1. CHAPTER 2
SHAFT POWER CYCLES

2. Chapter2 Shaft Power Cycles
There are two main types of power cycles;
1. Shaft power cycles : Marine and Land based power plants.
2. Aircraft propulsion cycles: Performance depends upon forward speed & altitude.
Chapter Shaft Power Cycles

3. SHAFT POWER CYCLES I Ideal Cycles
CHAPTER 2
SHAFT POWER CYCLES I
Ideal Cycles

4. Chapter2 Shaft Power Cycles
Ideal Cycles
The analysis is based on the :
perfection of individual components
w , h depend upon r and Tmax
w : Specific power output
h : Cycle efficiency
r : Pressure ratio
Tmax : Max. cycle Temperature
Chapter Shaft Power Cycles

5. Ideal Cycles - Assumptions
a) Compression and expansion processes are isentropic
b) The change of Kinetic Energy of the working fluid
between the inlet and outlet of each component is
negligible.
Chapter Shaft Power Cycles

6. Ideal Cycles - Assumptions
c) No pressure losses in the inlet ducting, combustion chambers, heat exchangers, intercoolers, exhaust ducting and ducts connecting the components.
d) The composition of the working fluid does not change and it is a prefect gas with
constant specific heats
Chapter Shaft Power Cycles

7. Ideal Cycles - Assumptions :
e) The mass flow rate of gas is constant
f) Heat transfer in the Heat Exchanger is complete; so in conjunction with (d)+(e), temperature rise on the cold side is equal to the temperature drop on the hot side.
(d,e) indicates that the combustion chamber is such
that it is as if heated by an external heat source.
Chapter Shaft Power Cycles

8. SIMPLE Gas Turbine CYCLE
The ideal cycle for a simple Gas Turbine is the BRAYTON (or JOULE) cycle.
Fig. 2.1 Simple Gas Turbine
Chapter Shaft Power Cycles

9. SIMPLE Gas Turbine CYCLE
Steady flow energy equation:
q = hII - hI + 1/2 ( vII2 - vI2) + w
where : q = heat transfer per unit mass flow.
w = work per unit mass flow.
w12 = - (h2 - h1) = - cp (T2 – T1)
q23 = (h3 - h2) = cp (T3 - T2)
w34 = (h3 - h4) = cp (T3 - T4)
Chapter Shaft Power Cycles

10. SIMPLE Gas Turbine CYCLE
The efficiency of the cycle is then :
Chapter Shaft Power Cycles

11. SIMPLE Gas Turbine CYCLE
The cycle temperatures can be related to the pressure ratio rp ;
rp = p2/p1 = p3/p4
For isentropic compression and expansion;
p/r = RT ; p/rg = const.
T2/T1 = rp(g-1)/g and T3/T4 = rp(g-1)/g
Chapter Shaft Power Cycles

12. The Efficiency of the Simple Gas Turbine Cycle
Chapter Shaft Power Cycles

13. The Efficiency of the Simple Gas Turbine Cycle
Then the cycle efficiency is;
where; ( 2.1 )
Chapter Shaft Power Cycles

14. SIMPLE Gas Turbine CYCLE
The specific work output w , depends upon the size of the plant for a given power.
It is found to be a function of not only pressure ratio, but also of maximum cycle temperature T3. Thus;
w = cp (T3-T4) - cp (T2-T1)
can be expressed as;
( 2.2 )
The specific work output is a function of " t " (T3/T1) and "rp" ;
w = w (t, rp).
Chapter Shaft Power Cycles

15. SIMPLE Gas Turbine CYCLE
Fig Efficiency and specific work output - Simple Cycle
FIG. 2.2 Efficiency and specific work output - simple cycle
Chapter Shaft Power Cycles

