20 Fig. 5.5
5.3.5 Component Matching
This is the time to clarify what appears to be a shortcoming or internal incon- sistency in the off-design calculation procedure. The heart of the matter is this:
the off-design equations are silent with regard to the rotational speeds of the ro- tating machines, despite the obvious fact that each compressor is mechanically connected via a permanent shaft to a turbine, whence they must always share the same rotational speed. The rotational speed will, in general, be different from the design point speed and, for this purpose, dimensionless compressor and turbine performance maps (e.g., Figs. 5.4 and 5.8) also contain data pertaining to rotational speed. It would seem, then, that the off-design equation set lacks some true physical constraints (i.e., Arc = Nt) and must therefore produce erroneous results. The fol- lowing discussion will demonstrate that this appearance is, fortunately, misleading.
The business of ensuring that all of the relationships that join a compressor and turbine are obeyed, including mass flow, power, total pressure, and rotational speed, is known as "component matching." The off-design calculation procedure of this textbook correctly maintains all known relationships except rotational speed.
The simplest and most frequently cited example of component matching found in the open literature is that of developing the "pumping characteristics" for the
"gas generator" (i.e., compressor, burner, and turbine) of a nonafterburning, single- spool turbojet (e.g., Refs. 1, 2, 5-7). Careful scrutiny of this component matching process reveals that the compressor performance map is used to update the estimate of compressor efficiency and to determine the shaft rotational speed; the turbine performance map and shaft rotational speed are then used only to update the estimate of turbine efficiency. In other words, the main use of enforcing Arc = Art is to provide accurate values of compressor and turbine efficiency.
If suitable compressor and turbine performance maps were available, they could, of course, be built into the off-design calculation procedure, and the iteration just described would automatically be executed internally. When such performance maps are not available, as is often the case early in a design study, the best approach is to supply input values of t/c and t/t based on experience. This "open-loop" method can also be employed later when satisfactory performance maps become available.
The principal conclusion is that accurate estimation of t/c and t/t at the off-design conditions has the same result as using performance maps and setting Nc = Nt.
Consequently, the off-design calculation procedure of this textbook is both correct and complete. An important corollary to this conclusion is that the "operating line"
(i.e., Jr or r vs rhv'CO/8) of every component in the engine is a "free" byproduct of the off-design calculations, even when the engine cycle is arbitrarily complex.
To make these conclusions even more concrete, it is useful to look more closely at the turbine. According to the typical turbine performance map of Fig. 5.8, this machine can provide the same work (i.e., 1 - rt) for a wide range of No = Nt, while t/t varies only slightly. Please recall that as long as the flow in the turbine
ENGINE SELECTION: PERFORMANCE CYCLE ANALYSIS 169 Station:
1 Stator 2 2R Rotor 3R 3
I I I I I
I I I I I
I ,or., : looo fps I I
I I ~
I
u2 = u2R ~ - ~ _ _ , , r / , ///]v
I 3R = w r~[ rm
a ~
Fig. 5.9 Single stage impulse turbine.
inlet guide vane and some downstream flow area remains choked and rh does not vary significantly, then Eq. (5.2) has demonstrated that ~rt and rt must be essentially constant. The question, then, is how the turbine flow conditions can adjust themselves in order to provide the s a m e rt at different values of (or. If the mechanics of adjustment are straightforward, then the entire process of component matching should be more easily comprehended.
Consider the single-stage, impulse, maximum work (i.e., no exit swirl), is- entropic, constant height turbine of Fig. 5.9 (see Ref. 2). At its design point, this turbine has a choked inlet guide vane and an entirely subsonic flow relative to the rotor. The flow angles are all representative of good practice. In short, this is a rather standard design.
Isentropic calculations have been performed at rotational speeds ± 1 0 % from design, which would encompass the entire operating range for most compressors.
The necessary condition for a solution was that rt have a design point value of 0.896. The results are displayed in Table 5.2.
These results confirm the message of the Euler turbine equation. Since (1 - rt) is proportional to ( o r m ( 1 ) 2 R - - 1.'3R), then M2, M e n , and M 3 R must increase in order to compensate for reductions in (orm, and vice versa. Nevertheless, even for such large differences in Wrm, the aerodynamic results are far from disastrous. For one thing, the inlet guide vanes remain choked (M2 > 1) and the rotor airfoils remain subsonic (M21¢ < 1 and M3R < 1) at all times. For another, the rotor airfoil relative inlet flow angle (/32) and the inlet flow angle to the downstream stator airfoils (~3) are well within the low loss operating range for typical turbine cascades. Finally, one might expect the frictional losses to increase and the efficiency to decrease as
(orm decreases and the blade scrubbing velocity increases, but only gradually.
