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

Подождите немного. Документ загружается.

APPENDIX H: MIXED TURBOFAN ENGINE PARAMETRIC 561

--a°{(l+fo---

&o gc

+(l+fo---

S--

F /~no

Pt9 ( Po'~yrr Y.fd Y.(cL TfcH Tfb YftH y.ftL Tt, M TfAB Yf n

=,,P9/

I/Pt9 "~

Pr9 = Prt9 ~'--~9 )

FAIR (3,

fo, T9, h9, Pr9, 4)9, Cp9,

R9, )/9, a9)

V9 = v/2gc(ht9 - h9)

M9 = V9/a9

F fl )V9 Mo

1 +or ao

fl "~ R9 T9/To

(1-

Po/P9) I

1 + ot ] Ro V9/ao

YO J "

2g~Mo F

ao /no

{

l + fo l ~r(~ \ao/

2gc l[I + fo- (I~)]V~- V~} +(CToL +CTol4)ho

~TH

~0 = ~THOP

fohpR

Appendix I

Mixed Flow Turbofan Engine Performance Cycle

Analysis Equations

Appendix I summarizes the complete performance or off-design cycle analysis

equations for mixed flow, afterburning, two-spool turbofan engine with bleed,

turbine cooling, and power extraction. For convenience in computer programming,

the required computer inputs and principal computer outputs are given. These are

followed by the cycle equations in their order of solution. Note that the iterative

solution procedure for M6, or', and rh0 follows that described in Sec. 5.2.6 and

depicted in Figs. 5.3a and 5.3b.

Inputs

Performance choices:

Flight parameters:

Throttle setting:

Exhaust nozzle setting:

Design constants:

re:

rl:

Others:

Reference condition:

Flight parameters:

Component behavior:

Others:

Engine control limits:

Outputs

Overall performance:

Component behavior:

Mo, To, Po

Tt4, Tt7

Po/P9

7"gd max, 2"fb, 7t'M max,

7t'ABR, 7t'n

Of, ~cL, I~cH, OtH, J~tL, l~b, l~mL, l~mn, ~mPL, OmPH

A4, A4.5, A6, A16, A6A, A8wo/AB

fl, e~, e2, hpR, PrOL, ProI4

MoR, Toe, PoR

7rfR, ~cLR, 27JcHR, 7"(tHR, 27JtLR

"gfR , "gcLR , "gcHR , ~tHR , "gtLR

M6R, MI6R, M6AR, M8R

rmlg, Zm2R, fR, fABR, M9R, M19R, Ore, Ot~

FR, m0R, SR

~cmax, Tt3max, Pt3max, %NL, %NH

F, rho, S, fo, Op, OrH, V9/ao, u

Pt9 / Pg, Pg / Po, Tg / To

7g f, 7gcL , 7gcH , 3"(tH , 7gtL

75f, "(cL, 75cH, "gtH, "gtL, "g,k

~ml, Zm2,

far

M6, M16, M6A, M8, M9

563

564 AIRCRAFT ENGINE DESIGN

Equations

Preliminary computations:

FAIR (1, 0, To, ho, PrO, ~b0,

CpO,

R0, Y0, ao)

Vo = Moao

hto = ho + V~

2gc

FAIR (2, 0,

Tto, hto, Prto, CtO, Cpto, Rto, )/tO,

ato)

rr = hto/ ho

rrr = P~O/Pro

OR spec

1 for Mo < 1

ORspec

= l -- 0.075(Mo - 1) 1"35 for 1 < Mo < 5

800

for 1 <Mo <5

ORspec

M4 +

935

7rJd = 7(d max OR spec

ht2 ~-- hto

P.z = e.o

7raBdry

= 1 -- (1 --

ZrABR)/2

Set initial values:

