Mattingly J.D., Heiser W.H., Pratt D.T. Aircraft Engine Design

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276 AIRCRAFT ENGINE DESIGN

0.30

0.25

0.20

0.15

0.10

M~ R =0.9

M 2 =0.9 .... " ...

M 2 =1.1 --

0.05 .... I .... i .... i ....

60 65 70 75 80

a 2 C)

Fig. 8.13 Stage axial velocity.

thermodynamic performance for choked and unchoked stages is improved by in-

creasing f2. This agrees with the conventional wisdom of the open literature and

explains the natural desire of the designer to increase wheel speed to the limit

allowed by materials and structural technology. The remainder of the discussion

therefore centers on the selection of or2.

Figure 8.8. The preceding engine cycle selection process has already deter-

mined the required turbine temperature ratio. The goal of the designer is to accom-

plish the desired work extraction with the minimum number of stages, which is

equivalent to finding the minimum practical value of rts. The results presented in

this figure demonstrate that 75ts diminishes as or2 increases over its expected range

for both choked and unchoked stages. Furthermore, the results suggest that rts

values of less than 0.85 are attainable. If higher values of rts are required, they

can easily be provided by reducing ~2 and/or ~2. However, they also reveal that

it is difficult to reach rt~ values much higher than about 0.88 unless the Mach

number assumptions are relaxed. This often motivates designers to shift the work

split between the low- and high-pressure compressors so that each turbine stage

is working hard and the total number of low- and high-pressure turbine stages is

minimized.

Figures 8.9 and 8.10. Creating sound aerodynamics for the turbine airfoils is

the heart of the matter for successful turbine design, just as it was for compressors.

The fundamental issue is that of avoiding boundary layer separation along the rear

portion of the rotor airfoil suction (convex) surface, where local Mach numbers

and adverse pressure gradients are the greatest. The smallest amount of separation,

even if reattachment follows, is disastrous for turbines because the large local Mach

numbers and dynamic pressures cause unacceptable aerodynamic (drag) losses.

DESIGN: ROTATING TURBOMACHINERY 277

Unfortunately, as the results presented in Fig. 8.9 reveal, the tendency to in-

crease stage work extraction by increasing a2 is accompanied by a surprisingly

rapid increase in the rotor flow turning angle. The streamline curvature effects

within the passage between adjacent rotor airfoils caused by this flow turning are

the principal contributor to the low suction surface static pressures and therefore

to the potential for boundary layer separation, especially when the average Mach

number is near sonic and shock waves can arise. Carefully tailoring the pressure

distribution around the complete airfoil profile by means of sophisticated com-

putational fluid dynamics (CFD) in order to resist separation despite very large

rotor flow turning angles is one of the major achievements of modern turbine tech-

nology (see Ref. 1). However, because the CFD must account for such exquisite

effects as the state of the boundary layer (for example, laminar, turbulent, or tran-

sitional), freestream turbulence levels, airfoil roughness, airfoil heat transfer, and

locally transonic flow, the application of these methods is beyond the scope of this

textbook.

Instead, we will capitalize on our general observation that skillful designers are

able to define rotor airfoil profiles that do not separate for flow turning angles

(/32 +/33) up to 120-130 deg provided that the rotor degree of reaction is at least

0.20. That is, the average static temperature and pressure drop significantly across

the rotor in order to partially counteract the adverse pressure gradient due to stream-

line curvature. Combining the results of Figs. 8.9 and 8.10, we see that these criteria

are met as long as or2 does not exceed approximately 70 deg, depending on the

exact value of f2. If some margin of safety is required, the selected value of a2

should be further reduced.

It is worthwhile to pause at this point to consider the relationship between com-

pressor and turbine airfoil design. In the compressor case, the adverse pressure

gradient caused by streamline curvature on the rear portion of the suction surface

is increased by the average static pressure increase across the row. Thus, the com-

pressor diffusion factor D, which is based on a simple estimate of their sum, is

a useful device. In the turbine case, it is reduced by the average static pressure

drop across the row. The flow turning angles of compressor airfoils are therefore

much smaller than turbine airfoils. Nevertheless, the streamline curvature effects

exceed the average static pressure drops in modern turbine stages, and, contrary

to the popular but naive notion, the flow runs "uphill" (pressure increasing) rather

than "downhill" where it matters most. Turbine and compressor airfoil designers

therefore actually share the adventure of working at the same limits allowed by

nature.

