Investigation of dynamic characteristics of a turbine-propeller engine

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RESEARCH MEMORANDUM

INVESTIGATION OF DYNAMIC CHARACTERISTICS OF A TURBINE-PROPELLER ENGINE By Frank L. Oppenheimer and /ames R. lacques Lewis Flight Propulsion Labora%ory Cleveland, Ohio CLASSIFIED DOCUMENT This document contains classified information affecting the National Defense of the United States within the meaning of the Espionage Act, USC 50:31 and 32. Its transmission or the revelation of its contents in any manner to an unauthorized person is prolflbitod by law.

Information so classified may be imparted only fe persons in the military and naval services of the United States, appropriate civilian officers and employees of the Federal Government who have a legitimate interest therein, and to United States citizens of known loyalty and discretion who of necessity must be informed thereof.

NATIONAL ADVISORY COMMITTEE

FOR AERONAUTICS

WASHINGTON September 5, 1951

NACARM ESIFI5

NATIONALADVISORY COMMITTEE FORAERONAUTICS

RESEARCH MEMORAI_UM INVESTIGATION OF DYNAMIC CHARACTERISTICS OF A TURBINE-PROPELLER ENGINE By Frank L. Oppenheimer and James R. Jacques SUMMARY Time constants that characterize engine speed response of a turbine- propeller engine over the cruising speed range for various values of constant fuel flo_ and constant blade angle were obtained both from steady-state characteristics and from transient operation.

Effects on time constant of magnitude and direction changes in blade angle over the cruising speed range were also observed. Magnitude Qf speed response to changes in fuel flow and blade angle was investi- gated over the cruising speed range and presented in the form of gain factors.

Results of the investigation indicated that at any given value of speed in the engine cruising speed range, time constants obtained both from steady-state characteristics and from transient operation agreed satisfactorily for any given constant fuel flow, whereas the time constants obtained from transient operation exceeded the time constants obtained from steady-state characteristics by approximately lA percent for any given blade angle. Over the entire cruising range of the engine, the time constants showed only a small variation with final engine speed and were independent of magnitude and direction of change in blade angle for constant fuel flow.

For values of constant fuel flow, speed-to-blade-angle gain increased linearly and rapidly with decreasing engine speed. For values of constant engine speed, this gain increased with fuel flow.

For values of constant blade angle, speed-to-fuel-flow gain increased rapidly with decreasing speed. The rate of increase of this gain with decreasing speed became greater at the lower values of speed. For values of constant speed, this gain increased with decreasing values of blade angle.

......... m1__ _ ".L_._, 2 NACA RM E51FI5 INTRODUCTION The dynamics of the engine have become of prime importance in the study of control systems for turbine-propeller engines (reference i).

This importance arises from the fact that a control must be matched to an engine for all conditions and therefore, in order to build good controls, the dynamics of the engine must be known. The time response of the engine speed to a step change in blade angle with fuel flow held constant or in fuel flow with blade angle held constant, and the magnitude of change in engine speed produced by a given cha_e in blade angle or fuel flow (ratio of change in engine speed to change in blade angle or fuel flow) represent two of th.e most important dynamic characteristics of the engine, time constant and gain factor, respectively.

The results of a previous inwestigation of a turbine-propeller engine (reference 2) show that values of the time constant can be determined from frequency response analysis of the engine.

The purpose of this investigation was to determine the time con- stants and gain factors of an engine over an extended range of oper- ating conditions in order to study the dynamics of turbine,propeller engines. In addition, a comparison is made between time constants obtained from steady-state data and time constants obtained by tran- sient operation of the system. The effects of magnitude and direction of change in the input variable on the time constant are discussed.

All turbine-propeller engine characteristics presented in this report were determined under sea-level static conditions.

ANALYSIS Time Constant from Steady-State Consideration The first method of obtaining the time constant involves the use of steady-state characteristic curves of the engine,propeller system (fig. 1). These curves show the variation of engine torque with engine rotative speed for values of constant fuel flow and for values of constant blade angle.

An analytical expression relating time constant to the steady- state characteristic curves of the engine system is desired. The first-order linear differential equation representing the dynamic response of the turbine-propeller engine (reference 2) is Jk#l_J_ J-X#_II J- S-A_kl_ _ _ NACA RM ESIFI5 t t

N(t) : _f(l - e-Y} + _i e--_

= log (_f - _i) - Log (Nf - N(t))

(3)

T

(_if - Ni)

t : T log (Nf-_(t)_

The last form of equation (3) shows that.the relation between t Nf - N i and the logarithm of the ratio Nf - N(t) is that of a straight line where T is the slope. Figure 2 shows a semilogarithmic plot of typical data, wherein (Nf - N(t)) is plotted on the logarithmic scale and time is plotted on the rectangular scale. The locus of log (Nf - N(t)) is observed to be a straight line. Thus the afore- mentioned method for obtaining the time constant is valid.

