# How Does a Regenerative Brayton Cycle Gas Turbine Operate?

• sawhai
I hope this helps to summarize the problem and give you some direction in finding a solution. In summary, the problem involves determining the net work output, back work ratio, water supply rate, and second-law efficiency for a gas turbine power plant operating on the regenerative Brayton cycle. The air can be modeled using air standard assumptions with variable specific heats, and the water supply rate can be found using an energy balance equation and considering the enthalpy change of water during evaporation.
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.

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

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.

## 1. What is a gas turbine for peaking power?

A gas turbine for peaking power is a type of power plant that uses a gas turbine engine to generate electricity during periods of high demand. It is typically used as a backup or supplemental power source to meet the peak energy needs of a grid.

## 2. How does a gas turbine for peaking power work?

A gas turbine for peaking power works by burning fuel, such as natural gas or diesel, in a combustion chamber. The resulting hot gases then expand through a turbine, causing it to spin and drive a generator to produce electricity. This process is known as the Brayton cycle.

## 3. What are the advantages of using a gas turbine for peaking power?

Some advantages of using a gas turbine for peaking power include its quick start-up time, high efficiency, and relatively low emissions compared to other types of power plants. It is also a flexible and scalable solution that can be easily integrated into existing power systems.

## 4. What are the limitations of a gas turbine for peaking power?

One limitation of a gas turbine for peaking power is its dependency on a continuous supply of fuel, which can be affected by fluctuations in prices or availability. It also has a relatively high initial cost and may require regular maintenance to ensure optimal performance.

## 5. How does a gas turbine for peaking power compare to other types of power plants?

Compared to other types of power plants, a gas turbine for peaking power has a shorter start-up time, making it ideal for meeting sudden spikes in energy demand. It also has a smaller footprint and produces lower emissions, but it may not be as cost-effective for continuous, baseload power generation.

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