16. SIMPLE Gas Turbine CYCLE
T3 : Maximum Cycle Temperature,
imposed by the metallurgical limit.
t = T3/T1 = for long life industrial plants,
t = for aircraft engines with cooled turbine blades.
From the T-S diagram, it is clear that when
rp= 1 or rp = (T3/T1)(g/g-1)  w = 0
Thus in between there is a maximum (or minimum) value for w
Chapter Shaft Power Cycles

17. SIMPLE Gas Turbine CYCLE
For any given value of "t" (T3/T1), the optimum value of rp for maximum specific work output can be calculated by differentiating eqn. 2.2 wrt. rp (g/g-1) and equating to zero.
The result is;
i.e. ( 2.3 )
Since
Chapter Shaft Power Cycles

18. SIMPLE Gas Turbine CYCLE
This is equivalent to;
So, w is maximum when compressor and turbine outlet temperatures are equal.
For all values of rp between 1 and ropt = [ (T3/T1) (g/2 (g-1) ) ] T4 > T2
and a heat exchanger can be incorporated to reduce the heat transfer from the external source and so increase the efficiency.
Chapter Shaft Power Cycles

19. Fig. 2.3 Simple cycle with heat - exchange
Heat Exchanger Cycle
Fig Simple cycle with heat - exchange
Chapter Shaft Power Cycles

20. Chapter2 Shaft Power Cycles
Heat Exchanger Cycle
The cycle efficiency h is;
with ideal HE T5 = T4
with the help of isentropic relations;
( 2.4)
Chapter Shaft Power Cycles

21. Heat Exchanger Cycle
Fig 2.4 Efficiency of a simple cycle with heat-exchange
for rp = 1 : h = 1- 1/t which is Carnot efficiency.
as T3 increases, t increases and then h increases
Chapter Shaft Power Cycles

22. Chapter2 Shaft Power Cycles
Heat Exchanger Cycle
Specific work output does not change with HE
thus is the same as the simple cycle.
To obtain an appreciable improvement in h by HE in
ideal cycles.
a) a value of rp < ropt
then work output is maximum.
b) It is not necessary to use a higher cycle pressure ratio as Tmax of the cycle is increased.
(a) is true for actual cycles whereas (b) requires modification
Chapter Shaft Power Cycles

23. Chapter2 Shaft Power Cycles
Reheat Cycle
Fig. 2.5 Reheat cycle
A substantial increase in specific work output can be obtained
by splitting the expansion and reheating the gas between
low-pressure and high-pressure turbines.
Chapter Shaft Power Cycles

24. Chapter2 Shaft Power Cycles
Reheat Cycle
Since the vertical distance between any pair of constant pressure lines increase with the increasing entropy
(T3 - T4) + (T5 - T6) > (T3 - T4 )
thus : wreheat > wsimple
w34 + w56 = Cp (T3 - T4) + Cp (T5 - T6)
= Cp (T3 - T4) + Cp (T3 - T6)
wt = Cp T3 (1-T4/ T3) + Cp T3 (1-T6/T5)
Chapter Shaft Power Cycles

25. Chapter2 Shaft Power Cycles
Reheat Cycle
since
Denoting
then P4 = P5
Chapter Shaft Power Cycles

26. Chapter2 Shaft Power Cycles
Reheat Cycle
To find P4 for maximum work output;
The result is;
Hence, P3/P4 = P4/P6
for maximum work output
the optimum splitting is an equal one.
Chapter Shaft Power Cycles

27. Chapter2 Shaft Power Cycles
Reheat Cycle
Specific work output of the cycle is then;
w = Cp (T3 - T4) + Cp (T5 - T6) - Cp (T2- T1)
Thus:
( 2.5 )
Then the efficiency;
( 2.6)
Chapter Shaft Power Cycles

28. Chapter2 Shaft Power Cycles
Reheat Cycle
Effect of Reheat :
increase in specific output
and decrease in efficiency.
Fig. 2.6
Work output vs. r
in a Reheat Cycle
EXERCISE :
For a simple Reheat Cycle, prove that specific work output is maximum when rp (g-1/g) =(T3/T1)2/3 = t2/3 .
Chapter Shaft Power Cycles

