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Homework Help: Gas turbine for peaking power

  1. Mar 10, 2012 #1
    1. The problem statement, all variables and given/known data
    A gas turbine power plant operates on the regenerative Brayton cycle as shown in the figure.
    Compression occurs in two stages, with interstage cooling, and expansion in the turbine
    likewise occurs in two stages, with interstage reheating. The cycle operates between the
    pressure limits of P1 = P9 = P10 = 100 kPa and P4 = P5 = P6 = 1200 kPa.
    Interstage cooling/heating occur at the thermodynamic optimum P2 = P3 = P7 = P8 = 346.4 kPa(i.e. the geometric mean of the intake air and combustor pressures). Air enters each
    compression stage at T1 = T3 = 300 K. Combustion gases enter the first and second stages of
    the turbine at T6 = 1400 K and T8 = 1300 K respectively. The compressor and the turbine both
    have an isentropic efficiency of 80%. The regenerator has an effectiveness of 75%; i.e.
    εregen = (h9 – h10)/(h9 – h4) = 0.75.
    Assuming that the gas power cycle can be modeled using the air standard assumptions, with
    variable (i.e. temperature-dependent) specific heats for air, and an air mass flow rate
    m = 90 kg/s, determine the following:
    (a). The net work output Wnet (MW) for the cycle.
    (b). The back work ratio rbw; i.e. the fraction of the turbine work output that is used to drive
    the compressor.
    (c). The water supply rate, mW (kg/s), needed for interstage cooling in the compressor, if
    liquid water at ambient temperature (300 K) is sprayed into the air between the two
    compressor stages to provide evaporative cooling.
    (d). The second-law efficiency η II = η th /η max for this gas turbine cycle; i.e. the ratio of the actual thermal efficiency to the maximum possible (Carnot) efficiency.

    2. Relevant equations
    Ein = Eout

    3. The attempt at a solution
    Parts a & b are done. I have done all the analysis across the power plant and have found all the temperatures in each stage (1-10). I have two questions:
    1- It mentions in problem statement that the air has variable specific heat, does it mean that I have to use different values for the specific heat in each stage like compressor, coolant, etc. depending on the temperature in that stage?
    2- For part C, how can I find the water supply rate in interstage cooling?

    Thank you
  2. jcsd
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