GALCIT REPORT NO.

THEORETICAL INVESTIGATION OF ACCELERATION

OF A TURBOJET ENGINE

Thesis by

Lt. Cdr. Loys M. Satterfield, USNLt* Cdr. John P. Wheatley, USN

hesis18

en*

library

U. S. Noral Postgraduate School

Annapolis, Md.

t

THEORETICAL INVESTIGATION OF ACCELERATION

o? a -ranaojET engine

eeia by

Lt. Cdr. Loys M. batterf ield, USN

Lt. Cdr. John P. uheatley, U39

In Partial Fulfillment of the Requirements for the

Degree of Aeronautical Engineer

California Institute of Technology

Pasadena, California

1947

Sis

AwKZJO"..LftDGBMSMT

The writers are sincerely grateful to Mr. W. D. Rannie for

hie assistance and consideration during the preparation of this

report.

NQ^ffi. JLOTTR2

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/

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\* Aa» ^3' etc Annular areas

•

«2

al

i a2 # 83' etC Local sonic velocities ft/aeo

• CLP

Specific heats ft - lbSlug - °R

Dc ^om^ressor inletMean diaraeter

ft

Dt Turbine mean diameter ft

Gross thrust lb

g Acceleration of gravity ft/sec

Polar moaient of inertiaof rotor o.7675

llach number

lb - ft - sec'

A liaaa rate of fluid flou slu ;s/sco

Rotational speed RP

Rotor acceleration Rev/sec'

Fx ^ree stream pre asure at ^/fta

station "x"

Psx stagnation pressure at 'ft'*station nxM

*x

%

Gqs conetant ft - lbslug - 3

H

Free stream te^eratureat station "x"

°R

Stagnation temperatureat station "xn

°R

Vx Fluid velocity at ft/secstation "xn

v;c jompressor power ft » lbsec

W-fc Turbine power ft - lbsec

\ o -.o .pressor flow coefficient 17= ttt" \l 8J5c P2 AcV z

Wc-f2.o Compressor power coefficient -^t" P A a

° o Compressor speed coefficient (Jc= —^

—

' t Turbine flow coefficient C * ^V"Y?SP+AtJ £

-*^t Turbine power coefficient _/2 = -x—

^t Turbine speed coefficient <C * -2lH* £*4_

J1 Ratio of specific heats CP

/~

7? ">? 77 Diffusor, burner, and' ( * nozzle efficiencies

^ fc

/As Tal1 area »**•

The failure of turbojet aircraft propulsion units to accelerate

rapidly to high thrust operation when emergencies arise in slow speed

flight has restricted their use in aircraft applications, and has also

concentrated considerable attention upon their acceleration characteristics

in an effort to produce better results* This thesis presents a method

of computing the acceleration of a particular turbojet by making use of

complete performance curves of the component parts of the turbojet.

The method presented here does not permit computation of the

acceleration for a particular operating condition as determined by those

variables usually considered independent; namely, (l) Flight Conditions

of velocity, density, pressure, and temperature, (8) Sngine rotor spaed

(3) fuel rate of flow, and (4) Tail cone area ratio. Computation using

these four independent variables was originally attempted in preparation

of this thesis. However, extreme complication in the computations dictated

that turbine inlet temperature and air mass rate of flow which are

normally dependent variables, should be considered independent. Fuel

rata of flow and tail cone area ratio are therefore considered dependent.

Therefore, in order to match a particular operatinc condition, it io

necessary to make a family of computations for various turbine inlet

temperatures (constant for each set) over a range of assumed air mass

flows.

Computations have bean performed for the ..estinghouse X19B axial

flow turbojet to illustrate application of the method and to show

qualitative and quantitative effects of variation of tail area ratio,

at two different turhine inlet temperatures.

EJTROlXJJTIoK

Daring emergency conditions which arise in aircraft landing

approach, a rapid increase in thrust is imperative, Ho-.Tever, current

turbojet engines are notoriously slow to accelerate from low to high thrust

conditions. Although a large volume of information is available concerning

equilibrium running conditions of turbojets, comparatively little ha:;

been published concerning acceleration. Accordingly the purpose of this

paper is to develop a method of computation of acceleration, and of thrust

during acceleration of a turbojet engine ; and further, to ascertain quali-

tative effects on acceleration and thrust of variation of tail area ratio

and turbine inlet temperature.

