1. AME 436 Energy and Propulsion
Lecture 14
Propulsion 4: Nonideal performance of airbreathing propulsion devices

2. Outline Component performance - definitions
AirCycles4Propulsion spreadsheet
Non-ideal performance of 'conventional' propulsion systems
Diffuser
Compressor
Burner
Turbine
Nozzle
Fan
Heat loss
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

3. Component performance
Diffusers (1  2) & nozzles (7  9) subject to stagnation pressure losses due to friction, shocks, flow separation
More severe for diffusers since dP/dx > 0 - unfavorable pressure gradient, aggravates tendency for flow separation
If adiabatic, Tt = constant, thus d  T2t/T1t = 1 and n  T9t/T7t = 1
If also reversible, d  P2t/P1t = 1 and n  P9t/P7t = 1, but d or n may may be < 1 due to losses; define performance
If reversible, d = d(-1)/ = 1, n = n(-1)/ = 1, but if irreversible d(-1)/ < 1 or n(-1)/ < 1 even though d = 1, n = 1
Define diffuser efficiency
d = d(-1)/ = 1 if ideal
Define nozzle efficiency
n = n(-1)/ = 1 if ideal
For nozzle - also need to consider what happens if Pexit ≠ Pambient, i.e. P9 ≠ P1
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

4. Compressors, fans & turbines
Compressors (2  3) & fans (2'  3') subject to losses due to
Separation of flow around compressor blades (again, unfavorable dP/dx)
Gas leakage between blade tips and compressor walls
How to define compression performance? (See Lecture 6)
If irreversible compressor or turbine, dS > Q/T; if still adiabatic
(Q = 0) then dS > 0
For same P ratio, more work input (more T) during compression, less work output (less T) during expansion through turbine
So define compressor efficiency comp as follows:
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

5. Compressors, fans & turbines
Fan efficiency fan defined similarly (note mass flow is  times higher than in main flow); problems not as severe since smaller pressure ratios
Turbines (4  5 and 5  6) have less fluid mechanics problems since dP/dx < 0, but need to bleed air from compressor through turbine blades for cooling (at least in first stages where T is high)
Define turbine efficiency turb as follows:
Same for fan turbine (if fan exists), just replace state 4 with 5 and replace 5 with 6
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

6. Component performance - combustors
Combustor (4  5) and afterburner (6  7) - stagnation pressure losses due to turbulence (required for mixing of fuel and air), heat addition at M > 0
Define combustor (burner) or afterburner performance in terms of stagnation pressure ratio b or ab (= 1 if ideal)
Of course for heat addition at finite M, stagnation pressure will always decrease; recall (lecture 12)
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

7. AirCycles4Propulsion.xls See also lecture 9 (AirCycles4Recips)
Thermodynamic model is exact, but heat loss, stagnation pressure losses etc. models are qualitative
Constant  is not realistic (changes from about 1.4 to 1.25 during process) but only affects results quantitatively (not qualitatively)
Heat transfer model
T ~ h(Twall -Tgas,t), where heat transfer coefficient h and component temperature Twall are specified - physically reasonable
Unlike AirCycles4Recips.xls, wall temperature Tw is specified separately for each component (diffuser, compressor, combustor, etc.) since each component feels a constant T, not the T averaged over the cycle
Increments each cell not each time step
Doesn't include effects of varying area, varying turbulence, varying time scale through Mach number, etc. on h
Work or heat in or out going from step i to step i+1 computed according to dQ = CP(Ti+1,t - Ti,t) or dW = - CP(Ti+1,t - Ti,t) (heat positive if into system, work positive if out of system)
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

8. AirCycles4Propulsion.xls Diffuser
Mach number decrements from flight Mach number (M1) to the specified value (must be zero except for hypersonic propulsion, discussed in lecture 15) after the diffuser in 25 equal steps
Stagnation pressure decrements from its value at M1 (P1t)
to dP1t = d/(-1)P1t in 25 equal steps
Static P and T are calculated from M and Pt, Tt
Sound speed c is calculated from T, then u is calculated from c and M
No heat input or work output in diffuser, but may have wall heat transfer
Fan flow diffuser exactly same as main flow diffuser except that mass flow rate is  times higher (d,main flow= d,fan flow)
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