29. Cycle with Reheat & Heat Exchange
The reduction in efficiency due to reheat can be overcomed by adding heat exchanger.
The high exhaust gas temperature is now fully utilized in the HE and the increase in work output is no longer offset by the increase in heat supplied.
Fig. 2.7
Reheat cycle with
Heat - Exchange
Chapter Shaft Power Cycles

30. Reheat cycle with Heat - Exchange
Fig. 2.8 Efficiency - reheat cycle with heat - exchange
Chapter Shaft Power Cycles

31. Cycle With Reheat & Heat Exchange
The reduction in efficiency due to reheat can be overcomed by adding a heat exchanger.
The higher exhaust gas temperature is now fully utilized in the HE and the increase in work output is no longer offset by the increase in heat supplied. 3 4 2 1 5 6 7 HE f 6
Chapter Shaft Power Cycles

32. Cycle With Reheat & Heat Exchange3 5 7 6 4 HE 2 8 1 s
Chapter Shaft Power Cycles

33. Cycle With Reheat, Intercooling & Heat Exchange3 4 2 5 6 7 HE f 1 8 10 9
LPC
HPC
LPT
HPT
Intercooler
Chapter Shaft Power Cycles

34. Cycle With Reheat, Intercooling & Heat Exchange5 7 9 6 8 HE 4 2 10 1 3 s
Chapter Shaft Power Cycles

35. SHAFT POWER CYCLES II Actual Cycles
CHAPTER 2
SHAFT POWER CYCLES II
Actual Cycles

36. Chapter2 Shaft Power Cycles
ACTUAL CYCLES
The performance of real cycles differ from that of ideal cycles for the following reasons :
a) Change in Kinetic Energy between inlet and outlet of each component can not necessarily be ignored.
b) Compression and expansion are actually irreversible and therefore involves an increase in entropy
c) Fluid friction causes pressure losses in components and associated ducts.
d) HE can not be ideal, terminal temperature difference is inevitable
Chapter Shaft Power Cycles

37. Chapter2 Shaft Power Cycles
ACTUAL CYCLES
e) Slightly more work than that required for the compression process will be necessary to overcome bearing and windage friction in the transmission between compressor and turbine and to drive ancillary components such as fuel and oil pumps. (hmech)
f) Cp and g changes throughout the cycle.
Cp = f(T) h= f(T) and chemical composition.
g) Combustion is not complete (hcomb)
Chapter Shaft Power Cycles

38. Chapter2 Shaft Power Cycles
ACTUAL CYCLES
The efficiency of any machine (which absorbs or produces work), is normally expressed in terms of the ratio of actual to ideal work transfers
For a compressor;
For a perfect gas;
h = Cp T ,
This relation is sufficiently accurate for real gasses under conditions encountered in a GT if a mean Cp over the relevant range of temperature is used
Chapter Shaft Power Cycles

39. Compressor and Turbine Efficiencies
Then for compressors;
( 2.7 )
Similarly for turbines the isentropic efficiency defined as;
( 2.8 )
Chapter Shaft Power Cycles

40. Chapter2 Shaft Power Cycles
ACTUAL CYCLES
For compressors: from equation 2.7
( 2.9 )
Similarly for turbines;
( 2.10 )
Chapter Shaft Power Cycles

41. Compressor & Turbine Efficiencies
Since
Thus ( 2.11 )
Since the vertical distance between a pair of constant pressure lines on the T-S diagram increases as entropy increases,
SDTs’ > DT’  hs > hc ( for compressors )
Chapter Shaft Power Cycles

42. Compressor and Turbine Efficiencies
Now consider an axial flow compressor consisting of a number of successive stages.
If the blade design is similar in successive blade rows it is reasonable to assume that the isentropic efficiency of a single stage hs remains the same through the compressor.
Then the overall temperature rise;
Chapter Shaft Power Cycles

