyright by Brij Bhooshan @ 2013 Page 3
3 Basic and Applied Thermodynamics By Brij Bhooshan
13.1 STEAM TURBINE
A steam turbine converts the energy of high-pressure, high temperature steam produced
by a steam generator into shaft work. The energy conversion is brought about in the
following ways:
1. The high-pressure, high-temperature steam first expands in the nozzles emanates
as a high velocity fluid stream.
2. The high velocity steam coming out of the nozzles impinges on the blades mounted
on a wheel. The fluid stream suffers a loss of momentum while flowing past the
blades that is absorbed by the rotating wheel entailing production of torque.
3. The moving blades move as a result of the impulse of steam (caused by the change
of momentum) and also as a result of expansion and acceleration of the steam
relative to them. In other words they also act as the nozzles.
A steam turbine is basically an assembly of nozzles fixed to a stationary casing and
rotating blades mounted on the wheels attached on a shaft in a row-wise manner. In
1878, a Swedish engineer, Carl G. P. de Laval developed a simple impulse turbine, using
a convergent-divergent (supersonic) nozzle which ran the turbine to a maximum speed
of 100,000 rpm. In 1897 he constructed a velocity-compounded impulse turbine (a two-
row axial turbine with a row of guide vane stators between them.
Auguste Rateau in France started experiments with a de Laval turbine in 1894, and
developed the pressure compounded impulse turbine in the year 1900.
In the USA , Charles G. Curtis patented the velocity compounded de Lavel turbine in
1896 and transferred his rights to General Electric in 1901.
In England , Charles A. Parsons developed a multi-stage axial flow reaction turbine in
1884.
Steam turbines are employed as the prime movers together with the electric generators
in thermal and nuclear power plants to produce electricity. They are also used to propel
large ships, ocean liners, submarines and to drive power absorbing machines like large
compressors, blowers, fans and pumps.
Turbines can be condensing or non-condensing types depending on whether the back
pressure is below or equal to the atmosphere pressure.
Normally a turbine stages is classified as
1- Impulse stage;
2- Reaction stage
An impulse stage is characterized by the expansion of the gas which occurs only in the
stator nozzles. The rotor blades act as directional vans to deflect the direction of flow.
Further they convert the kinetic energy of the gas in to work by changing the
momentum of the gas more or less at constant pressure.
A reaction stage is one in which expansion of the gas takes place both in the stator and
in the rotor. The function of the stator is the same as that in the impulse stage but the
function in the rotor is two fold
1. A rotor converts the kinetic energy of the gas in to work,
2. Contributes a reaction on the rotor blades.
The reaction force is due to the increase in the velocity of gas relative to the blades. This
results from the expansion of the gas during its passes through the rotor.
For more information log on www.brijrbedu.org
Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)
Copyright by Brij Bhooshan @ 2013 Page 4
4 Chapter 13: Steam Turbines
Classification
Based on the blade flow passage
In steam turbine thermal energy available with steam is converted in to kinetic energy
which in turned produces driving thrust on the shaft. Base upon the rotor blades the
flow passage may be of
1- Constant cross-section area type from blade inlet to exit;
2- Varying cross-section area type from blade inlet to exit.
Turbine having former type blading are termed as impulse turbine while later type are
in reaction type.
The mechanism of impulse and reaction forces getting by Newton’s Second law
F = m.a = m.(dV/dt)
F = mass flow rate × change in velocity
Tangential Force (Ft) = mass flow rate × change in tangential component of the velocity
The impulse force can be defined as the force because of change in tangential component
of velocity of fluid which may be due to change in direction or magnitude. Diagram 13.1
shows the impulse force generating because the use of the change in velocity of fluid.
Diagram 13.1
Diagram 13.1(a) the impulse force is available due to change in magnitude of velocity
and shall be given by the product of mass flow rate and change in velocity. In case B the
impulse force is generated due to change in direction of velocity and if the blade is
stationary and frictionless then there shall be no decrease in magnitude of velocity.
Reaction force is available when the tangential velocity of fluid is increased and is
opposite in reference to the direction of velocity.
In case Diagram 13.1(b), the total force exerted on the blade is actually a combination of
impulse and reaction. Impulse force is available in the entrance half of the blade where
jet impinges causing a force to right. While in the exit half the leaving jet exerts a
reactive force on the blade which also acts to right. Combined effect of the two forces on
the impulse force.
