13468-9-169P AID: 1825 | 05/12/2014

Two-stage gas turbine

Show the two-stage gas-turbine with regeneration, reheating and intercooling, on diagram as in Figure (1).

Use Ideal-gas specific heats of various common gases table to find specific heat capacity and specific heat ratio of air.

Find the pressure ratio across each stage in the given two-stage gas turbine .

Here, the overall pressure ratio of the two-stage gas turbine is r.

Substitute 16 for r to find .

Calculate the temperature at the end of the compression process for the two-stage gas turbine.

Here, the minimum temperature of air in the two-stage gas turbine cycle is , the specific heat ratio of air is k.

Substitute 4 for , 293 K for , and 1.4 for k.

Calculate the temperature at the end of the expansion process for the two-stage gas turbine .

Here, the maximum temperature of air in the two-stage gas turbine cycle is .

Substitute 4 for , 1073 K for , and 1.4 for k.

Find the heat input for the two-stage gas turbine .

Here, the specific heat of air at constant pressure is .

Substitute for , 1073 K for , and 722.1 K for .

Find the heat output for the two-stage gas turbine .

Substitute for , 293 K for , and 435.4 K for .

Find the thermal efficiency of the given two-stage gas turbine .

Substitute for , and for .

Hence, the thermal efficiency of the two-stage gas-turbine is .

Three-stage gas-turbine

Show the three-stage gas-turbine with regeneration, reheating and intercooling, on diagram as in Figure (2).

Find the pressure ratio across each stage in the given three-stage gas turbine .

Here, the overall pressure ratio of the three-stage gas turbine is r.

Substitute 16 for r to find .

Calculate the temperature at the end of the compression process for the three-stage gas-turbine.

Here, the minimum temperature of air in the three-stage gas turbine cycle is .

Substitute 2.52for , 293 K for , and 1.4 for k.

Calculate the temperature at the end of the expansion process for the three-stage gas turbine .

Here, the maximum temperature of air in the three-stage gas turbine cycle is .

Substitute 2.52 for , 1,073 K for , and 1.4 for k.

Find the heat input for the three-stage gas turbine .

Substitute for , 1,073 K for , and 824 K for .

Find the heat output for the three-stage gas turbine .

Substitute for , 293 K for , and 381.5 K for .

Find the thermal efficiency of the given three-stage gas turbine .

Substitute for , and for .

Hence, the thermal efficiency of the three-stage gas-turbine is . Also, the thermal efficiency of three-stage gas-turbine is found to be higher than the two-stage gas-turbine, due to the increase in the temperature at the end of the expansion process, and decrease in the temperature at the end of the compression process.