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NASA Technical Memorandum 83204

NASA-TM-8320419810024663

SIMPLIFIED OFF-DESIGN PERFORMANCEMODEL OF A DRY TURBOFAN ENGINE CYCLE

Frederick J. Lallman

September 1981

OCT 1 1981

~/\NGLE'f RESEARCd CENTE.'~

LIBRARY, NASA

/1""~f'tt"jt\l': ~'I'I~'~\~

Nl\SI\National Aeronautics andSpace Administration

Langley Research CenterHampton, Virginia 23665

https://ntrs.nasa.gov/search.jsp?R=19810024663 2020-03-27T02:40:01+00:00Z

SIMPLIFIED OFF-DESIGN PERFORMANCE MODEL OF ADRY TURBOFAN ENGINE CYCLE

, . Frederick J ..• Lallman

ABSTRACT

The specific thrust and fuel-air ratio for a dry turbofan engine cycle werecalculated for several power levels over a range of altitudes and Mach numbers.The engine has a design fan pressure ratio of 2.9, compressor pressure ratio of8.0, and bypass ratio of 0.6. Nominal engine component curves were picked toapproximate the calculated data to construct a simplified model of the off­design performance of the engine. The model was then used to construct asimplified design-point engine model for the full-power condition.

SUMMARY

The specific thrust and fuel-air ratio for a dry turbofan engine cycle werecalculated for altitudes of 0 and 10 kilometers and Mach numbers of 0, 1 and 2for a number of power settings, each specified by fan pressure ratio, compressorpressure ratio, and main burner temperature. Theoretical engine componentperformance curves, for which the specific heat is considered to be constant butunknown, were picked to approximate the calculated data for each engine compo­nent. The resultant curves form the basis or' an off-design performance model ofthe engine which does not require complicated equations to calculate specificheats, entropy functions, and enthalpy functions. The parameters were then setto their full-power values and the model was reduced to a simplified design­point model for the engine.

INTRODUCTI ON

In the study of integrated propulsion system and flight controls, it isnecessary to model the effects of varying flight conditions upon propulsionsystem operation. Perturbation models of engines used for multivariable controllaw design do not generally include these effects. The operation of an enginedepends upon the air entering it (specifically, the pressure and total tempera­ture at the face of the fan for a turbofan engin~. These, in turn, are depen­dent on the flight Mach number, altitude, and the inlet pressure recovery ratio.Inclusion of these effects into an integrated aircraft model enables the studyof interactions which may occur between flight modes such as the phugoid andvariations in the engine thrust and internal operating canditions. This rep~)Tt

describes the results of an effort which has sought to characterize the effectsof flight condition and inlet pressure recovery ratio upon the operatingparameters of a contemporary dry turbofan jet engine type.

IV Z/-3J;2.{) &~..

Two quantities which characterize the performance of a turbofan engine arethe specific thrust (ST) and the fuel-air ratio (Wf/W

a). The specific thrust is

the ratio of the net thrust force produced by the engine to the mass flow rateof the air entering the engine. Using this and the fuel-air ratio, the specificfuel consumption (SFC) of the engine may be computed. The specific fuel consump­tion is the ratio of fuel rate to the thrust force. Using this, the free-streamvelocity, and the heating value of the fuel, the efficiency of the engine may becomputed.

One method of calculating the performance of a turbofan engine is given inreference 1. This method involves complicated equations needed to calculatespecific heats, entropy nlnctions, and enthalpy functions. In an applicationwhere many of the parameters which define the engine are fixed or confined tonarrow ranges, the use of a complicated computer program as is given inreference 1 may not be necessary. In this case, the program may be used togenerate simplified functions defining the operation of the individual enginecomponents. These functions may then be assembled into a simplified model ofthe whole engine.

This report uses the data calculated by the computer program of reference 1·to construct a simplified model of the engine defined by tables I and II andfigure 1. The resultant model involves many nonlinear functions which have beenrepresented by algebraic equations. The specific thrust and fuel-air ratio arefunctions of flight condition (Mach number and ambient temperature), inletperformance (pressure recovery ratio), fan pressure ratio, compressor pressureratio, and burner temperature. A schematic diagram of the engine model ispresented in figure 2. The nonlinear functions in the model are presented asalgebraic equations in the text and in graphical form in figures 3 through 13.

