SHAFT%20POWER%20CYCLES - PowerPoint PPT Presentation

View by Category
About This Presentation
Title:

SHAFT%20POWER%20CYCLES

Description:

chapter 2 shaft power cycles – PowerPoint PPT presentation

Number of Views:68
Avg rating:3.0/5.0
Slides: 77
Provided by: edut1362
Category:

less

Write a Comment
User Comments (0)
Transcript and Presenter's Notes

Title: SHAFT%20POWER%20CYCLES


1
CHAPTER 2
  • SHAFT POWER CYCLES

2
  • 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.

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

4
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

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.

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

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.

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

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)

10
SIMPLE Gas Turbine CYCLE
  • The efficiency of the cycle is then

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

12
The Efficiency of the Simple Gas Turbine Cycle
13
The Efficiency of the Simple Gas Turbine Cycle
  • Then the cycle efficiency is
  • where ( 2.1 )

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).

15
SIMPLE Gas Turbine CYCLE
  • Fig. 2.2 Efficiency and specific work output -
    Simple Cycle

FIG. 2.2 Efficiency and specific work output -
simple cycle
16
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

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

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 gt T2
  • and a heat exchanger can be incorporated to
    reduce the heat transfer from the external source
    and so increase the efficiency.

19
Heat Exchanger Cycle
  • Fig. 2.3 Simple cycle with heat - exchange

20
Heat Exchanger Cycle
  • The cycle efficiency h is
  • with ideal HE T5 T4
  • with the help of isentropic relations
  • ( 2.4)

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

22
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

23
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.

24
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)

25
Reheat Cycle
  • since
  • Denoting
  • then P4 P5

26
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.

27
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)

28
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 .

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
30
Reheat cycle with Heat - Exchange
  • Fig. 2.8 Efficiency - reheat cycle with heat -
    exchange

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.

6
32
Cycle With Reheat Heat Exchange
T
3
5
7
6
4
HE
2
8
1
s
33
Cycle With Reheat, Intercooling Heat Exchange
34
Cycle With Reheat, Intercooling Heat Exchange
T
5
7
9
6
8
HE
4
2
10
1
3
s
35
CHAPTER 2
  • SHAFT POWER CYCLES
  • II
  • Actual Cycles

36
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

37
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)

38
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

39
Compressor and Turbine Efficiencies
  • Then for compressors
  • ( 2.7 )
  • Similarly for turbines the isentropic efficiency
    defined as
  • ( 2.8 )

40
ACTUAL CYCLES
  • For compressors from equation 2.7
  • ( 2.9 )
  • Similarly for turbines
  • ( 2.10 )

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 gt DT ? hs gt hc ( for compressors )

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

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

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 ? ?c dT'/dT const.
  • But for an isentropic process,
  • in differential form
  • dT' ? ? c dT
  • integrating between 1 2 (inlet outlet)
  • ( 2.12 )

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 )

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 )

47
Polytropic Efficiency
  • Fig. 2.10 Variation of turbine and compressor
    isentropic efficiency with pressure ratio
    for polytropic efficiency of 85

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 )
  • where
  • Here n is the coefficient for a polytropic
    process.

49
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

50
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

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)

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)

53
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.

54
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

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

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 -43100 kJ/kg

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

58
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

59
Fuel/Air Ratio, Combustion Efficiency and Cycle
Efficiency
  • Then the cycle efficiency is
  • where Qnet,p net calorific value -H25

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

61
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.

62
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.

63
(No Transcript)
64
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.

65
(No Transcript)
66
3.Heat Exchange Cycle with Reheat or Intercooling
  • Fig. 2.15 Cycle with Heat-Exchange and Reheat

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.

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.

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

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.

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

72
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.

73
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.

74
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

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.

76
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.
About PowerShow.com