Charles F. Herlihy
Aero 410
11/11/13
Aero 410 Computer Project #2
1.
a. For varying Compressor Pressure Ratio find:
i. TSFC at M=.1 to M=1.1
ii. T/Ma at M=.1 to M=1.1
b. Given T04 = 1950 oK. Find
i. TSFC at M=.1 to M=1.1
ii. T/Ma at M=.1 to M=1.1
c. Compressor Pressure Ratio kept at 12 find:
i. TSFC at 10k through 30k ft from M=.2 to M=.95
ii. T/Ma at 10k through 30k ft from M=.2 to M=.95
d. Compressor Pressure Ratio kept at 12 find how bypass ratio
affects:
i. TSFC at M= .9 at 30k ft
ii. T/Ma at M= .9 at 30k ft
e. Find with optimal values for Compressor Pressure Ratio and
Bypass ratio find:
i. Thrust developed at various altitudes
Page 3 (handwritten sheet with diagram) contains the corresponding
equations that lead to the plots below. The assumptions are as follows.
Pa/P7 = 1
CpH = 1243 J/kgK
Cpc = 1004 J/kgK
T02 = Ta
U = M(γRT).5
ηb = 1
Pa and Ta only vary with altitude
R = 287 J/kgK
Inlet diameter = 86.4in
Efficiencies throughout the turbo-jet are constant
QR = 45000KJ/kg
The code that generated the below plots is attached after the conclusion.
a.
Figure 1 Thrust Specific Fuel Consumption Versus Compressor Pressure Ratio
Figure 2 Specific Thrust versus Compressor Pressure Ratio
b.
Figure 3 Thrust Specific Fuel Consumption versus Compressor Pressure Ratio with
T04 = 1950K
Figure 4 Specific Thrust versus Compressor Pressure Ratio with T04 = 1950K
c.
Figure 5 Thrust Specific Fuel Consumption versus Compressor Pressure Ratio at
varying Altitudes and Mach Numbers
Figure 6 Specific Thrust versus Compressor Pressure Ratio at varying Altitudes and
Mach Numbers
d.
Figure 7 Thrust Specific Fuel Consumption versus Bypass Ratio
Figure 8 Specific Thrust Generated versus Bypass Ratio
e.
Figure 9 Thrust Developed at Various Altitudes
Conclusion
For parts a through c the bypass fan is removed from the system. For a,
thrust specific fuel consumption (TSFC) as well as specific thrust (T/ma) are
plotted against an increasing compressor pressure ratio ranging from 2 to 12
at Mach numbers from .1 to 1.1. What can be seen is that as the compressor
pressure ratio increases the turbo-jet becomes more efficient. Its TSFC is
decreasing at a rate that can be approximated as exponential. Interestingly
enough the T/ma increases with pressure ratio generating about 1500(m/s)
at M=.1 and a pressure ratio of 12. The turbo-jet is not only consuming less
fuel per unit thrust, but is also generating more power as compressor
pressure ratio increases. In part b very similar plots can be seen. The only
difference between a and b is the fixed combustion chamber inlet
temperature of 1950oK and the calculations being done at sea level instead
of 35000ft. The same conclusions can be deduced.
Part c is when the effects of altitude can truly be seen. Looking at Figure 5
and Figure 6, an inference about how altitude affects TSFC and T/ma can be
made. At 30000ft the TSFC is at its least value. This means that the engine
is more efficient at these higher altitudes. Similarly for T/ma the turbo-jet
appears to increase its efficiency at higher altitudes. At M=.2 and 30000ft
the jet delivers the most thrust, whereas at M=.95 at 10000ft the T/ma is at
a minimum for the plot.
Part d contains my favorite two plots. Optimization for bypass ratio under
the given conditions can be made. Although TSFC’s best value is found at a
low spike at a bypass ratio at about 50, specific thrust in this scenario is
actually negative. That clearly is not efficient nor correct. Studying these
plots more closely reveals that the optimal value for bypass ratio under
these given conditions occurs at about 25. The highest value of T/ma
happens here, and TSFC also has a local minimum here as well.
Initially the plot in part e appeared to be wrong. It seemed as though the
approximate linearly decreasing graph conflicted with the graphs in part c.
The efficiency, best viewed by specific thrust was consistently going up with
altitude. In e however the thrust values are decreasing with altitude. But this
actually does make sense. At higher altitudes the density of the air is going
down. Less air density to push, and at a lower temperature, yields less
thrust. The mass flow rate is decreasing as well. It varies with ambient
temperature, air density and Mach number. Mach number is the only
variable that is constant here and the others are decreasing with altitude.
Therefore, although specific thrust (efficiency) is increasing with altitude
(Figure 6) the actual thrust is decreasing (Figure 9).