SCOPE

The basic method developed in this analysis is general and may

be applied to any turbojet operating condition. However, this lethod

does not encompass thrust augmentation devices such as afterburning.

Application of the proposed, method is contingent upon complete experimental

performance data for the compressor, combustion chamber, and turbine, as

separate units, and in addition upon knowledge of diffuser and nozzle

efficiencies. The method is based upon the assumption that the steady

state performance data can be applied instantaneously, even under non-

stationary running conditions. Hence the accelerations are considered

as "slow* changes, and although this assumption is probably valid, the

final justification must come from comparison with tests.

The computations presentea are restricted to a single flight

condition. For this flight condition effects of variation of rotor speed

from idle to military rating, and of tail area ratio from 0.8 to 2.0,

are evaluated at two different turbine inlet temperatures.

PHOO&PPRS

In order to compute the acceleration of the rotor of the turbojet

engine it is necessary to know both the power required to drive the

compressor, «f , and the power output of the turbine, Wtf The excess

power, neglecting power required for the accessories, is then the power

available for the acceleration of the rotor. In operation, the magnitude

of these powers is determined by the independent variables: (l) Flight

conditions (2) Rotor speed, n, (3) Fuel rate of flow and (4) Tail area

ratio, Ag/Agp However, for the purpose of calculation, the independent

variables have been chosen to be: (l) Flight conditions (2) Air mass

rate of flow (3) Turbine inlet temperature, T4f and (4) Rotor speed,

leaving fuel rate of flow and tail area ratio as dependent variables.

This is completely explained in the discussion*

The first step used in calculating .

c and W^ was to find the

entrance conditions of the compressor* Flight velocity of the engine

was assumed to be 100 mph* Sea level standard conditions of density,

pressure and temperature were assumed* Then assuming lsentroplc flow

through the diffuser, a plot of Mg, Tg , and P2 , versus air mass flow,

A, was made by the use of a Collier diagram* (See Figure U) A

particular rotor speed was then assumed* Values of mass flow from

the lower limit of the compressor stall to the upper limit of the

critical flor were chosen* The compressor flow parameter, r^ and

speed parameter, (f^_ were calculated for each mass flow, and then

the compressor pressure ratio P3/P2 » the compressor power coefficient

_/Z c 9 and the compreaaor temperature ratio^T^/Tg, were found from

Figures 13, 14, and 15* With theae values It was possible to

determine:

a, P,.f*$

c) W^-Cl^AzQz

P4 waa assumed to be 0.98 P3. (See Figure 12). T4 was then taken

as the value desired: (8000 R for one case and 2200°R for the

second case). From these data it was possible to compute

w RAtlfT14

... . I

The turbine performance charts, Figures 16, 17, 18, and 19 were

entered and from them was obtained:

d) M s

°> T.

from these the following were computed:

a) ps « 3(i£

b) Wt= -R^At^

(Unless Pss/p exceeds the critical-then see

Appendix II)

With tills information the nozzle chart Figure 20 was entered

and Mfi

, ?^?~ 9 and A5/A5 were determined. From these data

T'-Ts(%)anc|

The acceleration of the turbojet rotor was then computed as

tl =: Wfc - Wc

4irxnl

pand the thrust

F= m(\4- V.)

for values of Mg less than one, When Pg/Pfiexceeds the critical

pressure ratio then the pressure at the nozzle outlet, Pg , exceeds

atmospheric pressure, P , and a pressure term in amount A c. ( ft - R>

)

Is added to the thrust. Uhder this condition, M^= I.Of and

the expression for the thrust becomes:

F- m(a^Vo) f At(P^R)

*?here Pft

ia determined from the known magnitude of ?5 and from that

pressure ratio, P5/P-, which makes the value of IAQequal to unity.

From the plots of ohe data obtained from the above calculations

(See Figures 1, 2, 4 t and 5) it was then possible to compute the

acceleration time for the rotor by taking time increments of the order

of a half a second and making the computation in a step by step process.

1. "Jet Propulsion", A reference text prepared by the staff

8

of the Guggenheim Aeronautical Laboratory and the Jet

Propulsion Laboratory, GALCIT, California Institute of

Technology, for the Air Technical Service Command.

