Module 1 Steam Engineering: Properties of steam - wet, dry and superheated steam - dryness fraction - enthalpy and internal energy - entropy of steam - temperature entropy diagram - process - Mollier chart - Rankine cycle for wet, dry and superheated steam. Steam Generators - classification - modern steam generators - boiler mountings and accessories. Module 2 Steam nozzles - Mass flow rate - throat pressure for maximum discharge - throat area - effect of friction - super saturated flow. Steam turbines: velocity triangles, work done, governing, and efficiencies. Module 3 Gas turbine Plants - Open and closed cycles - thermodynamics cycles - regeneration, re heating - inter cooling - efficiency and performance of gas turbines. Rotary Compressors - Analysis of rotary compressors - centrifugal and axial compressors. Combustion - combustion chambers of gas turbines - cylindrical, annular and industrial type combustion chamber - combustion intensity - combustion chambers efficiency - pressure loss combustion process and stability loop. Module 4 Introduction to solar energy - solar collectors - Liquid flat plate collectors - principle - thermal losses and efficiency - characteristics - overall loss coefficient - thermal analysis - useful heat gained by fluid - mean plate temperature - performance - focussing type solar collectors - solar concentrators and receivers - sun tracking system - characteristics - optical losses - thermal performance - solar pond - solar water heating - solar thermal power generation Module 5 Thermal power plants: layout and operation of steam and diesel power plants - coal burners - stockers - cooling ponds & towers - chimneys - draught - dust collectors - precipitators - feed water heaters - evaporators - steam condensers - coal handling - ash handling

1. THERMAL ENGINEERING

2. 2
Syllabus
Module 1
Steam Engineering: Properties of steam - wet, dry and superheated steam -
dryness fraction - enthalpy and internal energy - entropy of steam - temperature
entropy diagram - process - Mollier chart - Rankine cycle for wet, dry and
superheated steam. Steam Generators - classification - modern steam generators -
boiler mountings and accessories.
Module 2
Steam nozzles - Mass flow rate - throat pressure for maximum discharge - throat
area - effect of friction - super saturated flow.
Steam turbines: velocity triangles, work done, governing, and efficiencies.
Module 3
Gas turbine Plants - Open and closed cycles - thermodynamics cycles -
regeneration, re heating - inter cooling - efficiency and performance of gas
turbines. Rotary Compressors - Analysis of rotary compressors - centrifugal and
axial compressors. Combustion - combustion chambers of gas turbines -
cylindrical, annular and industrial type combustion chamber - combustion
intensity - combustion chambers efficiency - pressure loss combustion process
and stability loop.
Module 4
Introduction to solar energy - solar collectors - Liquid flat plate collectors -
principle - thermal losses and efficiency - characteristics - overall loss coefficient
- thermal analysis - useful heat gained by fluid - mean plate temperature -
performance - focussing type solar collectors - solar concentrators and receivers
- sun tracking system - characteristics - optical losses - thermal performance -
solar pond - solar water heating - solar thermal power generation (Description
Only)

3. 3
Module 5
Thermal power plants: layout and operation of steam and diesel power plants - coal
burners - stockers - cooling ponds & towers - chimneys - draught - dust collectors -
precipitators - feed water heaters - evaporators - steam condensers - coal handling - ash
handling.

4. 4
MODULE 1
Steam Engineering
Formation of steam -
Consider a cylinder fitted with a piston which can move freely upwards and
downwards in it.
(a) Let 1 kg of water at 0o
C under the piston
Let the piston is loaded with load w to ensure heating at constant pressure.
Now if heat is imparted to water, a rise in temperature will be noticed and this
rise will continue till boiling point is reached.
B.P of water, at normal atmospheric pressure of 1.01325 bar is 100o
C. But it
increases with the increase in pressure.
(b) The volume of water will increase slightly with the increase in temperature, but
increase in volume of water (or work) is generally neglected for all types of calculations.
The boiling temperature is known as the temperature of formation of steam or
saturation temperature.
(c) Now, if supply of heat to water is continued, it will be notices that rise of
temperature after the boiling point is reached nil but piston starts moving upwards which
indicates that there is increase in volume which is only possible if steam formation
occurs.
The heat being supplied does not show any rise of temperature but changes
water into vapour state (steam) and is known as Latent heat or hidden heat.

5. 5
So long as the steam is in contact with water, it is called wet steam.
(d) If heating of steam is further progressed such that all the water particles
associated with steam are evaporated, the steam so obtained is called dry and saturated
steam.
If vg m3
is the volume of 1 kg of dry and saturated steam then work done on the
piston will be
P (Vg - Vf), where ‗P‘ is the constant pressure (due to weight ‗W‘ on the
piston).
(e) If the supply of heat to the dry and saturated steam is continued at constant
pressure, there will be increase in temperature and volume of steam.
The steam so obtained is called super heated steam and it behaves like a perfect
gas.
Temperature Vs Total Heat Graph during steam formation
A represents the initial condition of water at 0oC and pressure p (in bar)
During the formation of the super heated steam, from water at freezing point,
the heat is absorbed in the following 3 stages.
The heating of water upto boiling temperature or saturation temperature (ts) is

6. 6
shown by AB.
AP known as sensible heat, liquid heat or total heat of water.
The change of state from liquid to steam is sown by BC PQ, latent heat of
vaporisation.
The super heating process is CD.
QR known as the heat of superheat.
LINE, AR represents the total heat of the super heated steam.
If the pressure is increased, the boiling temperature also increases.
The line passing through the points A, B, E, K  Saturated liquid line.
The line passing through the points L, F, C  Dry saturated steam line.
[Some times, these terms are briefly written as liquid line and dry steam line.
but the word saturated is always understood].
Note:
When the pressure and saturation temperature increases, the latent heat of
vaporisation decreases, it becomes ZERO at a point (N), where liquid and dry steam
lines meet.
The point N is known as critical point and at this point, the liquid and vapour
phases merge, and become identical in every respect.
The temperature corresponding to critical point N is known as critical
temperature and the pressure is known as critical pressure.
For steam, the critical temperature is 374.15o
C and critical pressure is 220.9 bar
Pc = 220.9 bar
Tc = 374.15oC
At critical point and above, there is no definite transition from liquid to vapour
and two phases cannot be distinguished visually. The latent heat of vaporisation is zero
at critical point and has no meaning at pressure higher than critical.

7. 7
At T = 273.16 k and P = 0.006113 bar ice, water and steam co-exist in the
thermodynamic equilibrium in a closed vessel and bcf (Belleni - 200) is called triple
point line. At lower pressures than this, ice sublimates to steam.
IMPORTANT TERMS RELATING STEAM FORMATION
1. Sensible Heat of water (hf)
It is defined as the quantity of heat absorbed by 1 kg of water when it is heated
from 0oC (freezing point) to boiling point.
If i kg of water is heated from 0o
C to 100o
C the sensible heat added to it will be
4.18 × 100 = 418 kJ
But if water is at say 20o
C initially then sensible heat added will be 4.18 × (100-
20) = 334.7 kJ
This type of heat is denoted by letter hf and its value can be directly read from
the steam tables.
The value of specific heat of water may be taken as 4.18 kJ/kg K at low
pressures but at high pressures it is different from this value.
2. Latent Heat or Hidden Heat (hfg)
It is the amount of heat required to convert water at a given temperature and
pressure into steam at the same temperature and pressure.
The value of L.H is not constant and varies according to pressure variation.
3. Dryness Fraction (x)
It is related with wet steam
Mass of dry saturated vapour to the total mass of the mixture.
x =
g g
g f
m m
m m m


mg = Mass of actual Dry steam
mf = Mass of water in suspension

8. 8
m = Mass of mixture = mg + mf
eg:- If in 1 kg of wet steam 0.9 kg is the dry steam and 0.1 kg water particles
then x = 0.9.
No steam can be completely dry and saturated, so long as it is in contact with
the water from which it is being formed.
The steam is called saturated when the molecules escaping from the liquid
become equal to the molecules returning to it.
Saturated steam may be dry or wet. When the saturated vapour contains
particles of liquid evenly distributed over the entire mass of vapour, it is called wet
saturated steam.
Wet steam is characterised by its dryness fraction.
Dryness fraction, x =
mass of day saturated vapour
mass of mixture
=
mg
m
x =
mass of dry vapour in the mixture
mass of the mixture
Q. Calculate the dryness fraction of steam which has 1.25 kg of water in suspension
with 40 kg of steam
=
g
g f
m
m m
=
40
0.97
40 1.25
4. Total heat or enthalpy of wet steam (h)
It is defined as the quantity of heat required to convert 1 kg of water at 0o
C into
steam at constant pressure.
5. Total heat of dry saturated steam
If steam is dry saturated, x = 1 and hg = hf + hfg

9. 9
6. Superheated steam
Total heat of super heating is always carried out at constant pressure.
It represents the quantity of heat required to convert 1 kg of water at 0o
C into
super heated steam at constant pressure.
 sup f fg ps sup sh h h c T T   
The value of specific heat of steam at constant pressure Cps depends upon the
degree of superheat and the pressure of steam generation. Its average value is taken from
2 to 2.1 kJ/kg K.
Water boils at 12o
C if pressure on the surface of water is kept at 0.014 bar.
7o
C if pressure 0.01 bar.
Advantages obtained by using ‘super heated’ steam
1. By super heating steam, its heat content and have its capacity to do work is
increased without having increase its pressure.
2. High temperature use of super heated steam results in an increase in thermal
efficiency.
3. Super heating is done in a super heater which obtains its heat from waste
furnace gases which would have otherwise passed uselessly up the chimney.
Volume of wet and dry steam
If steam has a dryness fraction of x.
1 kg of this steam will contain x kg of dry steam and (1 - x) kg of water.
Let ,
fv  volume of 1 kg of water
gv  volume of 1 kg of perfect dry steam
fv = specific volume of saturated liquid
fgv = specific volume of evaporation

10. 10
gv = specific volume of dry steam, then
[specific volume of a fluid is the volume occupied by a unit mass of the fluid]
Volume of 1 kg of wet steam = volume of dry steam + volume of water
[Since vf is very small as compared to gv , therefore the expression (1 - x) vf
may be neglected.
 Volume of 1 kg of wet steam = 3
gx v m
 g fx v 1 x v  
g f fxv v xv  
 f g fv x v v  
f fgv xv 
f fg fg fgv xv v v   
   f fg fgv v 1 x v   
 g fgv 1 x v  
Super heated Steam
The superheated steam behaves like a perfect gas and therefore, its volume can
be worked out by applying Charles law to steam at the beginning and at the end of super
heating process.
vg = Specific volume of dry steam at pressure P
Ts = Saturation temperature in K
Tsup = Temperature of super heated steam in K
Vsup = Volume of 1 kg of super heated steam at pressure P.
Then
g sup
s sup
PV PV
T T


11. 11
g sup
sup
s
V T
V
T

Internal Energy of steam
The actual Heat energy above the freezing point of water stored in steam is
known as internal energy of steam.
The work of evaporation is not stored in the steam as it is utilised in during
external work.
So the internal energy of steam could be found by subtracting work of
evaporation from the total heat.
u = h - pv
For wet steam
 f fg gu h xh pxv  
=  f fg gh h 100pxv  kJ/kg
Pressure on the piston in bar
= P × 105 N/m2
1 bar = 105 N/m2
For dry saturated steam
 f fg gu h h pv  
g gh 100pv  kJ/kg
For super heated steam
 f fg ps sup s supu h h C T T PV    
 g ps sup s suph C T T 100PV    
 