9. AirCycles4Propulsion.xls Compressor
Mach number is assumed to be zero throughout - calculations correct only if the Mach number after the diffuser is zero, thus P = Pt, T = Tt
Compression is done in two steps
(1) Wall heat transfer at constant pressure according to the same law as for the diffuser process (step i,a to step i,b)
(2) Compression according to the usual Pv relations, isentropic or with optional irreversibility comp (step i,b to step i+1,a)
comp = 1 corresponds to reversible adiabatic process
Compression ends at a pressure of cP2t where c is the specified pressure ratio and P2t is the pressure at the end of the diffuser process
Stagnation pressure increments in 25 equal steps
Work per step = CP(Ti+1,a,t - Ti,a,t)
Fan compressor follows exactly same as rules except that mass flow rate is  times higher and fan may be different from comp
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

10. AirCycles4Propulsion.xls Combustor and afterburner
Heat generation due to combustion is added in 25 equal steps (1/25 of the total for each 1/25 of the stagnation temperature change) during the process and heat is transferred to the wall according to the same law as always
Stagnation pressure drops in 25 equal increments so that the pressure after combustion P4t = bP3t (note b = 1 for ideal turbojet cycle), or for afterburner P7t = abP6t
Heat addition ends when the temperature T4t = T1 (i.e the turbine inlet temperature limit), or T7t = T1,ab (afterburner temperature limit)
Mach number is assumed to be zero throughout
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

11. AirCycles4Propulsion.xls Turbine
Expansion to pay for compressor work is done in two steps:
(1) Wall heat transfer at constant pressure according to the same law as for the diffuser process (step i,a to step i,b)
(2) Expansion according to the usual Pv relations, isentropic or with optional irreversibility turb (step i,b to step i+1,a)
turb = 1 corresponds to reversible adiabatic process
Each of 25 expansion steps provides (after accounting for losses due to irreversibility) 1/25 of the work required to drive turbine (calculated in compressor analysis)
Work per step = - CP(Ti+1,a,t - Ti,a,t),
Mach number is assumed to be zero throughout
Expansion through turbine to pay for fan work (if fan exists, i.e. a ≠ 0) - same as main turbine, except equate fan work to turbine work
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

12. AirCycles4Propulsion.xls Nozzle
Static (not stagnation) pressure decrements from value after afterburner to specified exhaust pressure in 25 equal steps
Stagnation pressure decrements from its value after afterburner (P7t) to nP7t = n/(-1)P7t in 25 equal steps
Static P and T are calculated from M and Pt, Tt
Sound speed c is calculated from T, then u is calculated from c and M
No heat input or work output in diffuser, but may have wall heat transfer
Heat transfer occurs according to usual law
Same rules apply to fan nozzle except
We go directly from state 3' (after fan compressor) through nozzle to state 9', no combustor or turbine
Mass flow rate is  times higher
Assume Pexit = Pambient always, i.e. P9' = P1
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

13. Turbojet cycle - diffuser - effect of d
Obviously thrust & overall decrease, TSFC increases as d decreases, but can have pretty bad diffuser (d ≈ 0.55) before thrust disappears
Basic turbojet
No fan
No afterburner
M1 = 0.8
c = 30
 = 5
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

14. Turbojet cycle - diffuser - effect of d
T2 is the same, regardless of d, since air decelerated to M = 0
s2 increases & P2 decreases with decreasing d
T3 same (since same c), T4 same (same  limit), T5 same (same work required to drive compressor)
If P2 is too low (note it can be < P1), after compressor/combustor/turbine, P5 is too low, can only expand back to u9 = u1, so no net thrust!
Basic turbojet
No fan
No afterburner
M1 = 0.8
c = 10.97
 = 5
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

15. Turbojet cycle - effect of comp
Obviously thrust & overall decrease, TSFC increases as comp decreases, but (again) can have pretty bad compressor (c ≈ 0.58) before thrust disappears
Basic turbojet
No fan
No afterburner
M1 = 0.8
c = 30
 = 5
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

16. Turbojet cycle - effect of comp
State 2 is the same since air decelerated isentropically to M = 0
T3 & s3 increases as comp decreases (more work required to drive compressor for same comp), T4 same (same  limit)
T5 lower as comp decreases (more turbine work to drive compressor)
If comp too low after paying for compressor work in turbine, P5 & T5 are too low, can only expand back to u9 = u1, so no net thrust!
Basic turbojet
No fan
No afterburner
M1 = 0.8
c = 10.97
 = 5
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

