The parametric calculations described in detail in the preceding section and embodied in the accompanying ONX computer program must be used repeatedly in order to find the best combinations of design parameters for an engine. Basically, a search must be conducted to find the influence of each of the design parameters and from that to find the combinations that work well at each of the important flight conditions. Selecting the flight conditions for study of a complex mission requires some judgment. As a minimum, one should examine engine behavior at the extreme conditions as well as at those conditions that play the greatest role in the constraint analysis or the mission analysis.
As each mission phase is studied, for each combination of input design pa- rameters the primary result will be the variation of uninstalled thrust specific fuel consumption (S) with uninstalled specific thrust (F/rho) as nc is varied, as shown in the carpet plots of Figs. 4.3 and 4.4. In this representation, the most desirable direction to move is always down and to the right. Unfortunately the laws of nature
Sample ONX Computer Output
O n - D e s i g n C a l c s ( O N X V 5 . 0 0 ) D a t e : X / X X / X X X : X X : X X P M F i l e : E 1 O N . o n x
T u r b o f a n E n g i n e w i t h A f t e r b u r n i n g u s i n g V a r i a b l e S p e c i f i c H e a t ( V S H ) M o d e l
* * * * * * * * * * * * * * * * * * * I n p u t D a t a * * * * * * * * * * * * * * * * * * * * * * * * *
M a c h N o = 1 . 6 0 0 A l p h a = 0 . 4 0 0
A l t ( f t ) = 3 5 0 0 0 P i f / P i c L = 3 . 8 0 0 / 3 . 8 0 0
TO ( R ) = 3 9 4 . 1 0 Pi d ( m a x ) = 0 . 9 6 0
P 0 ( p s i a ) = 3 . 4 6 7 P i b = 0 . 9 5 0
D e n s i t y = . 0 0 0 7 3 5 2 P i n = 0 . 9 7 0
( S l u g / f l ^ 3 ) E f f i c i e n c y
B u r n e r = 0 . 9 9 9
M e c h H i P r = 0 . 9 9 5 M e c h L o P r = 0 . 9 9 5
F a n / L P C o m p = 0 . 8 9 0 / 0 . 8 9 0 (ef/ecL)
T t 4 m a x = 3 2 0 0 . 0 R H P C o m p = 0 . 9 0 0 ( e c H )
h - f u e l = 1 8 4 0 0 B t u / l b m H P T u r b i n e = 0 . 8 9 0 ( e t H )
C T O L o w = 0 . 0 0 0 0 L P T u r b i n e = 0 . 9 0 0 (etL)
C T O H i g h = 0 . 0 1 5 0 P w r M e c h E f t L = 1 . 0 0 0
C o o l i n g A i r #1 = 5 . 0 0 0 % P w r M e c h E f t H = 0 . 9 9 0
C o o l i n g A i r # 2 = 5 . 0 0 0 % B l e e d A i r = 1 , 0 0 0 %
P 0 / P 9 = 1 . 0 0 0 0
** A f t e r b u r n e r **
T t 7 m a x = 3 6 0 0 . 0 R P i A B = 0 . 9 5 0
E t a A / B = 0 . 9 9 0
* * * M i x e r * * * Pi M i x e r m a x = 0 . 9 7 0
* * * * * * * * * * * * * * * * * * * * * * R E S U L T S * * * * * * * * * * * * * * * * * * * * * * * * * T a u r = 1 . 5 1 0
P i r = 4 , 2 3 7
Pi d = 0 . 9 2 4
T t 4 / T 0 = 8 . 1 2 0 P T O L o w = 0 , 0 0 K W P T O H i g h = 3 0 1 . 3 4 K W P t l 6 / P 0 = 1 4 . 8 7 6 P t 6 / P 0 = 1 3 . 7 9 2
Pi c = 1 6 , 0 0 0
Pi f = 3 . 8 0 0 0
T a n f = 1 . 5 3 7 2 E t a f = 0 . 8 6 8 1
Pi c L = 3 . 8 0 0
E t a c L = 0 . 8 6 8 1 Pi c H = 4 . 2 1 0 5 T a u c H = 1 . 5 7 3 4 E t a c H = 0 . 8 7 9 5 P i t H = 0 . 4 6 9 3 T a u t H = 0 . 8 4 5 7 E t a t H = 0 . 8 9 8 0 Pi t L = 0 . 4 9 3 9 T a u tL = 0 . 8 5 0 4 W i t h o u t A B
P t 9 / P 9 = 1 2 . 7 4 5
f = 0 . 0 3 1 2 7
F / m d o t S T 9 / T 0 V 9 / V 0 M 9 / M 0 A 9 / A 0 A 9 / A 8