Entropy of steam
1. The entropy of water at 0oC is taken as zero. The water is heated and

12. 12
evaporated at constant pressure. The steam is also super heated at constant pressure in
super heaters.
2. So the entropy of steam can be calculated from the formula for the change of
entropy at constant pressure.
Entropy of water
p
s
C dTdQ
d
T T

 
The total increase in entropy of water from freezing point to boiling point, may
be obtained by integrating the above expression within the limits 273 K and Ts K.
ss T p dT
so 273
s
C
d
T

 
s s
f p e p
T T
S C log 2.3C log
273 273
 
   
    
   
The value of Sf may be directly seen from the steam tables
Entropy Increase during Evaporation
When the water is completely evaporated into steam, it absorbs full latent heat
(hfg) at constant temperature T, corresponding to the given pressure.
Entropy =
Heat absorbed
Absolute temperature
 Increase of entropy during evaporation
fg
fg
h
S
T

If the steam is wet with dryness fraction x, the evaporation will be partial.
i.e., if evaporation is partial,
Heat absorbed = x hfg
 Increase of entropy,
fg
fg
xh
S
T


13. 13
Entropy of wet and dry steam
Entropy of wet and dry steam =
Entropy of water + Entropy during evaporation
=
fg
f f fg
xh
S S xS
T
   (wet steam)
=
fg
f f fg g
h
S S S S
T
    (dry steam)
Entropy of super heated steam
Heat absorbed; dQ = Cps dT
psdT
s
C
d
T
 [value taken × 1.67 kJ/kg K to 2.5 kJ/kg K]
sup sup
g s
S T
s pS T
dT
d C
T
  or
sup sup
sup g ps e p
T T
S S C log 2.3C log
T T
   
     
   
where  sup gS S is the increase in entropy.
Entropy of 1 kg of superheated steam is

sup
sup g ps
T
S S 2.3C log
T
 
   
 
TEMPERATURE - ENTROPY (T.S) DIAGRAM

14. 14
STEAM TABLES
The generation of steam at different pressures has been studied experimentally
and various properties of steam have been obtained at different conditions. The
properties have been listed in tables called steam tables. The steam tables are available
for
1. Saturated water and steam - on pressure basis.
2. Saturated water and steam - on temperature basis.
3. Super heated steam - on pressure and temperature basis for enthalpy,
entropy and specific volume.
4. Supercritical steam - on pressure and temperature basis above 221.2 bar
and 374.15o
C for enthalpy, entropy and specific volume.
Some important points regarding Steam Tables
(a) The steam table gives values for 1 kg of water and 1 kg of steam.
(b) The steam table gives values of properties from the triple point of water to
the critical point of steam.
(c) For getting values of thermodynamic properties, either saturation pressure or
saturation temperature need to be known. Pressure based steam table (i.e., extreme left
pressure column is placed) is used when pressure value is known, similarly temperature
based steam table is used when temperature value is known.

15. 15
(d) At low pressure the volume of saturated liquid is very small as compared to
the volume of dry steam and usually the specific volume of the liquid is neglected. but at
very high pressure the volume of liquid is comparable and should not be neglected.
(e) The specific enthalpy and specific entropy at 0o
C are both taken as zero and
measurements are made from 0o
C onwards.
(f) In computing properties for wet steam it should be noted that only hfg and sfg
are affected by dryness fraction but hf and sf are not affected by dryness fraction. This
means that for steam with dryness fraction x,
g f fgh h xh 
g f fgS S xS 
Property Table
Property Wet steam Dry steam Super heated steam
Volume   f g1 x v x v  gv sup
g
s
T
v .
T
Enthalpy f gfh xh f fg gh h h   g ps sup sah C T T 
Entropy f fgS xS f fg gS S S  sup
g ps n
s
T
S C l
T

Enthalpy - Entropy chart (Mollier chart)
Most of the thermodynamic systems deal with flow of steam in steady
condition where change in enthalpy is encountered.

16. 16
The most convenient method of computing change in enthalpy is the enthalpy-
entropy chart.
Saturated liquid region is not required for solving engineering problems and
therefore only a part of chart near saturated vapour region and super heat region is
shown.
This chart is very useful for solving problems on nozzles and steam power
plants.
1. Dryness fraction lines
2. Constant volume lines
3. Constant pressure line
4. Isothermal lines
5. Isentropic lines
6. Throttling lines
RANKINE CYCLE
M.Rankine (1820-1872), a Professor at Glasgow University
It is also a reversible cycle but it differs from the Carnot cycle in the following
respects:
(i) The condensation process is allowed to proceed to completion; the exhaust
steam from the engine/turbine is completely condensed. At the end of condensation
process the working fluid is only liquid and not a mixture of liquid and vapour.

17. 17
(ii) The pressure of liquid water can be easily raised to the boiler pressure
(pressure at which steam is being generated in the boiler) by employing a small sized
pump.
In addition, the steam may be super heated in the boiler so as to obtain exhaust
steam of higher quality. That will prevent pitting and erosion of turbine blades.
Steam power plant working on ideal Rankine cycle
The various elements are:
A boiler which generates steam at constant pressure
An engine or turbine in which steam expands isentropically and work is done.
A condenser in which heat is removed from the exhaust steam and it is
completely converted into water at constant pressure
A hot well in which the under state is collected
A pump which raises the pressure of liquid water to the boiler pressure and
pumps it into the boiler for conversion into steam.

18. 18
Consider a steady flow conditions at all states and 1 kg of steam is circulating
through the cycle.
The heat supplied by the boiler per kg of steam generated
Heat absorbed = Q1 = (h2 – h1) = (h2 – h4) - (h1 – h4)
where,
Wp = (h1 – h4) is called pump work per kg of steam.
Heat rejected into the condenser = Q2 = (h3 – h4)
Net work done per kg of steam = Q1 - Q2
= (h2 – h4) - Wp - (h3 – h4)
= (h2 – h3) - Wp
= WT - WP
Where,
WT = Turbine work = (h2 – h3) = isentropic enthalpy drop during expansion
Rankine efficiency = R
1
Network done W
Heat supplied Q
  
=
 
 
1 2 P
1 3 P
h h W
h h W
 
 
The pump work (WP) is very small as compared to turbine work (h2 – h3) and
heat added (h2 – h1), therefore it can be fairly neglected.
WP = ( P1 - P2) V4
P1 = Boiler pressure, P2 = Condenser pressure
V4 = Specific volume of saturated liquid at condenser pressure.
The field pump handles liquid water which is in compressed, which means with
the increase in pressure its density or specific volume undergoes a little change. Using
general property relation for reversible adiabatic compression, we get,

19. 19
Tds = dh - vdp
ds = 0
dh = v dp
 h = v  P ... (since change in specific volume is negligible)
hf2 - hf3 = V1 (P1 - P2)
When P is in bar and v is in m3
/kg, we have
hf2 - hf3 = V4 (P1 - P2) × 105
J/kg
The Rankine efficiency without pump work is
1 2
R
1 f 3
h h
h f

 

............ (1)
State 3 (i.e., at the end of isentropic expansion) must be known then only h3 can
be determined. State 3 is located from the steam table by equating entropy S2 and S3 or
by drawing a vertical line on the Mollier chart from State 1 to condenser pressure.
Modified Rankine Cycle (Steam Engine Cycle)
In the steam engine the expansion is not continued up to the point 2 as the stroke
will be too long and as the work obtained is very small at the tail end of the stroke which
is not even sufficient to overcome the frictional resistances near the end of the stroke.
Therefore in actual practice the expansion is terminated at point 5 instead of 2 and the
steam is released at constant volume. This causes a sudden pressure drop from P2 to P2
to Pb (back pressure) at constant volume due to the steam communicating with outside
atmosphere. This is represented by 56 fig. This reduces the stroke length of the engine
without any appreciable change in the work done.

20. 20
Specific Steam Consumption (S.S.C)
It is defined as the steam consumption (kg/s) to produce unit power (kW)
S.S.C =
 1 2
Mass flow rate per hour kg/s 3600
kg/kWhr
Net power output kW h h
 

(h1 - h2) kJ work is obtained from 1 kg of steam.
1 kW hr = 3600 kJ
S.S.C =
 1 2
3600
kg/kWhr
h h
In case of steam power plant, the specific steam consumption is an indicator of
the relative size of the plant.
Work ratio (Wr) : It is the ratio of network done to the turbine work.
 
 
1 2 P
r
1 2
h h W
W
h h
 


Relative Efficiency or Efficiency Ratio
Relative Efficiency =
Thermal Efficiency
Ranking Efficiency
Q. A simple Rankine cycle steam power plant operates between the temperature of
260o
C and 95o
C. The steam is supplied to the turbine at a dry saturated condition.
In the turbine it expands in an isentropic manner. Determine the efficiency of the
Rankine cycle followed by the turbine and the efficiency of the carnot cycle

21. 21
operating between these two temperature limits. Draw the T - S and H - S
diagrams.
Solution:
T1 = 260o
C = 260 + 273 = 533 K ; T2 = 95o
C = 95 + 273 = 368 K.
From steam table, At 260o
C, P2 = 46.94 bar 1 95o
C, P2 = 0.845 bar.
The initial and final conditions of steam are shown in the H-S diagram.
h1 = 2800 kJ/kg;
h2 = 2170 kJ/kg;
From steam tables at temperature 95o
C,
hf3 = 398 kJ/kg
Efficiency of Rankine cycle, 1 2
R
1 f 3
h h
h f

 

=
2800 2170
2800 398


= 0.262 = 26.2%
Efficiency of Carnot cycle, 1 2
c
1
T T
T

 
=
533 368
533

= 0.3096 = 30.96%
Ranking cycle for wet dry and super heated steam
The value of h1 and h2 may be determined by using steam tables
h1 = hg = 2796.4 kJ/kg ; Sg = 6.001 kJ/kg
hf3 = hf = 398 kJ/kg = 2270.2 kJ/kg
Sf3 = Sf = 1.25 kJ/kg ; Sfg = 6.167 kJ/kg K

22. 22
Dryness fraction at 2
S1 = S2
6.001 = 1.25 + x × (6.167)  x = 0.77
h2 = hf + x hfg
= 398 + 0.77 × 2270 - 2 = 2146 kJ/kg
Specific Steam Consumption
It is the mass of steam that must be supplied to a steam engine or turbine in
order to develop a unit amount of work or power out put.
The amount of work or power out put is usually expresses in kilowatt hour
(kWh).
W = J/s
S.S.C =
1 2
Mass flow rate per hour kg/s kg 3600
Net power out put kW kWS h h
  

