126 AIRCRAFT ENGINE DESIGN
feature is activated by following the directions at the bottom of the ONX input data window for the mixed flow turbofan engine.
The final safety net is that the ONX computer program has been arranged to override the input of M6 if M16 is out of limits in order to obtain a legitimate solution. Even if the solution is not a useful one (i.e., M16 "~ 0), the results will indicate the right direction. If no solution is possible, the printout will tell which of the two mixer entry total pressures was too high.
4.3.5 The Good News
Applying the ONX parametric engine cycle computer program to a new set of requirements is an exhilarating experience. The tedious work is done so swiftly and the results are so comprehensive that natural curiosity simply takes over. Almost any search procedure from almost any starting point quickly leads to the region of most promising results. The influence of any single input parameter on all of the output quantities can be immediately determined by changing its value only slightly. This is the basis of sensitivity analysis (see Sec. 4.4.5). The behavior of each component can also be clearly traced and the possibility of exceeding some design limitation (e.g., compression ratio or temperature) easily avoided.
In addition to fun, there is also learning. Armed with computational power and an open mind, the best solutions made possible by natural laws literally make themselves known. Simultaneously, the payoff made possible by various tech- nological improvements or changes in the ground rules is determined. For the moment, each participant really is like an engine company preliminary design group, with similar capabilities and limitations. No wonder it is exhilarating.
ENGINE SELECTION: PARAMETRIC CYCLE ANALYSIS
190 = 1.07
50
127
40
Alt (k ft)
30
20
10
0
0.0 0.5 1.0 1.5 2.0
M0
Critical flight conditions vs theta zero (00) for standard day.
Fig. 4 . E l
all possible combinations of aircraft flight conditions and engine design points.
Instead, a few critical flight conditions having significantly different characteristics and/or large fuel usage (small FI) may be used to establish important trends. For the AAF of the RFP, the following represent such a sample:
1) Takeoff, 100°F at 2,000 ft--High thrust is required at a flight condition (00 > 1.07) where the engine operation is Tt4 limited. This is not plotted in Fig. 4.E 1 because the flight condition does not occur on a standard day.
2) Subsonic Cruise Climb (BCM/BCA), 0.9M/42 k f t i L o w fuel consumption is required in phases 3-4 (I-I = 0.9736) and 10-11 (FI = 0.9698).
3) Supersonic Penetration and Escape Dash, 1.5M/30 kft--High thrust is re- quired to permit low fuel consumption without afterburning (supercruise) in phases 6-7 segment G (FI = 0.9382) and 8-9 (FI = 0.9795).
4) Supersonic Acceleration, 1.2M/30 k f t i B o t h high thrust and low fuel con- sumption with afterburning are required in phases 6-7 segment F (FI = 0.9837) and 7-8 segment K (FI = 0.9828).
4.4.2 Component Design Performance Parameters
Referring to the data of Table 4.4, and recognizing that the AAF engine will use the most advanced engine technology available, the design will be based on the following component performance parameters and information:
128 AIRCRAFT ENGINE DESIGN
Description Input value
Polytropic efficiency
Fan (ef) 0.89
Low-pressure compressor (eeL) 0.89
High-pressure compressor (ecu) 0.90
High-pressure turbine (etH) 0.89
Low-pressure turbine (etD 0.91
Total pressure ratio
I n l e t (Ygd max) 0 . 9 7
Burner (zrb) 0.96
Mixer (ZrM max) 0.97
Afterburner (ZrAB) 0.95
Nozzle (zrn) 0.98
Component efficiency
Burner (Ob) 0.995
Afterburner 0/AS) 0.97
Mechanical
Low-pressure spool (OmL) 0.995
High-pressure spool (0m/4) 0.995
Power takeoff LP spool (l]meL) 0.995
Power takeoff HP spool (tlmeu) 0.995
Fuel (JP-8) heating value (heR) 18,400 Btu/lbm Main burner exit (Tt4 max ) _~< 3400 ° R
Afterburner (TtT) 3600°R
Turbine cooling air
Tt4max > 2 4 0 0 ° R 61 = 62 = (Tt4max - 2 4 0 0 ) / 1 6 , 0 0 0
Tt4max ~-~ 2400°R sl = 62 = 0
4.4.3 Analysis of Results
The O N X parametric computer program accompanying this textbook was used to study 60 different design point combinations of the design parameters Zrc, zrf, or, Tt4, and Tt7 for the three flight conditions selected as critical for fuel consumption in Sec. 4.4.1. The carpet plots in Figs. 4.E2-4.E6 are the results of this study for the most promising combinations of design choices. The results are plotted as uninstalled specific fuel consumption vs uninstalled specific thrust. The required uninstalled specific fuel consumption (S) is plotted in order to allow for convenient comparison with the estimated value of the uninstalled fuel consumption. Please note that ~ = 0 corresponds to a zero bypass turbofan, normally known as a turbojet. Incorporation of the engine control into the parametric analysis requires that Tt4 be limited to values less than Tt4ma x for flight conditions where 00 is less than the throttle ratio (TR). The value of Tt4 for these flight conditions can be calculated using (see Appendix D)
00 ,~ "max (4.35)
Zt4 = ~ 1 , 4
S (i/h)
1.10
1.05
1.00
0.95
0.90
0.85
0.80
T a r g e t o r G o a l
I I I
5O
Fig. 4.E2
I ' I
°=05 t /_
, I , , , , I ,
55 60
F / rh o (Ibf/lbm/s) B C M / B C A , Tt4 = 2613°R, no AB.