The values for the fan pressure ratio, compressor pressure ratio, andburner temperature were then set to their full-power values. With these vari­ables fixed, the engine model is reduced to a design-point performance model.The specific thrust and fuel-air ratio become functions of flight condition andinlet performance. A schematic of the design-point model is presented infigure 14. Many of the nonlinear functions in this model are the same as wasdiscussed above. Additional nonlinear functions were derived. These arepresented as algebraic equations in the text and in graphical form in figures 15through 17.

SYMBOLS

b

CP

g

h

bypass ratio

ospecific heat, J/kg- K

2gravitationa~ acceleration ~onstant (9.81 m/sec )

,

alti~ude, m

2

HVF

M

M

P

R

R

SFC

ST

STl

ST2

T

v

vc

Vcd

W/Wc a

Wf/Wa

o

y

n

e

L':.h

heating value of fuel, J/kg

Mach number

molecular weight, kg/kmole

pressure, Pa

ogas constant, J/kg- K

ouniversal gas constant (8.314 J/ K-kg-mole)

inlet pressure recovery ratio

specific fuel consumption, kg/N-sec

specific thrust, N-sec/kg

contribution of engine core to specific thrust, N-sec/kg

contribution of bypass to specific thrust, N-sec/kg

temperature, oK

velocity, m/sec

velocity coefficient of the main nozzle

velocity coefficient of the duct nozzle

coolant flow ratio

fuel-air ratio

pressure relative to sea-level standard {lOl.4 kPa)

ratio of specific heats

efficiency

temperature relative to sea-level standard (288.2 oK)

enthalpy change, J/kg

oentropy .change, 'J/kg- K

Subscripts

a

B

air

burner

3

C compressor

F fan

f fuel

g gas

s static

SL sea-level

T turbine

Integer subscripts refer to engine stations depicted in figure 1.

o free-stream

1 fan face

l' fan exhaust

2 compressor exhaust

3 main burner

4 turbine exhaust

5 main nozzle entrance

6 main nozzle exit

7 duct nozzle entrance

8 duct nozzle exit

ENGINE MODEL DEVELOP~ffiNT

The performance model of the dry turbofan engine developed in this reportis depicted in figure 2. This model is based on the theoretical performancecharacteristics of the individual engine components of reference 1. The charac­teristics are obtained by manipulating the equations of reference 1 with thespecific heats, C, held constant. The ~esultant equations: are then fitted to

. p. .... data obtained by executing the program of reference lover a range of operatingconditions. If the specific heats; do not vary radically, then the derivedformulae for the en.gine component characteristics will at least be of the properform, if not having the precise numbers. In each case, the derived formulae are

4

fitted to data which are calculated by the more exact program. This data ispresented with the fitted formulae in figures 3 through 13.

The specific heat used in the data calculations is a fourth order poly­nomial function of temperature and is also a function of the fuel-air ratio ofthe gas being considered. Treating the specific heat to be a constant, theenthalpy change and entropy change reduce to the following approximations:

T.6.h = J

T2 C (T)dT '" C

p(T2-TI )

1 p

T2 C (T)

In [~:].6.~ = J P dT '" CT T P1

(1)

(2)

These approximations are used throughout the following development.

The engine data were calculated by the program of reference 1. Thecharacteristics of the engine are given in table I. The data were calculated forMach numbers of 0, 1 and 2 at sea level and 10 kilometers altitude. At eachflight condition, the fan pressure ratio, compressor pressure ratio, and burnertemperature were varied according to the schedule of table II.

Those terms involving Cp

are treated as unknowns in the process of fitting the theoretical formulae tothe calculated data.

The individual engine components are examined in the following sections.This development follows the derivations of reference 1. The approximations ofequations 1 and 2 are applied in each instance. In addition, the effects of thefuel combustion products upon the thermodynamic properties of the gases invarious parts of the engine are ignored. For each engine component, the theo­retical (approximation) formula is given followed by a formula (with numbers)which has been picked to approximate the calculated data. Note that wheneverthe specific heat, C , appears in the theoretical formulae, its value is

p "obscured by the effects of the approximations used.