=
 1 2
3600
kg/kWhr
h h
Q. A steam power plant uses steam at a pressure of 50 bar and temperature 500o
C
and exhausted into a condenser where a pressure of 0.05 bar is maintained. The
mass flow rate of the steam is 150 kg/sec. determine (a) the Rankine engine
efficiency (b) Power developed (c) specific steam consumption (d) Heat rejected
into the condenser per hour (e) Carnot efficiency.
P1 = 50 bar, P2 = 0.05 bar
From steam tables:
50 bar 263.99o
C (Saturation Temperature)
Page - 44 (Properties of super heated steam)
h1 = 3433.8 and S1 = 6.9770 kJ
S1 = S2

23. 23
6.977 = f 3 fgS xS
6.977 = 0.4764 + x × 7.9187, x 0.82 
 h2 = hf2 = x hfg = 137.8 + 0.82 × 2423.8 = 2125.316 kJ/kg
Vf3 = 1.005 × 10-3
m3
/kg
hf3 = 137.82 kJ/kg
(a) Rankine Engine Efficiency = 1 2
1 3
h h 3433.8 2125.316
h h 3433.8 137.82
 

 
= 0.3969 = 39.69%
(b) Power developed = ms × work done per kg = 150 × (h1 - h2)
= 150 × 1308.384
= 196257.6 kW = 196.257 mW
(c) S.S.C =
1 2
3600 3600
h h 1308.384


= 2.751 kg/kW hr
(d) Heat Rejected into the condenser = Q2 = ms (h2 - h3)
= 150 (2125.316 - 137.8)
= 298127.4 kJ/s
(e) Carnot efficiency, c =
 
 
2
1
273 32.9T
1 1
T 273 263.9

  

= 0.43 = 13%
P1  Boiler Pressure, P2 = Condenser Pr
V3  Specific volume of saturated liquid at the condenser pressure
WP = (P1 - P2) V3
(f) Ranking cycle efficiency,
 
 
1 2 P
R
1 f 3 P
h h W
h h W
 
 
 

24. 24
=
   
   
3433.7 2125.316 50 0.05 /10
3433.7 137.8 50 0.05 /10
  
  
=
1308.384 4.995
100 39.6%
3295.9 4.995

 

Q. Dry saturated steam at 10 bar is supplied to a prime mover and the exhaust
takes place at 0.2 bar. Determine the Rankine Efficiency, efficiency ratio and
specific steam consumption of the prime mover, if the indicated thermal efficiency
is 20%. Also find the percentage change in the Rankine efficiency, if steam is
initially 90% dry.
From Mollier chart, h1 = 2775 kJ/kg, h2 = 2150 kJ/kg
From steam tables, we find that enthalpy of water at 0.2 bar,
hf3 = 251.5 kJ/kg
Rankine Efficiency, 1 2
R
1 f 3
h h
h h

 

=
2775 2150
2775 251.5


= 0.247 or 24.7%
Efficiency ratio =
Indicated thermal efficiency
Ranking efficiency
0.2
0.247
 = 0.81 or 81%
Specific Steam Consumption =
1 2
3600
h h
=
3600
2775 2150
= 5.76 kg/kWh
Percentage change in the Rankine efficiency if the steam is initially 90% dry
h1 = 2580 kJ/kg, h2 = 2030 kJ/kg
Rankine efficiency,

25. 25
2 3
R
2 f 3
h h
h h

 

=
25080 2030
2580 251.5


= 0.236 or 23.6%
Percentage change in Rankine Efficiency
=
24.7 23.6
100 4.45%
24.7

 
Q. In a Rankine cycle, the steam at turbine inlet is saturated at a pressure of 30 bar
and the exhaust pressure is 0.25 bar. Determine, (i) Pump-Work (ii) Turbine
power. (iii) Rankine efficiency (iv) condenser heat flow (v) dryness at the end
of expansion. Assume flow rate of 10 Kg/s.
P1= 30 bar
P2 = .05 bar
(i) Pump work per 1 Kg.
 p 4 3 fW m P P V 
5
1 (30 .04) .00102 10 3KJ     
Power required for the pump
10 3KJ
30KW
sec

 
(ii) Turbine Power
From steam table for 30 bar, dry sale steam
h1 = kg, 2803 KJ/Kg
at (1) entropy
S1 = Sg1 = 7.831 KJ/kgK
at .2 steam is wet steam
2 f 2 2 2 2S S x Sfg 0.893 x x...   
Since 1-2 is an isentropic process
S1 = S2

26. 26
 7.831= 0.893 + x2 × .........
x2 = 0.763
Enthalpy at 2, (wet steam of x2 dry)
2 f 2 2 2h h x hfg 
= 272 + 0.763 × 2346
Turbine power = 10× (2803-2062) KJ/s. = 7410 KW
(iii) Rankine Efficiency
1 2 p
1 3 p
h h W
h (h w )
 

 
=
 
(2803 2062) 3
2803 272 3
 
 
=0.292 or 29.2%
(iv) heat flow rate in the condenser
= m(h2–h3) = 10× (2062–272) = 17900 KW
(v) Dryness at the end of expansion = 0.763 = 76.3%
Thermodynamic Processes of steam
Constant volume process
V1 = x1Vg1 , V2 = x2Vg2
(i) W 1 – 2 = 0 dv = 0
(ii) U1 = h1 – 100P1V1 = h1–100P1 X1 Vg1
U2 = h2–P2V2100 = h2–P2X2Vg2100.....(Wet)
= h2–P2Vg2 100.........(dry saturated)
= h2–P2 Vsup 100 ...........(super heated)
(iii) heat absorbed, q12 = du + w 1–2 = U2–U1
Applying first law energy equation
2
1
Q u pdv  

27. 27
 2 1 2 1U U P(V – V )  
if initially steam is wel. V1 = X1Vg1
Finally super heated V2 = Vsup
Constant Temperature Process
 in wet steam region (hynerbolic in super heated steam region)
 will be a constant pressure process also during
 Condensation & evaporation
Q = h2 – h1
W = P1 (V2–V1)
 Limited to wet steam region only
Hyperbolic Process
 Process PV = C
 Hyperbolic process is also an isothermal process in the superheated
steam regions.
2 2
2
11 1
vc
W pdv dv clog
v v
 
   
 
 
2
1
1
V
W P V1log
V

Q u w 
  2
2 1 1 1
1
V
U U P V loge
V
 
    
 
    2
2 2 2 1 1 1 1 1
1
V
h P V h P V P V log
V
 
      
 
  2
2 1 1 1
1
V
Q h – h P V log
V
 
   
 

28. 28
Isentropic Process
Q u w 
Q = O adiabalic
W = U1–U2
Steady flow reversible
W = h1–h2
1 1 1 2 2 2
1 2
u P V Q W U P V
h h
   

Polytropic Process
steam follows the low PVn
= C
Work done 1 1 2 2P V P V
W
n 1



Applying first law energy equation to the non flow process.
Q u W 
=   1 1 2 2
2 1
P V P V
U U
n 1
 
  
 
    1 1 2 2
2 2 2 1 1 1
P V P V
h P V h P V
n 1

    

   2 1 1 1 2 2
1
h h P V P V 1
n 1
 
     
 
   2 1 1 1 2 2
n
Q h h P V P V
n 1
   

Throttling Process
 Const. enthalpy in the absence of heat and work transfer enthalpy
remains constant.
h1 = h2
 during throttling pressure always falls

29. 29
Process Wo Qn
Isochoric O U2–U1
Isobaric  2 1P V V 2 1h h
Isothermal 2 1P(V V ) h2–h1
Hyper bolic 2
1 1
1
V
P V loge
V
 
 
 
  2
2 1 1 1
1
V
h h P V loge
V
 
   
 
Isentropic U2–U1 0
Polytropic 1 1 2 2P V P V
n 1


   2 1 1 1 2 2
n
h h P V P V
n 1
  

throttling process h1 = h2
STEAM GENERATORS
In simple a boiler may be defined as a closed vessel in which steam is produced
from water by combustion of fuel.
According to American Society of Mechanical Engineers (A.S.M.E.) a „steam
generating unit‟ is defined as: “A combination of apparatus for producing, furnishing or
recovering heat together with the apparatus for transferring the heat so made available
to the fluid being heated and vapourised”.
The steam generated is employed for the following purposes:
For generating power in steam engines or steam turbines.
(ii) In the textile industries for sizing and bleaching etc. and many other industries like
sugar mills ; chemical industries.
(iii) For heating the buildings in cold weather and for producing hot water for hot water
supply.
The primary requirements of steam generators or boilers are

30. 30
The water must be contained safely.
(ii) The steam must be safely delivered in desired condition (as regards its pressure,
temperature, quality and required rate).
CLASSIFICATION OF BOILERS
The boilers may be classified as follows:
1. Horizontal, Vertical or Inclined
If the axis of the boiler is horizontal, the boiler is called as horizontal, if the axis is
vertical, it is called vertical boiler and if the axis is inclined it is known as inclined
boiler. The parts of a horizontal boiler can be inspected and repaired easily but it
occupies more space. The vertical boiler occupies less floor area.
2. Fire Tube and Water Tube
In the fire tube boilers, the hot gases are inside the tubes and the water surrounds the
tubes. Examples : Cochran, Lancashire and Locomotive boilers.
Boiler Terms
Shell. The shell of a boiler consists of one or more steel plates bent into a cylindrical
form and riveted or welded together. The shell ends are closed with the end plates.
Setting. The primary function of setting is to confine heat to the boiler and form a
passage for gases. It is made of brickwork and may form the wall of the furnace and the
combustion chamber. It also provides support in some types of boilers (e.g., Lancashire
boilers).
Grate. It is the platform in the furnace upon which fuel is burnt and it is made of cast
iron
bars. The bars are so arranged that air may pass on to the fuel for combustion. The area
of the grate on which the fire rests in a coal or wood fired boiler is called grate surface.
Furnace. It is a chamber formed by the space above the grate and below the boiler shell,
in which combustion takes place. It is also called a fire-box.