= 6 2 . 8 5 9 l b f / ( l b m / s )
= 1 . 1 3 8 6 ( l b m / h r ) / l b f
= 2 . 5 4 2 8
= 2 . 2 6 8
= 1,439
= 1.136
= 2 . 3 7 2 T h r u s t = 1 2 5 7 2 l b f T h e r m a l E f t = 5 5 . 8 9 % P r o p u l s i v e E f t = 6 1 . 6 2 %
a 0 (ft/sec) = 9 7 4 . 7 V 0 (ft/sec) = 1 5 5 9 . 4 M a s s F l o w = 2 0 0 . 0 l b m / s e c A r e a Z e r o = 5 . 4 2 2 s q f i A r e a Z e r o * = 4 . 3 3 6 s q f t T t 1 6 f f 0 = 2 . 3 1 2 4 T t 6 / T 0 = 5 . 7 7 0 2 T a u m l = 0 . 9 6 8 4 T a n m 2 = 0 . 9 7 4 2
T a n M = 0 . 8 2 0 6
Pi M = 0 . 9 7 7 1
T a u c L = 1 . 5 3 7 2
M 6 = 0 . 4 0 0 0
M 1 6 = 0 . 5 1 5 9
M 6 A = 0 . 4 3 3 1
A I 6 / A 6 = 0 . 1 8 4 4 G a m m a M = 1 . 3 1 6 5
C P M = 0 . 2 8 4 9
E t a t L = 0 . 9 0 7 0 W i t h A B
P t 9 / P 9 = 1 2 . 4 1 8
f = 0 . 0 3 1 2 7
f A B = 0 . 0 3 2 2 2
F / m d o t = 1 1 0 . 6 3 4 l b f / ( l b m / s ) S = 1 . 6 8 7 8 ( l b m l h r ) / l b f
T 9 / T 0 = 5 . 3 3 6 4
V 9 / V 0 = 3 . 1 4 2
M 9 / M 0 = 1 . 4 1 6
A 9 / A 0 = 1 . 7 7 5
A 9 / A 8 = 2 . 4 8 9
T h r u s t = 2 2 1 2 7 l b f T h e r m a l E f f = 4 7 . 4 0 % P r o p u l s i v e E f t = 4 9 , 0 1 %
118
E N G I N E S E L E C T I O N : P A R A M E T R I C C Y C L E A N A L Y S I S 119
S
( l / h )
1.25 . . . . i . . . . i . . . . i . . . . i . . . . i . . . . i . . . .
1.20 ~'~ -- S ~
0.3
1.15 0.4
0.5
s 1.10 O,'h)
1 . 0 5 a ~
1.00
f ~ , . = (.= 24
0.95
0 , 9 0 i i t i I i i , , I . . . . I . . . . I . . . . I . . . . I . . . .
30 35 40 45 50 55 60 65
F / rh o (lbf/lbm/s)
Fig. 4.3 Parametric performance of mixed flow turbofans (no AB).
2.05
2.00
1.95
1.90
1.85
1.80
1.75
1.70
1.65 90
' ' ' ' 1 ' ' ' ' 1 I ' ' ' ' 1 ' ' ' '
' 2 4
~ = 0
12
16
24
I I I I I I I I ' I , , i , l J , , , I , , , ,
95 100 105 110
F / th o (lbf/lbm/s)
Fig. 4.4 Parametric performance of mixed flow turbofans (w/AB).
115
120 AIRCRAFT ENGINE DESIGN
do not always fully cooperate, and there is usually a tradeoff between S and F/rho, where one can be improved only at the expense of the other. Be prepared for intu- ition to go wrong at this point because increases in cycle temperatures (e.g., rz) and component pressure ratios (e.g., zrc) do not always lead to improved performance.
You may find recourse to propulsive, thermal, and overall efficiency and Eq. (4.32) to be helpful in discovering the root cause of parametric performance trends. This explains why they are always included in the output quantities. To make use of the computed results, initial goals must be established for S and F/rho, as described next.
4.3.1 Uninstalled Specific Fuel Consumption (S)
Clear targets can be set for S because of the initial expectations already es- tablished by mission analysis. The main caution to be raised is that the mission analysis is based on installed specific fuel consumption (TSFC), while the cycle analysis yields uninstalled specific fuel consumption (S). A good rule of thumb is that installed exceeds uninstalled by 0 to 10%, depending on the situation (see Chapter 6), or a conservative average value of about 5%. Hence, the most revealing way to display the parametric analysis results is to plot the target or goal value of S on the carpet plot of S vs F/rho.
