In a gas turbine plant working on Brayton cycle, the air at inlet is 27°C, 0.1 MPa. The pressure ratio is 6.25 and the maximum temperature is 800°C. The turbine and compressor efficiencies are each 80%. Find compressor work, turbine work, heat supplied, cycle efficiency and turbine exhaust

Question

In a gas turbine plant working on Brayton cycle, the air at inlet is 27°C, 0.1 M [latex]P_{a}[/latex]. The pressure ratio is 6.25 and the maximum temperature is 800°C. The turbine and compressor efficiencies are each 80%. Find compressor work, turbine work, heat supplied, cycle efficiency and turbine exhaust temperature. Mass of air may be considered as 1 kg. Draw T-s diagram. (N.U.)

Accepted Answer

Refer Fig. 40.
Given : [latex]T_{1} = 27 + 273 = 300 K ; p_{1} = 0.1 MP_{a} ; r_{p} = 6.25, T_{3} =[/latex] 800 + 273 = 1073 K ;
[latex]η_{comp.} = η_{turbine} [/latex]= 0.8.
For the compression process 1–2, we have

[latex] \frac{T_{2}}{T_{1}} = (\frac{p_{2}}{p_{1}})^{\frac{γ - 1}{γ}} = (r_{p})^{\frac{γ - 1}{γ}} = (6.25)^{\frac{1.4 - 1}{1.4}} =[/latex] 1.688

or [latex]T_{2} [/latex] = 300 × 1.688 = 506.4 K

Also, [latex]η_{comp.} = \frac{T_{2} - T_{1}}{T_{2}′ - T_{1}} or 0.8 = \frac{506.4 - 300}{T_{2}′ - 300}[/latex]

or [latex]T_{2}′ = \frac{506.4 - 300}{0.8} [/latex] + 300 = 558 K

∴ Compressor work, [latex]W_{comp.} = 1 × c_{p} × (T_{2}′ - T_{1})[/latex]

= 1 × 1.005 (558 – 300) = 259.29 kJ/kg.

For expansion process 3–4, we have

[latex] \frac{T_{3}}{T_{4}} = (\frac{p_{3}}{p_{4}})^{\frac{γ - 1}{γ}} = (r_{p})^{\frac{γ - 1}{γ}} = (6.25)^{\frac{1.4 - 1}{1.4}} =[/latex] 1.688

or [latex]T_{4} = \frac{T_{3}}{1.688} = \frac{1073}{1.688}[/latex] = 635.66 K

Also, [latex]η_{turbine} = \frac{T_{3} - T_{4}′}{T_{3} - T_{4}} or 0.8 = \frac{1073 - T_{4}′}{1073 - 635.66}[/latex]

or [latex]T_{4}′[/latex] = 1073 – 0.8 (1073 – 635.66) = 723.13 K

∴ Turbine work, [latex]W_{turbine} = 1 × c_{p} × (T_{3} – T_{4}′)[/latex] (neglecting fuel mass)

= 1 × 1.005 (1073 – 723.13) = 351.6 kJ/kg.

Net work output, [latex] W_{net} = W_{turbine} – W_{comp.}[/latex] = 351.6 – 259.29 = 92.31 kJ/kg

Heat supplied, [latex] Q_{s} = 1 × c_{p} × (T_{3} – T_{2}′)[/latex]

= 1 × 1.005 × (1073 – 558) = 517.57 kJ/kg.

Cycle efficiency, [latex]η_{cycle} = \frac{W_{net}}{ Q_{s}} = \frac{92.31}{517.57}[/latex] = 0.1783 or 17.83%.

Turbine exhaust temperature, [latex]T_{4}′[/latex] = 723.13 K or 450.13°C.
The T-s diagram is shown in Fig. 40.

Question 8.38: In a gas turbine plant working on Brayton cycle, the air at ...

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