Reaction force available due to increase in tangential velocity of fluid can be seen in case
of nozzle due to acceleration of fluid.
Diagram 13.2
Based on cylinder flow arrangement:
a) Single flow single casing turbine;
Fr = m (0 V1) = m V1
V1 > 0
Fv
Fr
V0 = 0
Impulsive force due to change in direction of
velocity.
(b)
Impulse force due to change in
magnitude of velocity
(a)
For more information log on www.brijrbedu.org
Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)
Copyright by Brij Bhooshan @ 2013 Page 5
5 Basic and Applied Thermodynamics By Brij Bhooshan
b) Double flow single casing turbine;
c) Tipple cross flow compound turbine with double row;
d) Cross flow compound turbine with single row;
e) Cross flow compound turbine with double row
Based on the direction of flow:
a) Radial flow turbine;
b) Axial flow turbine;
c) Tangential flow turbine
In Radial flow turbines the steam is inject in middle near shaft and steam flow radially
outwords through the successive moving blades placed concentrically. In radial flow
turbines there are no stationary blades so pressure drop occurs in moving blade passage
concentric moving blades rings are designed to move in opposite directions.
In tangential flow turbines the nozzle directs steam tangentially into bucket at the
periphery of single wheel and steam reverses back and re-enters other bucket at its
periphery. This is repeated several times as steam follows the helical path. Tangential
flow turbines are very robust but less efficient.
In axial flow turbines steam flows along the axis of turbine over blades. These axial flow
turbines are well suited for large turbogenrators and very commonly used presently.
Based on the No. of stages:
a) Single stage turbine;
b) Multi stage turbine
Single stage turbines have the expansion occurring in single stage while in multi stage
turbines the expansion occurs in more than one stage of turbine.
Based on speed of turbine
a) Low speed steam turbine < 3000;
b) Normal speed steam turbine = 3000;
c) High speed steam turbine > 3000
Based on pressure in steam turbine
a) Low pressure steam turbine < 20 kg/cm2.
b) Medium pressure steam turbine < 20 kg/cm2.
c) High pressure steam turbine < 20 kg/cm2.
d) Super pressure steam turbine < 20 kg/cm2.
According to Method of governing
Turbine with throttle governing: in which fresh steam enters through one or more
simultaneously operated throttle valves.
Turbine with nozzle governing: in which fresh steam enters through two or more
consecutively opening regulators.
Turbine with by-pass governing: in which steam turbines besides being fed to the 1st
stage as also directly fed to one, two or even three intermediate stages of the turbine.
For more information log on www.brijrbedu.org
Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)
Copyright by Brij Bhooshan @ 2013 Page 6
6 Chapter 13: Steam Turbines
According to heat drop pressure:
a) Condensing turbine with generators;
b) Condensing turbine with one or two intermediate stage extractions.;
c) Back pressure turbine;
d) Non-condensing turbine;
e) Pass-out turbine;
f) Topping turbine;
g) Back pressure turbine with steam extraction from intermediate stages at specific
pressure;
h) Low pressure turbine;
i) Mixed pressure turbine.
According to usage in industry:
a) Stationary turbine with constant speed of rotation - primarily used for driving
alternators.
b) Stationary steam turbine- with variable speed meant for driving turbo-blowers,
air circulators, pump, etc.
c) Non-stationary turbines with variable speed turbine of this type are usually
employed in steamers, ships and railway locomotive.
13.2 IMPULSE TURBINES
Impulse turbines (single-rotor or multi-rotor) are simple stages of the turbines. Here the
impulse blades are attached to the shaft. Impulse blades can be recognized by their
shape. They are usually symmetrical and have entrance and exit angles respectively,
around 20°. Because they are usually used in the entrance high-pressure stages of a
steam turbine, when the specific volume of steam is low and requires much smaller flow
than at lower pressures, the impulse blades are short and have constant cross sections.
The Single-Stage Impulse Turbine
The single-stage impulse turbine is also called the de Laval turbine after its inventor.