07ftH ~--- 7"(tHR, 7rtL ~ 7t'tLR, "t'tH ~--- "~tHR, "~tL ~- "CtLR

7t'f ~ 7~fR , T(cL = 7~cLR, 7~cH ~ 7t;cH R

r f = rfR, TcL = rcLR, 7~cH = TcHR

"Eml ~--- "CmlR, rm2 -~- "Cm2R,

f = fR

M4-~- l, M4.5 = 1,

M6A =M6AR, M8 =M8R

FAIR(l, f, Tt4,

ht4, Prt4,

~t4,

Cpt4, Rt4,

}'t4,

at4)

ht4.5 = ht4Zml ~tHTm2

f4.5 = f(1 -/5 - el - e2)/(1 -/5)

FAIR

(2, f4.5,

Tt4.si,

ht4.5,

ert4.5,

t~t4.5,

¢pt4.5,

gt4.5, )/t4.5, at4.5)

ht5 = ht4.5r;tL

FAIR (2, f4.5, Ttsi, hts,

Prts, (bts, Cpts, Rts, Yts,

ats)

ht6A = ht5~mR

f6A

= f4.5( 1 -- fl)/(1 + Ot -- /5)

FAIR

(2,

f6a,

Tt6A,

ht6a, ert6a, ~)t6A, ¢pt6a, Rt6A, Yt6a, at6a)

ht3 =

htOrcLrcH

FAIR (2, 0,

Tt3,

ht3, Prt3,

~t3,

Cpt3, Rt3,

Yt3,

at3)

or' = or/{(1 + f)(1 -/5 - el - e2) + el + e2}

FAIR(I, f, Tt4, ht4,

Prt4, C~t4, Opt4, Rt4,

Yt4,

at4)

f4.5 = f(1 --/5 -- Sl - e2)/(1 --/5)

TURBC(Tt4, f, A4/A4.5, M4,

M4.5, 0ttt, Tt4.5i,

Tt3, /5, el, e2, :rrtH, rtH,

Tt4.5)

TURB(Tt4.5,

f4.5,

A4.5/A6,

M4.5,

M6, OtL, Tt5i,

7rtL, rtL,

Tt5)

7:x = hta/ ho

APPENDIX I: MIXED TURBOFAN ENGINE PERFORMANCE 565

-[- (el

"CtH -}-

82)

"~cL rcH TrOmPL

thoho ]

× {(rcL - 1)e/(rf - 1)R + a}

rcL = 1 + (rf - 1) (rcL

1)R

(rl -

rcn= 1 { }

"[- (1-- TtH) TIm H

(1-

"[- EI'~cH

Tr TcL

(1 + or)

Pro

fl - ¢1 - e2)(1 + f)

7:r 7:cL ~mPH

rhoho

ht2 = hto

Prt2 = Prto

htl3 =" ht2"~ f

ht2.5 = ht2"CcL

ht3 ~-" ht2.5~cH

htl3i

= h/2{1 +

rlf(zf -

1)}

ht2.5i

= h/2{1 +

rlcL('rcL --

1)}

ht3i

= ht2.5{1 +

rlct/(rct/- 1)}

FAIR (2, 0, Ttl3,

htl3,

Prtl3,

~btl3,

Cptl3,

Rtl3, Ytl3, atl3)

FAIR

(2, 0,

Ttl3i,

htl3i, ertl3i,

~b/13i,

Cptl3i, Rtl3i, )/tl3i, atl3i)

FAIR (2, 0, Tt2.5,

ht2.5, Prt2.5,

q~t2.5,

cpt2.5, Rt2.5,

Yt2.5, at2.5)

FAIR

(2, 0,

Tt2.si,

ht2.si, Prt2.5i, ~)t2.5i, Cpt2.5i, Rt2.5i, Yt2.si, at2.5i )

FAIR

(2, 0,

Tt3,

ht3, ert3,

~t3, Cpt3,

Rt3, Yt3, at3)

FAIR

(2, 0,

Zt3i, ht3i, Prt3i, ~t3i, Cpt3i, Rt3i, Yt3i, at3i)