31. 31
Water space and steam space. The volume of the shell that is occupied by the water is
termed water space while the entire shell volume less the water and tubes (if any) space
is called steam space.
Mountings. The items such as stop valve, safety valves, water level gauges, fusible
plug, blow-off cock, pressure gauges, water level indicator etc. are termed as mountings
and a boiler cannot work safely without them.
Accessories. The items such as superheaters, economisers, feed pumps etc. are termed
as accessories and they form integral part of the boiler. They increase the efficiency of
the boiler.
Water level. The level at which water stands in the boiler is called water level. The
space above the water level is called steam space.
FIRE TUBE BOILERS
The various fire tube boilers are described as follows:
Simple Vertical Boiler
It consists of a cylindrical shell, the greater portion of which is full of water
(which surrounds the fire box also) and remaining is the steam space. At the bottom of
the fire box is grate on which fuel is burnt and the ash from it falls in the ash pit.
The fire box is provided with two cross tubes. This increases the heating surface and the
circulation of water. The cross tubes are fitted inclined. This ensures efficient circulation
of water. At the ends of each cross tube are provided hand holes to give access for
cleaning these tubes. The combustion gases after heating the water and thus converting it
into steam escape to the atmosphere through the chimney. Man hole, is provided to clean
the interior of the boiler and exterior of the combustion chamber and chimney. The
various mountings shown in Figure are (i) Pressure gauge, (ii) Water level gauge or
indicator, (iii) Safety valve, (iv) Steam stop valve, (v) Feed check valve, and (vi) Man
hole. Flow of combustion gases and circulation of water in water jackets are indicated by
arrows

32. 32
The rate of production in such a boiler normally does not exceed 2500 kg/hr and
pressure is normally limited to 7.5 to 10 bar.
A simple vertical boiler is self-contained and can be transported easily.
Cochran Boiler
It is one of the best types of vertical multi-tubular boiler, and has a number of horizontal
Dimensions, working pressure, capacity, heating surface and efficiency are given below:
Shell diameter 2.75 m
Height 5.79m
Working pressure 6.5 bar (max. pressure = 15 bar)
steam capacity 3500 kg/hr (max. capacity = 4000 kg/hr)
Heating surface 120m2
Efficiency 70 to 75% (depending on the fuel used)

33. 33
Cochran boiler consists of a cylindrical shell with a dome shaped top where the
space is provided for steam. The furnace is one piece construction and is seamless. Its
crown has a hemispherical shape and thus provides maximum volume of space. The fuel
is burnt on the grate and ash is collected and disposed of from ash pit. The gases of
combustion produced by burning of fuel enter the combustion chamber through the flue
tube and strike against fire brick lining which directs them to pass through number of
horizontal tubes, being surrounded by water. After which the gases escape to the
atmosphere through smoke box and chimney. A number of hand-holes are provided
around the outer shell for cleaning purposes.
The various boiler mountings shown in Figure are : (i) Water level gauge, (ii)
Safety valve, (iii) Steam stop valve, (iv) Blow off cock, (v) Man hole and, (vi) Pressure
gauge.

34. 34
The path of combustion of gases and circulation of water are shown by arrows in Fig.
11.2.
Cornish Boiler
This form of boiler was first adopted by Trevithick, the Cornish engineer, at the time of
introduction of high-pressure steam to the early Cornish engine, and is still used. The
specifications of Cornish boiler are given below
No. of flue tubes One
Diameter of the shell 1.25 w 1.75 m
Length of the shell 4 to 7 m
Pressure of the steam 10.5 bar
Steam capacity 6500 kg/h.
It consists of a cylindrical shell with flat ends through which passes a smaller
flue tube containing the furnace. The products of combustion pass from the fire grate
forward over the brickwork bridge to the end of the furnace tube; they then return by the
two side flues to the front end of the boiler, and again pass to the back end of a flue
along the bottom of the boiler to the chimney

35. 35
The various boiler mountings which are used on this boiler are : (i) Steam stop
valve, (ii) Pressure gauge, (iii) Water gauge, (iv) Fusible plug, (v) Blow off cock, (vi)
High steam low water safety valve, (vii) Feed check valve and (viii) Man hole.
The advantage possessed by this type of boiler is that the sediment contained in
the water falls to the bottom, where the plates are not brought into contact with the
hottest portion of the furnace gases. The reason for carrying the product of combustion
first through the side flues, and lastly through the bottom flue, is because the gases,
having parted with much of their heat by the time they reach the bottom flue, are less
liable to unduly heat the plates in the bottom of the boiler, where the sediment may have
collected.
Lancashire Boiler
This boiler is reliable, has simplicity of design, ease of operation and less
operating and maintenance costs. It is commonly used in sugar-mills and textile
industries where alongwith the power steam and steam for the process work is also
needed. In addition this boiler is used where larger reserve of water and steam are
needed.
The specifications of Lancashire boiler are given below
Diameter of the shell 2 to 3 m
Length of the shell 7 to 9 m
Maximum working pressure
Steam capacity 9000 kg/h
Efficiency 50 to 70%
The Lancashire boiler consists of a cylindrical shell inside which two large tubes
are placed. The shell is constructed with several rings of cylindrical from and it is placed
horizontally over a brickwork which forms several channels for the flow of hot gases.
These two tubes are also constructed with several rings of cylindrical form. They pass

36. 36
from one and of the shell to the other and are covered with water. The furnace is placed
at the front end of each tube and they are known as furnace tubes. The coal is introduced
through the fire hole into the grate. There is low brickwork fire bridge at the back of the
gate to prevent the entry of the burning coal and ashes into the interior of the furnace
tubes.
The combustion products from the grate pass up to the back end of the furnace
tubes, and then in downward direction. Thereafter they move through the bottom
channel or bottom flue up to the front end of the boiler where they are divided and pass
up to the side flues. Now they move along the two side flues and come to the chimney
flue from where they lead to the chimney. To control the flow of hot gases to the
chimney, dampers (in the form of sliding doors) are provided. As a result the flow of
airto the grate can be controlled. The various mountings used on the boiler are shown in
Figure.
In Cornish and Lancashire boilers, conical shaped cross tubes known as galloway
tubes (not shown) may be fitted inside the furnace tubes to increase their heating
surfaces and circulation of water. But these tubes have now become absolete for their
considerable cost of fitting. Moreover, they cool the furnace gases and retard
combustion.

37. 37
Locomotive Boiler
It is mainly employed in locomotives though it may also be used as a stationary
boiler. It is compact and its capacity for steam production is quite high for its size as it
can raise large quantity of steam rapidly.
Dimensions and the specifications of the locomotive boilers (made at Chitranjan
works in India) are given below

38. 38
Barrel diameter 2.095 m
Length of the barrel 5.206 m
Size of the tubes (superheater) 14cm
The locomotive boiler consists of a cylindrical barrel with a rectangular fire box
at one end and a smoke box at the other end. The coal is introduced through the fire hole
into the grate which is placed at the bottom of the fire box. The hot gases which are
generated due to burning of the coal are deflected by an arch of fire bricks, so that walls
of the fire box may be heated properly. The fire box is entirely surrounded by water
except for the fire hole and the ash pit which is situated below the fire box which is
fitted with dampers at its front and back ends. The dampers control the flow of air to the
grate. The hot gases pass from the fire box to the smoke box through a series of fire
tubes and then they are discharged into the atmosphere through the chimney. The fire
tubes are placed inside the barrel. Some of these tube are of larger diameter and the
others of smaller diameter. The superheater tubes are placed inside the fire tubes of
larger diameter. The heat of the hot gases is transmitted into the water through the
heating surface of the fire tubes. The steam generated is collected over the water surface.

39. 39
A dome shaped chamber known as steam dome is fitted on the upper part of the
barrel, from where the steam flows through a steam. pipe into the chamber. The flow of
steam is regulated by means of a regulator. From the chamber it passes through the super
heater tubes and returns to the superheated steam chamber (not shown) from which it is
led to the cylinders through the pipes, one to each cylinder.
In this boiler natural draught cannot be obtained because it requires a very high
chimney which cannot be provided on a locomotive boiler since it has to run on rails.
Thus some artificial arrangement has to be used to produce a correct draught. As such
the draught here is produced by exhaust steam from the cylinder which is discharged
through the blast pipe to the chimney. When the locomotive is standing and no exhaust
steam is available from the engine fresh steam from the boiler is used for the purpose.
The various boiler mountings include
Safety valves, pressure gauge, water level indicator, fusible plug, man hole, blow-off
cock and feed check valve.
Merits
1. High steam capacity.
2. Low cost of construction.
3. Portability.
4. Low installation cost.
5. Compact.
Demerits
1. There are chances to corrosion and scale formation in the water legs due to the
accumulation of sediments and the mud particles.
2. It is difficult to clean some water spaces.
3. Large flat surfaces need bracing.
4. It cannot carry high overlo1ds without being damaged by overheating.
5. There are practical constructional limits for pressure and capacity which do not meet
requirements.

40. 40
Scotch boiler
The scotch type marine boiler is probably the most popular boiler for steaming
capacities upto about 1000 kg/hr and pressure of about 17 bar. It is of compact size and
occupies small floor space.
Figure shows a single ended scotch type marine boiler. It consists of a cylindrical
shell in which are incorporated one to four cylindrical, corrugated steel furnaces. The
furnaces are internally fired and surrounded by water. A combustion chamber is located
at the back end of the furnace and is also surrounded by water. Usually each furnace has
its own combustion chamber. A nest of fire tubes run from the front tube plate to the
back tube plate. The hot gases produced due to burning of fuel move to the combustion
chambers (by means of the draught). Then they travel to the smoke box through the fire
tubes and finally leave the boiler via uptake and the chimney.
In a double ended scotch boiler furnaces are provided at each end. They look like
single ended boilers placed back to back. A doub‘e ended boiler for same evaporation
capacity, is cheaper and occupies less space as compared to single ended boiler.

41. 41
WATER TUBE BOILERS
The types of water tube boilers are given below
Babcock and Wilcox Water-tube Boiler
The water tube boilers are used exclusively, when pressure above 10 bar and
capacity in excess of 7000 kg of steam per hour is required. Babcock and Wilcox water-
tube boiler is an example of horizontal straight tube boiler and may be designed for
stationary or marine purposes.
The particulars (dimensions, capacity etc.) relating to this boiler are given below
Diameter of the drum 1.22 to 1.83 m
Length 6.096 to 9.144 m
Size of the water tubes 7.62 to 10.16 cm
Size of superheater tubes 3.84 to 5.71 cm
Working pressure 40 bar (max.)
Steaming capacity 40000 kg/h (max.)
Efficiency 60 to 80%
Figure shows a Babcock and Wilcox boiler with longitudinal drum. It consists of
a drum connected to a series of front end and rear end header by short riser tubes. To
these headers are connected a series of inclined water tubes of solid drawn mild steel.
The angle of inclination of the water tubes to the horizontal is about 15° or more.
A hand hole is provided in the header in front of each tube for cleaning and inspection of

42. 42
tubes. A feed valve is provided to fill the drum and inclined tubes with water the level of
which is indicated by the water level indicator. Through the fire door the fuel is supplied
to grate where it is burnt. The hot gases are forced to move upwards between the tubes
by baffle plates provided. The water from the drum flows through the inclined tubes via
downtake header and goes back into the shell in the form -of water and steam via uptake
header. The steam gets collected in the steam space of the drum. The steam then enters
through the antipriming pipe and flows in the superheater tubes where it is further heated
and is finally taken out through the main stop valve and supplied to the engine when
needed.
At the lowest point of the boiler is provided a mud collector to remove the mud
particles through a blow-down-cock.
The entire boiler except the furnace are hung by means of metallic slings or
straps or wrought iron girders supported on pillars. This arrangement enables the drum
and the tubes to expand or contract freely. The brickwork around the boiler encloses the
furnace and the hot gases.