Figure 8.11.

The stage exit flow angle or swirl, which should be kept small

whether or not another stage follows. In the former case, a small or3 reduces the

total flow turning for the succeeding inlet stator. In the latter case, the need for

turbine exit guide vanes and their accompanying diffusion losses is reduced or

avoided.

The consensus of the turbine design community is that or3 should not exceed

about 40 deg. The results presented in this figure show that meeting this criterion

depends strongly on both oe2 and f2, as well as whether the stage is choked or

unchoked. In some cases, this criterion could restrict ~3 to values less than 70 deg.

A somewhat subtle but important point is that designing the low-pressure turbine

to rotate in the opposite direction can accommodate large amounts of exit swirl from

278 AIRCRAFT ENGINE DESIGN

the high-pressure turbine. The so-called counter-rotating, low-pressure turbine will

thus require an inlet guide vane with little tuming, or perhaps no inlet guide vane

at all. This complicates the bearing and support system because the shafts must

also counter-rotate, but the overall result must be beneficial because many modem

engines apply this approach.

The computations also show that the stator degree of reaction exceeds that of

the rotor, and that the stator flow tuming (aa + a2) is less than that of the rotor

(especially for inlet guide vanes where al is zero). Consequently, the aerodynamic

design of rotor airfoil profiles is usually more difficult than that of stator airfoils,

justifying our focus on rotor airfoil design.

Figure 8.12.

Because the individual turbine stator and rotor airfoils are

heavy and expensive, especially cooled airfoils that employ exotic materials, ela-

borate manufacturing processes, and intricate intemal flow passages, it is im-

portant to reduce their number to the extent possible. The Zweifel coefficient

(Ref. 12) provides a reliable and straightforward method for making an initial

estimate of the minimum solidity and number of required airfoils (see Ref. 11,

Sec. 9.5).

Put simply, the Zweifel coefficient Z is a measure of how closely the turbine

designer can tailor the pressure distribution around the airfoil profile to conform

to the ideal of static pressure equal to stagnation pressure along the entire pres-

sure (concave) surface and exit static pressure along the entire suction (convex)

surface. This rectangular pressure distribution has no adverse pressure gradients

and thus is free of boundary layer separation. This ideal pressure distribution has

Z = 1 according to the mathematical definition of the Zweifel coefficient (see

Ref. 11, Sec. 9.5). Most importantly, the CFD procedures that have enabled air-

foil designers to increase the flow tuming angles for modest degrees of reaction

have simultaneously enabled them to achieve Zweifel coefficients one or more for

stators and rotors. Thus, Eq. (8.52) can be used to estimate the minimum rotor

solidity based on a maximum assumed value of Z.

Figure 8.12.

This figure reveals that the minimum rotor solidity is of the order

of one for Z = 1, and that it decreases rapidly as or2 increases for both choked and

unchoked stages. The designer is therefore encouraged to select higher values of

a2 in order to reduce the number of rotor airfoils.

Figure 8.13.

The dimensionless stage axial velocity is an indicator of the

throughflow area that will be required by the stage and hence of the height of the

airfoils and the rotor centrifugal stress (see Sec. 8.2.3). The results presented in

this figure show that u diminishes rapidly as or2 increases for both choked and

unchoked stages and is independent of f2. The designer is therefore encouraged to

choose values of or2 less than 70 deg in order to increase u and thus obtain shorter,

lighter airfoils, and rotor blades that have lower centrifugal stresses. This evidently

creates another conflict between stage performance and airfoil life.

General conclusions.

