BRAYTON CYCLE

The air standard Brayton or Joule cycle is a constant pressure cycle used in gas turbine power plants. The p-v and T-S diagrams are shown in Fig 9.12. It consists of the following processes:

1−2: Isentropic compression in the compressor

2−3: Constant pressure heat addition.

3−4: Isentropic expansion of air

4−4: Constant pressure heat rejection

Consider 1 kg of working fluid

From first law of thermodynamics for steady flow, rejecting ΔKE and ΔPE, we have

δ_q – δ_w = dh

Heat added, q_s = h₃ – h₂ = c_p (T₃ – T₂)

Heat rejected q_r = h₄ – h₁ = c_p (T₄ – T₁)

Net work done by turbine, w_net = q_s – q_r = c_p [(T₃ − T₂) − (T₄ − T₁)]

Also work done by turbine, w_t = h₃ − h₄ = c_p (T₃ − T₄)

Work consumed by compressor, w_c= h₂ − h₁ = c_p (T₂ − T₁)

w_net = c_p [(T₃ − T₄) − (T₂ − T₁)] = c_p [(T₃ − T₂) − (T₄ − T₁)]

Thermal efficiency,

Figure 9.12 Brayton (or Joule) cycle: (a) p-v diagram, (b) T-s diagram

From isentropic compression process 1 – 2, we have

and from isentropic expansion process 3 – 4,

The variation of thermal efficiency v’s pressure ratio is shown in Fig. 9.13. The thermal efficiency increases with increasing values of pressure ratio. This cycle is used in gas turbines.

w_t = work done by turbine

w_c = work supplied to compressor

Pressure ratio for maximum work,

 

W = mc_p [(T₃ – T₂) – (T₄ – T₁)]

 

= mc_p [(T₃ – T₄) – (T₂ – T₁)]

 

Figure 9.13 Efficiency v’s pressure ratio in simple Brayton cycle