How Does a Regenerative Brayton Cycle Gas Turbine Operate?

[sawhai]

Homework Statement

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.

Homework Equations

Ein = Eout

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

 

[KataKoniK]

for your question. it is important to carefully analyze and understand the problem statement before attempting to solve it. In this case, the problem statement mentions that the air can be modeled using air standard assumptions, with variable specific heats. This means that the specific heat of air can vary with temperature, but it can still be approximated using a single value for each stage. You can use the average specific heat for each stage, calculated using the temperature range for that stage.

For part C, you can use the energy balance equation (Ein = Eout) to find the heat transfer rate between the air and water. This can then be used to determine the mass flow rate of water needed for interstage cooling. You can also consider the enthalpy change of the water during evaporation to find the water flow rate.