These results are clearly in agreement with the conven-

tional wisdom of turbine stage design. In particular, they support the universal

drive for increasing f2 to the limit allowed by materials and structures. Further-

more, they support the contention that the best choice of a2 is in the range of

60-75 deg. Finally, they provide a sound basis for initial estimates for the detailed

TURBN computations that must be carried out for your specific turbine stage de-

signs. Four sets of representative initial design choices that meet all of the design

DESIGN: ROTATING TURBOMACHINERY 279

Table 8.2 Summary of representative initial turbine

stage design choices for

M3R =

0.9, % = 1.30,

gccm =

7378 ft2/(sZ-°R), and Z = 1

M2 1.1 0.9

S2 = 0.2 13l 2 67 deg 61 deg

rts 0.860 0.880

f12 "~ f13

116 deg 103 deg

°Rt

0.199 0.458

0~3 41.2 deg 40.2 deg

ffxr

1.25 1.09

U~ V'

0.217 0.226

g2 = 0.3 or2 72 deg 72 deg

rts

0.811 0.831

f12 + f13 120 deg 116 deg

°Rt 0.294 0.463

a'3 31.1 deg 40.0 deg

crxr 0.92 0.67

u/V'

0.171 0.144

criteria with

M3R

= 0.9, Ft = 1.30,

gcCpt =

7378 ft2/(s2-°R), and Z = 1 are

presented in Table 8.2 for your reference. This compilation indicates that, for a

given f2, increasing M2 can decrease rt~, but the airfoil aerodynamics are nearer

to the edge.

8.2.2.2 Stage pressure ratio

(:rrts).

Once the turbine stage temperature

ratio

rts

and the flowfield and airfoil characteristics are established, several avenues

are open for calculating the stage pressure ratio. The most simple and direct method

is to apply Eq. (4.9d-CPG), so that

~rts = rt~ '/(y'-l)e"

(8.53)

and

1-- Vts

.(×,-1)/×, (8.54)

Ors 1 - nts

This method will provide a useful and adequate starting point for turbine design.

If necessary or desired, it may be refined using the standard design tools detailed

in Ref. 11 and contained in the AEDsys TURBN subroutine.

Example case:

An uncooled, single-stage turbine is to be designed with the

following conditions:

M: = 1.1 M3R = 0.9

Tt2 = Ttl

= 3200°R

gcCpt

= 7378 ft2/(s2-°R)

ot2 = 70 deg Yt = 1.3

= 1200 ft/s Z = 1

280

Then

AIRCRAFT ENGINE DESIGN

V' = 4859 ft/s Eq. (8.37)

f2 = 0.2470 Eq. (8.38)

V2 = 2693 ft/s Eq. (8.39)

u = 921 ft/s Eq. (8.40)

v2 = 2531 ft/s Eq. (8.41)

v2n = 1331 ft/s Eq. (8.42)

f12 = 55.31 deg Eq. (8.43)

Tt2R = Tt3R =

2886°R Eq. (8.44)

/33 = 64.60 deg Eq. (8.45)

/32 + f13 = 119.9 deg Eq. (8.46)

v3 = 740 ft/s Eq. (8.47)

~3 = 38.79 deg Eq. (8.48)

T3 = 2573°R Eq. (8.49)

rs = 0.8337 Eq. (8.50)

°Rt = 0.2540 Eq. (8.51)

tTxr

~---

1.307 Eq. (8.52)

If one chooses to assume

---- ets = 0.90, then zrts = 0.4166 [Eq. (8.53)] and r/ts =

90.88% [Eq. (8.54)]. The results for this stage are summarized in Table 8.3.

8.2.2.3 Recapitulation.

The turbine stage design procedure of Sec. 8.2.2

and the method of computing the stage pressure ratio have been integrated into

the TURBN program of AEDsys in order to serve as the first step in the design

process. You will quickly find that this has several important benefits, including

the ability to quickly explore the entire range of design parameters and make

promising initial choices, and then to transfer all of the input that the complete

TURBN computation requires. The complete TURBN computation is very similar

to that used in industry, 7,8,11 and the initial Sec. 8.2.2 design will require only minor

and entirely transparent tweaking in order to produce a worthy result that meets

all of the imposed constraints.