43. 43
The various mountings used on the boiler are shown in Figure.
A Babcock Wilcox water tube boiler with cross draw differs from longitudinal
drum boiler in a way that how drum is placed with reference to the axis of the water
tubes of the boiler. The longitudinal drum restricts the number of tubes that can be
connected to one drum circumferentially and limits the capacity of the boiler. In the
cross drum there is no limitation of the number of connecting tubes. The pressure of
steam in case of cross drum boiler may be as high as 100 bar and steaming capacity upto
27000 kg/h.
Stirling Boiler
Stirling water tube boiler is an example of bent tube boiler. The main elements of
a bent type water tube boiler are essentially drum or drums and headers connected by
bent tubes. For large central power stations these boilers are very popular. They have
steaming capacities as high as 50000 kg/h and pressure as high as 60 bar.
Figure shows a small-sized stirling water tube boiler. It consists of two upper
drums known as steam drums and a lower drum known as mud or water drum. The
steam drums are connected to mud drum by banks of bent tubes. The steam and water
space of the steam drums are interconnected with each other, so that balance of water
and steam may be obtained. For carrying out cleaning operation a man hole at one end of
each drum is provided. The feed water from the economiser (not shown) is delivered to
the steam drum-i which is fitted with a baffle. The baffle deflects the water to move
downwards into the drum. The water flows from the drum 1 to the mud drum through
the rearmost water tubes at the backside. So the mud particles and other impurities will
move to the mud drum, where these particles may be deposited. As this drum is not
subjected to high temperature, so the impurities may not cause harm to the drum. The
blow-off cock blows off the impurities. The baffle provided at the mud drum deflects the
pure water to move upwards to the drum 1 through the remaining half of the water tubes
at the back. The water also flows from it to the drum 2 through the water tubes which are
just over the furnace. So they attain a higher temperature than the remaining portion of
the boiler and a major portion of evaporation takes place in these tubes. The steam is

44. 44
taken from the drum 1 through a steam pipe and then it passes through the superheater
tubes where the steam is superheated, Finally the steam moves to the stop valve from
where it can be supplied for further use. The combustion products ensuing from the grate
move in the upward and downward directions due to the brickwall baffles and are finally
discharged through the chimney into the atmosphere. Fire brick arch gets incandescent
hot and helps in combustion and preventing the chilling of the furnace when fire door is
opened and cold air rushes in. The steam drums and mud drum are supported on steel
beams independent of the brickwork. It is lighter and more flexible than the straight tube
boilers. But it is comparatively more difficult to clean and inspect the bent tubes.

45. 45
BOILER MOUNTINGS AND ACCESSORIES
Boiler Mountings. These are different fittings and devices which are necessary
for the operation and safety of a boiler. Usually these devices are mounted over boiler
shell. In accordance with the Indian boiler regulation the following mountings should be
fitted to the boilers
Two safety valves
• Two water level indicators
• A pressure gauge
• A steam stop valve
• A feed check valve
• A blow-off cock ;1
.An attachment for inspector‘s test gauge
A man hole
• Mud holes or sight holes.
Boilers of Lancashire and Cornish type should be fitted with a high pressure and
low water safety valve
All land boilers should have a fusible plug in each furnace.
Boiler Accessories. These are auxiliary plants required for steam boilers for
their proper operation and for the increase of their efficiency. Commonly used boiler
accessories are
• Feed pumps
• Injector

46. 46
• Economiser
• Air preheater
• Superheater
• Steam separator
• Steam trap.
BOILER MOUNTINGS
The various boiler mountings are discussed as follows
Water Level Indicator
The function of a water level indicator is to indicate, the level of water in the
boiler con8tdntly. It is also called water gauge. Normally two water level indicators are
fitted at the front end of every boiler. Where the boiler drum is situated at considerable
height from the floor, the water gauge is often inclined to make the water level visible
from any position. When the water being boated in the boiler transforms into steam the
level of water in the boiler shell goes on decreasing. For the proper working of the
boiler, the water must be kept at safe-level. If the water level falls below the safe level
and the boiler goes on producing steam without the addition of feed water, great damage
like crack and leak can occur to the parts of the boiler which get uncovered from water.
This can result in the stoppage of steam generation and boiler operation.
Figure shows a Hopkinson‘s water gauge. It is a common form of glass tube
water-level gauge. A is the front end plate of the boiler. F is a very hard glass tube
indicating water level and is connected to the boiler plate through stuffing boxes in
hollow gun metal castings (B, C) having flanges X, Y for bolting the plate.

47. 47
For controlling the passage of steam and water cocks D and E are
provided. When these cocks are opened the water stands in the glass tube at the same
level as in the boiler. K is the drain cock to blow out water at intervals so as not to allow
any sediments to accumulate. Upper and lower stuffing boxes are connected by a hollow
metal column G. Balls J and H rest in the position shown in the normal working of the
gauge. When the glass tube breaks due to rush of water in the bottom passage the balls
move to dotted positions and shut off the water and steam. Then the cocks D and E can
be safely closed and broken glass tube replaced. M, N, P and .R are screwed caps for
internal cleaning of the passage after dismantling. L is the guard glass ; it is tough and
does not give splinters on breaking. Thus when the gauge glass breaks, and this guard
glass which normally will hold flying pieces, also gives way, the pieces will not fly one
and hurt the attendant.
Pressure Gauge
The function of a pressure gauge is to measure the pressure exerted inside the
vessel. The gauge is usually mounted on the front top of the shell or the drum. It is
usually constructed to indicate upto double the maximum working pressure. Its dial is

48. 48
graduated to read pressures in kg‘cm2 (or bar) gauge (i.e., above atmospheric). There are
two types of pressure gauges: (i) Bourdon tube pressure gauge and (ii) Diaphragm type
pressure gauge. A pointer, which rotates over a circular graduated scale, indicates the
pressure.
A pressure gauge is known as compound pressure gauge if it is designed in such
a fashion so as to measure pressures above and below the atmosphere on the same dial.
Figure shows a Bourdon pressure gauge (single tube) a common type of pressure
gauge used. The essential feature of this gauge is the elliptical spring tube which is made
of a special quality of bronze and is solid drawn. One end A is closed by a plug and the
other is connected with a block C, the block is connected with a syphon tube (which is
full of condensed water). The steam pressure forces the water from the syphon tube into
elliptical tube and this causes the tube to become circular is cross-section. As the tube is
fixed at C, the other end A moves outwards. This outward movement is magnified by the
rod R and transmitted to toothed sector T. This toothed sector is hinged at the point H
and meshes with the pinion P fixed to the spindle of the pointer N. Thus the pointer
moves and registers the pressure on a graduated dial.
The movement of the free end of the elliptical tube is proportional to the
difference between external and internal pressure on the tube. Since the outside pressure

49. 49
on the tube is atmospheric, the movement of the free end is a measure of the boiler
pressurô above atmospheric i.e., gauge pressure.
Figure shows a U-tube syphon which connects the gauge to the boiler. The U-
tube syphon is connected to the steam space of the boiler and contains condensed steam
which enters the gauge tube. The condensed water transmits pressure to the gauge, and
at the sametime prevents steam from entering the pressure gauge. In case steam passes
into the gauge tube it will expand the tube and reading obtained will be false.
Furthermore metal may be affected. Plug R is used for connecting the inspector‘s
standard gauge and testing accuracy of boiler pressure gauge while in service. Plug Z is
employed for cleaning the syphon. Three way cock S is used for either connecting the
boiler pressure gauge to steam space or inspector‘s pressure gauge to the steam space.
The double-tube Bourdon gauge is more rigid than the single tube and more suitable for
locomotive
and portable boilers.
Safety Valves
The function of a safety valve is to release the excess steam when the pressure of
steam inside the boiler exceeds the rated pressure. As soon as the pressure of steam
inside the boiler exceeds the rated pressure the safety valve automatically opens and

50. 50
excess steam rushes out into the atmosphere till the pressure drops down to the normal
value. A safety valve is generally mounted on the top of the shell.
As per boiler regulations every boiler must be fitted at least with two safety
valves.
The various types of safety valves are enumerated and discussed as follows:
1. Dead weight safety valve.
2. Lever safety valve.
3. Spring loaded safety valve.
4. High steam and low water safety valve.
Dead Weight Safety Valve
Figure shows a dead weight safety valve. A is the vertical cast iron pipe through
which steam pressure acts. B is the bottom flange directly connected to seating block on
the boiler shell communicating to the steam space. V is the gun metal valve and VS is
the gun metal valve seat. D is another cast iron pipe for discharge of excess steam from
the boiler. W are the weights in the form of cylindrical disc of cast iron. WC is the
weight carrier carrying the weights W. The cover plate C covers these weights. The
steam pressure acts in the upward direction and is balanced by the force of the dead
weights W. The total dead-weights consist of the sum of the weights W, weight of the
valve V, weight of the weight carrier and weight of the cover plate C.
When the steam pressure is greater than the working pressure it lifts the valve
with its weights. So the steam escapes from the boiler and the steam pressure thereby
decreases.

51. 51
Merits of dead weight safety valve
1. Simplicity of design.
2. Gives quite a satisfactory performance during operation.
3. It cannot be easily tempered from the pressure adjustment view-point.
Demerits:
1. Unsuitable for use on any boiler where extensive vibration and movement are
experienced (e.g. locomotive and marine work).
2. It is not suitable for high pressure boilers because a large amount of weight is required
to balance the steam pressure.
Uses. It is mainly used for low pressures, low capacity, stationary boilers of the Cornish
and Lancashire types.
Lever Safety Valve
It consists of a lever and weight W. The valve (r1ade of gun metal) rests on the
valve seat (gun metal) which is screwed into the valve body ; the valve seat can be
replaced if required. The valve body is fitted on the boiler shell. One end of the lever is
hinged while at the other is suspended a weight W. The strut presses against the valve

52. 52
on seat against the steam pressure below the valve. The slotted lever guide allows
vertical movement to the lever.
When the steam pressure becomes greater than the normal working pressure, the
valve is lifted with the lever and the weight. Consequently, the steam escapes through
the passages between the valve and seat and the steam pressure decreases. The
disadvantages of this valve is that it admits of being tempered with, and the effect of a
small addition to the weight is magnified considerably in its action on the valve. Figure
shows the loading arrangement on the lever
Economiser
An economiser is a device in which the waste heat of the flue gases is utilised for
heating the feed water.
Economiser are of the two types (i) Independent type, and (ii) Integral type.
Former is installed in chamber apart from the boiler setting. The chamber is situated at
the passage of the flow of the flue gases from the boiler or boiler to the chimney. Latter
is a part of the boiler heating surface and is installed within the boiler setting.
Figure shows an independent type vertical tube economiser (called Green‘s
economiser). It is employed for boilers of medium pressure range upto about 25 bar. It
consists of a large number of vertical cast iron pipes P which are connected with two
horizontal pipes, one at the top and the other at the bottom. A is the bottom pipe through
which the feed water is pumped into the economiser. The water comes into the top pipe

53. 53
B from the bottom pipe (via vertical pipes) and finally flows to the boiler, The flue gases
move around the pipes in the direction opposite to the flow of water. Consequently, heat
transfer through the surfaces of the pipes takes place and water is thereby heated. A
blow-off cock is provided at the back end of vertical pipes to remove sediments
deposited in the bottom boxes. The soot of the flue gases which gets deposited on the
pipes reduces the efficiency of the economiser. To prevent the soot deposit, the scrapers
S move up and down to keep the external surface of the pipe clean (for better heat
transfer). By-pass arrangement enables to isolate or include the economiser in the path
of flue gases.

