CHAPTER 2

- 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 2

- SHAFT POWER CYCLES
- I
- Ideal 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

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.

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

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.

SIMPLE Gas Turbine CYCLE

- The ideal cycle for a simple Gas Turbine is the

BRAYTON (or JOULE) cycle. - Fig. 2.1 Simple Gas Turbine

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)

SIMPLE Gas Turbine CYCLE

- The efficiency of the cycle is then

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

The Efficiency of the Simple Gas Turbine Cycle

The Efficiency of the Simple Gas Turbine Cycle

- Then the cycle efficiency is
- where ( 2.1 )

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).

SIMPLE Gas Turbine CYCLE

- Fig. 2.2 Efficiency and specific work output -

Simple Cycle

FIG. 2.2 Efficiency and specific work output -

simple cycle

SIMPLE Gas Turbine CYCLE

- T3 Maximum Cycle Temperature,
- imposed by the metallurgical limit.
- t T3/T1 3.5 -4 for long life industrial

plants, - t 5-5.5 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

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

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 gt T2 - and a heat exchanger can be incorporated to

reduce the heat transfer from the external source

and so increase the efficiency.

Heat Exchanger Cycle

- Fig. 2.3 Simple cycle with heat - exchange

Heat Exchanger Cycle

- The cycle efficiency h is
- with ideal HE T5 T4
- with the help of isentropic relations
- ( 2.4)

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

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 lt 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

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.

Reheat Cycle

- Since the vertical distance between any pair of

constant pressure lines increase with the

increasing entropy - (T3 - T4) (T5 - T6) gt (T3 - T4 )
- thus wreheat gt 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)

Reheat Cycle

- since
- Denoting
- then P4 P5

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.

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)

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 .

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

Reheat cycle with Heat - Exchange

- Fig. 2.8 Efficiency - reheat cycle with heat -

exchange

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.

6

Cycle With Reheat Heat Exchange

T

3

5

7

6

4

HE

2

8

1

s

Cycle With Reheat, Intercooling Heat Exchange

Cycle With Reheat, Intercooling Heat Exchange

T

5

7

9

6

8

HE

4

2

10

1

3

s

CHAPTER 2

- SHAFT POWER CYCLES
- II
- Actual 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

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)

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

Compressor and Turbine Efficiencies

- Then for compressors
- ( 2.7 )
- Similarly for turbines the isentropic efficiency

defined as - ( 2.8 )

ACTUAL CYCLES

- For compressors from equation 2.7
- ( 2.9 )
- Similarly for turbines
- ( 2.10 )

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 gt DT ? hs gt hc ( for compressors )

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

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 gt hst .
- Fig. 2.9 Definition of Isentropic
- and Small Stage Efficiencies

Polytropic Efficiency

- Isentropic efficiency of an elemental stage in

the process such that it is constant throughout

the whole process. - For a compression process ? ?c dT'/dT const.
- But for an isentropic process,
- in differential form
- dT' ? ? c dT
- integrating between 1 2 (inlet outlet)
- ( 2.12 )

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 )

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 )

Polytropic Efficiency

- Fig. 2.10 Variation of turbine and compressor

isentropic efficiency with pressure ratio

for polytropic efficiency of 85

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 )
- where
- Here n is the coefficient for a polytropic

process.

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

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

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)

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)

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.

Variation of Specific Heat

- Cp/ Cv Cp - Cv R
- Cp g R/( g -1 ) g R /( g - 1 )M
- for air Cpa 1.005 kJ/kg K , ga 1.4
- for combustion gasses Cpg 1.148 kJ/kgK ,
- gg 1.333
- Rair 0.287 kJ/kg-K
- Cp changes with T, but the change with p is

negligible

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

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 -43100 kJ/kg

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

Fuel/Air Ratio, Combustion Efficiency and Cycle

Efficiency

- For an air mass flow ma total fuel consumption

is - fma.
- The specific fuel consumption
- kg/kW-h
- wN specific net work output in kW/( kg/s ) of

air flow

Fuel/Air Ratio, Combustion Efficiency and Cycle

Efficiency

- Then the cycle efficiency is
- where Qnet,p net calorific value -H25

CHAPTER 2

- SHAFT POWER CYCLES
- III
- Comparative Performance of Practical Cycles

1. Simple GT Cycle

- Fig. 2.12 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.

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 ? 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.

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2.Heat Exchange Cycle

- 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.

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3.Heat Exchange Cycle with Reheat or Intercooling

- Fig. 2.15 Cycle with Heat-Exchange and Reheat

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.

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.

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

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.

Cogas Cycles

- Fig.2.15 T-H diagrams for single and dual

pressure COGAS schemes

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 20C DTpinchpt 20C
- if the boiler is to be of economic size.

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.

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 43-50

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.

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 - 443
- 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.