Temperature and Pressure Variables

The temperature and pressure variables used in reference 1 and in thetheoretical formulae given below are absolute values denoted by T and P. Thetemperature and pressure variables used in the fitted formulae are relative tostandard sea-level values and are qenoted by e and 0, respectively. Therelationships between these variables are"

e T= T

SL(3)

5

Po = PSL

where TSL is the standard sea-level temperature of 288.2 oK

PSL is the standard sea-level pressure of 101.4 kPa.

Engine Inlet

(4)

The variation of the standard ambient temperature of reference 2 withaltitude is depicted in figure 3a. The temperature decreases linearly withaltitude until it reaches 75.19 percent of its sea-level value at 11 kilometersaltitude after which it is constant until 20 kilometers altitude.

The inlet velocity is a function of Mach number and ambient temperature.

(5)

where Vo is the airplane air speed

MO is the airplane Mach number

80s

is the ambient temperature-1

y is the ratio of specific heats of the ambient air equal to (I-RIC) .p

The inlet total temperature ratio is a function of Mach number.

2'" 1 + .199 MO

(6)

This formula is depicted in figure 3b.

The inlet total pressure ratio is a function of the total temperatureratio.

3.518.(7)

This formula is depicted in figure 3c .•

'.

6

Diffuser

The total temperature across the diffuser is constant and the totalpressure ratio of the diffuser is the pressure recovery ratio, rIO',

(8)

(9)

Fan

The enthalpy change of the fan (a measure of the fan work) is a function ofthe fan pressure ratio and the total temperature of the air entering the fan.

[ [',11']

Ra

Cp ~ " 353000[ [,,~,] .2805 _ ~ (10)

where °1,/°1 is the fan pressure ratio

nF

is the fan efficiency.

The fan temperature ratio is a function of the enthalpy change.

1 + 3.162 x 10-6(ll)

Equations 10 and 11 are depicted in figures 4 and 5. Since the variations inthe data used for figures 4 and 5 are weak functions of the fan intake tempera­ture, only the data for the maximum temperature (sea-level, Mach 2) and theminimum temperature (10 kilometers altitude, zero velocity) are shown on thesefigures. ..

Compressor

The enthalpy change of the compressor is a function of the compressqrpressure ratIo and the total temper~ture of the air entering the compres~or.

7

[ ["12,]

Ra

Cp l [ [0 ] .2654 lJ'" 3853000 0

1

2, - lJ (12) I

where °2/ °1

, is the compressor pressure ratio

nC is the compressor efficiency.

The compressor temperature ratio is a function of the enthalpy change

Equations 12 and 13 are depicted in figures 6 and 7.

Main Burner

(13)

The fuel-air ratio is a function of the temperature change across the mainburner.

(14)

where W IW is the coolant flow ratioc a

HVP is the heating value of the fueln

Sis the efficiency of the burner

6p is the temperature of the fuel.

This formula is depicted in figure 8.

Turbine

The enthalpy change of the turbine is equal to the sum of the enthalpychanges of the fan and compressor with allowance made for the higher airflow ofthe fan.

8

(15)

where b is the bypass ratio.

The temperature drop across the turbine is a function of the enthalpychange.

(16)

The pressure ratio across the turbine is a function of the temperatureratio

where nT

is the efficiency of the turbine.

Equations 16 and 17 are depicted in figures 9 and 10.

(17)

The exhaust gas of the turbine is a mixture of gas from the main burner anda portion of cooling air from the compressor. The temperature of the turbineexhaust is determined by equating the energy of the gas mixture to the energiesof each of the components.

(18)

where W jW is the cooling flow ratio. A fit of the data yieldsc a

85

~ .3652 + .1010 82

+ .7856 84 (19)

Figure 11 illustrates the correlation between the calculated and approximatedvalues of the turbine exhaust temperature.

