THERMODYNAMICS OF CONSTANT PRESSURE GAS TURBINE: BRAYTON CYCLE

1 Efficiency

The Brayton cycle is shown on p-V and T-s diagrams in Fig. 16.4. During this cycle, air is drawn into the compressor at point 1 and then compressed isentropically along the process 1-2. Process 2-3 represents the burning of the oil at constant pressure p₂. Process 3-4 is the isentropic expansion of the gases through the turbine. Process 4-1 represents the exhausting and cooling of the gases at constant pressure p₁.

For 1 kg of air,

Compressor work, w_c = w₁₋₂ = h_2 − h₁ = c_p (T_2 − T₁)

Heat supplied, q = q₂₋₃ = h₃ − `h₂ = c_p (T₃ − T₂)

Turbine work, w_t = w₃₋₄ = h_3 − h₄ = c_p (T₃ − T₄)

Net work done, w_net = w_t − w_c = c_p [(T₃ − T₄) − (T₂ − T₁)]

Figure 16.4 Brayton cycle for constant pressure gas turbine: (a) p-V diagrams, (b) T-s diagrams

Let  be the pressure ratio and 

For the adiabatic compression process 1-2, we have

and for the adiabatic expansion process 3-4, we have

But p₁ = p₄ and p₂ = p₃

∴ 

Thermal efficiency, 

Figure 16.5 Variation of thermal efficiency with pressure ratio

The variation of thermal efficiency with r_p is shown in Fig. 16.5.

2 Specific Output

Specific output 

For maximum specific output, 

or 

Figure 16.6 Variation of specific output with pressure ratio

Hence, for maximum work output, the temperature after compression must be equal to the exhaust gas temperature, which depends on the expansion ratio. The variation of specific output with r_p is shown in Fig. 16.6.

3 Maximum Work Output

Maximum work output,

 

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

= c_p [T₃ + T₁ − T₄ − T₂]

4 Work Ratio

5 Optimum Pressure Ratio for Maximum Specific Work Output

w_net = w_t − w_c = c_p (T₃ − T₄) − c_p (T₂ − T₁)

w_net will be maximum, when 

Let 

From Eq. (16.3), we have

Combining with Eq. (16.7), we get