~ f = Prtl3i/ ert2

7rcL = Prt2.5i / ert2

7TcH -~- Prtsi / Prt2.5

Yfc = 7"(cLTrcH

rc = rcL rcn

ftemp=f

FAIR(l, f,

Tt4,

ht4, Prt4,

¢t4,

Cpt4, Rt4, Yt4, at4)

ht4 -- ht3

f--

hpRrlb -- ht4

if If -

ftemp[ > 0.0001 goto 2

ht6 = ht5

Zt6 = Tt5

htl6 = htl3

Ttl6 =

Ttl3

et6 = Po 7Tr 27Jd 2"[cL Y~'cH 2"gb 2"~tH 2"[tL

f4.5 = f(1 - fl - el - e2)/(1 -/3)

566 AIRCRAFT ENGINE DESIGN

RGCOMPR (1, Tt6, M6, f4.5,

TtT, PtP,

MFP6)

P6 = Pt6/PtP

T 6 = Tt6/TtT

etl6 ~- PoTt'rTt'dTf f

(Pt)=Ptl6/P6

T 16

RGCOMPR (1,

Tt16, 1, O, TtT, PtP, MFP16)

(Pt/P)16 >PtP

then M6 = M6 - 0.01 goto 1

(Pt/P)16

< 1 then M6 = M6 - 0.01 goto 1

RGCOMPR (3,

Tt16,

M16, 0,

ZtZ, ( Pt/ P)16, MFP16)

Z16 =

Ttl6/TtT

, Ptl6A16MFPI6 / Tt6

anew= Pt6A6MFP6 V Tt16

, a'.ew-- a'

Olerro r = Ol t

a = ct'ne w

{(1 + f)(1 - fl - e~ - e2) + el + e2}

• l

Oterro r

> 0.001 then

calculate a new or'using Newtonian iteration

goto 1

end if

FAIR(l, f4.5, T6, h6,

Pr6,

46,

¢p6, R6,

~'6, a6)

FAIR(l, 0, T16, hi6,

Prl6,

~b16,

Cpl6,

R16, Y16, a16)

ht6 + olthtl6

ht6a

1 +or'

ht6A

rJ M --

ht6

f6A

= f4.5 (1 --/3)/(1 + Ot --/3)

FAIR (2,

f6a,

Tt6a, ht6a, ert6a, ~t6A, Cpt6A, gt6A, Yt6a, at6a)

1 ot ~ / R/R~ 1 + y6M2 + t~' ~1 + Y16M26 }l/

Constant

1 -4-[ V

Y6 M6

~'~-- MI6

RGCOMPR (1,

Tt6A, M6A, f6a, TtT6A, PtP6A, MFP6A)

Tt6a

T6A--

TtT6A

FAIR(l,

f6A, T6A, h6a, Pr6A, ~6A, Cp6A, R6A, Y6A, a6A)

-- 1 + Y6AM2A

M6anew

V Y6A Constant

error = I a.ew -- [

M6Aerro r >

0.001 then

M6A = M6Ane w

goto 3

APPENDIX I: MIXED TURBOFAN ENGINE PERFORMANCE 567

T~t6A MFP6 1 + or'

2Tmideal

-~ "Vl~t6 MFP6A 1 + A16/A6

7rM = 7"t'M max ~M ideal

Pt9

-- = J'gr T(d TgcL YgJcH T(b T('tH T(tL 2"gM 7rAB dry ~n

RGCOMPR (3, Tt6a, m9, f6a, TtT9, Pt9/ Po, MFP9)

if M9 > 1 then M8 = 1 else/148 = M9

RGCOMPR (1,

Tt6a, m8, f6a, TtT8, PtP8,

MFP8)

a,S'rD

T(MT"gAB dry

A8 ~/

Tt6

MFP6 ---- lvlr r s -~-~-~7 A6 Tt6a

RGCOMPR (4,

Tt6, M6new, f4.5, TtT6, PtP6, MFP6)

1146 .....