1.15
1.10
1.05 E
1.00 (l/h)
0.95
0.90
0.85 55
' I ' ' I '
~
0.3, , , , I , , , , I ,
60 65
F / rh o (lbf/lbm/s) Fig. 4.E3 B C M / B C A , Tt4 = 2776°R, no AB.
65
70
129
4.6
4.4
4.2
4.0
3.8
3.6
3.4
3.2
Tt4 = 2613°R .. . .
Tt4 = 2776°R - - a=0.3
r S
J S
S
S
J a = 0 . 4 o~= 0.3
- ~ o~= 0.4
~ ~ a = 0 . 5
. . .
10 15 20 25 30
zcc
Fig. 4.E4 BCM/BCA, fan pressure ratio vs compressor pressure ratio, Tt4 -- 2613 and 2776°R.
S (l/h)
1.45 1.40 1.35 1.30 1.25 1.20 1.15 1.10
1.05 55
' ' ' ' I ' ' ' ' I ' ' ~ I '
a = ~ 0"3
, , , , z ~ , , , ~ ~ - ,
~.°
, . . . . , ,60 65 70
F / rh o (lbf/lbm/s) Fig. 4.E5 1.5M/30 kft, Tt4 = 3200°R, no AB.
I I I
75
130
ENGINE SELECTION: PARAMETRIC CYCLE ANALYSIS 131
S (l/h)
2.00 1.95 1.90 1.85 1.80 1.75 1.70 1.65 1.60
~=5
a= 0.4 c¢=0
15
Target or Goal
2 5 ~ m _m
95 100 105 110 115 120
F / rh 0 (lbfflbrrds)
Fig. 4.E6 1.2M/30 kft, Tt4 - - 3059°R, Tt7 = 3600°R.
The design Tt4 and the target or goal S values are presented in Table 4.El for the three flight conditions of interest.
Subsonic cruise climb BCM/BCA, 0.9M/42 kft. Examination of the carpet plots of the computed results in Figs. 4.E2 and 4.E3 reveals that the uninstalled specific fuel consumption (S) and specific thrust (F/rho) depend strongly upon bypass ratio (or) and compressor pressure ratio (Trc). Comparison of Figs. 4.E2 and 4.E3 shows the familiar result that both S and F/rho increase along with peak cycle temperature (Tt4). On the other hand, Fig. 4.E4 shows that fan pressure ratio (:rf) increases with Jrc and Tt4 and decreases with ~. Consequently, the focus here
Table 4.El Combustor temperatures and fuel consumption goals
Altitude, Target or goal
Flight condition Mach kft 0o Tt4ma x Tt4 TSFC S a
BCM/BCA 0.9 42 0.8737 3200 2613 1.015 0.964
3400 2776
Supercruise 1.5 30 1.151 3200 3200 1.203 1.143
Acceleration 1.2 30 1.023 3200 3059 1.714 1.629
aBased on data in Sec. 3.4.1 and a 5% installation loss.
132 AIRCRAFT ENGINE DESIGN
will be upon the selection of useful ranges of t~ and Zrc, and consideration of Tt'f and Tt4 will be delayed pending later results.