Diagram 13.3 Schematic diagram of an Impulse Turbine
The turbine consists of a single rotor to which impulse blades are attached. The steam is
fed through one or several convergent-divergent nozzles which do not extend completely
For more information log on www.brijrbedu.org
Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)
Copyright by Brij Bhooshan @ 2013 Page 7
7 Basic and Applied Thermodynamics By Brij Bhooshan
around the circumference of the rotor, so that only part of the blades is impinged upon
by the steam at any one time. The nozzles also allow governing of the turbine by
shutting off one or more them.
The velocity diagram for a single-stage impulse has been shown in Diagram 13.3.
Diagram 13.4 shows the velocity diagram indicating the flow through the turbine
blades.
Diagram 13.4 Velocity diagram
Velocity Diagram and Calculations for Impulse Turbine
Let us consider
V1 = absolute velocity of steam at inlet to moving blade or velocity of steam leaving
nozzle.
V2 = absolute velocity of steam at exit of moving blade
V1w = Whirl velocity at inlet to moving blade or tangential component of absolute
velocity at inlet to moving blade.
V2w = Whirl velocity at exit of moving blade or tangential component of absolute velocity
at exit of moving blade.
V1a = Flow velocity at inlet to moving blade or axial component of absolute velocity at
inlet to moving blade.
V2a = Flow velocity at exit of moving blade or axial component of absolute velocity at exit
of moving blade.
Vr1 and Vr2 = Inlet and outlet relative velocity (Velocity relative to the rotor blades.)
U = mean blade speed / linear velocity of blade ( dN/60)
d = mean diameter of wheel
N = speed in rpm
m = mass of steam flowing over blade
ρ = Ratio of linear velocity of blade and absolute velocity of steam at inlet to moving
blade = U/V1
K = Co-efficient of blade velocity
= Angle of absolute velocity w.r.t. the direction of blade motion
1 = Angle of absolute velocity at inlet to moving blade or nozzle angle.
2 = Angle of absolute velocity at outlet to moving blade or inlet angle of fixed blade in
next stage.
β = Angle of relative velocity w.r.t. the direction of blade motion
β1 = Angle of relative velocity at inlet or inlet angle of moving blade
V2a
U
Vr2
V2
U V2w
U V1w
V1 V1a Vr1
V2a
Vr2
V2
V2w
U V1w
V1
V1a Vr1
For more information log on www.brijrbedu.org
Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)
Copyright by Brij Bhooshan @ 2013 Page 8
8 Chapter 13: Steam Turbines
β2 = Angle of relative velocity at exit or exit angle of moving blade
Let the mass flow rate be m, kg/sec
Tangential Force
FT = m × change of tangential component of velocity or whirl velocity.
FT = m(V2 cos 2 V1 cos 1) = m(V2 cos 2 + V1 cos 1)
FT = m Vw [13.1]
Driving Thrust
FD = FT = m(V2 cos 2 + V1 cos 1)
FD = m Vw [13.2]
From Velocity triangles
V2 cos 2 + V1 cos 1 = Vr2 cos 2 + Vr1 cos 1
Vw = Vr
FD = m Vw = m Vr
FD = m(Vr2 cos 2 + Vr1 cos 1) [13.3]
Rate of work done or the rotor
W = FD U = m Vw U [13.4a]
Work done per unit of steam mass flow
W = FD U = Vw U [13.4b]
Rate of work done will be the power produced by the turbine stage
W = mU (V1 cos 1 U) (1 + KZ) [13.6
where K = Vr2/Vr1, Ratio of cosines of blade angles (Z) = cos β2/cos β1.
For perfectly smooth and symmetrical blade both K and Z shall have unity value i.e. K =
1, Z = 1.
Therefore for simple impulse turbine stage having perfectly smooth and symmetrical
blade, rate of work done,
W = mU (V1 cos 1 U)
From Diagram U = AB, ΔCw = EF
W = m × AB × EF
Second Approach: The work is available at rotor can also be obtained using steady
flow energy equation b/w section 1 and 2. Assuming no change in P.E. from inlet to exit
across the moving blade and no heat interaction across the stage, the SFEE can be given
be
For more information log on www.brijrbedu.org
Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)
Copyright by Brij Bhooshan @ 2013 Page 9
9 Basic and Applied Thermodynamics By Brij Bhooshan
In case of impulse stage of change in enthalpy from section 1 and 2 can be given by the
change in K.E. associated with relative velocity from 1 to 2.
Rate of work done
For perfectly smooth moving blade Vr1 = Vr2, h1 – h2 = 0.