43. Compressor and Turbine Efficiencies
The difference between hc and hs will increase with the number of stages i.e. with the increase of pressure ratio.
A physical explanation is that the increase in temperature due to friction in one stage results in more work being required in the next stage.
A similar argument can be
used to show that for a turbine
ht > hst .
Fig. 2.9 Definition of Isentropic
and Small Stage Efficiencies
Chapter Shaft Power Cycles

44. Polytropic Efficiency
Isentropic efficiency of an elemental stage in the process such that it is constant throughout the whole process.
For a compression process η c = dT'/dT = const.
But for an isentropic process,
in differential form
dT' = η  c dT
integrating between 1 & 2 (inlet & outlet)
( 2.12 )
Chapter Shaft Power Cycles

45. Polytropic Efficiency
So hc can be computed from measured values of P and T at the inlet an outlet of the compressor, as;
( 2.13 )
Finally the relation between hc & hc ;
( 2.14 )
Chapter Shaft Power Cycles

46. Polytropic Efficiency
Similar relations can be obtained for turbines since ,
It can be shown that for an expansion between turbine inlet 3 and outlet 4;
( 2.15 )
( 2.16 )
Chapter Shaft Power Cycles

47. Polytropic Efficiency
Fig Variation of turbine and compressor isentropic efficiency with pressure ratio for polytropic efficiency of 85 %
Chapter Shaft Power Cycles

48. Polytropic Efficiency
In practice, as with hc and ht , it is normal to define the polytropic efficiencies in terms of stagnation temperatures and pressures.
( 2.17 )
where
( 2.18 )
Here n is the coefficient for a polytropic process.
Chapter Shaft Power Cycles

49. Chapter2 Shaft Power Cycles
Pressure Losses
Fig. 2.11
Pressure losses
Pb = Pressure loss in Combustion Chamber
Pha = Frictional pressure loss on the air side of HE
Phg = Frictional pressure loss on the gas side of HE
Chapter Shaft Power Cycles

50. Chapter2 Shaft Power Cycles
Pressure Losses
Pressure losses cause a decrease in the available turbine pressure ratio.
Po3 = Po2 - Pb - Pha
Po4 = Pa + Phg
It is better to take Phg & Pb as fixed proportions of compressor delivery pressure; Then;
Chapter Shaft Power Cycles

51. HEAT EXCHANGER EFFECTIVENESS
Turbine exhaust gasses reject heat at the rate of:
mt Cp46 (T04-T06)
Compressor delivery receives heat at a rate of:
mc Cp25 (T05-T02)
If mc = mt
Then Cp46 (T04-T06) = Cp25 (T05-T02)
Chapter Shaft Power Cycles

52. HEAT EXCHANGER EFFECTIVENESS
One possible measure of performance is the ratio of the actual energy received by the cold air to the maximum possible value. Thus;
HE effectiveness = Cp25 (T05-T02) / Cp24 (T04-T02)
over the mean temperature ranges if Cp25 = Cp24
HE effectiveness = ( T05-T02) /(T04-T02)
Most generally :
HE effectiveness = mcCp25( T05-T02) / mtCp24(T04-T02)
Chapter Shaft Power Cycles

53. Chapter2 Shaft Power Cycles
MECHANICAL LOSSES
In all Gas Turbines, the power necessary to drive the compressor is direct,
so any loss that occurs is due to bearing friction and windage ;
this amounts to about 1 %
If the transmission efficiency is hm, then
wct = Cp12 (T02-T01)/hm ( hm = 99 % )
Any power used to drive auxillary components
such as fuel and oil pumps, gearing losses are ussually accounted for by subtracting from the net output.
Chapter Shaft Power Cycles

54. Variation of Specific Heat
Cp/ Cv = Cp - Cv = R
Cp = g R/( g -1 ) = g R /( g - 1 )M
for air Cpa = kJ/kg K , ga =1.4
for combustion gasses Cpg = kJ/kgK ,
gg =1.333
Rair = kJ/kg-K
Cp changes with T, but the change with p is negligible
Chapter Shaft Power Cycles

