AME 436	Assigned: 4/18/08
Problem Set #6	Due: 4/25/08 at 4:30 pm in my office mailbox (OHE 430J) (fax to me at 213-740-8071 if you’re off campus)

Problem #1 (from last year’s final exam)

In an ideal t_l-limited turbojet with afterburner how would the T-s diagram be affected if

a) The compressor is irreversible, but all other components are still ideal

b) A new turbine with a higher maximum allowable inlet temperature is used, thus t_l increases (but the afterburner temperature limit t_l,_AB does not change.)

c) There are pressure losses in both the main burner and the afterburner (all other components are still ideal)

d) A new fuel with a larger heating value per unit mass is used

Show your results on the T-s diagrams below. In some cases there may be no change to the cycle. Assume that the compressor pressure ratio is the same for all cycles. When useful, add statements like “this DT = that DT,” “this area = that area,” etc. Please make your modifications clear; cycles that look like random scribbles and have no explanations don’t get much credit!

a)
	The compressor is irreversible, but all other components are still ideal.
b)
	A new turbine with a higher maximum allowable inlet temperature is used, thus tl increases (but the afterburner temperature limit tl,AB does not change.)
c)
	There are pressure losses in both the main burner and the afterburner (all other components are still ideal.)
d)
	A new fuel with a larger heating value per unit mass is used.

Problem #2 (from last year’s final exam)

The following 5 changes to a t_l-limited turbofan engine flying at subsonic conditions (M₁ < 1) are being considered:

1) Increase the fan air bypass ratio (a) by a factor of 2

2) Increase the flight Mach number (M₁) by a factor of 2

3) Increase the turbine inlet temperature limit (t_l) by a factor of 2 (yeah, right…)

4) Increase the compressor pressure ratio (π_c) by a factor of 2 (ditto…)

5) Increase the fuel heating value (Q_R) by a factor of 2

Briefly explain:

a) Which of these would increase thermal efficiency the most?

b) Which of these would decrease overall efficiency the most?

c) Which of these would increase specific thrust the most?

Problem #3 (from last year’s final exam)

Two hypersonic engine designs, A and B, are being considered for a high-speed transport aircraft operating at a flight Mach number of 5.

Engine A produces a flow at the exit with a stagnation pressure 80 times the ambient pressure and a stagnation temperature 12 times the ambient temperature.

Engine B produces a flow at the exit with a stagnation pressure 100 times the ambient pressure and a stagnation temperature 10 times the ambient temperature.

Because these two engines are made by rival companies with trade secrets, little is known about what happens inside the engines. It is not known for either engine it uses a compressor or not, whether combustion occurs at constant P, T, A or none of the above, if the diffuser is reversible or not, nor is t_l known. All that is known is that for both engines (1) the same fuel is used, (2) reversible adiabatic expansion occurs in the exhaust nozzle to ambient pressure, (3) during the expansion the gas has constant specific heats with g = 1.4, and (4) the fuel to air ratio (FAR) is much less than 1.

a) Which engine, A or B, has the higher specific thrust?

b) Which engine, A or B, has the higher thrust specific fuel consumption?

Problem #4

For a turbofan with bypass ratio (a) = 5, g = 1.4 for all processes, compressor pressure ratio (p_c) = 30, fan pressure ratio (p_c’) = 2, flight Mach number 0.8, turbine inlet temperature = 1500K, ambient pressure 0.25 atm, ambient temperature 225 K, and the following component efficiencies:

a) For the ideal cycle (all component efficiencies = 1), determine the temperature, pressure and Mach number at each station 1, 2, 3, 4, 5, 6 and 9. Assume FAR << 1. You can use aircycles4recips.xls to check your results, but you need to show the calculations that led to your results.

b) From these results, determine the specific thrust, thrust specific fuel consumption, thermal efficiency, propulsive efficiency, and overall efficiency.

c) Repeat (a) and (b) for a non-ideal cycle with no heat losses but the following component efficiencies:

Component	Component efficiency
Diffuser	0.97
Compressor	0.85
Burner	0.99
Turbine	0.90
Nozzle	0.98
Fan	0.85

For the non-ideal cycle your results will be slightly (but only slightly) different than those of aircycles4recips.xls due to the way the spreadsheet breaks the compression and expansion processes up into 25 smaller parts.

Problem #5

For turbofan of Problem #4 (g = 1.4 for all processes, compressor pressure ratio (p_c) = 30, flight Mach number 0.8, turbine inlet temperature = 1500K, ambient pressure 0.25 atm, ambient temperature 225 K), using aircycles4propulsion.xls, determine what combination of bypass ratio (a) and fan pressure ratio (p_c’) (changing nothing else) gives the minimum thrust specific fuel consumption under the following 3 conditions:

a) Ideal cycle (all component efficiencies = 1)

b) Component efficiencies as in Problem #4, part (c), with drag coefficient = 0

c) Component efficiencies as in Problem #4, part (c), with drag coefficient = 0.2

You don’t have to show any calculations as you did in Problem 4, just use the spreadsheet to find the optima under these conditions, but answer the following questions:

1) Why was the answer to (a) a ® ∞, p_c’ ® 1?

2) Why was the optimum a smaller for part (c) than (b)?