17. Turbojet cycle - burner - effect of burner
Obviously thrust & overall decrease, TSFC increases as
burner decreases, but can have really lousy burner ≈ 0.13 before thrust disappears
Basic turbojet
No fan
No afterburner
M1 = 0.8
c = 30
 = 5
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

18. Turbojet cycle - burner - effect of burner
States 2 & 3 are the same, independent of what burner does
T4 same for all (same  limit) but as burner decreases, P4 decreases, thus s4 increases
T5 same for all (same turbine work required to drive compressor)
If burner too low after paying for compressor work in turbine, P5 & T5 are too low, can only expand back to u9 = u1, so no net thrust!
Basic turbojet
No fan
No afterburner
M1 = 0.8
c = 10.97
 = 5
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

19. Turbojet cycle - turbine - effect of turb
Obviously thrust & overall decrease, TSFC increases as turb decreases, but can again can have low turb ≈ 0.57 before thrust disappears
Basic turbojet
No fan
No afterburner
M1 = 0.8
c = 30
 = 5
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

20. Turbojet cycle - turbine - effect of turb
States are same, independent of turb
T5 also independent of turb (same work required to drive compressor) but s5 increases as turbine decreases
If turb too low after paying for compressor work in turbine, P5 is too low, can only expand back to u9 = u1, so no net thrust!
Basic turbojet
No fan
No afterburner
M1 = 0.8
c = 10.97
 = 5
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

21. Turbojet cycle - nozzle - effect of n
Obviously thrust & overall decrease, TSFC increases as turb decreases, but can again can have low turb ≈ 0.56 before thrust disappears
Interesting that d, comp, turb, nozzle at Thrust = 0 are all about the same!
Basic turbojet
No fan
No afterburner
M1 = 0.8
c = 30
 = 5
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

22. Turbojet cycle - nozzle - effect of n
States are same, independent of turb
If nozzle too low, can only expand back to u9 = u1, so no net thrust!
Note that even for zero-thrust cycle, there is still some decrease in T after turbine to create u9; if u9 = 0 then thrust is negative!)
Basic turbojet
No fan
No afterburner
M1 = 0.8
c = 10.97
 = 5
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

23. Turbojet cycle - nozzle - effect of Pexit ≠ Pamb
Thrust & overall decrease, TSFC increases if P9 ≠ P1, but performance very insensitive to P9/P1 (note horizontal scale is logarithmic)
Basic turbojet
No fan
No afterburner
M1 = 0.8
c = 30
 = 5
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

24. Turbojet cycle - nozzle - effect of Pexit ≠ Pamb
States are same, independent of P9/P1
If P9 too low, negative (P9 - P1)A9 term in the thrust equation balances the positive a[(1+FAR)u9 - u1], so no net thrust, even though u9 increases as P9 decreases
If P9 too high, u9 = 0; analysis fails at higher P9 although even at P9 = P5, there is still net thrust (although mdota[(1+FAR)u9 - u1] term is zero, (P9 - P1)A9 term generates thrust)
Basic turbojet
No fan
No afterburner
M1 = 0.8
c = 10.97
 = 5
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

25. Turbofan cycle - effect of fan
Obviously thrust & overall decrease, TSFC increases as fan decreases, but can have low fan ≈ 0.33 before thrust disappears
Actually thrust ≠ 0 at this point; at this point fan work is so large that turbine exit pressure = ambient pressure; beyond this point analysis fails since turbine work insufficient to supply greedy fan
Turbofan
 = 2
No afterburner
M1 = 0.8
c = 30
c' = 2
 = 5
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

26. Turbofan cycle - effect of fan
States are same, independent of turb
If fan too low, fan work is so large that turbine exit pressure P6 = ambient pressure P9, beyond this point analysis fails since turbine work insufficient to supply greedy fan
Turbofan
 = 2
No afterburner
M1 = 0.8
c = 10.97
c' = 2
 = 5
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

27. Turbojet cycle - effect of heat loss
No fan
No afterburner
M1 = 0.8
c = 10.97
 = 5
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

