When performing an analysis on this jet engine, there are great deals of
calculations necessary to conduct. To first gain a grasp of what is occurring, a simple
analysis was conducted for ideal conditions. This involved calculating the temperature
and pressure at the compressor outlet, having assumed that it was ideal, isentropic
compression and knowing the compression ratio. Also, the adiabatic flame temperature in
the combustor was calculated first assuming a stoichiometric combustion, then by
determining the amount of excess air flowing through the combustor and reevaluating the
adiabatic flame temperature. Next, the turbine exit conditions were found based on the
assumption that the work of the compressor was equal to the work of the turbine. In
addition to this assumption, it was assumed that the expansion in the turbine was
isentropic, which allowed the provided efficiency to be used for calculations of the exit
temperature. Finally, the temperature at the nozzle exit was calculated as well as the
nozzle efficiency. The final exit velocity was then determined based on the nozzle
efficiency.
The following table provides the determined values calculated in the simple
analysis:
Compressor Exit Temperature
471.242 K
Compressor Exit Pressure
344.505 kPa
Adiabatic Flame Temperature
944.473 K
Turbine Exit Temperature
773.272 K
Turbine Exit Pressure
141.949 kPa
Nozzle Exit Temperature (static)
711.437 K
Nozzle Exit Temperature (stagnation)
773.272 K
Nozzle Efficiency
87.08 %
Jet Exit Velocity
377.795 m/s
Using the data collected during lab, an analysis of the performance of the jet was
conducted assuming constant specific heat values. This consisted of first finding the mass
flow rate of air through the system from the inlet velocity, determined from the Pitot
tube, and the thrust force generated. This mass flow rate was used with the measured
mass flow rate of fuel to find the actual air to fuel ratio. After finding a compressor exit
temperature assuming that it was isentropic compression (effectively having an efficiency
of 100%), an actual compressor efficiency was calculated using the temperatures
recorded. Using the same procedure, an efficiency for the turbine was calculated. Also,
an efficiency for the nozzle was calculated using the temperatures between the turbine
exit and the nozzle exit. Lastly, the heat lost in the combustor was determined by the
energy of the reactants entering and the energy of the products leaving the combustor.
This entire method was conducted for each of the four levels of engine speed.
The following table provides the determined values calculated in the constant
specific heat analysis:
Idle
50,000 RPM 65,000 RPM 80,000 RPM
Constant Cp
Mass Flow Rate of Air (kg/s)
0.181
0.244
0.291
0.430
Actual Air to Fuel Ratio
185.238
160.033
119.250
123.284
Compressor Efficiency (%)
40.888
52.575
55.798
65.588
Turbine Efficiency (%)
344.195
269.944
158.086
117.108
Nozzle Efficiency (%)
-2789
-2275
-1316
-1456
Heat Loss in Combustor (kW) -4.018
-6.252
-10.005
-14.303
An analysis was also conducted on the experimental data assuming non-constant
specific heat values. The primary concern for this analysis was that the specific heat
value at any given point was dependent upon the temperature at that point. Based on that
specific heat value, an enthalpy was determined. To overcome the obstacle of finding the
specific heat values, the constants for air that apply to the third order polynomial
expression of specific heat as a function of temperature were used. This approach to
determining the specific heat values neglects the addition of fuel to the mixture after the
combustion process. Using a reference temperature of 298K, the enthalpy values for a
specific temperature were calculated by integrating the specific heat as a function of
temperature. Likewise, the entropies at any given temperature were calculated as a
function of a reference temperature and pressure as well as the temperature and pressure
of the desired entropy. Assuming isentropic compression in the compressor or isentropic
expansion in the turbine, an isentropic exit temperature was calculated. This isentropic
temperature was compared to the actual exit temperatures, which determined the
efficiencies. The calculations for mass flow rate of air, the air to fuel ratio, and the heat
lost in the combustor were the same as in the constant specific heat analysis, and were
therefore not conducted again.
The following table provides the efficiencies determined using non-constant
specific heat values at the four engine speeds:
Idle
50,000 RPM 65,000 RPM 80,000 RPM
Non-constant Cp
Compressor Efficiency (%) 40.775
52.391
55.420
65.016
Turbine Efficiency (%)
376.740 293.520
171.091
127.411
Nozzle Efficiency (%)
-3035
-2461
-1420
-1580
The following three figures depict the relationship between the constant specific
heat analysis and the non-constant specific heat analysis for compressor, turbine, and
nozzle efficiencies at the four engine speeds:
Compressor Efficiency versus Engine Speed
70
65
Efficiency (%)
60
55
50
45
40
idle
50,000
65,000
Engine Speed (RPM)
constant specific heat
non-constant specific heat
80,000
Turbine Efficiency versus Engine Speed
400
350
Efficiency (%)
300
250
200
150
100
idle
50,000
65,000
80,000
Engine Speed (RPM)
constant specific heat
non-constant specific heat
Nozzle Efficiency versus Engine Speed
-1000
Efficiency (%)
-1500
-2000
-2500
-3000
-3500
idle
50,000
65,000
80,000
Engine Speed (RPM)
constant specific heat
non-constant specific heat
As it can be seen, the differences between the constant specific heat analysis and
the non-constant specific heat analysis are minimal. For all three components of the
engine, the same overall trends occur for both analyses. The compressor performed more
efficiently as the engine speed increased. It was expected to do so, becoming closer to an
ideal condition of isentropic compression. The turbine becomes less efficient as engine
speed is increased. As it can be observed from the calculated values for nozzle efficiency,
the values seem extremely out of place, not only being negative but also on the
magnitude of thousands. This can be accounted for the fact that the temperatures recorded
at the nozzle exit were higher than the nozzle entrance, or turbine exit. This temperature
increase is most likely the result of heat lost from the combustor.
A T-s diagram was created for the experimental data. This graph, shown in Figure
_, shows the similarity of our experimental data to the ideal Brayton Cycle. However, the
random point around 800 K inside the closed process is the fifth state point, at the nozzle
exit. The red line depicts what was expected. It was expected that the temperature would
decrease in the nozzle and the air/fuel mixture would return to atmospheric pressures. It
was found, however, that the temperature increased in the nozzle portion of the engine as
explained previously.
The plots in Figure _ show the operating curve for the compressor and Figure _
for the turbine at the four different engine speeds. These curves plot the pressure ratio of
either the compressor or turbine versus the Mach number at that point in the engine. The
red diamond represents idle conditions, blue at an engine speed of 50,000 RPM, green at
a speed of 65,000 RPM, and fuchsia at 80,000 RPM.
m'air.0 T 1.07 10
5
P1.0
6 10
m'air.1 T 1.1
5
P1.1
5 10
5
m'air.2 T 1.2
P1.2
4 10
5
m'air.3 T 1.3
P1.3
3 10
5
1.2
1.4
1.6
1.8
2
2.2
2.4
P02.0 P02.1 P02.2 P02.3



P1.0 P1.1 P1.2 P1.3
m'air.0 T 03.05.5 10 5
P03.0
m'air.1 T 03.1
5 10
5
4.5 10
5
P03.1
m'air.2 T 03.2
P03.2
m'air.3 T 03.3
P03.3
4 10
5
1.2
1.4
1.6
1.8
P03.0 P03.1


P04.0 P04.1
P03.2 P03.3

P04.2 P04.3
2
2.2