54. 54
The use of an economiser entails the following advantages
1. The temperature range between various parts of the boiler is reduced which results in
reduction of stresses due to unequal expansion.
2. If the boiler is fed with cold water it may result in chilling the boiler metal. Hot feed
water checks it.
3. Evaporative capacity of the boiler is increased.
4. Overall efficiency of the plant is increased.
Air Preheater
The function of the air pre-heater is to increase the temperature of air before it
enters the furnace. It is generally placed after the economiser ; so the flue gases pass
through the economiser and then to the air preheater. An air-preheater consists of plates
or tubes with hot gases on one side and air on the other. It preheats the air to be supplied
to the furnace. Preheated air accelerates the combustion and facilitates the burning of
coal.
Degree of preheating depends on
Type of fuel,
(iii) Rating at which the boiler and furnace are operated.
There are three types of air preheaters
1. Tubular type

55. 55
2. Plate type
3. Storage type.
Figure shows a tubular type air preheater. After leaving the boiler or
economiser the gaseous products of combustion travel through the inside of the tubes of
air preheater in a direction opposite to that of air travel and transfer some of their heat to
the air to be supplied to the furnace. Thus the air gets initially heated before being
supplied to the furnace. The gases reverse their direction near the bottom of the air
heater, and a soot hopper is fitted to the bottom of air heater casing to collect soot.
In the plate type air preheater the air absorbs heat from the hot gases being
swept through the heater at high velocity on the opposite side of a plate. Figure shows a
self explanatory sketch of a storage type air preheater (heat exchanger).

56. 56
Finally the gases escape to the atmosphere through the stack (chimney). The
temperature of the gases leaving the stack should be kept as low as possible so that there
is minimum loss of heat to the stack. Storage type air preheaters are employed widely in
larger plants.

57. 57
MODULE II
Steam Nozzles & Steam Turbines
Introduction
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: The highpressure, high-temperature steam first expands in the
nozzles emanates as a high velocity fluid stream.
1. 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.
2. 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

58. 58
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.
Flow through Nozzles
A nozzle is a duct that increases the velocity of the flowing fluid at the expense
of pressure drop. A duct which decreases the velocity of a fluid and causes a
corresponding increase in pressure is a diffuser . The same duct may be either a nozzle
or a diffuser depending upon the end conditions across it. If the cross-section of a duct
decreases gradually from inlet to exit, the duct is said to be convergent. Conversely if the
cross section increases gradually from the inlet to exit, the duct is said to be divergent. If
the cross-section initially decreases and then increases, the duct is called a convergent-
divergent nozzle. The minimum cross-section of such ducts is known as throat. A fluid
is said to be compressible if its density changes with the change in pressure brought
about by the flow. If the density does not changes or changes very little, the fluid is said
to be incompressible. Usually the gases and vapors are compressible, whereas liquids are
incompressible .
Steam Nozzles
 A steam nozzle is a passage of varying resection, which converts heat energy of
steam into Kinetic Energy as the steam expands from higher pressure to lower
pressure.
Purpose
 to produce high velocity jet of steam to run in steam turbines.
 The amount of energy so converted depends upon the pressure ratio and the type
of expansion
 Isentropic expansion provides the maximum expansion
 Generally nozzles are so shaped that isentropic expansion is obtained.

59. 59
Types of Nozzles
(1)Convergent Nozzle
 area diminishes from inlet section to at let section
 useful up to a pressure ratio of 0.58 using saturated steam.
(2)Divergent Nozzle
(3)Convergent Divergent
 Nozzle with divergent part in addition to the convergent part to obtain more
pressure drop acceleration is .....
 divergent portion is long
 T is divergent angle
 Least cross section is called throat.
Two Functions of turbine nozzle
(i) a portion heat energy to kinetic energy
(ii) In Impulse turbine directs high velocity steam to turbine blades.
Reaction turbines – nozzle movable
Flow of Steam Trhough Nozzle
Consider a unit mass flow of steam through a nozzle.
Applying steady flow energy equation to the sections 1 and 2.
2 2
1 2
1 2
V V1 1
h R h W
1000 2 2 1000
     
h = enthalpy
V = velocity
W = work transfer
Q = heat transfer
Since expansion. is isentropic and there is no external work done during the flow of

60. 60
steam W = Q = O
2 2
2 1
1 2
V V1
h h
1000 2 2
 
   
 
 2 2
2 1 1 2V V h h 2000   
2
2 1 1 2V V 2000(h h )  
Since V1 <<V2
2 1 2V 2000(h h )  = d44.72 h
This is the general energy equation irrespective of the shape of the nozzle.
Mass of steam discharged through nozzle
The flow of steam through the nozzle may be represented by an eqn of the form
Pvn
= constant
n = 1.135 for saturated steam
= 1.3 for superheated steam
Steam performs works upon itself by accelerating itself to a high velocity.
As the steam pressure drops its enthalpy is reduced. This reduction of the
enthalpy must be equal to the increase in KE.
heat drop = work done percentage of steam during cycle.
2 2
2 1
1 1 2 2
V V n
(P V P V )
2 2 n 1
  

V1<<V2
2
2
1 1 2 2
V n
(P V P V )
2 n 1
 

2 2
1 1
1 1
P Vn
P V (1
n 1 P V
 


61. 61
we know that n n
1 1 2 2P V P V
2 1
1 2
V P
1/ n
V P
 
 
 

2
2 2 1
1 1
1 2
V P Pn
P V 1 1/ n
2 n 1 P P
  
       
2
1 1
1
Pn n 1
P V 1
n 1 P n
    
         
2
2 1 1
1
Pn n 1
V 2 P V 1
n 1 P n
   
   
   
Volume of steam flowing per second
= A × V2
Specific volume of steam V2 m3
/Kg
mass of steam discharged per second
2
Volumeof steamdischargedper
Specificvolumeof 1Kgof steant at P

2
2
AV
V

n 1
n
2
1 1
2 1
PA n
2 P V 1
V n 1 P
 
  
        
1/ n
2 1
1 2
V P
V P
 
 
 
½
1
2 1
2
P
V V
P
 
  
 
1/ n
1
1 2
P1 1
V2 V P
 
  
 

62. 62
1/ n
1 2
1 1
1 2 1
P PA n n 1
m 2 P V 1
V P n 1 P n

     
       
    
n 1
1/ n
n
2 2
1 1
1 1 1
P PA 2n
P V 1
V P n 1 P

  
    
          
 
n 1
2/ n
n
1 2 2
1 1 1
P P P2n
A 1
n 1 V P P
 
    
            
 
n 1
n
1 2 2
1 1 1
P P P2n
A 2/ n
n 1 V P P
 
    
           
Condition for Maximum Discharge through a nozzle (critical pressure ratio)
n 1
2/ n
n
1 2 2
1 1 1
P P P2n
m A
n 1 V P P
 
    
           
A nozzle is designed for maximum discharge by designing a certain throat pressure.
There is only one value of the ratio 2
1
P
P
, which produces maximum discharge.
The portion of the equation which contains 2
1
P
P
is differentiated and equated to zero, for
maximum discharge.
n 1
n
2 2
1 12
1
P Pd 2
0
P n PP
d
P
 
    
              
 
2 n 1
1 1
n n
2 2
1 1
P P2 n 1
0
n P n P

 
   
    
   

63. 63
1
n
2 2
1 1
P P2 2 n n 1
n P n n P
    
   
   
2 n
1/ n
n
2 2
1 1
P P N 1 n
P P n 2


    
     
   
1 n
n
2
1
P N 1
P 2

  
 
 
 
n n
1 n 1 n2
1
P n 1 n 1
P 2 2

      
    
   
n
n 1n 1
2

 
 
 
n
n 12
n 1
 
 
 
P2
P1
is called critical pressure ratio and the pressure P2 at the throat is known as
critical pressure.
STAGNATION, SONIC PROPERTIES AND ISENTROPIC EXPANSION IN NOZZLE
The stagnation values are useful reference conditions in a compressible flow.
Suppose the properties of a flow (such as T, p, ρ etc.) are known at a point. The
stagnation properties at a point are defined as those which are to be obtained if the local
flow were imagined to cease to zero velocity isentropically. The stagnation values are
denoted by a subscript zero. Thus, the stagnation enthalpy is defined as
For a calorically perfect gas, this yields,

64. 64
which defines the stagnation temperature. It is meaningful to express the ratio of
in the form
or,
If we know the local temperature (T) and Mach number (Ma), we can fine out the
stagnation temperature . Consequently, isentropic relations can be used to obtain
stagnation pressure and stagnation density as.
In general, the stagnation properties can vary throughout the flow field.
However, if the flow is adiabatic, then is constant throughout the flow. It
follows that the and are constant throughout an adiabatic flow, even in the
presence of friction. Here a is the speed of sound and the suffix signifies the stagnation
condition. It is understood that all stagnation properties are constant along an isentropic
flow. If such a flow starts from a large reservoir where the fluid is practically at rest,
then the properties in the reservoir are equal to the stagnation properties everywhere in
the flow (Fig. 1.1).

65. 65
Fig 1.1 An isentropic process starting from a reservoir
There is another set of conditions of comparable usefulness where the flow is sonic,
Ma=1.0. These sonic, or critical properties are denoted by asterisks: and. .
These properties are attained if the local fluid is imagined to expand or compress
isentropically until it reachers Ma=1.
We have already discussed that the total enthalpy, hence , is conserved so long the
process is adiabatic, irrespective of frictional effects. In contrast, the stagnation pressure
and density decrease if there is friction.
From Eq.(1), we note that
or,
is the relationship between the fluid velocity and local temperature (T), in an adiabatic
flow. The flow can attain a maximum velocity of

66. 66
As it has already been stated, the unity Mach number, Ma=1, condition is of special
significance in compressible flow, and we can now write from Eq.(2), (3) and (4).
For diatomic gases, like air , the numerical values are
The fluid velocity and acoustic speed are equal at sonic condition and is
or,
We shall employ both stagnation conditions and critical conditions as reference
conditions in a variety of one dimensional compressible flows.
Effect of Area Variation on Flow Properties in Isentropic Flow
In considering the effect of area variation on flow properties in isentropic flow, we shall
concern ourselves primarily with the velocity and pressure. We shall determine the
effect of change in area, A, on the velocity V, and the pressure p.
From Bernoulli's equation, we can write

67. 67
or,
Dividing by , we obtain
---- 1.1
A convenient differential form of the continuity equation as
Substituting from Eq. (1.1)
-----1.2
Invoking the relation ( ) for isentropic process in Eq. (1.2), we get
-----1.3
From Eq. (1.3), we see that for Ma<1 an area change causes a pressure change of
the same sign, i.e. positive dA means positive dp for Ma<1. For Ma>1, an area change
causes a pressure change of opposite sign.
Again, substituting from Eq.(1.1) into Eq. (1.3), we obtain
-------1.4

68. 68
From Eq. (1.4), we see that Ma<1 an area change causes a velocity change of
opposite sign, i.e. positive dA means negative dV for Ma<1. For Ma>1, an area change
causes a velocity change of same sign.
These results are summarized in Fig.1.1, and the relations (1.3) and (1.4) lead to
the following important conclusions about compressible flows:
1. At subsonic speeds (Ma<1) a decrease in area increases the speed of flow. A
subsonic nozzle should have a convergent profile and a subsonic diffuser should
possess a divergent profile. The flow behaviour in the regime of Ma<1 is
therefore qualitatively the same as in incompressible flows.
2. In supersonic flows (Ma>1), the effect of area changes are different. According
to Eq. (1.4), a supersonic nozzle must be built with an increasing area in the flow
direction. A supersonic diffuser must be a converging channel. Divergent nozzles
are used to produce supersonic flow in missiles and launch vehicles.
Fig 1.2 Shapes of nozzles and diffusersin subsonic and supersonic regimes
Suppose a nozzle is used to obtain a supersonic stream staring from low speeds
at the inlet (Fig.1.2). Then the Mach number should increase from Ma=0 near the inlet to
Ma>1 at the exit. It is clear that the nozzle must converge in the subsonic portion and
diverge in the supersonic portion. Such a nozzle is called a convergent-divergent nozzle.