Increasing ot alone causes both F/rho and S to decrease, in accordance with normal expectations for subsonic turbofan engines, as the available exhaust kinetic energy is spread over more incoming air. Because the slope of the line of constant Zrc shows that F/rho is decreasing percentage-wise roughly twice as fast as S, it does not seem advisable to choose an ot greater than 0.5. Conversely, because S meets the target or goal for moderate to high pressure ratios, no a less than 0.3 should be considered. Thus, the best ~ for this flight condition is probably in the range of 0.3-0.5.
Increasing Zrc alone produces a more complex behavior of F/rho and S because a maximum of F/rho occurs while S continuously decreases. This behavior is typical of turbine engines, as demonstrated in Refs. 1 and 2. The maximum value of F/rho is due to the simple fact that increasing values of Jrc (and thus Tt3) eventually limit the amount of fuel than can be added before the allowable Tt4 is reached. One should logically select values of Zrc that are located below the knee of the curve, but not so far below that F/rho is falling rapidly for slight reductions in S. Moreover, no Zrc should be chosen that exceeds reasonable expectations, with that value today being in the range of 35-40. Computations reveal, however, that Zrc cannot reach that limit at high Mach flight conditions before Tt3 exceed s current capabilities (Zt3max > 1700°R). Taken together, these reasons indicate that Zrc should be held in the range of 20-30 for this flight condition.
Supersonic penetration and escape dash, 1.5M/30 kft. Very similar re- marks to those just stated, both qualitative and quantitative, can be made about the influence of zrc, zrf, a , and Tt4 on S and F/rho at this flight condition. The main differences, as illustrated by the carpet plot of Fig. 4.E5, are that F/rho decreases more rapidly with zrc as well as less rapidly with a in the critical area below the knee and that there is no sign of choking of the core flow at the highest allowable values of zr¢. Taking these factors into account, including the special need for high thrust at this flight condition, the useful ranges of parameters are 15 < Zrc < 25 and 0.3 < a < 0.4.
Supersonic acceleration, 1.2M/30 kft. The carpet plot of the computed results in Fig. 4.E6 reveal that both S can be reduced and F/mo increased by increasing 7r¢ and reducing ~. Again, changing either Tt4 or Tt7 would have the usual effect of increasing both S and F/rno.
By this time it has become clear that the desired fuel consumption goals can be achieved at some flight conditions, but not all. Consequently, the focus of our search must continue to be on reduced fuel consumption over the entire mission.
Otherwise, the takeoff weight (WTo) of the AAF will certainly grow beyond the initial estimate of Chapter 3 and, because Eq. (3.49), which determines Wro, is extremely nonlinear, Wro could become unacceptably large. While it is still possible that S will be reduced when the engine is throttled back to the required thrust, or the installation penalties will be less than estimated, or the TSFC models of Table 4.El are conservative, nothing may yet be taken for granted.
Consequently, the engine performance information generated at this flight condi- tion shows that 20 < zr¢ < 30 and 0 < ~ < 0.4. The results obtained so far suggest
ENGINE SELECTION: PARAMETRIC CYCLE ANALYSIS 133 that Tt4 and Tt7 must be limited in order to achieve acceptable fuel consumption, even though increasing them will increase specific thrust and thereby reduce the size of the required engine. Their limits will be arbitrarily selected a s Zt4 ~-- 3200°R and T,7 = 3600°R because even these values will push the material and cooling ca- pabilities expected to be available for the AAF (see Table 4.4). These assumptions, as well as any others, can be changed if later calculations indicate a positive benefit.
4.4.4 Integrated Results: Range of Design Choices
Before the final ranges of interest for key engine reference point parameters are selected, two facts must be recognized. First, it makes sense to state them only in conjunction with a specific flight condition (i.e., P0, To, and M0), preferably one that will be near the final reference point. Because the AAF must operate well over the 0.9 < M0 < 1.8/30-45 kft range, it is reasonable to conclude that the reference point will be in the vicinity of 1.5M/35 kft. Second, any selection must take into account the normal behavior of parameters when the engine is operating off-design. A sensible goal is for the key engine parameters to be in their best ranges at all critical operating points. Thus, the engine will appear to be properly designed for each.
