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
6.11__ - 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:

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.b) determine the energy consumed by the compressor [w

_{C}= -328kJ/kg], and the temperature at the outlet of the compressor [T_{2}= 587K].c) determine the heat energy absorbed by the working gas in the combustion chamber [q

_{H}= 754kJ/kg].d) determine the temperature [T

_{4}= 975K] and the pressure [P_{4}= 546kPa] at the outlet of the gas generator turbine.e) determine the temperature [T

_{5}= 627K] and energy output of the power turbine [w_{PT}= 382.5kJ/kg].f) 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:**

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.

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.

b) 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.

c) determine the heat energy absorbed by the working gas in the combustion chamber (q

_{H}- kJ/kg).

d) 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.

e) determine the temperature (T

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

f) 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
6.12** is an extension to this exercise in
which we consider non-isentropic compressor and turbines.