Hence for stage with smooth blade
From velocity triangle at inlet
From velocity triangle at outlet
Combining above two we get,
We know that
The rate of work done
Axial thrust
Axial component of velocity or flow velocity change causes creation of axial thrust. Axial
thrust due to change in momentum because of change in flow velocity
Blading/ Diagram Efficiency
Stage/ Gross Efficiency
Stage efficiency refers to the ratio of work done and energy supplied to the stage. Energy
supplied to the stage can be accounted by the change in enthalpy between section 0 and
1 i.e. inlet of nozzle to exit of nozzle.
Stage efficiency is thus the output of stage divided by the available energy for the stage.
Energy supplied to stage = m(h0 –h1)
For more information log on www.brijrbedu.org
Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)
Copyright by Brij Bhooshan @ 2013 Page 10
10 Chapter 13: Steam Turbines
Nozzle Efficiency
It is the ratio of K.E. available and enthalpy change occurring across the nozzle i.e.
between inlet and outlet (Sec. 0 to 1)
Overall Efficiency
The overall efficiency of stage can be given by the ratio of work delivered at turbine
shaft to the energy supplied to the stage.
where ηm = mechanical efficiency.
Optimization of Turbine Stage
Turbine being work producing machine is designed with the aim of providing maximum
work output. The ηD of the turbine should be maximized as it indicates the rate of work
done per unit of energy supplied to the rotor.
Work output per unit time in a simple impulse turbine stage is
m, V1, U, , K, Z = Dependable quantity
Thus the work cannot be maximized by only selecting the minimum value of angle 1
and so requires optimization of turbine stage performance with respect to some other
parameter.
The ηD should be maximized with respect to suitable parameter.
Let ρ = U/V1, then
K = 1, Z = 1, for perfectly smooth and symmetrical blade.
Second order differential of ηD with respect to ρ indicates that the diagram efficiency is
maximum corresponding to the blade speed-steam velocity ratio given as
For more information log on www.brijrbedu.org
Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)
Copyright by Brij Bhooshan @ 2013 Page 11
11 Basic and Applied Thermodynamics By Brij Bhooshan
Hence, maximum diagram efficiency,
For perfectly smooth and symmetrical blade maximum diagram efficiency,
Max. Rate of Work done
Wmax = mU2 (1 + KZ)
For perfectly smooth and symmetrical blade K = 1, Z = 1.
Wmax = 2mU2
The variation of diagram efficiency can be plotted with varying blade, steam velocity
ratio as shown in Diagram 13.5.
Diagram 13.5
13.3 METHODS OF REDUCING WHEEL OR ROTAR SPEED
Under the handling simple impulse turbine that if the steam is expanded from the boiler
pressure to condenser pressure in one stage the speed of the rotor becomes tremendously
high which crops up practical complicacies. There are several methods of reducing this
speed to lower value, all these methods utilize a multiple system of rotor in series, keyed
on a common shaft and the steam pressure or jet velocity is absorbed in stages as the
steam flows over the blades. This is termed as compounding. Compounding is a
thermodynamic means for reducing the speed of turbine where speed reduction is
realized without employing a gear box.
Compounding in Impulse Turbine
If high velocity of steam is allowed to flow through one row of moving blades, it produces
a rotor speed of about 30000 rpm which is too high for practical use.
It is therefore essential to incorporate some improvements for practical use and also to
achieve high performance. This is possible by making use of more than one set of
For stage with losses
For K=1, Z=1
For more information log on www.brijrbedu.org
Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)
Copyright by Brij Bhooshan @ 2013 Page 12
12 Chapter 13: Steam Turbines
nozzles, and rotors, in a series, keyed to the shaft so that either the steam pressure or
the jet velocity is absorbed by the turbine in stages. This is called compounding. Two
types of compounding can be accomplished:
(a) velocity compounding;
(b) pressure compounding; and
(c) velocity- pressure compounding.
(Either of the above methods or both in combination are used to reduce the high
rotational speed of the single stage turbine).
The Velocity - Compounding of the Impulse Turbine
The velocity-compounded impulse turbine was first proposed by C.G. Curtis to solve the
problems of a single-stage impulse turbine for use with high pressure and temperature
steam. The Curtis stage turbine, as it came to be called, is composed of one stage of
nozzles as the single-stage turbine, followed by two rows of moving blades instead of
one.