(Restricted)

2. Westinghouse Aviation Gas Turbine Report No. A-502, Oot. 1946.

3* B. Pinkel and L. R. Turner, "Thermodynamic Data for the

Computation of the Performance of Exhaust Gas Turbines,"

NACA Advance Restricted Report 4B25.

4. Curtiss VTright corporation, "A Simplified Method of Calculating

and Presenting Turbo-Jet Perfonuance, " Confidential Report

No. 11-46-3, Oct. 1946.

5. Glenn L. Martin Co., "Acceleration characteristics of westing-

house Model X19B Turbo-Jet Engine," Flight Report Ito. 37-6833,

Jan. 16, 1946.

6. Glenn L. Martin Co«, "Report on the Operational Characteristics

of the Westinghouse Model X19B Turbo-Jet Engine Installed in

a JM-1 Flying Test Bed", Engineering Report Ho. 2482,

Oct. 15, 1946.

RESULTS

PaOCSDUKS FOR COMPUTATION OF TURBOJET ACCBLSRATICW

1* Given the following atoospheric flight and diffuser conditions:

?ot

T°, Ho, ^2. Assume the independent variables n and m.*

3, Compute M ? T2 <™d P2 :

~?

if-') T . T r. +^M^+ 2

P2 - P.

IM)

4« Compute non-dimencional compressor parameters I c and (£ :

C= M^f<£ =

a z

5, Hnter compressor perfoimanoe charts for the particular turbojet

under consideration (See Figures 13, 14, and 15), From these

charts determine:

fta) Compressor pressure ratio, p

b) Compressor power coefficient, -i.Z.c

c) Compressor temperature ratio, —

r

6* From the above data determine the following:

») p3 =Pz(t2)b) Wc

= Slc Pz Ac a z

*3ee discussion on selection of m

7. Enter combustion chamber performance chart for the ;ular turbojet

under consideration and determine pressure ratio vP3 . (See Figure 1

Compute Rv '-

R - ?{%

• Compute \ t and (T-t :

r*- c?VV£&

8

Note that 1^ involves introducing another independent variable, "77 •

For analysis of tliio subject see discussion.

9. Enter turbine performance charts for the particular turbojet under

consideration (See Figure 16, 17, 18 and 19), From these charts

determine:

a) P4

) -^O

d)

Ts

10. From these dita compute the following:

b ) Wt =Jlt R,.A t a

'4Vr411. Compute nozzle ore3sure ratio

Pt^ ft

12. Enter nozzle performance chart (See Figure 20) and determine M^i

~^°/Ts and ^Ms • Bacn installation will have a different chart

depending upon nozzle geometry. Ho;vever f for short tail pipes and

small area ratios flow is nearly iser.troplo. ..hen nozzle efficiency

is known, the foregoing quantities may be determined by computation

similar to those for the diffuser.

13. From these data compute the following:

15

Vfc= MfcYFRTfc

14* Turbojet acceleration

_Wt__VVcn " 4ir*n I

p

15, Turbojet thrust

a) Then Mfe < \0 :

b) ..hen *% exceeds the critical pressure ratio and l\=|.0

F«m(cj(,-V.) +

A

t (pt -P.)

(See Appendix IX)

Application of this method to the particular cases selected for

demonstration produced the ultimate results shown in Figures 1, 2, Sa #

and 3b, The effects of tail area ratio and rotor speed on thrust and

on acceleration are shown in Figures 1 and 2, whioh were derived from

figures 7-10, Figures 3a and 3b show effects of rotor speed and tail

area ratio on time required to accelerate to a particular engine sx>eed a

The method of computation proposed in this paper is staple in

form, but the calculations are lengthy and the method requires some

practice to estimate quickly the proper range of mass flows to select

for the --alculatijns. This is to be expected since the maso flow is

not, in fact, an independent variable* However it has been chosen

as such for the purpose of ease of computation. The independent

variables in the unsteady state condition are: (l) Flight conditions

(velocity, density, temperature and pressure) (2) Rotor speed

(3) Fuel mass rate of flow and (4) Tail area ratio. (This contrasts

with the steady state or equilibrium condition where the rotor speed

Is a dependent variable)*

In the method outlined in this paper the fuel mass rate of flow

hat; been replaced as an independent variable by the use of a constant

turbine inlet temperature. The independent variables used then are:

(1) Flight conditions (2) Air mass rate of flow (3) Turbine inlet

temperature and (4) Rotor speed. Since the flight conditions have been

held constant throughout the series of computations made here, there

remain only three independent variables.

