steam cycle1

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    STEAM CYCLE

    For the steam cycle below, calculate the total electrical efficiency. The following is

    given:

    Mechanical efficiency turbine 0.96Efficiency generator 0.95

    Efficiency boiler 0.92

    Isentropic efficiency turbine 0.75

    The rest of the given values are given on the figure

    Turbine G

    m =120 kg/s

    p =110 bar

    t = 525 deg C

    m = 19 kg/s

    p = 20 bar

    p = 0.8 bar

    p = 1.5 bar

    p = 6.0 bar

    h = 900 kJ/kg h = 450 kJ/kg

    h= 390 kJ/kg

    h = 480 kJ/kg

    h= 640 kJ/kg

    Boiler

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    HINTS

    Hint 1 (-2p):The total electrical efficiency is defined as the power output dividedwith the thermal power obtained from the boiler. Start calculate the power output

    from the steam turbine

    Hint 2 (-5p):In order to find the steam turbine power output, you have to calculate

    the enthalpies and mass flows from the steam extractions. The enthalpies can all be

    found in an h-s diagram on the expansion line drawn from turbine from inlet to the

    outlet to the condenser.

    h2s

    h2

    0,8 bar

    1,5 bar

    6 bar

    20 bar110 bar

    525 deg C h1

    a

    b

    c

    Hint 3 (-3p): The steam extraction mass flows can be found via heat balances on the

    feed water preheaters. Heat balance on the high pressure preheater gives data to

    calculate the boiler power.

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    SOLUTION

    Start calculating the power output from the turbine.

    First we draw the expansion line, from the inlet conditions (1) to the condenserpressure. The enthalpy h2 can be found, as we know the isentropic efficiency of the

    turbine, as follows:

    h2 = 3427 0.75*(3427-2370) = 2634 kJ/kg, (where 2370 is the enthalpy of the

    isentropic expansion process).

    h2s

    h2

    0,8 bar

    1,5 bar

    6 bar

    20 bar

    110 bar

    525 deg C h1

    a

    b

    c

    Enthalpies at extractions can be read on the expansion line at the given pressures on

    an enthalpy entropy diagram.

    ha = 3115 kJ/kg

    hb = 2920 kJ/kg

    hc = 2720 kJ/kg

    The water enthalpy into the boiler is found through a heat balance over the high

    pressure preheater, and then we calculate the power in the boiler Pboiler:

    MWP

    kgkJh

    h

    Boiler

    in

    in

    4.292)7.9903427(*120

    /7.990

    120*64019*311519*900120*

    =

    +=+

    The fuel input to the boiler becomes:

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    MWP

    Qboiler

    boilerfuel 8.317

    92.0

    4.292===

    &

    The flows

    bm and

    cm are given through heat balances over the feed water tank andover the low pressure feed water preheater:

    Feed water tank:

    640*120900*19480*)19120(2920* =++

    bb mm

    skgmb /6.4

    Low pressure preheater:

    skgm

    mm

    c

    cc

    /82.3

    480*4.96450*390*4.962720*

    +=+

    The electrical power generated is:

    MW

    Pel

    9.7695.0*96.0*

    )]2.26342720(*58.92)27202929(4.96)29203115(*101)31153427(*120[

    +++=

    The total efficiency of the plant can be calculated as:

    24.08.317

    9.76==

    fuel

    eltot

    Q

    P

    &