The three critical operating points were therefore added to scaled Figs. 4.6 and 4.8, which are representative of the type of engine emerging for the AAF application, and the results reproduced here as Figs. 4.E7 and 4.E8.
30
25 Ec
20
15
10
5 0.0
I ' ' ' ~ 1 ' I ' ' I
I I , , I , J , , I , , , ,
0.5 1.0 1.5 2.0 2.5
Mo
Alt (kft) 40 30 20 10 SL
Fig. 4.E7 Compressor integrated results.
134 A I R C R A F T ENGINE DESIGN
a 0.6
0.5
0.4
0.3
I ' ' ' ' I ' ' ' ' I ' ' ' '
0 . 2 . . . . I . . . . I , ~ , t , ~ , ~ I , ~ t
0.0 0.5 1.0 1.5 2.0 2.5
MO
Alt (kft) SL
10 2O 3O 4O
Fig. 4.E8 Bypass ratio integrated results.
Referring to Fig. 4.E7, it can be seen that both the desired and available 7rc decrease with M0, so that selecting the range 15 < :re < 25 at 1.5M/35 kft will provide the desired zrc at other flight conditions. In other words, using the trends of Fig. 4.E7 and imagining that the reference point is moved through the range 15 < Zrc < 25 at 1.5M/35 lift, one sees that the desirable 7rc at other flight conditions will be included.
Referring to Fig. 4.E8, it can be seen that the situation is different, and that only the relatively small range of 0.3 < ot < 0.4 at the reference point of 1.5M/35 kft will provide desirable ot at the other critical flight conditions.
The foregoing reasoning leads to the final choices for the most promising ranges of key engine design parameters:
1.2_<Mo_< 1.6 3 0 < h < 4 5 k f t
15 < zr~ _< 25 0.3 <¢z < 0 . 4 3 _ < 7 r / ~ 5 Tt4 < 3200°R Tt7 < 3600°R 0.35 < M6 < 0.45
ENGINE SELECTION: PARAMETRIC CYCLE ANALYSIS 135 A good first design should have both the compressor pressure ratio and the combustor exit temperature at their maximum values at a theta break 00 equal to the TR (see Appendix D). In this case the TR has initially been chosen to be 1.07, which would correspond, for example, to 1.318 Mach at 30 kft or 1.454 Mach at any altitude above the tropopause. Consequently, the selection of h depends on the choice of M0 and vice versa.
4.4.5 Sensitivity Analysis
The power of the parametric engine cycle performance calculations can be better understood and appreciated by means of this final investigation known as a sensitivity analysis. This is a process in which the percentage change of all output quantities with respect to the percentage change of each independent input quantity is determined by varying the input parameters only slightly and one at a time. For example, if one is interested in how sensitive the specific fuel consumption (S) is to the cycle bypass ratio (~) alone, one would form the quantity
($2 - $1)/$1 ~S (ot2 - o~1)/Oll got
from two successive reference point calculations that differ only in 6or << or. Such ratios, in the limit, represent the mathematical slopes or derivatives that are gen- erally too difficult to obtain in closed form for such a complex set of equations.
The qualitative meaning of these ratios is easy to grasp. When they are very small compared to one, the input variable has little influence on the output variable. If the entire array were very small compared to one, the design point would be located on some type of a plateau, perhaps near to an optimum. Those ratios of the order of one offer the opportunity for improvement and point out the desired direction of change.
Consider the sensitivity of specific thrust and thrust specific fuel consumption to changes in flight conditions and engine design choices for a mixed flow turbofan engine having the component performance design values corresponding to those of the printout reproduced in Sec. 4.2.7, which has the engine reference point
M 0 = 1.6 ~ = 0.4 Alt = 3 5 k ~ ~ 4 = 3200 °R
~c = 16 ~7 = 3600 °R
~ f = 3.8 Po/P9 = 1
Table 4.E2 presents the computed sensitivity of F/rho and S to changes in the design choices at the engine reference point. These data were obtained from a fractional change of +0.05 in each design choice given. Because S and F/rho are at a minimum and maximum respectively for Po/P9 = 1.0, the sensitivities are shown for a (+) and ( - ) variation in P0/P9. From the table, the sensitivity of thrust specific fuel consumption to a change in bypass ratio, for example, is seen to be
3S - 0.0723 mil power got
= +0.0341 max power
136 AIRCRAFT ENGINE DESIGN Table 4.E2 Sensitivity analysis
Military power Maximum power
Fractional
Variation of/with F /rho S F /rho S
Tt 4 +1.0526 +0.5872 +0.2165 -0.0976
Tt7 +0.8437 +0.8411
rrc -0.0914 -0.1464 +0.0301 -0.0375
7/'f -0.0091 +0.0069 -0.0063 +0.0068
ot -0.2098 -0.0723 -0.0369 +0.0341
M6 -0.0026 +0.0034 -0.0022 +0.0023
Po/P9 -0.0039 +0.0034 -0.0033 +0.0034
+0.0042 -0.0052 +0.0035 -0.0045
Mo -0.5956 +0.0706 -0.1965 +0.0613
Alt +0.1900 -0.0362 +0.1109 -0.0715
neither of which shows a significant sensitivity of S to or. Fortunately, this insen- sitivity is not typical of all of the results of the analysis.