8.2.2.4 Airfoil geometry.

The situation in unchoked turbines is similar to

that in compressors except that the deviations are markedly smaller owing to the

thinner boundary layers. Hence, using the nomenclature of Fig. 8.3,

Yl -- Y2

~t - (8.55)

DESIGN: ROTATING TURBOMACHINERY

Table 8.3 Summary of example case stage properties

(et

= 0.90)

281

Property/station 2 2R 3R 3

Tt, °R 3200 2886 2886 2668

Pt/Pt~ 0.4166

e/erl 0.3563

V, ft/s 2693 1618 2148 1182

u, ft/s 921 921 921 921

v, ft/s 2531 1331 1940 740

c¢, deg 70.0 38.79

/~, deg 55.31 64.60

is a good estimate.7'

More importantly, however, when the turbine airfoil cascade

exit Mach number is near one, the deviation is usually negligible because the

cascade passage is similar to a nozzle. In fact, the suction (or convex) surface

of the airfoils often has a flat stretch between the throat and the trailing edge,

which evokes the name "straight-backed," or may even be slightly concave. Finally,

the simple concept of deviation loses all meaning at large supersonic exit Mach

numbers because expansion or compression waves emanating from the trailing

edge can dramatically alter the final flow direction. This is a truly fascinating field

of aerodynamics, but one that requires study beyond the scope of this textbook. 7

8.2.2.5 Radial variations. The compressor radial variation material of Sec.

8.2.1 is also generally applicable to turbines. However, because the mass flow rate

per unit annulus area (that is, rh/A = Pt/MFP~c~t) is higher in turbines than

compressors, turbine airfoils are correspondingly shorter. The result is little radial

variation of aerodynamic properties from hub to tip except possibly in the last few

stages of the low-pressure turbine. If the aerodynamic design of these stages began

as free vortex, the rotor degree of reaction would be the same as for compressors

[Fig. 8.6 and Eq. (8.27)], other than the sign of the pressure change across the stage.

Consequently, the most difficult airfoil contours to design would be at the hub of

the rotating airfoils and the tips of the stationary airfoils. It is therefore possible to

find portions of some airfoils near the rear of highly loaded (that is, high work per

stage) low-pressure turbines where the static pressure actually rises and boundary

layer separation is hard to avoid. In these cases, contemporary turbine designers

employ CFD to develop non-free or controlled vortex machines that minimize these

troublesome effects and maintain high efficiency at high loading by requiring less

work to be produced at the hub and

tip. 13

8.2.2. 6 Turbine cooling.

The gas temperatures in modem turbines are high

enough to destroy any available materials in short order unless they are protected

by cooling air. The unwanted or nuisance heat may be carded or convected away by

air flowing within the airfoils or prevented from reaching the airfoils by means of

an unbroken extemal blanket of air. The amount of air required to accomplish the

necessary cooling depends entirely upon the cooling configuration, the perversity

of nature causing simpler configurations to require more cooling air. 1

282 AIRCRAFT ENGINE DESIGN

0.6

0.5-

0.4-

0.3-

0.2

Fig. 8.14

IIlil I I ill

WITH IMPINGEMENT/

/ WITHOUT IMPINGEMENT

I I till t I I I ~

0.4 0.6 0.8 1.0 2.0 3.0 4.0

Coolant Flow, Percent of Engine Flow

Leading edge turbine cooling effectiveness. ~4

The cooling effectiveness is usually defined as

do _ Tg - Tm

(8.56)

7~- Tc

where

Tg, Tm, and Tc are

the mainstream gas, average metal, and cooling air tem-

peratures, respectively. Please note that the cooling air temperature Tc can be less

than the compressor discharge temperature Tt3 if the fluid is taken from an earlier

compressor stage or, in future designs, if the fluid is cooled by exchanging heat with

fan discharge air or fuel. An attractive property of do is that it must lie between

zero and one--the higher the better. Figure 8.14 provides some typical leading

edge cooling effectiveness design data. If, for example, impingement (created by

a cooling flow insert that directs the flow against the inside wall) is considered and

Tg = 2400°F, Tc = 1200°F, and

T m =

2000°F, then do must be at least 0.333, and

the coolant flow must be 0.70% of engine flow or more. An unfortunate property

of do is that it must be determined experimentally in all but the simplest cases.