In figure 2:

tI = T(log_f - Log l)

tI represents time when Nf - N(t) = i; t 2 = T(log Nf - log u) t 2 represents time when Nf - N(t) = u; t 2 - t I = -7 log u + 7 log i = _(-log u) t 2 - t I = T when u = e -I = 0.368 Therefore the length of the projected segment on the time axis between the points Nf - N(t) = i and Nf - N(t) = 0.368 is the time con- stant 7. The term (Nf - N i) is a constant and does not affect the slope 7.

APPARATUS AND PROCEDURE Engine Installation The principal components of the engine used in this investigation are an axial-flow compressor, reverse-flow combustion chambers, and a single-stage direct-coupled turbine. A two-stage planetary gear system provided a speed reduction between the turbine and the propeller.

A 12-foot, l-inch-diameter_ four-bladed propeller was installed on the engine. The pitch-changing mechanism maintains a linear relation between the position of the input lever, or beta arm, and the blade angle, as noted in reference 2.

NACARMESIFIS __ 3

Ip II_%1 A_ - AWf

+ Ie d RI_--INP _ Ne

(1)

All symbols are defined in %he appendix.

The time constant that characterizes the response of equation (1) therefore is Ip IP+ I e R- _ + I e R 2

: _ (2)

8Qe From knownmoments of inertia and values of 8N--j from the slopes of steady-state characteristic curves_ this expression is used to obtain time constants.

Time Constant from Transient Operation The second method Of determining the time constant requires observation of the engine speed response under actual transient condi- tions of operation. A step input in fuel flow or blade angle results in a speed response that is observed by the use of a photorecording oscillograph.

Although time constants could be most readily determined from measuring the time for the speed change to reach 65.2 percent of its final value_ this method is subject to inaccuracy. Therefore 3 a semilog method developed by Harold Gold of the Lewis laboratory is used. The basis for this method is as follows: A step change in fuel flow or blade angle in an ideal first-order linear system produces an exponential change in speed with time. Such an expo- nential curve_ rising from an initial value at zero time to some final value_ is expressed in the following form:

NACARM ESIFI5

In order to vary blade angle_ a hydraulic actuator was conhected

to the beta arm. Fuel flow was varied by means of a _ydraullc

actuator attached to the engine fuel regulator valve.

Instrumentation

Steady-state measurements were taken of fuel flow, blade augle,

turbine outlet temperature, engine torque, and engine speed. These

variables also were measured during transient conditions of operation.

Transient fuel flow was indicated by the use of an aneroid-type

pressure sensor with a strain-gage element to measure total fuel pres-

sure in the main fuel line immediately upstream of the engine fuel

manifold. The strain-gage element was connected to a bridge circuit

in a strain analyzer, where the resulting signal was amplified and fed

to a photorecording oscillograph. Steady-state measurement of fuel

flow was obtained by use of a rotameter installed in the main fuel line.

Blade-angle position was measured by use of a potentiometer,

actuated by the propeller blade, that varied the flow of current in an

electric circuit in direct proportion to the blade position. For

steady-state measurements, the current was measured by a milliammeter;

during transient conditions the circuit was switched to a recording

oscillograph element. A conventional slip-ring arrangement was used

to complete the circuit between the potentiometer on the propeller hub

and the recording device.

The ring gear of the planetary reduction unit of the engine is

restrained by a self-balancing hydraulic system. Under transient

conditions of operation, the torque output of the engine was indicated

by the pressure required to act on the hydraulic piston to maintain

balance. This pressure was measured by an aneroid-type pressure sensor

with a straln-gage element. The signal was amplified and fed to an

oscillograph unit. For steady-stage torque output measurement_ the

pressure was measured by a Bourdon-type gage. Because this measurement

was made under steady-state conditiozs_ it was also an indication of

torque input. The methods of analysis applied to this investigation

did not require utilization of transient torque measurement.

Transient speed measurement was facilitated by a direct-current

generator gearedto the engine. The voltage generated was propor-

tional to engine speed. This voltage was applied to an oscillograph

element.