Diagram 13.6 Velocity Compounding arrangement
Steam is expanded through a stationary nozzle from the boiler or inlet pressure to
condenser pressure. So the pressure in the nozzle drops, the kinetic energy of the steam
increased due to increase in velocity. A portion of this available energy is absorbed by a
row of moving blades. The steam (whose velocity has decreased while moving blades)
then flows through the second row of blades which are fixed. The function of these fixed
blades is to re-direct the steam flow without altering its velocity to the flowing next row
moving blades where again work is done on them and steam leaves the cut away section
of such a stage and changes in pressure and velocity as the steam passes through the
nozzle, fixed blades and moving blades. In the Curtis stage, the total enthalpy drop and
hence pressure drop occur in the nozzles so that the pressure remains constant in all three
rows of blades.
Velocity is absorbed in two stages. In fixed (static) blade passage both pressure and
velocity remain constant. Fixed blades are also called guide vanes. Velocity compounded
stage is also called Curtis stage. The velocity diagram of the velocity-compound Impulse
turbine is shown in Diagram 13.6.
The fixed blades are used to guide the outlet steam/gas from the previous stage in such a
manner so as to smooth entry at the next stage is ensured.
M = Moving Blade,
F = Fixed Blade,
N = Nozzle
N M F M
Leaving velocity Ve
Back pressure pe
Boiler
pressure pi
Entering
velocity Vi
Steam out
Steam in
For more information log on www.brijrbedu.org
Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)
Copyright by Brij Bhooshan @ 2013 Page 13
13 Basic and Applied Thermodynamics By Brij Bhooshan
Diagram 13.7 Velocity diagrams for the Velocity-Compounded Impulse turbine
The blade velocity coefficient may be different in each row of blades
Work done (W) = mU (∆Vw1 ∆Vw2) [13.8a]
End Thrust = mU (∆Vf1 ∆Vf2) [13.8b]
The optimum velocity ratio will depend on number of stages and is given by
Work is not uniformly distributed (1st >2nd )
The first stage in a large (power plant) turbine is velocity or pressure
compounded impulse stage.
Diagram 13.8 Pressure-Compounded Impulse Turbine
Pressure Compounding or Rateau Staging
To alleviate the problem of high blade velocity in the single-stage impulse turbine, the
total enthalpy drop through the nozzles of that turbine are simply divided up,
essentially in an equal manner, among many single-stage impulse turbines in series
Stages
1 2 3
N M N M N M
Initial Steam Velocity
Boil
er
Pre
ssu
re
Exhaust Pressure
Lost
Velocity
First Stage
Vf1
U
21 21 11
11
Vr11
V11
Vr21
V21
Vw1
Second Stage
Vf2
U
22 22 21
12
Vr12
V12
Vr22
V22
Vw2
For more information log on www.brijrbedu.org
Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)
Copyright by Brij Bhooshan @ 2013 Page 14
14 Chapter 13: Steam Turbines
(Diagram 13.8). Such a turbine is called a Rateau turbine, after its inventor. Thus the
inlet steam velocities to each stage are essentially equal and due to a reduced Δh.
Diagram shows rings of fixed nozzle in corporate between the rings of moving blades.
The steam at boiler pressure enters the first set of nozzles and expands partially. The
kinetic energy of the steam thus obtained is absorbed by the moving blades (stage 1).
The steam is expands partially in the second set of nozzles where its pressure again falls
and the velocity increases, the kinetic energy so obtained is absorbed by the second ring
of moving blades (stage 2). This is repeated in stage 3 and steam is finally leaves the
turbine at low velocity and pressure. The number of stages (or pressure reduction)
depends upon the number of rows of nozzles through which the steam must pass.
This is most efficient turbine since the speed ratio remains constant built it is expensive
owning to a large number of stages.
Pressure- Velocity Compounding
This method of compounding is the combination of velocity and pressure compounding.
The total drop in steam pressure is divided into stages and velocity obtained in each
stage is also constant during each stages. The rings of nozzles are fixed at the begning of
each stage and pressure remains constant during each stages. The change in pressure
and velocity are as shown in Diagram 13.9.