Specific Thrust"

The specific thrust of the engine is

9

ST = (20)

where Vo is the free-stream velocity

V6 is the exit velocity of the main nozzle

V8 is the exit velocity of the duct nozzle

W/Wa is the fuel-air ratio

b is the bypass ratio.

The first term of equation 20 is the contribution to the specific thrust of thecore of the engine, the second term is the contribution of the engine bypass,and the third term is the effect of the momentum of the inlet air. The specificthrust, in this paper, is defined as the amount of thrust force produced permass flow of the total intake air of the engine and its units are'newtons forceper kg/sec mass rate. These three terms are computed separately as indicated infigure 2. In this figure, the first term of equation 20 is denoted by STI andthe second term by ST2.

Main Nozzle

The component of tre specific thrust produced by the main nozzle is afunction of the nozzle pressure ratio and the temperature of the gas entering it.

STI Vc-- = -:-----c:-r;::- 1 + byes ~l [o':J

R

'Me:g P "'482.9 ~l _[0°:

5

] -.2698 (21)

where V is the main nozzle velocity coefficient. This formula is depicted inc

figure 12.

Duct Nozzle

The component of the specific thrust produced by the duct nozzle is afunction of the nozzle pressure ratio and the temperature of the gas entering it.

ST2 bVcd-- =1 b I2gcpTsL/6V +,

10

RM Cg P ",273.9 ~l

-2660(22)

where Vcd is the duct nozzle velocity coefficient. This formula is depicted in

figure 13.

DESIGN-POINT MODEL

This section uses the engine performance model developed in the previoussection to generate a design-point engine model. The design point (full power)condition is specified by the fan pressure ratio, the compressor pressure ratio,and the burner temperature. The fan pressure ratio sets the ratio of fanenthalpy change with fan intake temperatures ~hf/8l (Fig. 4). This, in turn,

sets the fan temperature ratio, 8ll~1 (Fig. 5). The compressor pressure ratio,

°2/°11 , sets the ratio of compressor enthalpy change with compressor intake

temperature, ~hc/8l1 (Fig. 6). This, in turn, sets the compressor temperature

ratio, 82/8 11 (Fig. 7). These quantities and the selected burner temperature

are used to reduce the .engine performance model to the design-point engine modelof figure 14.

The design-point model is developed for the parameters of table IIcorresponding to the maximum power level angle (PLA) setting.

The engine inlet and diffuser models are the same as in the previoussection.

The fan model reduces to the following:

(23)

= 1.387 (24)

where equations 23 and 24 were obtained from the approximations of equations 10and 11.

The compressor model reduces to the following:

~h

__c_ = 282100811

11

(25)

82 1.864~-

(26)

where equations 25 and 26 were obtained "from the approximations of equations 12and 13.

The fuel-air ratio reduces to

Wf

_W- - .02332 - .01086 81a

where equation 27 was obtained from the approximation of equation 14 withequations 24 and 25. This formula is depicted in figure 15.

The temperature drop across the turbine becomes

(27)

(28)

where equation 28 was obtained by the combination of equations 15, 16, 23, 24and 25.

The pressure ratio across the turbine becomes

[1.016 - .3908 8 ]4.2901

(29)

where equation 29 was obtained by combining equation 28 with the approximationof equation 17. This formula is depicted in figure 16.

The turbine exhaust temperature becomes

85

= 4.677 - 1.234 81 (30)

where equation 30 was obtained by combining equations 19, 24, 26 and 28. Thisformula is depicted in figure 17.

The errors which are apparent in figures 15 through 17 are caused by anaccumulation of small errors in the engine performance model developed in the

12

previo~s section. The coefficients of equations 27, 29 and 30 were adjusted tomore closely fit the calculated values. The adjusted formulae follow:

Wfwe = .02264 - .00988 81a

°4 [.9973 _ .3647 81,]4.290

~=

85 = 4.759 - 1.272 81

These formulae are depicted in figures 15 through 17.

(31)

(32)

(33)

•

The models for the main nozzle and the duct nozzle remain the same as inthe previous section.