As a starting point in the calculation a rotor speed and turbine

inlet J, eiperature are selected. Then for each air mass flow chosen,

values of tail area ratio, acceleration, and thrust are obtained. This

makes tail area ratio, acceleration, and thrust a function of the air mass

rate of flow. Other sets of calculations may be obtained by varying the

rotor speed and the turbine inlet temperature and repeating the procedure.

The geometric configuration of the unit imposes certain natural

limitations upon the selection of the air mass rate of flow. If m is

chosen too low, the compressor operates in a stalled conditions. This

is obviously undesirable. Under certain conditions of higher mass flow

a Maeh number of unity is reached at some point in the unit and a

condition of oritioal flow exists due to sonic velocity in the turbine

nozzle throat. This occurs when the value of /1 exceeds a critical

value (In this case 0.482) and i3 clearly shown in Figure 10. Under

certain conditions of hi$i A **hen the critical flow limit is not reached,

a value of m may be chosen so high that the stayaati .n pressure in the

tail pipe is less than the atmospheric pressure. This obviously is a

physically impossible condition and occurs whon too high a value of A

is selected. The fallacy does not become apparent in the calculations

until the point of entry into the nozzle chart (Figure 20), when the

tall area ratio appears to be something "greater than infinite".

She turbine inlet temperature is controlled directly by the mass

rate of fuel flow into the combustion chamber. iJowever, since the

calculation of the turbine inlet temperature is a process involving the

combustion efficiencies and the heating value of the fuel it wtiS

not considered to be within the Bcopo of this report to carry out these

calculations. The assumption was therefore made that a sufficient amount

of fuel was consu-ned in order to provide the required T . In order to

ascertain the effects of turbine inlet temperature variation, calcula-

tions were for a T. of 2000°R which is approxi mately the maximum

allowable for continuous operation of the meetinghouse XL93 (1960°R)

and for a T4 of 200°? higher,

Sxact information regarding pressure drop across the combustion

chamber was not available until after calculations were completed.

The estimate used in these calculations (^^/p3 " O.OZ.) was subsequently

found to agree reasonable w*l.\ with data from tests made on the combustion

chamber of this unit by westinghouse. (See Figure 12).

No allowance has been made in this analysis for mass of fuel

added , air leakage between compressor and turbine, or power required

for accessories. The effects of these small quantities t end to compensate

*ach other*

Figures 1, and 2 show the effects on acceleration and thrust of

variation of rotor speed and tail area ratio at a particular turbine

inlet temperature. Jcoiparison of t lase two charts shows that temporarily

exceeding the peak continuoue allowable temperatures of the meetinghouse

XI93 produces a slight increase in acceleration at low rotor speed, but

also introduces the danger of operating within the compressor stall*

It ie interesting to note that acceleration may be obtained only

at t.<e expense of thrust. This further aggravates the problem of thrust

requirements under emergency conditions.

convergence of lines of constant tail area ratio as their ma^nltud*

increases shows that increasing tail area ratio above 2.0 produces only

light gain in acceleration.

Figures 3a and 3b show the effects of rotor speed and tail area

ratio on time required to accelerate to a particular engine speed.

Jecauae the accelerations is a function of the small difference betueen

large turbine and compressor rs, accuracy of the results is subject

to question, and should be verified by experimental data.

Pertinent extracts from a report on flight tests of a XI

conducted by the Glenn L. Hart in Jompany are s_,c are G. Since

manual control of fuel flow was used in these tests, a constant turbine

inlet temperature could not be .aintained. ^n effort isas made, i>ov¥9ver,

to follow a procedure wnich would produce maximum acceleration. No

rational estimate of turbine inlet temperatures used in the tests is

possible* However, sinoo maximum acceleration was their oal, it is

presumed that t ese temperatures were at or near the maximum allowable

(1960°R) during mo3t of the run. Tail area ratio was neld constant,

but at a value not specified* Ho?«ver, esti:oates derived from a

photograph of this installati n indicts thexail area ratio was

approximately 2.0. Acceleration times, then, would be roughly comparable

to tiiose shown in Figure 3a, for a tail area ratio of approxixetel;.' 2.C.