The totality of results must be used with care. On the one hand, reference point values of S may be different than the corresponding off-design values that will be computed later. Also, installation effects will vary with distance from the final reference point. On the other hand, it is needlessly restrictive to require that the specific fuel consumption be less than or equal to the target value at every flight condition. It is necessary only that the total fuel consumption, integrated over the entire mission, meets its goal. Therefore, a higher fuel consumption on one leg may be traded for a lower fuel consumption on another, provided that the integrated gains equal or outweigh the losses. A good general rule is to concentrate on reducing S for those legs using the most fuel (i.e., smallest 17) in the mission analysis.
4.3.2 Uninstalled Specific Thrust (F/mo)
Because the physical size of the engine (i.e., rho design) is not known at this point, no stated target for F/rho exists. Although the size of the engine can always be increased to provide the needed total thrust, it is always desirable to achieve large values of F/rho in order to decrease the size (as well as the initial and maintenance cost, volume, and weight) of the engine. Once again, it should be noted that a constraint analysis is based on installed thrust (T), while the cycle analysis yields uninstalled thrust (F), with F exceeding T by 0 to 10% depending on the situation and distance from the final design point.
A good general rule here is to concentrate on increasing F/rho for those legs that formed the boundary of the solution space in the constraint analysis. The lower thrust required for flight conditions away from that boundary will be attained by reducing Tt7 and/or Tt4. In fact, for flight conditions that require considerably less than the available thrust, it is more realistic to run these parametric computations at less than the maximum values of Tt7 and/or Tt4.
Even though no precise goal for F/rho is available, ballpark figures can be easily generated using ONX, a representative sample of which is given in Table 4.1.
ENGINE SELECTION: PARAMETRIC CYCLE ANALYSIS 121 These numbers will also be useful in the initial estimation of
Pro Pro F
Cro -- rhoho Fho rho (4.33)
4.3.3 Parametric vs Performance Behavior
During this process of selecting a set of reference point parameters for each critical flight condition, it is important to remember that the final engine will always be running off-design and will therefore behave differently at each operating point.
Thus, it makes little sense to try to find an engine, for example, of f i x e d rrc, try, or, and Zt4 that works reasonably well at every operating point. It is, however, desirable to have the selected sets of reference point parameters generally follow the natural path of a single engine running off-design. Applying this logic will increase the probability of success of a design.
But how is this natural path established in advance? There is no simple answer to this question, but some good approximations are available. The best would be to run several off-design computations (see Chapter 5) for promising designs in order to generate directly applicable guidance. This would be equivalent to coupling parametric and performance computations in an iterative manner and, time permitting, offers a rich design experience. A simple and direct, but less reliable, method is to use the typical off-design parameter behavior information of Figs. 4.5-4.11, which are generated by the performance computer program portion
22
18
14
10
6
' ' ' ' I ' ' ' ' I '
0.0 0.5 1.0
' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' '
X
\
\
\
' ' ' I I I i I i I I I I [ I i I I
1.5 2.0 2.5 3.0 Mo
Aft (kft) 40 30 20 I0 SL
Fig. 4.5 Compressor pressure ratio (~'c) performance characteristics for a turbojet with TR = 1.0.
2 2 ' ' ' ' l ' ' ' ' l ' ' ' ' l ' ' ' ' l
14 18
\
\
\
10
Air (kft) 40 30 20 10 SL
2 , , J = I , , = = I ~ , , , i .... i ....
0.0 0.5 1.0 1.5 2.0 2.5
Mo
Fig. 4.6 Compressor pressure ratio (Trc) performance characteristics for a low bypass ratio mixed flow turbofan with T R = 1.065.
4.5 I ' ' ' ' 1 ' ' ' ' 1 '
4.0
3.5
3.0
2.5
2.0
I '
Alt (kft) 40 30 20 10 SL
1 . 5 i i , I , , , , I , , , , I , , , , I , ~ , ,
0.0 0.5 1.0 1.5 2.0 2.5
Mo
Fig. 4.7 Fan pressure ratio ('/l'f) performance characteristics for a low bypass ratio mixed flow turbofan with T R = 1.065.
122
1.1 I , , , , I , i , , I ' ' ' ,
Alt (kft) SL 10 20
1.0
0.9 30
40
0 . 8 a
0 . 7
0 . 6
0 . 5 . . . . I ~ , , , I , , ~ , I , , , , I , , , ,
0.0 0.5 1.0 1.5 2.0 2.5
Mo
Fig. 4.8 B y p a s s r a t i o (c~) p e r f o r m a n c e c h a r a c t e r i s t i c s f o r a l o w b y p a s s r a t i o m i x e d f l o w t u r b o f a n w i t h T R = 1.065.