170 AIRCRAFT ENGINE DESIGN Table 5.2 Turbine off-design performance Quantity - 10% Design + 10%
Wrm, ft/s 900 1000 1100
M2 1.22 1.10 1.02
0/2, deg 50.6 52.0 52.4
f12, deg 35.2 32.6 28.4
MzR 0.947 0.804 0.708
M3R 0.820 0.804 0.790
0/3, deg -4.2 0 3.5
rt 0.899 0.896 0.898
Tt2 = 2800°R; y = 1.33; gcR = 1716 ft2/(s2--¢~R).
This turbine therefore performs gracefully as expected, providing the same rt with slight changes in Ot for a wide range of Arc = Nt, all of the while remaining choked.
5.3.6 Engine Performance Program Predictions
The engine performance portion (referred to as Engine Test) of the AEDsys program, based on the equations developed in this chapter, can determine the performance of many types of engines at different altitudes, Mach numbers, and throttle settings. The accuracy of the resulting computer output depends on the validity of the assumptions specified in Sec. 5.2.2. The engine speed (N) is not incorporated in the off-design equations and is needed only when the efficiency of the rotating components (fan, compressor, or turbine) vary significantly over the operating speed (N) of the engine. Thus, the assumption of constant component efficiency (Of, 0eL, 0cH, Or/4, and OtL) removes the engine speed from the system of equations for prediction of off-design performance. This absence of engine speed from the off-design equations allows the determination of engine perfor- mance without the prior knowledge of each component's design point (knowl- edge of each component's design point and off-design performance by way of a map is required to include engine speed in the off-design performance). As shown in the maps of Figs. 5.4, 5.5, and 5.8, the efficiency of a rotating compo- nent remains essentially constant along the operating line in the 70-100% engine speed range of design N/x/-O. However, a significant reduction in component ef- ficiency occurs when the engine speed exceeds 110% or drops below 60% of design N / v"O.
The component maps of Figs. 5.4, 5.5, and 5.8 give considerable insight into the variation of engine speed with changes in flight conditions. High values of fan or compressor pressure ratio correspond to high engine speed and low val- ues of pressure ratio correspond to low engine speed. Figures 4.5, 4.6, 4.7, 4.9, and 4. l0 show that pressure ratio increases with altitude and decreases with Mach number with Tt4 held constant. Thus, engine speed increases with altitude and decreases with Mach number with Tt4 held constant. The operating regimes where the assumption of constant component efficiency may not apply then correspond
ENGINE SELECTION: PERFORMANCE CYCLE ANALYSIS 171 to the regions of high-altitude/low Mach number and low-altitude/high Mach number flight. Some of the high-altitude/low Mach number region is excluded from the operational envelope of many aircraft because of its low dynamic pres- sure and the high coefficient of lift (CL) required to sustain flight. Some of the low-altitude/high Mach number region is excluded from the operational envelope of many aircraft because of the structural limits of the airframe and the presence of very high dynamic pressure in this flight region.
The effect of decreasing component efficiency is to reduce the pressure ratio, engine air mass flow rate, and thrust and increase the thrust specific fuel consump- tion from that predicted by the off-design computer program. The magnitude and range of this effect depends on each component's design and design point, which are not known at this point in the analysis.
The predicted performance of the engine over the aircraft mission is used to select the best engine cycle, size the selected engine, and select component design points. Output of the performance portion (Engine Test) of the AEDsys computer program can be used to create plots of the compressor operating line at full throttle, as shown in Fig. 5.10, and the variation of the compressor pressure ratio at full throttle with changes in the flight condition, as shown in Fig. 5.11. However when the maximum compressor pressure ratio that the engine control system will allow is equal to the sea-level static value, the control system limits the fuel flow and the compressor pressure ratio is limited as shown at low Mach/high altitude in Fig. 5.11.
8
Compressor 6 Pressure Ratio (n,.) 5
3 50
i i i i i , i , i i , i t i i i i i i
60 70 80 90 100
% C o r r e c t e d M a s s F l o w R a t e
Fig. 5.10 Predicted compressor operating llne.
172 AIRCRAFT ENGINE DESIGN
40 kft
Compressor 7
Pressure Ratio (z~)
6
3 J L ~ L I ~ ~ i ~ I ~ , , , I ~ ~ , ,
0.0 0.5 1.0 1.5
M0
Fig. 5.H Predicted compressor pressure ratio at full throttle (TR = ]).
2.0