28. Turbojet cycle - effect of heat loss
With moderate heat loss, T2 & T3 decrease (given my choice of component wall temperatures, 300K for diffuser & compressor, 900K thereafter), and since P3/P2 is set by choice of c, s3 decreases
Heat addition is greater, because need to add more heat to get to  limit limit (starting from lower T, plus heat loss during heat addition)
Since heat addition at constant pressure and same maximum temperature, T4 is the same with heat loss
Heat loss during turbine & nozzle expansion also result in decreased T; since P9 is fixed, lower T9 means lower s9
Note that s decreases during nozzle expansion, even though T9 < Twall - heat transfer is based on stagnation temperature of gas, not static temperature, since heat loss occurs at the walls, and gas must decelerate to M = 0 at wall, Tt, not T, is a better temperature to use in heat tranfer estimates
(Actually, how nearly this happens depends on the wall “accommodation coefficient" and other gasdynamic effects that we won't discuss in this course)
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

29. Turbojet cycle - effect of heat loss
For ridiculously high wall heat loss coefficient, gas temperature follows wall temperature during compression (constant-T compression, like Stirling cycle), then heat is added at constant P, then during turbine & nozzle expansion, gas must follow constant-P path again until Tt = 900K (turbine & nozzle wall temperature) is reached, then remainder of turbine work can be extracted isothermally (again like Stirling cycle), then gas can expand adiabatically through nozzle (no change in Tt during nozzle expansion if adiabatic, and it will be adiabatic if gas Tt = wall T)
Effect of heat losses on performance (plot next page)
Heat losses barely affect specific thrust, can get about the same thrust per unit mass flow independent of heat losses since the pressures don't change much, thus velocities don't change much
Similarly, since pressures don't change much, velocities don't change much, thus propulsive efficiencies don't change much
HOWEVER, much more heat must be added when heat losses are present, thus TSFC goes WAY up, similarly thermal efficiency and overall efficiency go way down
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

30. Turbojet cycle - effect of heat loss
No fan
No afterburner
M1 = 0.8
c = 10.97
 = 5
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

31. Combination of all non-ideal effects
Spec. Thrust
TSFC
Thermal Eff.
Prop. Eff.
Overall Eff.
Specific impulse (sec)
Ideal
0.9314
2.5193
0.5504
0.5770
0.3176
5247.4
Non-ideal
0.3800
6.2803
0.1976
0.6445
0.1274
2104.9
Turbofan, no afterburner
M1 = 0.8, c = 10.97,  = 5
c' = 2,  = 2
diffuser = 1 or 0.9
comp = 1 or 0.9
πburner = 1 or 0.9
turb = 1 or 0.9
nozzle = 1 or 0.9
fan = 1 or 0.9
h = 0 or 0.02 (all wall temperatures = average gas temp for that component)
Drag coefficient = 0 or 0.2
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

32. How accurate is aircycles4recips.xls?
Real engine: GE90-85B turbofan, no afterburner
Static sea level (M1 = 0, T1 = 300K, P1 = 1 atm) or cruise (M1 = 0.83, T1 = 219K, P1 = atm)
Reported properties: c = 39.3; c' = 1.65;  = 8.4; Inlet area = 7.66 m2; CD = 0 (drag not included in reported performance)
Guessed properties
Turbine inlet temp. = 1700K   = 5.67 (static) or 7.76 (cruise)
diffuser = 1 (static) or 0.97 (cruise); comp = 0.9; burner = 0.98; turb = 0.9; nozzle = 0.98; fan = 0.9
h = 0.01 (all wall temperatures = average gas temp for that component)
Results (very sensitive to diffuser because of huge fan air flow!)
Spec. Thrust (static)
TSFC (static)
Spec. Thrust (cruise)
TSFC (cruise)
Spreadsheet
0.988
1.095
0.774
2.355
Actual
0.788
1.183
??? (air flow not reported)
2.213
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

33. Example - numerical
For a nonideal turbofan with bypass ratio () = 8,  = 1.35, compressor pressure ratio (c) = 30, fan pressure ratio (c') = 1.8, flight Mach number (M1) = 0.8, turbine inlet temperature = 1800K, ambient pressure (P1) = 0.25 atm and ambient temperature (T1) = 225 K, with P9 = P1 and FAR << 1, and component efficiencies as follows: diffuser (d) = 0.97, compressor (hc) = 0.90, combustor (b) = 0.98, turbine (ht) = 0.90, nozzle (d) = 0.98, fan (hf) = 0.90, determine the following (this is the same as the example in lecture 13 except non-ideal components are presumed here):
T, P and M after the diffuser (station 2)
T, P and M after the compressor (station 3)
(c) T, P and M after the combustor (station 4)
M4 = 0; P4t = P4 = (b)P3t = 0.98(11.0 atm) = 10.7 atm ; T4t = T4 = 1800K
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