The sensitivity of cooling flow requirements to do and

should not be underes-

timated. If the preceding example were repeated without impingement, the coolant

flow would jump to almost 1.1%, a factor of 1.6. If the example were repeated with

an advanced material allowing

to increase to 2100°F, the coolant flow would

drop to 0.55%.

This exercise pertains only to the leading edge cooling of one airfoil row, the job

being complete only when all parts of all airfoils are safe from the heat. This leads to

two important conclusions. First, the turbine cooling designer must have data avail-

able to ensure that all surfaces, including the endwalls, can be protected and how

much cooling air is needed. Second, the seemingly small amounts in the preceding

example really do add up when all of the threatened surfaces are accounted for,

the total cooling flow of modem machines being in the range of 15-25%. These

engines therefore take onboard an enormous amount of air that is compressed, led

through wondrously complex labyrinths, and expanded with no other purpose than

DESIGN: ROTATING TURBOMACHINERY 283

Table 8.4a Range of axial flow turbine design parameters

Parameter Design range

High-pressure turbine

Maximum

AN 2

Stage loading coefficient 7t

Exit Mach number

Exit swirl angle

Low-pressure turbine

Inlet corrected mass flow rate

Hub/tip ratio at inlet

Maximum stage loading at hub

Exit Mach number

Exit swirl angle

4-5 x 101° in 2. rpm 2

1.4-2.0

0.4-0.5

040 deg

40-44 lbrrd(sec-ft 2)

0.35-0.50

2.4

0.4-0.5

04-40 deg

helping the turbine survive. Such air does not pass through the burner and, unless

afterburning is present, does not contribute to the thrust of the engine.

8.2.2. 7 Range of turbine design parameters.

Table 8.4a gives the range

of some typical turbine design parameters that can be used for guidance. The stage

loading coefficient ~p is a parameter frequently used in the turbine literature as a

rough measure of how hard each turbine stage is working and is defined as

-- gccptA Tt

(8.57)

(wr) 2

You will find it interesting to calculate the stage loading coefficients of the turbines

The comparison of the Pratt and Whitney JT3D and JT9D engines of Table 8.4b

reveals typical design values and the leading trends in turbine technology. Note es-

pecially the increase of high-pressure turbine inlet temperature and cooling airflow

and the low-pressure turbine stage loading coefficient. These were all necessary

to make it possible to greatly increase the overall pressure ratio (that is, the ther-

mal efficiency) and the bypass ratio (that is, the propulsive efficiency), and thus

dramatically reduce the specific fuel consumption (that is, the overall efficiency).

These changes combined with the absolute size of the engines, as indicated by the

core engine flow, to increase the total power required from the turbines at takeoff

to more than 130,000 hp.

8.2.3 Engine Life

8.2.3.1 Background.

Every part of the engine must be certain to last its in-

tended design lifetime. The fundamental truth, therefore, is that a successful engine

design must simultaneously meet its aerodynamic, thermodynamic, and structural

requirements. Because one of the structural requirements is to reduce the weight,

cost, and complexity of the parts, their durability margins must be minimized.

The primary concern is for the heavy rotating and highly pressurized parts that can

harm or destroy the parent aircraft if large pieces of them are inadvertently set free.

284 AIRCRAFT ENGINE DESIGN

Table 8.4b Comparison of Pratt and Whitney engines

Parameter JT3D JT9D

Year of introduction 1961 1970

Engine bypass ratio 1.45 4.86

Engine overall pressure ratio 13.6 24.5

Core engine flow, lbm/s 187.7 272.0

High-pressure turbine

Inlet temperature, ° F 1745 2500

Power output, hp 24,100 71,700

Number of stages 1 2

Average stage loading coefficient 1.72 1.76

Coolant plus leakage flow, % 2.5 16.1

Low-pressure turbine

Inlet temperature, ° F 1410 1600

Power output, hp 31,800 61,050

Number of stages 3 4

Average stage loading coefficient 1.44 2.47

Coolant plus leakage flow, % 0.7 1.4

These are exemplified by long first-stage fan blades, blades and disks of cooled

high-pressure turbines, and outer cases of main combustors. Because engine life is

so critical, engine structural design has become an extremely sophisticated science

and art. Proving that the engine meets its life requirements is one of the major steps

in the development process.