69. 69
A convergent-divergent nozzle is also called a de Laval nozzle, after Carl G.P. de Laval
who first used such a configuration in his steam turbines in late nineteenth century (this
has already been mentioned in the introductory note). From Fig.1.2 it is clear that the
Mach number must be unity at the throat, where the area is neither increasing nor
decreasing. This is consistent with Eq. (1.4) which shows that dV can be non-zero at the
throat only if Ma=1. It also follows that the sonic velocity can be achieved only at the
throat of a nozzle or a diffuser.
Fig 1.3 A convergent-divergent nozzle
The condition, however, does not restrict that Ma must necessarily be unity at the throat,
According to Eq. (1.4), a situation is possible where at the throat if dV=0 there.
For an example, the flow in a convergent-divergent duct may be subsonic everywhere
with Ma increasing in the convergent portion and decreasing in the divergent portion
with at the throat (see Fig.1.3). The first part of the duct is acting as a nozzle,
whereas the second part is acting as a diffuser. Alternatively, we may have a convergent-
divergent duct in which the flow is supersonic everywhere with Ma decreasing in the
convergent part and increasing in the divergent part and again at the throat (see
Fig. 1.4).

70. 70
Fig 1.3 Convergent-divergent duct with at throat
Fig 1.4 Convergent-divergent duct with at throat
Isentropic Flow of a vapor or gas through a nozzle
First law of thermodynamics:

71. 71
(if )
where is enthalpy drop across the nozzle
Again we know, Tds = dh - νdp
For the isentropic flow, dh = νdp
or,
or,
Assuming that the pressure and volume of steam during expansion obey the law pνn
=
constant, where n is the isentropic index

72. 72
Now, mass flow rate
Therefore, the mass flow rate at the exit of the nozzle
=
The exit pressure, p2 determines the for a given inlet condition. The mass flow rate is
maximum when,
For maximum ,

73. 73
n = 1.4, for diatomic gases
for super saturated steam
for dry saturated steam
for wet steam with dryness fraction x
For , (50%drop in inlet pressure)
If we compare this with the results of sonic properties, as described in the earlier
section, we shall observe that the critical pressure occurs at the throat for Ma = 1. The
critical pressure ratio is defined as the ratio of pressure at the throat to the inlet pressure,
for checked flow when Ma = 1
Expansion of Steam in a Nozzle
Figure 1.5 Super Saturated Expansion of Steam in a Nozzle
 The process 1-2 is the isentropic expansion. The change of phase will begin to
occur at point 2
 vapour continues to expand in a dry state
 Steam remains in this unnatural superheated state untit its density is about eight
times that of the saturated vapour density at the same pressure
 When this limit is reached, the steam will suddenly condense

74. 74
 Point 3 is achieved by extension of the curvature of constant pressure line
from the superheated region which strikes the vertical expansion line at 3 and
through which Wilson line also passes. The point 3 corresponds to a metastable
equilibrium state of the vapour.
 The process 2-3 shows expansion under super-saturation condition which is not
in thermal equilibrium
 It is also called under cooling
 At any pressure between and i.e., within the superheated zone, the
temperature of the vapous is lower than the saturation temperature corresponding
to that pressure
 Since at 3, the limit of supersaturation is reached, the steam will now condense
instantaneously to its normal state at the constant pressure, and constant enthalpy
which is shown by the horizontal line where is on normal wet area
pressure line of the same pressure .
 is again isentropic, expansion in thermal equilibrium.
 To be noted that 4 and are on the same pressure line.
Thus the effect of supersaturation is to reduce the enthalpy drop slightly during
the expansion and consequently a corresponding reduction in final velocity. The
final dryness fraction and entropy are also increased and the measured discharge
is greater than that theoretically calculated.
Degree of super heat =
= limiting saturation pressure
= saturation pressure at temperature shown on T-s diagram
degree of undercooling - -

75. 75
is the saturation temperature at
= Supersaturated steam temperature at point 3 which is the limit of supersaturation.
Supersaturated vapour behaves like supersaturated steam and the index to expansion
Problems
Qn.1. Steam is expanded in a set of nozzles from 10 bar and 2000C to 5 bar. What type
of nozzle is it? Neglecting the initial velocity find minimum area of the nozzle required
to allow a flow of 3 kg/s under the given conditions. Assume that expansion of steam to
be isentropic.
Solution. Steam pressure at the entry to the steam nozzles,
p1 = 10 bar, 200o
C
Steam exit pressure, p1 = 5 bar
We know that,
 
13n
0.3n 12
1
p 2 2
p n 1 1.3 1
   
    
    
4.333
2
0.5457
2.3
 
  
 
2 1p p 0.5457 10 0.5457 5.5 bar    
Since throat pressure (p2) is greater than the exit pressure, the nozzle used is
convergent divergent nozzle. The minimum area will be at throat, where the pressure is

76. 76
5.5 bar.
From Mollier chart, 1 2h h 120 kJ / kg
Specific volume, 3
u 0.345 m / kg
Velocity at the throat, 2C 44.72 120 489.88 m/s 
Throat area, 2
2
2
mv 3 0.345
A 0.0021 m
C 489.88

  
Qn.2. Steam having pressure of 10.5 bar and 0.95 dryness is expanded through
convergent-divergent nozzle and the pressure of steam leaving the nozzle is 0.85 bar.
Find the velocity at the throat for maximum discharge conditions. Index of expansion
may be assumed as 135. Calculate mass rate of flow of steam through the nozzle.
Solution. The pressure at throat for maximum discharge,
n 1.135
n 1 1.135 1
2 1
2 2
p p 10.5
n 1 1.135 1
    
    
    
8.41
2
10.5 6.06 bar
2.135
 
  
 
The velocity C2 at throat for maximum discharge is given by (eqn. 11)
 5
2 1 1
n 1.135
C 2 p v 2 10.5 10 0.95 0.185
n 1 1.135 1
     
 
443 m/s
[C2 can also be obtained with the help of steam tables or Mollier chart also]
n n
1 1 2 2p v p v
 1.135 1.135
210.5 0.95 0.185 6.06 v  
3
2v 0.285 m / kg
Mass flow rate, 2 2
2
A C 1 443
m
u 0.285

 
2
1554.4 kg/ m of throat area

77. 77
Qn. 3 A convergent-divergent nozzle is to be designed in which steam initially at 14
bar and 800C of superheat is to be expanded down to a back pressure of 1.05 bar.
Determine the necessary throat and exit diameters of the nozzle for a steam discharge of
500 kg/hour, assuming that the expansion is in thermal equilibrium throughout and
friction reheat amounting to 12% of the total isentropic enthalpy drop to be effective in
the divergent part of the nozzle.
Solution. o
1 sup sp 14 bar, t t 80 C  
o
sup s 3t t 80 195 80 275 C; p 1.05bar     
We know that,
n 1.3
n 1 1.3 12
1
p 2 2
0.546
p n 1 1.3 1
    
     
    
ie, 2 1p p 0.546 14 0.546 7.64 bar    
From Mollier chart, h1 = 2980 kJ/kg, h2 = 2850 kJ/kg
h3 = 2490 kJ/kg, 3x 0.921 
u2 = 0.287 m3
/kg (From Mollier chart)
d 1 2h h h 2980 2850 130 kJ / kg    
d 1 3h h h 2980 2490 490 kJ / kg     

78. 78
For throat:
2 dC 44.72 h 44.72 130 509.8 m/s  
Now, 2 2 2
2
A C A 509.8
m
u 0.287

 
6 2
2
m 0.287 500 0.287
A 7.82 10 m
509.8 3600 509.8
 
    

ie, 2 5
2D 7.82 10
4

 
or
1/ 25
2
7.82 10 4
D 0.009978 m or 9.9 mm
  
    
ie, Throat diameter = 9.9 mm.
At exit:
 3 dC 44.72 kh 44.72 1 0.12 490 928.6m/s     
3
3
3 3 gu x u 0.921 1.69 1.556 m / kg    
23
3
3
m u 500 1.556
A 0.0002327 m
3600 928.6c
 
   

ie, 2
3D 0.0002327
4


or,
1/ 2
3
0.0002327 4
D 0.0172m or 17.2 mm
 
  
 
Qn. 4 Dry saturated steam enters the Steam nozzle at a pressure of 15 bar and is
discharged at a pressure of 2.0 bar. If the dryness fraction of discharge steam is 0.96,
what will be the final velocity of steam? Neglect initial velocity of steam.
If 10% of heat drop is lost in friction, find the percentage reduction in the final
velocity.

79. 79
Solution: Initial pressure of steam, p1 = 16 bar, x1 = 1.
Final pressure of steam, p2 = 2.0 bar, x2 = 0.96
From steam tables:
At p1 = 15 bar, x1 = 1 : h1 = hg = 2789.9 kJ/kg.
At p2 = 2 bar: 2fh 504.7 kJ / kg , 2fgh 2201.6 kJ / kg
2 22 f 2 fh h x h 504.7 0.96 2201.6 2618.2kJ / kg     
The velocity of steam at discharge from nozzle in S.I. units is given by:
 2 d 1 2C 44.72 h 44.72 h h  
 44.72 2789.9 2618.2 585.9 m/s  
ie, Final velocity of steam = 585.9 m/s.
In case 10% of heat drop is lost in friction, nozzle co-efficient.
= 1.0 – 0.1 = 0.9
Hence the velocity of steam = d44.72 kh
 44.72 0.9 2789.9 2618.2 555.9 m/s  
Percentage reduction in velocity =
585.9 555.9
100 5.12%
585.9

 
Qn. 5. Steam initially dry and saturated is expanded in a nozzle from 15 bar at 3000C to
1.0 bar. If the frictional loss in the nozzle is 12% of the total heat drop calculate the mass
of steam discharged when exit diameter of the nozzle is 15 mm.
Solution: Pressure, p1 = 15 bar, 300o
C
Pressure, p2 = 1.0 bar
Frictional loss in nozzle = 12%

80. 80
-efficient, k = 1 – 0.12 = 0.88.
Exit diameter of nozzle, d2 =15 mm
Neglecting the velocity of steam at inlet to the nozzle, the velocity of steam at
exit from the nozzle is given by
 2 d 1 2C 44.72 kh 44.72 0.88 h h    
 44.72 0.88 3037 2515 958.5 m/s   
Dryness fraction of steam at discharge pressure, 2x 0.93 
Specific volume of dry saturated steam at 1.0 bar, 2
3
gv 1.694 m / kg .
Hence mass of steam discharged through nozzle per hour
 
2
2
2 2
2 g
/ 4 15/1000A C
3600 3600 387 kg / h
x u 0.93 1.694
  
    


81. 81
STEAM TURBINES
Turbines
 We shall consider steam as the working fluid
 Single stage or Multistage
 Axial or Radial turbines
 Atmospheric discharge or discharge below atmosphere in condenser
 Impulse/and Reaction turbine
Impulse Turbines
Impulse turbines (single-rotor or multirotor) 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. 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 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 Fig. 2.1.
Figure 2.2 shows the velocity diagram indicating the flow through the turbine
blades.