Thus hear one or more ‘curtis stage’ velocity compound followed by ‘Rateau stage’ reduce
pressure to a moderate level with high proportion to work per stage and then the highly
efficient ‘Rateau stage’ absorb the remaining energy available.
Diagram 13.9 Pressure- Velocity Compounding Impulse Turbine
13.4 REACTION TURBINE
A reaction turbine, therefore, is one that is constructed of rows of fixed and rows of
moving blades. The fixed blades act as nozzles. The moving blades move as a result of
the impulse of steam received (caused by change in momentum) and also as a result of
expansion and acceleration of the steam relative to them. In other words, they also act
as nozzles. The enthalpy drop per stage of one row fixed and one row moving blades is
divided among them, often equally. Thus a blade with a 50 percent degree of reaction, or
a 50 percent reaction stage, is one in which half the enthalpy drop of the stage occurs in
the fixed blades and half in the moving blades. The pressure drops will not be equal,
N M F M N M F N
Initial Steam Velocity
Boil
er
Pre
ssu
re
Exhaust Pressure
Lost Velocity
For more information log on www.brijrbedu.org
Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)
Copyright by Brij Bhooshan @ 2013 Page 15
15 Basic and Applied Thermodynamics By Brij Bhooshan
however. They are greater for the fixed blades and greater for the high-pressure than
the low-pressure stages.
The moving blades of a reaction turbine are easily distinguishable from those of an
impulse turbine in that they are not symmetrical and, because they act partly as
nozzles, have a shape similar to that of the fixed blades, although curved in the opposite
direction. The schematic pressure line (Diagram 13.10) shows that pressure
continuously drops through all rows of blades, fixed and moving. The absolute steam
velocity changes within each stage as shown and repeats from stage to stage. Diagram
13.11 shows a typical velocity diagram for the reaction stage.
Diagram 13.10 Three stages of reaction turbine indicating pressure and velocity distribution
Pressure and enthalpy drop both in the fixed blade or stator and in the moving blade or
Rotor
A very widely used design has half degree of reaction or 50% reaction and this is known
as Parson's Turbine. This consists of symmetrical stator and rotor blades.
Diagram 13.11 The velocity diagram of reaction blading
The velocity triangles are symmetrical and we have
Energy input per stage (unit mass flow per second)
Fixed Blade
U
F M F M F M
Initial Steam Velocity
Boil
er
Pre
ssu
re
Exhaust Pressure
Lost Velocity
For more information log on www.brijrbedu.org
Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)
Copyright by Brij Bhooshan @ 2013 Page 16
16 Chapter 13: Steam Turbines
From the inlet velocity triangle we have,
Work done (for unit mass flow per second) = W = UΔVw
Therefore, the Blade efficiency
Put ρ = U/V1, then
For the maximum efficiency dηB/dρ = 0, and we get
from which finally it yields
Diagram 13.12 Velocity diagram for maximum efficiency
Absolute velocity of the outlet at this stage is axial (see Diagram 13.12). In this case, the
energy transfer
(ηB)max can be found out by putting the value of ρ = Cosα1 in the expression for blade
efficiency
η is greater in reaction turbine. Energy input per stage is less, so there are more number
of stages.
13.5 STAGE EFFICIENCY AND REHEAT FACTOR
The Thermodynamic effect on the turbine efficiency can be best understood by
considering a number of stages between two stages 1 and 2 as shown in Diagram 13.13.
The total expansion is divided into four stages of the same efficiency ηs and pressure
ratio.
U
For more information log on www.brijrbedu.org
Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)
Copyright by Brij Bhooshan @ 2013 Page 17
17 Basic and Applied Thermodynamics By Brij Bhooshan
Diagram 13.13 Different stage of a steam turbine
The overall efficiency of expansion is η0. The actual work during the expansion from 1 to
2 is
R.F is 1.03 to 1.04
If ηS remains same for all the stages or ηS is the mean stage efficiency.
We can see:
This makes the overall efficiency of the turbine greater than the individual stage
efficiency.
The effect depicted by Eqn (13.b) is due to the thermodynamic effect called "reheat". This
does not imply any heat transfer to the stages from outside. It is merely the
reappearance of stage losses an increased enthalpy during the constant pressure
heating (or reheating) processes AX, BY, CZ and D2.
Entropy
Enthalpy
W
px
Wa py
A pz
p2
p1 1
Z
Y
X
2
2 D
C B
A