Question

Air enters the compressor of an air-standard Brayton cycle with a volumetric flow rate of 60 m3/s at 0.8 bar, 280 K. The compressor pressure ratio is 20, and the maximum cycle temperature is 2100 K. For the compressor, the isentropic efficiency is 92% and for the turbine the isentropic efficiency is 95%. Determine
(a) the net power developed, in MW

(b) the rate of heat addition in the combustor, in MW

(c) the thermal efficiency of the cycle

Answer 1

Answer:

a) The Net power developed in this air-standard Brayton cycle is 43.8MW

b) The rate of heat addition in the combustor is 84.2MW

c) The thermal efficiency of the cycle is 52%

Explanation:

To solve this cycle we need to determinate the enthalpy of each work point of it. If we consider the cycle starts in 1, the air is compressed until 2, is heated until 3 and go throw the turbine until 4.

Considering this:

$h_{i} =T_{i}C_{pair}=T_{i}1.005\frac{KJ}{Kg K}$

$\mu_{comp}=\frac{h_{2S}-h_{1}}{h_{2}-h_{1}}$

$\mu_{comp}=\frac{h_{3}-h_{4}}{h_{3}-h_{4S}}$

$G_{m} =\frac{PMG_{v}}{TR} =59.73\frac{Kg}{s}$

Now we can calculate the enthalpy of each work point:

h₁=281.4KJ/Kg

h₂=695.41KJ/Kg

h₃=2105KJ/Kg

h₄=957.14KJ/Kg

The net power developed:

$P_{net}=P_{Tur}-P_{Comp}=G_{m}((h_{3}-h_{4})-(h_{2}-h_{1}))$

The rate of heat:

$Q=G_{m}(h_{3}-h_{2})$

The thermal efficiency:

$\mu_{ther}=\frac{P_{net}}{Q}$