We wish to do an ideal thermodynamic analysis
of the **General Electric T700 gas turbine**
engine, which is used to power the **Army
Black Hawk helicopter**. Consider the schematic diagram
of the engine shown in the figure below:

Notice 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
**axial/centrifugal 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.

__Problem
6.10__ - Assume
that the compressor and both turbines are isentropic, and that
the combustion process occurs at constant pressure (isobaric).
Using the information shown on the schematic diagram above, do
the following:

- 1) 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. - 2) determine the energy consumed by the compressor
[w
_{C}= -328kJ/kg], and the temperature at the outlet of the compressor [T_{2}= 587K]. - 3) determine the heat energy absorbed by
the working gas in the combustion chamber [q
_{H}= 754kJ/kg]. - 4) determine the temperature [T
_{4}= 975K] and the pressure [P_{4}= 546kPa] at the outlet of the gas generator turbine. - 5) determine the temperature [T
_{5}= 627K] and energy output of the power turbine [w_{PT}= 382.5kJ/kg]. - 6) given that the mass flow rate of the working gas through the system is 4.6 kg/s, determine the power output of the power turbine [1.76MW].

(Data obtained through private communication
with **Dr.
Tom Scott**)

**Note:** Because
of the large temperature variation throughout this problem we
will need to consider the temperature dependence of the **Specific Heat
Capacities of Air**. All thermo texts that we know of present
a method of doing this using the tabulated function s^{}0, relative
pressure P_{r}, and relative specific volume v_{r}.
We prefer the simpler approach of using a constant specific heat
capacity C_{P} and ratio of specific heats k, where the
values are chosen at the average system temperature. This has
always provided an answer within around 1% accuracy. In the above
schematic diagram we see that the temperature extremes of the
system are 16°C - 1000°C (289 K - 1273 K), giving an average
temperature of 781 K. From the table of
**Specific
Heat Capacities of Air** we see that at 800 K, C_{P}
= 1.099 [kJ/kg.K] and the ratio of specific heat capacities k
= 1.354, thus we use those values throughout this problem.

**Solution Approach:**

- 1) 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.

Unlike the case with a pure fluid such as steam the*h-s*diagram is not drawn to scale, however is sketched in order to provide an intuitive graphical understanding of the problem. Furthermore, for an ideal gas the enthalpy is proportional to the temperature, hence the y-axis can be considered either an enthalpy or temperature axis. The various temperatures and pressures shown on this diagram are evaluated and plotted as we progress with the solution.

Notice that the various temperatures and pressures shown on this diagram are evaluated and plotted as we progress with the solution.

- 2) determine the energy consumed by the compressor
(w
_{C}- kJ/kg), and the temperature at the outlet of the compressor (T_{2}).

Ideally both the compressor and the turbine are isentropic devices, thus given the pressure ratio, in order to determine the temperature we consider the**isentropic relations**developed for an ideal gas.

- 3) determine the heat energy absorbed by
the working gas in the combustion chamber (q
_{H}- kJ/kg).

- 4) determine the temperature (T
_{4}) and the pressure (P_{4}) at the outlet of the gas generator turbine.

Once more. since both turbines are isentropic, we use the pressure temperature relations developed for an**isentropic process**of an ideal gas.

- 5) determine the temperature (T
_{5}) and energy output of the power turbine (w_{PT}- kJ/kg).

- 6) given that the mass flow rate of the working gas through the system is 4.6 kg/s, determine the power output of the power turbine (MW).

Note that the actual power output of the T700
engine is around 1800 hp, which is significantly less than the
above value. This is because we have assumed that the compressor
and both turbines are isentropic, which will never occur in practice.
**Problem 6.11** is an extension
to this exercise in which we consider non-isentropic compressor
and turbines.

______________________________________________________________________________________

Engineering Thermodynamics by Israel Urieli is licensed under a
Creative Commons Attribution-Noncommercial-Share
Alike 3.0 United States License