55. Fuel/Air Ratio, Combustion Efficiency and Cycle Efficiency
Combustion problem in GT is to calculate the Fuel/Air (F/A) ratio = "f" required to transform unit mass of air at T02 and f kg of fuel at the fuel temperature Tf to ( 1 + f ) kg of products at T03 .
Since the process is adiabatic, the energy equation is simply;
where mi = mass of product i per unit mass of air
hi = its specific enthalpy
Chapter Shaft Power Cycles

56. Fuel/Air Ratio, Combustion Efficiency and Cycle Efficiency
Making use of the enthalpy of reaction unit mass of fuel at a reference temperature of 25oC
H25 = - ( net calorific value) = Qnet,p ; the equation can be expanded as
Cpg = Specific heat of products
over the temperature range 298K T03
H25 = Enthalpy of reaction (lower heating value)
a negative quantity = [ kJ/kg]
Chapter Shaft Power Cycles

57. Fuel/Air Ratio, Combustion Efficiency and Cycle Efficiency
Therefore, for a given fuel and the values of T02 & T03 ; "f" can be calculated.
A chart is given in the book to determine the "f" for a given combustion temperature rise (T03-T02) for various T02 's.
A convenient method of allowing for combustion losses is to introduce a combustion efficiency defined by
Chapter Shaft Power Cycles

58. Fuel/Air Ratio, Combustion Efficiency and Cycle Efficiency
For an air mass flow ma ; total fuel consumption is
f*ma.
The specific fuel consumption;
[ kg/kW-h ]
wN = specific net work output in kW/( kg/s ) of air flow
Chapter Shaft Power Cycles

59. Fuel/Air Ratio, Combustion Efficiency and Cycle Efficiency
Then the cycle efficiency is
where Qnet,p = net calorific value = -H25
Chapter Shaft Power Cycles

60. SHAFT POWER CYCLES III Comparative Performance of Practical Cycles
CHAPTER 2
SHAFT POWER CYCLES
III
Comparative Performance of Practical Cycles

61. Fig. 2.12 Cycle efficiency and specific output of simple gas turbine
1. Simple GT Cycle
Fig Cycle efficiency and specific output of simple gas turbine
With component losses : h (T03, rp) for each cycle max. temperature T03, h has a peak value at a paticular rp.
Chapter Shaft Power Cycles

62. Chapter2 Shaft Power Cycles
1. Simple GT Cycle
Optimum press ratio for maximum efficiency differs from that for maximum specific work output.
But h(rp) is quite flat around the peak so. the lowest rp which will give an accepted performance is chosen.
As T03 increases higher rp is advantageous
As T03 increases η increases. Therefore component losses compared to net work output gets less important.
As T03 increases ws increases appreciably. This is important for aircaft GT since SIZE of GT is smaller for a given power.
*Increasing Ta ; wnet and efficiency h both decreases.
Chapter Shaft Power Cycles

64. Fig. 2.13 Heat - exchange cycle
HE slightly reduces ws due to additional pressure losses.
But effects h (increases) and reduces the optimum press ratio for hmax.
Chapter Shaft Power Cycles

65. Chapter2 Shaft Power Cycles

66. 3.Heat Exchange Cycle with Reheat or Intercooling
Fig Cycle with Heat-Exchange and Reheat
Chapter Shaft Power Cycles

67. 3.Heat Exchange Cycle with Reheat or Intercooling
With HE, addition of REHEAT improves the specific work output considerably without loss of efficiency.
The gain in efficiency due to Reheat obtained with the ideal cycle is not realized in practice
* partly because of the additional pressure loss in the reheat chamber and the inefficiency of the expansion process,
* but primarily because the effectiveness of the HE quite low and the additional energy in the exhaust gas is not wholly recovered.
Chapter Shaft Power Cycles