Referring to Table 4.E2, and recalling that everything possible must be done to reduce S, particularly at military power, there seem to be several useful indications, namely:
1) An overall mission improvement in fuel consumption can be achieved by reducing both Tt4 and TtT, but only at the expense of a considerably larger reduction in F/rho, and hence an increase in the size of the engine(s). The message here confirms earlier conclusions regarding the necessity to put upper limits o n Tt4 and Tt7 in order to achieve fuel consumption goals. In that sense no real benefits result from making the engine "hotter."
2) Relatively large changes of zr¢, zrf, and ot are required to measurably impact F/rho and S, particularly in maximum power. The most promising possibility is to increase Zrc, which improves both F/rho and S with and without afterburning.
Next in line for consideration is an increase of zrf, provided that the decrease of military power F/rho is tolerable. Because changing ot has such conflicting effects, no clear advice for its final selection is yet available.
3) Changing M6 has no performance consequences. Performance cannot be improved by changing P9/Po and, as expected, it will suffer if P9 is taken far from P0 and the exhaust nozzle is incorrectly expanded.
4) For completeness, the sensitivity of engine performance to reference point Mach number and altitude has also been included. The large apparent benefits of reducing Mach number and increasing altitude are illusory, because the flight conditions are specified by the RFP and the gains would be lost when the engine is returned to the present reference point (i.e., 1.5M/35 kft). Nevertheless, in order to understand engine behavior more fully, recall that for any single exhaust stream jet engine
F ~7ofh?R
mo aoMo
ENGINE SELECTION: PARAMETRIC CYCLE ANALYSIS 137 and
S - l'h f __ aoMo F 7ohl, R
where 770 is the overall cycle energy conversion efficiency from fuel energy to thrust work (see Appendix E). Because 7o varies relatively slowly with flight conditions, the overwhelming effect of decreasing M0 or decreasing a0 (i.e., increasing alti- tude) is to improve both F / m o and S. Thus, the ranges of M0 and h are retained in the parameters only to allow the effects of different mission balance points to be examined.
These sensitivity analysis results lead to the conclusions that 7gf and 7rc should be selected from the high ends of their respective ranges, while Tt4 and/or Tt7 should be allowed to drift down from their limiting values. Meanwhile, changes of o~ and M16 will not have a significant impact on the leading propulsion performance parameters.
References
IOates, G. C., The Aerothermodynamics of Gas Turbine and Rocket Propulsion, 3rd ed., AIAA Education Series, AIAA, Reston, VA, 1997.
2Mattingly, J. D., Elements of Gas Turbine Propulsion, McGraw-Hill, New York, 1996.
3"Gas Turbine Engine Performance Station Identification and Nomenclature." Society of Automotive Engineers, Aerospace Recommended Practice (ARP) 755A, Warrendale, PA, 1974.
4Reynolds, W. C., and Perkins, H. C., Engineering thermodynamics, 2nd ed., McGraw- Hill, New York, 1977.
5U.S. Dept. of Defense, "Model Specification for Engines, Aircraft, Turbojet," Military Specification MIL-E-5008B, Washington, DC, Jan. 1959.
6Oates, G. C., "Performance Estimation for Turbofans with and Without Mixers," Journal of Propulsion and Power, Vol. 1, No. 3, 1985, pp. 252-256.
7 Gordon, S., and McBride, B., "Computer Program for Calculation of Complex Chemical Equilibrium Compositions," NASA SP-273, 1971.