3 2 ' I ' I
3 0
2 8
2 6
2 4
2 2
I I
40k-20k
~ O ] O k
20 , , , I , , , I , , , I , , , I , , ,
0.0 0.2 0.4 0.6 0.8 1.0
Mo
F i g . 4.9 C o m p r e s s o r p r e s s u r e r a t i o (Trc) p e r f o r m a n c e c h a r a c t e r i s t i c s f o r a h i g h b y p a s s r a t i o t u r b o f a n w i t h T R = 1.035.
123
: ~ l J 120k.40 k
1.52
1 . 5 0
1 . 4 8
1 . 4 6
1 . 4 4
1 . 4 2
1 . 4 0
1 . 3 8
rq
1 . 3 6 , , , I , , , I , , , I , , , I , L ,
0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1.0
M o
Fig. 4.10 Fan pressure ratio
(Tif)
performance characteristics for a high bypass ratio turbofan with T R = 1.035.1 0 . 0 I ' I I I '
9 . 0
a s
8 . 0
20k-40k
7 . 5 , i , , , i , , , l , , , I , , ,
0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0
M o
Fig. 4.11 Bypass ratio (c~) performance characteristics for a high bypass ratio turbofan with T R = 1.035.
1 2 4
ENGINE SELECTION: PARAMETRIC CYCLE ANALYSIS 125 of the AEDsys program developed in Chapter 5. Please note that the high- and low-pressure turbine total temperature and total pressure ratios are almost constant [see Eqs. (4.21c) and (4.22c) and Appendix D] and that afterburner operation has no effect on these results because it is assumed (and almost universally true) that the nozzle throat area (As) is controlled to make the mixer and all upstream components oblivious to the afterburner conditions by maintaining a constant value of the pressure at the mixer exit. Also, the results shown for 40 kft represent those for all altitudes above the tropopause. Another means to understand and predict off-design behavior is to employ the algebraic methods found in Appendix D.
Figures 4.5-4.11 all display the unmistakable signature of performance analysis, namely the theta break imposed by the control system at 00 = Oooreak = T R (see Appendix D). We will explain in much greater detail how to integrate performance analysis computations into the search for promising reference points in Sec. 4.4.4.
4.3.4 Influence of the Mixer
One of the things about to be encountered is the remarkable impact of the seemingly innocuous mixer on the range of acceptable design parameters for mixed exhaust flow engines. The main reason for this influence is that the fan and core streams are not separately exhausting to atmosphere, where their behavior would be uncoupled and the only physical constraint would be Pt > Po, but they are brought together in pressure contact within confined quarters. For this situation, the operating parameters are much more restricted because neither M6 nor M16 can be less than zero (reverse flow) or greater than one (choked). In tact, it is desirable that neither M6 nor M16 even begin to approach zero because the corresponding flow area would increase the engine cross-sectional (or frontal) area beyond reason.
Finally, common sense would encourage keeping design point values of M6 and MI6 in the range of 0.4-0.6 because they are certain to migrate away during off- design operation and therefore should start off with some cushion.
It is challenging to balance rrc, try, or, and Tt4 in order to make M6 and M16 behave properly. One available life preserver is to recognize that this desired behavior requires Pt6 approximately equal to Ptl6, or
Pt6 Po~rT"fdYfcLYrcHYrbYrtHrftL Ptl6 POTfr~dTg f
which reduces to
7licLJ~'c.HJ'gtHJ'CtL/Yr f ~ - - 1 ~'~ 1 (4.34)
7 r b
and then to use Eqs. (4.21c) and (4.22c) to reveal how to make yrc~/, Yrtn, and ZrtL bring Pt6 and Ptl6 together. For example, if Zrc~/, zra4, and ZrtL are too large, Eq. (4.22c) clearly shows that rtL, and therefore rrtL, Can be reduced by increasing o/or ygf and by decreasing rx. The physical interpretation of this is that the low pressure turbine drives the increase of fan airflow and pressure ratio. Also, as rx and the capacity for each pound of air to do work in the low pressure turbine decrease, zrtL must decrease in order to maintain the same power output. A valuable feature of the ONX computer program is its ability to calculate the fan pressure ratio (7rf) for a given bypass ratio (or), or Vice versa, that automatically matches the total pressures at stations 6 and 16 using the complete Eqs. (4.21a) and (4.22a). This
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.