It will become clear in what follows that there is a strong interaction between

aerodynamic, thermodynamic, and structural design decisions. The obvious im-

plication is that everyone involved will make better decisions if they are aware of

all of the possible consequences in advance. At least the participants will be less

likely to be unpleasantly surprised.

The lives that the engine parts must endure can be remarkably strenuous, and

they are highly dependent upon the mission of the parent aircraft. To appreciate this

point, one need only recognize the difference between the operation or "usage" of

fighter and transport engines. Fighter engines experience far more throttle move-

ments or maneuver transients per flight hour and are therefore more susceptible to

fatigue-type failures. Transport engines run for long times at elevated temperatures

and have greater design lifetimes and are therefore more susceptible to creep-type

failures. Both are exposed to considerably more severe duty during pilot training

than during normal operations or even combat.

There is a special message for both the engine builder and user here, namely,

that the initial "mission usage" specification plays a pivotal role in determining

the eventual success of the aircraft. Once agreed to by contract, the engine builder

will deliver an engine that will run soundly for the desired time under the specified

operating conditions. However, to the extent that the actual mission usage of the

engine departs from the original specifications the risk of unanticipated or "show-

stopping" failures increases. It is therefore to everyone's advantage to specify the

DESIGN: ROTATING TURBOMACHINERY 285

mission usage correctly at the outset. Furthermore, it is essential that the parts be

realistically exposed to the life-consuming portions of the engine usage spectrum

early and repeatedly in the development process. This is done best with the safety

and control made possible by simulated altitude testing in ground test facilities

and must be continued until the required engine durability has been confidently

demonstrated.

This foreword is meant to underscore the overwhelming importance of structural

design for modern aircraft engines. What follows next is an abbreviated, qualitative

introduction to the design process. The reader should be aware that much has been

written on this subject, and that adequate reference material exists to satisfy almost

any curiosity. We are indeed fortunate to be able to include an excellent review of

Turbine Engine Life Management, authored by Dr. William Cowie, a pioneer and

foremost expert in the field, as Appendix N. You will find this to supply a unique

and invaluable background for the engine design process.

The first step in the iterative structural design process is to estimate the stresses

that will be experienced by each part. The stresses stem from the environment to

which the parts are exposed and can, in turn, be regarded as the forcing functions

that consume available life. The second step is to evaluate the response of the parts

in terms of their life expectancy. Both steps require intimate knowledge of many

properties of the materials involved. If the life of any given part is inadequate (or

excessive), its design is changed, and the process is repeated until a satisfactory

solution is found.

We are about to embark on the development of several structural design tools

consistent with the philosophy of this textbook. Their focus will be on the main

source of stresses in rotating parts--the centrifugal force. For the sake of perspec-

tive, it is well to bear in mind the fact that the centrifugal force experienced by

an element of material rotating at 10,000 rpm and a radius of 1 ft is equivalent to

34,000 g!

Nevertheless, there are many other forces at work that can consume the life (or

destroy) stationary or rotating parts, all of which must eventually be accounted

for in the design and test process. Some of the most important, not necessarily in

order of importance, include the following:

1) Airfoil bending moments are caused by the pressure differences across the sta-

tionary and rotating airfoils (or their lift) and are greatest where they are fastened.

The centrifugal force can also cause airfoils with complex three-dimensional

shapes to twist and bend.

2) Flutter (self-induced vibration) is an unsteady aerodynamic phenomenon

that airfoils and/or disks can spontaneously experience, in which they vibrate at a

system natural frequency and for which the driving energy is extracted from the

flowing gas. This is most commonly found in fan and compressor airfoil rows and

comes in many varieties (for example, supersonic flutter, stall flutter, and choke

flutter). Once flutter begins, the life of the parts is measured in minutes because

of the large stresses and high frequency vibrations (> 1000 Hz) that result. Flutter

must be avoided at any cost, but the analysis tools are beyond the scope of this

textbook.

3) Airfoils, disks, and other flowpath parts are exposed to unsteady aerodynamic

forces, such as buffeting (forced vibration) and high cycle fatigue (HCF) that result

from temporally and/or spatially nonuniform flows. Care must be taken to avoid