68. 3.Heat Exchange Cycle with Reheat or Intercooling
Reheat has not been widely used in practice because the additional "CC" and the associated control problems
Can off-set the advantage gained from the decrease in size of the main components consequent upon the increase in specific output.
Intercooling, although increases specific output and cycle efficiency; intercoolers tend to be bulky and if they require cooling water, the self contained nature of the GT is lost.
In practice most GT utilize either a higher pressure ratio simple cycle or a low pressure ratio HE cycle.
The other additions to the cycles mentioned do not nominally show sufficient advantage to offset the increased complexity and capital cost.
Chapter Shaft Power Cycles

69. Cogas Cycles and Cogeneration Schemes
In the exhaust gases from a GT there is still an ample amount of energy. This energy could be utlized.
The only limitation is the exhaust temperature (Stack Temp.) should not be reduced much below 170oC to avoid dewpoint corrosion problems due to the sulphur content of the fuel.
The exhaust heat could be used in various ways.
It could be wholly, used to produce steam in a waste heat boiler for a steam turbine to angment the shaft power produced, it is called as COGAS-"Combined Gas/Steam Cycle Power, "plant
Chapter Shaft Power Cycles

70. Cogas Cycles and Cogeneration Schemes
Alternatively the exhaust heat maybe used to produce hot water or steam for same chemical process, for district or factory heating, for a distillation plant,
(for and absorption refrigerator in water chilling or air conditioning plant).
The shaft power there will normally be used to produce electricity
This system is refered to as a
COGENERATION or TOTAL ENERGY PLANT.
Chapter Shaft Power Cycles

71. Cogas Cycles
Fig.2.15 T-H diagrams for single and dual pressure COGAS schemes
Chapter Shaft Power Cycles

72. Chapter2 Shaft Power Cycles
Cogas Cycles
For any given T03 of GT rc increases  T04 (exhaust) decreases. Thus the heat available to the steam cycle decreases.
Dh gas (fall in boiler) = Dh (rise between feedwater inlet and steam outlet)
DTterminal ≥ 20°C & DTpinchpt ≥20°C
if the boiler is to be of economic size.
Chapter Shaft Power Cycles

73. Chapter2 Shaft Power Cycles
Cogas Cycles
A reduction in T4;
 Psteam decrease that can be used for steam cycle.
In the combined plant, therefore, selection of a higher compressor pressure ratio to improve the gas turbine efficiency may lead to a fall in steam cycle efficiency and no net gain in overall thermal efficiency.
In practice, however, a higher pressure ratio is accompanied by a higher turbine inlet temperature and the most advanced combined cycles use high pressure ratio gas turbines.
Chapter Shaft Power Cycles

74. Chapter2 Shaft Power Cycles
Cogas Cycles
Most COGAS plants are produced by adding a suitable exhaust heated Rankine Cycle conditions which matches best to GasTurbine.
COGAS plants for large base load generating stations hoverall is not the ultimate citerion.
The cost of electricity sold is ultimate and this also depends on the capital cost of the plant.
Due to the abundancy of choices it is very difficult to optimize these cycles. These have efficiencies %
Chapter Shaft Power Cycles

75. Cogeneration Plant Fig. 2.16 Cogeneration plant
This one is suitable for applications in which the required ratio of heat output to electrical output might vary over a wide range.
Chapter Shaft Power Cycles

76. Chapter2 Shaft Power Cycles
Cogeneration Plant
When only power required,then waste heat boiler is completely bypassed.
When max. heat/power ratio is required the HE is bypassed and supplemantary fuel is burnt in the boiler.
The overall efficiency may be defined as
h = [( net work + useful heat output ) / unit air mass flow ] / [ f.Qnet,p ]
Useful heat output per unit air mass flow is
Cp [ Tin ]
For high values of Q/HP rc has little effect on h
rc choosen to give wmax ,hence minimum capital cost.
Heat exchanger useful for small Q/Power ratios.
Chapter Shaft Power Cycles