---- Im6

m6newl

if M6

.....

> 0.0005 then

if M6 >

M6,ew

then M6 = M6 - 0.0001 else M6 = M6 + 0.002

goto 1

end if

RGCOMPR (1, Tt4 , M4, f,

TtT, PtP, MFP4)

1 + fR

Po(1

+ ot)rrr rrd gcL ~cH MFP4

/Tt4R

thOnew

= thor 1 +~-f- {Po (1

+ ~)

~r ~d ~cL ~cH}R

MFP4R .I r,4

• thOnew -- 17110

mOerror = thOR

if th0

.....

> 0.001 then mo =

thOnew

goto 1

f7 = f6a

FAIR (1, f7, T,7,

ht7, Prt7, (9t7, Cpt7, Rt7, Yt7, at7)

ht7 - ht6a

fAB--

t]ABhpR -- ht6A

f7 new "~ f6A Jr- fAB

f7error = If7.ew --

f71

th7error

> 0.00001 then fv =

f7new

goto 4

Tt7 -- Tt6 a

%AB

= 100

Tt7 R -- Tt6 A

7tAB .~- TfaBdry -~- 0.01 X %AB(TrAB R -- 7rABdry )

Pt9

-- ~ 7rr J'(d 7"(cL ~cH 7rb 7rtH 7"(tL 7"gM J'~AB 2"gn

Pt9 Pt9 P9

P9 POPO

Tt9 = Tt7

RGCOMPR (3, Tt9, M9, fT,

TtT, Pt9/P9, MFP9)

568 AIRCRAFT ENGINE DESIGN

rn 9 ---- rh 0 (1 + f7) 1 1 + ot

Pt9 ~ PO 7"(r ~d ~cL 7~cH 7rb 2"t'tH ~tL 7~M 7tAB Ten

m9v'T~

A9--

Pt9MFP9

T9 = Tt9/TtT

FAIR (1, fT, T9, h9,

er9,

~9,

Cp9, e9, }'9,

a9)

V9 = M9a9

f(1 - fl - el - E2)

-[-

fAs(1 + ot -- fl)

fo=

l+ot

- gc a7

( fl )R9Tv/To(1-Po/Pg)}

+ l+fo 1-7-or RoV9/ao Yo

S-

F/fno

RGCOMPR (1,

Tto, Mo, O, TtT,

PtP,

MFPo)

,~o,/-T~

Ao----

PtoMFPo

%RPMLp spool

= lO0/

hovr(vf --

V[ho'crQ:f --

1)]R

%RPMHp Spoor

= 100~/

horr rcL ( VcH

[horrrcL(rcH-

1)]R

2gcMo F /{(

)(V9") 2 }

rh, -- ao ao l + fo l ~ot -- - M2

\ao

O0 = rlrHOe

If any of the control limits (zrc,

Tt3, Pt3,

etc.) are exceeded, then reduce

Zt4 and

go to 1. A Newtonian iteration scheme is used to rapidly converge on the value of

Zt4

that meets the most constraining control limit.

Appendix J

High Bypass Ratio Turbofan Engine

Cycle Analysis

This material is included in case nonaflerburning, separate exhaust flow, high

bypass ratio turbofan engine cycles are under consideration. They are strong candi-

dates for any application where high thrust and low fuel consumption are required

and the flight Mach number never exceeds approximately 0.9. Consider the high

bypass ratio turbofan engine shown in Figs. J.la and J.lb. The station numbers

of locations indicated there will be used throughout this appendix and include the

following:

Station Location

2.5

3.1

4.1

4.4

4.5

Far upstream or freestream

Inlet or diffuser entry

Inlet or diffuser exit, fan entry

Fan exit

Low-pressure compressor exit

High-pressure compressor entry

High-pressure compressor exit

Burner entry

Burner exit

Nozzle vanes entry

Modeled coolant mixer 1 entry

High-pressure turbine entry

for zrm definition

Nozzle vanes exit

Coolant mixer 1 exit

High-pressure turbine entry

for

rtH

definition

High-pressure turbine exit

Modeled coolant mixer 2 entry

Coolant mixer 2 exit

Low-pressure turbine entry

Low-pressure turbine exit

Core exhaust nozzle entry

Core exhaust nozzle exit

Bypass exhaust nozzle entry

Bypass exhaust nozzle exit

569

570

AIRCRAFT ENGINE DESIGN

Fig. J.la Reference stations--high bypass ratio turbofan engine.