82. 82
Figure 2.1 Schematic diagram of an Impulse Trubine
and = Inlet and outlet absolute velocity
and = Inlet and outlet relative velocity (Velocity relative to the rotor blades.)
U = mean blade speed
= nozzle angle, = absolute fluid angle at outlet
It is to be mentioned that all angles are with respect to the tangential velocity ( in the
direction of U )
Figure 2.2 Velocity diagram of an Impulse Turbine

83. 83
and = Inlet and outlet blade angles
and = Tangential or whirl component of absolute velocity at inlet and outlet
and = Axial component of velocity at inlet and outlet
Tangential force on a blade,
(mass flow rate X change in velocity in tangential direction)
or,
Power developed =
Blade efficiency or Diagram efficiency or Utilization factor is given by
or,
stage efficiency
or,
or,

84. 84
Optimum blade speed of a single stage turbine
where, = friction coefficient
= Blade speed ratio
is maximum when also
or,
or,
is of the order of 180
to 220

85. 85
Now, (For single stage impulse turbine)
The maximum value of blade efficiency
For equiangular blades,
If the friction over blade surface is neglected
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
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 and (b) pressure
compounding
Either of the above methods or both in combination are used to reduce the high
rotational speed of the single stage turbine.

86. 86
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. These two rows are separated by one row of fixed blades attached to the turbine
stator, which has the function of redirecting the steam leaving the first row of moving
blades to the second row of moving blades. A Curtis stage impulse turbine is shown in
Fig. 23.1 with schematic pressure and absolute steam-velocity changes through the
stage. 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.
Figure 2.3 Velocity Compounding arrangement
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 Figure 2.3.

87. 87
Figure 2.4 Velocity diagrams for the Velocity-Compounded Impulse
turbine
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.
K, the blade velocity coefficient may be different in each row of blades
Work done =
End thrust =
The optimum velocity ratio will depend on number of stages and is given by
• Work is not uniformly distributed (1st >2nd )

88. 88
• The fist stage in a large (power plant) turbine is velocity or pressure compounded
impulse stage.
Pressure Compounding or Rateau Staging
The Pressure - Compounded Impulse Turbine
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
(Figure 2.5). 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.

89. 89
Figure 2.5 Pressure-Compounded Impulse Turbine
Pressure drop - takes place in more than one row of nozzles and the increase in kinetic
energy after each nozzle is held within limits. Usually convergent nozzles are used
We can write
where is carry over coefficient
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, 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 (Fig. 2.5) shows that pressure continuously drops
through all rows of blades, fixed and moving. The absolute steam velocity changes

90. 90
within each stage as shown and repeats from stage to stage. Figure 2.6 shows a typical
velocity diagram for the reaction stage.
Figure 2.5 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
Degree of Reaction =
or,
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.

91. 91
Figure 2.7 The velocity diagram of reaction blading
The velocity triangles are symmetrical and we have
Energy input per stage (unit mass flow per second)
From the inlet velocity triangle we have,

92. 92
Work done (for unit mass flow per second)
Therefore, the Blade efficiency
Reaction Turbine, Continued
Put then
For the maximum efficiency and we get
from which finally it yields
Figure 2.8 Velocity diagram for maximum efficiency

93. 93
Absolute velocity of the outlet at this stage is axial (see figure 2.8). In this case,
the energy transfer
can be found out by putting the value of in the
expression for blade efficiency
is greater in reaction turbine. Energy input per stage is less, so there are more
number of stages.
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 Figure 25.2
Figure 2.9 Different stage of a steam turbine

94. 94
The total expansion is divided into four stages of the same efficiency and pressure
ratio.
The overall efficiency of expansion is . The actual work during the expansion from 1
to 2 is
Reheat factor (R.F.)=
Problems
Qn. 1 In a De Laval turbine steam issues from the nozzle with a velocity of 1200 m/s.
The nozzle angle is 200, the mean blade velocity is 400 m/s, and the inlet and outlet
angles of blades are equal. The mass of steam flowing through the turbine per hour is
1000 kg.
Calculate:
(i) Blade angles.
(ii) Relative velocity of steam entering the blades.
(iii) Tangential force on the blades.
(iv) Power developed.
(v) Blade efficiency.
Take blade velocity co-efficient as 0.8.

95. 95
Solution. Absolute velocity of steam entering the blade, C1 = 1200 m/s
o
Mean blade velocity, Cbl = 400 m/s
Blade velocity co-efficient, K = 0.8
Mass of steam flowing through the turbine, ms = 1000 kg/h.
Ref. Procedure of drawing the inlet and outlet triangles (LMS and LMN
respectively is as follows:)
Select a suitable scale and draw line LM to represent Cbl (= 400 m/s)
At point L make angle of 20o
1 =
(1200 m/s). Join MS produces M to meet the perpendicular drawn from S at P. Thus
inlet triangle is completed.
By measurement: 1
o
r30 , C 830 m/s  
o
30   
Now, 2 1r rC KC 0.8 830 664 m/s   
At point M make an angle of 30o
cut the length MN to represent
 0rC 664m/s . Join LN. Produce L to meet the perpendicular drawn from N at Q.
Thus outlet triangle is completed.
o
30  
(ii) Relative velocity of steam entering the blade, 1rC
1rC MS 830 m/s 
(iii) Tangential force on the blades:
Tangential force    1 0s w w
1000
m C C 1310 363.8 N
60 60
   


96. 96
(iv) Power developed, P:
 1 2s w w bl
1000 1310 400
P m C C C kW 145.5 kW
60 60 1000

    

(v) Blade efficiency, bl
 1 2bl w w
bl 2 2
1
2C C C 2 400 1310
72.8%
C 1200
  
   
Qn. 2 A stage of a turbine with Parson‘s blading delivers dry saturated steam at 2.7 bar
from the fixed blades at 90 m/s. The mean blade height is 40 mm, and the moving blade
exit angle is 200. The axial velocity of steam is ¾ of the blade velocity at the mean
radius. Steam is supplied to the stage at the rate of 9000 kg/h. The effect of the blade tip
thickness on the annulus area can be neglected. Calculate:
(i) The wheel speed in r.p.m.;
(ii) The diagram power;
(iii) The diagram efficiency;
(iv) The enthalpy drop of the steam in this stage.
Solution. The velocity diagram is shown in Fig. 19.47 (…) and the blade wheel annulus
is represented in Fig. 19.47 (b).
Pressure = 2.7 bar, x = 1, C1 = 90 m/s, h = 40 mm = 0.04 m.
1 0
o
f f bl20 , C C 3/ 4C      = 9000 kg/h
Rate of steam supply
(i) Wheel speed, N:
o o
f bt 1C 3/ 4 C C sin 20 90sin 20 30.78 m/s   
blC 30.78 4/3 41.04 m/s  

97. 97
The mass flow of steam is given by : f
2
C A
m
u

(where A is the annulus area, and u is the specific volume of the steam)
In this case, gu u at 2.7 bar = 0.6686 m3
/kg
s
9000 30.78
m
3600 0.6686
   or 29000 0.6686
A 0.054 m
3600 30.78

 

(where D is the mean diameter, and h is the mean blade height)
0.054 D 0.04    or
0.054
D 0.43 m
0.04
 

Also, bl
DN
C
60

 or
0.43 N
41.04
60
 

41.04 60
N 1823 r.p.m.
0.43

 


98. 98
(ii) The diagram power:
Diagram power s blm C C
Now, 1 blC 2C cos C    o
2 90 cos20 41.04 128.1 m/s    
 Diagram power =
9000 128.1 41.04
13.14 kW
3600 1000
 


(iii) The diagram efficiency:
Rate of doing work per kg/s = blC C 128.1 41.04Nm/s  
Also, energy input to the moving blades per statge
0 1 1 1
2 2 2 2 22 2 2
r r 1 r r21 1 1
1
C C C C CC C C
C
2 2 2 2 2 2
 
        0r 1C C
Referring to ... we have
1
2 2 2
r 1 bl 1 blC C C 2C C cos   
2 2 o
90 41.04 2 90 41.04 cos20     
8100 1684.28 6941.69  
1rC 53.3 m/s 
Energy input =
2
2 53.3
90 6679.5 Nm per kg /s
2
 
 Diagram efficiency =
128.1 41.04
0.787 or 78.7%
6679.5


(iv) Enthalpy drop in the stage:
Enthalpy drop in the moving blades
0 1
2 2 2 2
r rC C 90 53.3
2.63 kJ / kg
2 2 1000
 
  

 0 1r rC C
 Total enthalpy drop per stage = 2 × 2.63 = 5.26 kJ/kg

99. 99
Module III
GAS TURBINES
The gas turbines are mainly divided into two groups:
1. Constant pressure combustion gas turbine
(a) Open cycle constant pressure gas turbine
(b) Closed cycle constant pressure gas turbine
2. Constant volume combustion gas turbine.
In almost all the fields open cycle gas turbine plants are used. Closed cycle plants were
introduced at one stage because of their ability to burn cheap fuel
Merits of gas turbines
(I) Merits over IC engines:
1. The mechanical efficiency of a gas turbine (95%) is quite high as compared with
IC engines (85%0 since the IC engine has a large number of sliding parts.
2. A gas turbine does not require a fly wheel as the torque on the shaft is continuous
and uniform. Whereas a flywheel is a must in case of an IC engine.
3. The weight of gas turbine per H.P developed is less than that of an I.C engine.
4. The gas turbine can be driven at very high speeds (40000 r.p.m) whereas this is
not possible with I.C engines.
5.the components of gas turbine can be made lighter since the pressure used in it are
very low, say 5 bar compared with I.C engine say 60 bar.

100. 100
6. In the gas turbine the ignition and lubrication systems are much simpler as
compared with I.C engines.
7. Cheaper fuels such as par affine type, residue oils or powdered coal can be used
whereas special grade fuels are employed in petrol engine to check knocking or
pinking.
8. The exhaust from gas turbine is less polluting comparatively since excess air is
used for combustion.
9. Because of low specific weight the gas turbines are particularly suitable for use in
aircrafts.
Demerits of gas turbines
1. The thermal efficiency of a simple turbine cycle is low (15 to 20%) as
compared with I.C engines (25 to 30%).
2. With wide operating speeds the fuel control is comparatively difficult.
3. Due to higher operating speeds it is imperative to have a speed reduction
device.
4. It is difficult to start a gas turbine as compared to an I.C engine.
5. The gas turbine valves need a special cooling system.
6. One of the main demerits of a gas turbine is its very poor thermal efficiency at
part loads, as the quantity of air remains same irrespective of load, and output
is reduced by reducing the quantity of fuel supplied.
7. Owing to the use of nickel chromium alloy, the manufacture of the blades is
difficult and costly.