34. Example - numerical (continued)
(d) T, P and M after the compressor turbine (station 5). Balance turbine & compressor work:
(e) T, P and M after the fan turbine (station 6)
For the fan stream, T2' = T2 = 250.2K and P2' = P2 = atm (same as main stream)
Then we need to compute the fan stream work and equate it to the turbine work:
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

35. Example - numerical (continued)
(e) T, P and M after the nozzle (station 9, and 9' for the fan stream) (note that for the fan stream, nothing happens between stations 3 and 6)
Specific thrust (ST) (recall FAR << 1 and P9 = P1 by assumption)
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

36. Example - numerical (continued)
(g) TSFC and overall efficiency
Recalling that only 1/(1+a) of the total air flow is burned,
note that compared to the ideal cycle, TSFC suffers less (2.52 vs = 8.6% increase) than
ST (0.647 vs = 12.5% decrease)
(h) Propulsive efficiency
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

37. Example - numerical (continued)
(i) Thermal efficiency
Note that hthhp = (0.516)(0.615) = = ho as advertised. Note that compared to the ideal cycle, thermal and overall efficiencies decreased (as expected) but propulsive efficiency actually increased slightly due to lower exit velocities.
(j) Specific impulse
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

38. Example - graphical
In an ideal -limited afterburning turbojet, how would the T-s diagrams be affected if
(a) The turbine is irreversible, but all other components are still ideal
The cycles are the same up to the end of the first heat addition process. The turbine work (thus DT) does not change, but the irreversibility during expansion increases the entropy, so that afterburning heat addition occurs along a lower constant-pressure curve up to the same temperature limit. Although not shown, since the afterburner DT is the same for the modified cycle, the heat addition, thus area under the T-s curve, is the same for the modified afterburner.
(b) A new compressor is used with a higher pressure ratio, but this compressor is irreversible (all other components are still ideal)
The compression process ends at a higher pressure and (since it is irreversible) a higher entropy than the base cycle. Heat addition then occurs along this constant-pressure curve up to the turbine temperature limit. More work, thus more DT, is required from the turbine, so the afterburning heat addition occurs along a lower constant pressure curve.
Same T
(a)
(b)
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

39. Example - graphical
In an ideal turbofan, how would the T-s diagrams be affected if
(a) The fan is removed and the redesigned turbine that drives the compressor is irreversible
The cycle is the same up to the end of heat addition. The DT and thus the T after the compressor turbine is the same but the entropy is higher. There is no fan turbine. Expansion through the nozzle continues to ambient pressure.
(b) There are substantial pressure losses in the combustor
The cycle is the same up to the end of the compression process. Heat addition occurs at decreasing pressure but up to the same temperature limit as the base cycle. The compressor and fan work requirements are unchanged, so the temperatures at states 5 and 6 are unchanged. 4 4'
(a)
(b)
(a) 5 5' 3 6 6' 2
AME Spring Lecture 14 - Nonideal effects in propulsion cycles

40. Summary - non-ideal effects
Irreversible diffusion, compression, expansion all reduce thrust & o
Stagnation pressure loss in diffuser - less expansion possible at end of cycle
More T (thus more work) to drive compressor
More P needed to extract turbine work required to drive compressor
Surprisingly, component efficiency at thrust = 0 nearly same for diffuser, compressor, turbine, nozzle! ( )
Effect of combustor pressure loss relatively small
Pexit ≠ Pambient (P9 ≠ P1) reduces thrust & o but effect is small
Heat transfer to/from gas during cycle
Modeling of heat losses different for steady flow device
Each component has its own T (unlike unsteady flow engines - use 1 wall temperature)
Stagnation vs. static temperature
As with unsteady flow engines, it takes more work to compress a hot gas than a cold gas, lowers o - best performance at h = 0
AME Spring Lecture 14 - Nonideal effects in propulsion cycles