The component z, Jr, efficiencies, and assumptions of Chapter 4 apply to this

engine with the exception of those referring to the mixer and afterburner. Unlike

the engine of Chapters 4 and 5, this turbofan does not have afterburning, and both

the core (rhc) and bypass (rhv) airflows pass through separate nozzles. The total

pressure ratio of the bypass air stream's nozzle is defined as

7~nf ~--

Ptl9/Ptl7

The mass flow ratios of Eqs. (4.4a), (4.4b), (4.4c), (4.4d), (4.4e), (4.4h), (4.8i), and

(4.8j) apply as does the turbine cooling model of Chapter 4 shown in Fig. 4.2.

This turbofan engine is modeled as having fixed convergent nozzles for both

the core and bypass air streams. Thus, the exit pressure is equal to the ambient

pressure for unchoked nozzle operation and the exit pressure is greater than the

ambient pressure when the nozzle flow is choked.

The following sections outline development of both parametric and performance

cycle analysis equations for this turbofan engine.

power extraction

PTOL PTOn

113 ~ [ • bleed air coolin~ air #2 ~.

• ~r~ ~coPrt ~ . coolin~~ir#l~ ~~ ~

31 I I I I I

13.I 4 4.1 high-pressure turbine 4.4 4.5 5

[ high-pressure spool I

2.5

low-pressure spool

Fig. J.lb Reference stations---bleed and turbine cooling airflows.

APPENDIX J: HIGH BYPASS RATIO TURBOFAN ENGINE 571

Parametric Analysis

The uninstalled thrust for a turbofan engine with separate exhausts streams is

given by

= --(th9V 9 .3¢_/,h19V19 _//'/0 Vo) -~- A9(P9 -

Po) +

A19(P19 -

eo)

which can be rearranged into its nondimensional form as

(1 + fo(1 + a)

- j~) V9 -~- ot gl---~9 -

(l -~- ot)Mo

ao ao

R9 T9/To

(1 -

Po/P9)

(J.1)

Fgc _ ~ +

(1 -F

fo(1 + or) -- fl)-~o V9/ao Yo

rhoao 1 + ot

R,9 r~9/ro (i - Po/P~9)

+or

Ro Vl9/ao Yo

The velocity and temperature ratios required in Eq. (J. 1) are obtained using the

methods of Chapter 4. For the core airstream, they are

g9~ 2

M2"~.'Cml'tStHgm2 gtL h9

where h9 is determined from

ht9

and the pressure ratio

Pt9 (eo"~r~dgcL~cH~b~,tH~tL~ n

---~9 = t'9/

For the bypass airstream, they are

a---o/ -- -~r ~ Y htl---9

where

h19

is determined from

htl9

and the pressure ratio

Ptl9 (Po'~Trr2.lj d

The independent design variables for this engine are the fan pressure ratio (zrf),

the overall cycle pressure ratio (zrc), and the bypass ratio (or). The pressure ratio

across the high-pressure compressor is obtained from

7gcH = 7~c/~cL

The temperature ratios across the fan (l:f), the low-pressure compressor (VcL), and

the high-pressure compressor (rcH) are related to their pressure ratios by Eqs. (4.7b),

(4.7c), and (4.7d), respectively. The temperature ratios across the high-pressure

turbine (VtH) and low-pressure turbine (rtL) are obtained from power balances of