Question

A gas-turbine power plant operates on the simple Brayton cycle between the pressure limits of 100 and 1200 kPa. The working fluid is air, which enters the compressor at 300K at a rate of 150 m3/min and leaves the turbine at 773K. Using variable specific heats for air and assuming a compressor isentropic efficiency of 82 percent and a turbine isentropic efficiency of 88 percent, determine:

(a) the net power output

(b) the back work ratio

(c) the thermal efficiency

Answer 1

The Brayton cycle is the ideal cycle for gas-turbine engines in which the working fluid undergoes a closed loop. That is the combustion and exhaust processes are modeled by constant-pressure heat addition and rejection, respectively. The Brayton ideal cycle is made up of four internally reversible processes:

1-2 isentropic compression (in the compressor)

2-3 const. pressure heat-addition (in the combustion chamber)

3-4 isentropic expansion (in the turbine)

4-1 constant pressure heat rejection

the p-v and T-s diagrams are shown in the image below:

the processes of the cycle are given in the table below

air is the working fluid with a variable specific heat

T1=300K

from the tables, we can obtain the values of S1 and h1.

s1 = 5.7159KJ/Kg.k

h1 = 303.6KJ/Kg

p1 = 12oo kPa

s1= s2

P2= 1200kPa

the solutions are given in the images below

 

 

 

 

 

 

 

 

 

the net power output is 659.73 kW

the back work ratio is 0.625

the thermal efficiency of the cycle is 0.3193/31.93%