Engine speed had a tendency to drift slightly under steady-state

conditions, even though input variables were held constant. In order

to obtain an accurate indication of steady-state speed immediately

6 NACARME51FI5

before and after each transient run, a means of effectively increasing

the scale sensitivity of the speed indicator was incorporated in the

measuring system. A mechanical differential and a synchronous electric

motor were utilized in the measuring circuit to make possible speed

measurement from an initial value of ll,O00 rpm to a final value of

15,000 rpm, thereby expanding the cruising speed range of the engine

over the full scale range of the indicator. One input shaft of the

differential was driven by an engine tachometer pad; another was driven

by the synchronous motor. By means of proper gear ratios, operation of

the synchronous motor caused 0 rpm of the output shaft of the differ-

ential at 10,500 rpm engine speed. As the engine speed increased, the

differential output shaft imparted rotational motion to a three-phase

tachometer generator, connected to the indicator. Speeds from ll,000

to 13,000 rpm were accurately indicated.

Turbine outlet temperature was measured with one chromel-alumel

thermocouple and recorder for steady-state operation and with three

chromel-constantan thermocouples and oscillograph for transient opera-

tion. All thermocouples were located in the same vertical plane inked-

lately behind the turbine. Transient turbine outlet temperatures were

not utilized in this investigation.

A lO-cycle-per-second timing signal generated by an audio-

oscillator was recorded on the oscillograph film to show the time

variation of the recorded variables.

Steady-state values were recorded before and after each transient

run to provide calibrations for measurement of parameters under tran-

slent conditions •

Table I indicates the steady-state and transient characteristics

of the instruments used.

Procedure Steady-state runs. - In order to obtain engine time constants from steady-state characteristics, a map of engine torque against engine speed was utilized. This map (fig. l) presents engine torque against engine speed for lines of constant fuel flow and constant blade angle in the cruising speed range. The fuel flow varied from 700 to 1250 pounds per hour and the blade angle from 15 ° to 29 ° . Maximum torques in the torque-speed curves were limited by an allowable safe operating turbine outlet temperature of 1265 ° F.

Transient runs. - In order to obtain time constants and gain factors under transient conditions of operation, step changes were made in speed over the cruising speed range. Both increasing and decreasing incremental changes in speed at a given operating point were recorded

NACARM ESIFI5

on a photorecording oscillograph. The magnitude of these changes was

approximately 400 rpm. To facilitate comparison of t_me constants from

transient operation with time constants from steady-state characteris-

tics approximately the same ranges of constant fuel flow and constant

blade angle were used for both transient and steady-state operation.

The values of constant fuel flow and constant blade angle used in the

transient runs were

flow 700, 750, 820, 883_ 950_ i000, 1066, and 1126

15.00, 17.10, 18.90, 21.00_ 23.00_ 25.00, and Blade angle (deg) : 27.03 A reproduction of typical transient data recorded on the oscillo- graph is presented in figures 3(a) and 3(b).

Magnitude and direction effects. - Effects of magnitude and direc- tion of speed change on the engine time constant over the cruising engine speed range from ll,000 to 13,000 rpmwere investigated. The variations in speed to determine these effects were obtained by varying blade angle while maintaining a constant fuel flow. In order to cover the cruising engine speed range, an operating speed of approximately 12,000 rpm was chosen. Using this value of initial speed_ step changes in blade angle first were made to produce incremental changes in speed from 200 to 1000 rpmboth above and below this starting point.

Using approximately 12,000 rpm as the final value_ step changes in blade angle then were made to produce incremental changes in speed of 200 to 1000 rpm from initial speeds above and below this approximate final speed point. Time constants were obtained for all of the incre- mental speed changes.

RESULTS AND DISCUSSION Experimentally Determined Time Constant from Steady-State Characteristics of Engine Values of time constant from steady-state characteristics for various_values of constant fuel flow and constant blade angle are presented in figure 4. All values of time constant are corrected to NACA standard sea-level temperature and pressure.

Experimentally Determined Time Constant from Transient Operation of Engine The faired curves in figure 5 show time constant variation with speed for various values of constant fuel flow and constant blade angle from transient operation.

NACA RMESIF15

÷ Comparison of Time Constants A comparison of figures 5(a) and 5(b) indicates that the average value of time constant for constant blade angle exceeds the average value of time constant for constant fuel flow by approximately 13 per- cent for all values of speed in the engine cruising speed range.

Although this correlation is satisfactory for controls work, it indi- cates a lag in the fuel system as compared to blade angle response.

A comparison of figures 4(a) and 5(a) indicates that the average values of time constant for constant fuel flow from steady-state char- acteristics agree satisfactorily with average values of time constant from transient operation for all values of speed in the engine cruising speed range. Figure 6(a) presents the variation with speed of the time constant from steady-state characteristics and time con- stant from transient data at the minimum and maximum values of fuel flow.