CONCLUDING REMARKS

Two simplified performance models for a dry turbofan engine have beendeveloped. The first model produces the specific thrust and fuel-air ratiogiven the flight condition, air inlet performance, fan and compressor pressureratios, and the burner temperature. Specific values for the fan and compressorpressure ratios and the burner temperature were set in this model to produce adesign-point model. Several nonlinear algebraic formulas for the performance ofthe individual engine components were derived by generating simplified theo­retical math models which were then fitted to calculated data. Because of therelative simplicity of these models, they can be used for calculations of engineperformance where computational efficiency and speed are important factors.

REFERENCES

1. Vanco, Michael R.:Computer Program for Design-Point Performance ofTurbojet and Turbofan Engine Cycles. NASA TM X-1340, February 1967.

2. Anon.: U.S. Standard Atmosphere, 1962. December 1962 .

13

Table 1.- Engine Characteristics.

Variable

nCnTnFHVF

r 3 2,VcVcdtv IWc a

nbPLA

b

Pl,IPlP/P lT

3

Description

Compressor Efficiency

Turbine Efficiency

Fan Efficiency

Heating Value' of Fuel

Main Burner Pressure Ratio/

Main Nozzle Velocity Coefficient

Duct Nozzle Velocity Coefficient

Coolant Flow Ratio

Main Burner Efficiency

Power Lever Angle

Bypass Ratio

Fan Pressure Ratio

Overall Pressure Ratio

Main Burner Temperature

Value

.88

.90

.90

46.7

.95

.96

.96

.158

.98

20-83

0.6

.98-2.9

5.54-23.0

1372-1559

Units

mJ/kg

degrees

Table 11.- Part-Power Schedules.

PLA Pl,IPl P/Pl , 83

20 .98 6.65 4.76

30 1.37 6.07 4.86

40 1.68 6.59 4.97

50 1.84 7.53 5.07

60 2.03 8.19 5.17

70 2.23 8.70 5.27

83 2.90 7.93 5.41•

7 8

CO/fPfU55tJR.

o 1

l' COfJLrj/UT => Aile h-o~-+ Fu€t.. h.ow

Figure 1.- Schematic Diagram of Dry Turbofan Engine.

ST~

5T1..fe-;

ye;,I~ 5TZ STZlL-1--...:....~.:.-I'~ ~'- --.J

9"

t:: LG,/81 Ft']7

h 11~c.

bieo G,F,~ JQ -:-F'J 3eo. eo.Mo

~ LL lCh:J 3b

Fr.7 1- FIJ 6

Ll hgJ, J" r$0 I;-dos

£"1'\0 ~os

Figure 2.- Dry Turbofan Engine Performance Model.

1

2.

- - - -------IIIIIII

~.".._.""..., u....·• ..~_,..,••~....."'.......~

o 11 ,,0h., km

a) Standard Atmospheric Temperature

..

1~-2­

1 + .. 19<JM

0 -----1 -i1

!12

b) Inlet Total Temperature

/0

/~o-fJo5

3.5/eS (~:J

: ...\ ~

0 1- 2ea-Bas

c) Inlet Total Pressure

Figure 3.- Inlet Parameters.

-I . _... --"-"'-""

? $(,-. f:, I

o

I.05 -r-

1III

I

li

10 -t-.

. . h Ipy Change. '.4.- Fan Ent a .Figure

[1,/0,

I. if.

1.2.,

1.0

o

Figure 5.- Fan Temperature Ratio.

· ..

Llhc J-0-, KO~, IJ

.2

!.1 T

I

I!

M h<> z. 0

6. 0 IOliW\

Figure 6.- Compressor Enthalpy Change.

'.

..

Z.O

o

o IOl<.~

o ~

o t\.

<> (;

~-------t··_---./

l·t)o

Figure 7. -. Compres;sor I Temperature Ratio. ,

•

..'

,020

W."- hWa.- M 0 '0 k'nt-~- ....._.-

.0" 0 0 ~

I [] ~

2- <> ¢)

J)/l.

,008

,001{.-

o L..--_"-'-'-"'-+-'_'__'_~. I--..._... '.'''__''1 2.

Figure 8.- Fuel-air Ratio.

-1---1.3 +

~ - (7.2.

