**Problem 6.12 - Actual Power Output of the T700 Gas
Turbine Engine**

In **Solved
Problem 6.11** we did an ideal
thermodynamic analysis of the General Electric T700 helicopter gas
turbine engine, shown in the following schematic diagram:

Notice again that there are two turbines operating on independent output shafts. The High Pressure (first) turbine, named the Gas Generator turbine, is directly connected by a shaft to the compressor. Its sole purpose is to drive the the compressor, thus the energy output of this turbine must equal the energy consumed by the compressor. The Low Pressure (second) turbine, named the Power turbine, is connected via gearing to the helicopter rotor.

Notice that in **Solved
Problem 6.11** we assumed that the
compressor and both turbines were isentropic. In this exercise we
wish to extend the analysis to non-isentropic compressor and
turbines. Assume that the compressor adiabatic efficiency η_{C}
= 88%, and that each turbine has an adiabatic efficiency
η_{T} = 86%. Using
the information shown on the schematic diagram above, do the
following:

a) Sketch the entire process on an

*h-s*diagram, clearly showing the 5 stations on the diagram and the relevant isentropic and constant pressure lines. Indicate the relevant actual and isentropic work values on the sketch.b) determine the actual energy consumed by the compressor [w

_{C,act}= 373 kJ/kg], and the actual temperature at the outlet of the compressor [T_{2a}628K].c) determine the heat energy absorbed by the working gas in the combustion chamber [q

_{H}= 709 kJ/kg].d) determine the actual temperature [T

_{4a}= 934K] and the pressure [P_{4}366 kPa] at the outlet of the gas generator turbine.e) determine the actual temperature [T

_{5a}] and energy output of the power turbine [w_{PT,act}252 kJ/kg].f) given that the mass flow rate of the working gas through the system is 4.6 kg/s, determine the actual power output of the power turbine [1161 kW].

g) determine the thermal efficiency (η

_{th}) of the T700 gas turbine, compare this value to the equivalent reversible thermal efficiency and discuss your results.

*Derive* all equations used
starting from the basic energy equation for a flow system, the
equation of enthalpy for an ideal gas (Δh), the basic definition of
compressor and turbine adiabatic efficiencies (η_{C},η_{T}),
the basic definition of heat engine thermal efficiency (η_{th}),
and the temperature/pressure relation for the isentropic process of
an ideal gas:

Use specific heat values for air at 800K (C_{P}=
1.099 [kJ/kg.K], k = 1.354)

(**Hint:** refer
to the **Adiabatic
Efficiency Summary Sheet** to determine the
effect of compressor and turbine efficiency. Don't forget that the
gas generator turbine *must* always
supply the power required by the gas compressor)