The agreement is close enough that quantitative values may be considered

roughly correct, and the qualitative effects may be considered reliable.

OOHOLUoIQBS

1. Acceleration characteristic*: or ?bojet may be computed by the

method presence:! in this report, provided adequate experimental data

for component parts is available.

2. Results obtained through use of this method agree closely enough with

experimental data so that quantitative values obtained may be considered

roughly correct, and qualitative effects may be considered reliable.

3. This method is not applicable for prediction of a schedule of accelera-

tion for a turbojet under actual operating conditions until extensive

calculations have been made over a complete range of turbine inlet

temperature and flight conditions,

4. Increasing tail area ratio increases acceleration but with diminishing

effect as tail area ratio gets larger. \

5. Increasing peak temperature increases acceleration at all rotor speeds.

*2h» relative increase is much greater at higher speeds.

6. Increasing peak temperature tends to induce earlier compressor stall.

7. Acceleration of a turbojet under any condition is slow when compared to

a reciprocating engine.

REFERENCES

1. "Jet Propulsion", A reference text prepared by the staff

s

of the Guggenheim Aeronautical Laboratory and the Jet

Propulsion Laboratory, GALCIT, California Institute of

Technology, for the Air Technical Service Command,

(Restricted)

2. Westinghouse Aviation Gas Turbine Report No. A-302, Oct. 1946.

3. B. Pinkel and L. R. Turner, Thermodynamic Data for the

Computation of the Performance of Exhaust Gas Turbines,

"

NAJA Advance Restricted Report 4B25.

4. Jurtiss Wright corporation, "A Simplified Method of Calculating

and Presenting Turbo-Jet Performance," Confidential Report

No. 11-46-3, Oct. 1946.

5. Glenn L. Martin Co., "Acceleration characteristics of westing-

house Model X19B Turbo-Jet Engine," Flight Report No. 37-6233,

Jan. 16, 1946.

6. Glenn L. Martin Co., "Report on the Operational characteristics

of the Westinghouse Model X19B Turbo-Jet Snglne Installed in

a JM-1 Flying Test Bed", Engineering Report No. 2468,

Oct. 15, 1946.

I

FIGURE 1

Turbojet Rotor Acceleration

vs. Tail Area Ratio at Various

Rotor SpeedsTurbine /nlet Temperature - 2000 >P

Sea Level Standard Coa/d/t/o/vs

Flight Velocity - /OOMPH

100 120 140 /60 ISO 200 220 240 2&0 2SO

Rotor Spsed - R.PS.

FIGURE 2

Turbojet Rotor Accelerationvs Rotor Speed at Various

j

Tail Area Ratios \

, . . — j

Turbihe /met 7ea/pe#atc/re 2200*^

.

Sea LEhFi Standard Coa/d/t/o<vs

ft/GUT YEioc/rr - /OOMPH

-20

-30

-40

Critical Flow

^K Limt'tthj Linz

noCompressor SfatI \

j,

Llrnehnq L/ne —z_—*\j .'

\

100

•• '

fc

—

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ROTO* SP£££>-£PS.

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FIGURE 4Tursojet- -Rotor Acceierat/on

vs. Tail /Irea Rat/o for W\r/ou5

I

! Rotor SpeedsT(JR.B/N£ /HLET T£MP£/?ATU/?E ZOOQ'fc

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n Critical How

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FIGURE 5Turbojet Rotor Acceleration

vs Ta/l Area Rat/o for Var/ous

Rotor SpeedsTurb/ne /nlet Temperature 2200°/?

Sea Level Standard Cond/t/onsFi/g#t VEioarr - 100MPH

100 ZPSISO20022525027?300Compressor Sfa//

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0.8 /.0 /.2 J.4

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FIGURE 15

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FIGURE 14

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DATE DUB

25M»y'49

20 May 5 (

6AP'5i

Thesis

S 18 Satterfield

8109

Theoretical investi-

gation of acceleration

of a turbojet engine.

thesS18

Theoretical investigation of acceleratio

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