Io-------t-----I-----lr---+\---I.2.5" .so .7~ 1.00 I,ZS- X 10 6o

1

3,5

~-e4- 0 '0 k'htlo

.3 0 0 6

I 0 ~

Z ¢ <>

Figure 9;- TUrbine Temperature Drop.

..

. 'l

Figure 10.- Turbine Pressure Ratio.

2.slope -: i.

~_-------11---'---

3

·---1+

•

Figure 11.- Turbine Exhaust Temperature .

.'.

400

IIS- ",'

M h 0 IOkwt

0 0 ~

I 1°~

2- 0,Q

__ I ( C482.8 1/ 1 - ~)- .~?%.605

,,---' ----.._._+-- .. _ ...S ------:---;.:.Lj .

/0o.

300

5Tl N·_ . -secr;:;- ,-

yes k3

Figure 12'.- Mai N, ,,' nozzle.

•

..

250

A __----e:;· -

213.8 '1 _(~)-.266O'1/ 60S

1501"'\

0 0

I 0100

2- V

50

5T.2 N-set-,-.,Je,: k~

200

5'o '--I-----+-----t-.---.--il----I t

10 /S ;'0 25£,1£os

Figure 13.- Duct Nozzle.

..

LLr"o

Figure 14.- Design-Point Model.

r

• ..

5T...

,016

,0/2.

,008

,004-

~"~..,,-_.

o 10i

I i lJ

2, 1o

3/

. .

o t-..-------,---~t_--.---,-.__t--- ..--..- ...--..-c-.-.---..-___1.5 /. 0 I. 5" 8; 2,0

Figure 15.- Fuel-air Ratio.

r

.3

~.t 0 IOkm----,.....~- ,....-.-.~... ~,""'-~~_ ..,., .'~~...... '."......

o 0 1.\

,I [J ~!

t!O t)

... ;::._ '~;>J--.,< ,..... ,"',,'

f '70_··Z V:,I.

...........

-~~

L...----'-------i·-·-··....··-·-·------····-··---i··-·----·· ._-''\;-~---,.5 1.0 /-5" ~ 2.0v,

o

.1

.2.

Figure 16.- Turbine Pressure Ratio.

o 10 km

3

1.5 1.0 1.5 2.0

•

..

Figure 17.- Turbine Exhaust Temperature.

1. Report No.

NASA TM-83204I2. Government Accession No. 3. Recipient's Catalog No.

4. Title and Subtitle

Simplified Off-Design Performance Model ofa Dry Turbofan Engine Cycle

7. Author(s)

Frederick J. Lallman

9. Performing Organization Name and Address

NASA Langley Research CenterHampton, VA 23665

12. Sponsoring Agency Name and Address

National Aeronautics and Space AdministrationWashington, DC 20546

15. Supplementary Notes

5. Report Date

September 19816. Performing Organization Code

505-34-33-028. Performing Organization Report No:

10. Work Unit No.

". Contract or Grant No.

13. Type of Report and Period Covered

Technical Memorandum

14. Sponsoring Agency Code

--_._---------------------------------------------....j16. Abstract

The speCific thrust and fuel-air ratio for a dry turbofan engine cycle were calculatedfor several power levels over a range of altitudes and Mach numbers. The engine has adesign fan pressure ratio of 2.9, compressor pressure ratio of 8.0, and bypass ratioof 0.6. Nominal engine component curves were picked to approximate the calculateddata to construct a simplified model of the off-design performance of the engine. Themodel was then used to construct a simplified design-point engine model for the full­power condition.

17. Key Words (Suggested by Author(s))

engine modelturbofansteady state performance

18. Distribution Statement

Unclassified - Unlimited

Subject Category 07

19. Security Classif. (of this report)

Unclassified20. Security Classif. (of this pagel

Unclassified21. No. of Pages

3222. Price"

A03

N-305 For sale by the National Technical Information Service. Springfield. Virginia 22161

DO NOT REMOVE SLIP FROM MATERIAL

Delete your name from this slip when returning materialto the library.

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( J/. 1£// / V/"'/T7/ -//1...£4/ ..../ r v -v

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NASA Langley (Rev. May 1988) RIAD N-75

,