A comparison of figures 4(b) and 5(b) indicates that for any given value of constant blade angle the time constants from transient data exceed the time constants from steady-state characteristics by approxi- mately 14 percent for all values of engine speed in the cruising speed range. Figure 6(b) presents variation with speed of time constants from steady-state characteristics and time constants from transient data at the minimum and maximum values of blade angle.

Time Constant Variation with Changes in Magnitude or Direction of Speed Increments Figure 7 presents the effect on time constant from transient oper- ation of covering the speed range in increasing and decreasing incre- ments of from 200 to 1000 rpm and for a fuel flow of 950 pounds per hour. The time constants resulting from these incremental changes are presented as a function of the final engine speed and are shown by data points. The behavior of average time constants as a function of final speed for incremental changes of 400 rpm over the cruising speed range is indicated by the line for comparison of time constant at final speed for varied incremental speed changes. The results indicate that increasing or decreasing changes in speed up to and including a magnitude of 1000 rpm can be made with no appreciable variation in the value of the time constant within the experimental error. Furthermore_ the variation of time constant versus final engine speed is of such

NACARMESIF15 9

small magnitude as to indicate that incremental changes in speed larger

than 1000 rpm can be made with no appreciable variation in the value of

the time constant.

Experimentally Determined Gain Factors from Transient Operation

of Engine

In order to measure the speed-to-blade-angle-gain factor and the

speed-to-fuel-flow-gain factor, the initial and final values of speed

for known changes in blade angle or fuel flow were utilized. Figures 8

and 9 present speed-to-blade-angle-gain factor and speed-to-fuel-flow-

gain factor_ respectively, versus speed for the incremental changes in

speed used to investigate time constants.

Figure 8 indicates that the speed-to-blade-angle-gain factor varies

linearly with engine speed and the rate of change in gain factor with

speed is approximately the same for all values of constant fuel flow.

The gain factor increases very rapdil_ both with a decrease in engine

speed for a given constant fuel flow and with increasing values of con-

stant fuel flow at a given engine speed. This condition indicates that

decidedly large values of gain factor exist at the lower portion of the

cruising speed range for high values of fuel flow.

Figure 9 indicates that for values of constant blade angle the

speed-to-fuel-flow-gain factor increases as the engine speed decreases.

This increase is not linear as the gain factor increases more rapidly

for a given blade angle with changes in speed as the engine speed is

decreased. For a given value of engine speed the gain factor increases

as the value of constant blade angle _ecreases. The combination of low

speeds and small blade angle gives maximumgain factors.

SUMMARY OF RESULTS The following results apply to time constant and gain factor behavior of a turbine-propeller engine in sea-level static operation: i. For all values of speed in the engine cruising speed range_ average values of time constant for constant fuel flow obtained from both steady-state characteristics and from transient operation agreed satisfactorily_ whereas the time constants obtained from transient operation exceeded the time constants obtained from steady-state char- acteristics by approximately 14 percent for any given blade angle.

2. Over the entire cruising range of the engine, the time constants showed only a small variation with final engine speed and were independent of magnitude and direction of change in blade angle for constant fuel flow.

i0 NACARMESIFIS

Z. For values of constant fuel flow_ speed-to-blade-angle gain

increased linearly and rapidly with decreasing engine speed. For values

of constant engine speed_ this gain increased with fuel flow. Conse-

quently high speed-to-blade-angle gain existed at a combination of low

speed and high fuel flow.

4. For values of constant blade angle_ speed-to-fuel-flow gain

increased rapidly with decreasing speed. The rate of increase of this

gain with decreasing speed became greater at the lower values of speed.

For values of constant speed, this gain increased with decreasing values

of blade angle. Consequently_ high speed-to-fuel-flow gain existed at

a combination of low speed and low blade angle.

Lewis Flight Propulsion Laboratory,

National Advisory Committee for Aeronautics_

Cleveland, Ohio.

NACAI_MESLFI$ ii

APPENDIX - SYMBOI_

polar moment of ine_iaof engine, (lb)(ft)(seo)(rad)(min)/

I e revolution polar moment of inertia of propeller, (Ib)(ft)(sec)(rad)(min)/ Ip revolution engine speed_ rpm N e final engine speed, rpm initial speed of engine at time 0_ rpm Ni propeller speed; rpm

N(t)

speed of engine at time t, rpm torque input to engine_ ib-ft Qe torque output of propeller, ib-ft

%

R gear ratio of engine speed to propeller speed t time_ sec time when t is tl, sec t I time when t is t2_ sec t 2 u value of

_f - N(t) when t is t2

fuel flow, ib/hr

wf

propeller blade angle_ deg A incremental change ambient static pressure NACA standard sea level pressure ambient static temperature NACA standard sea level temperature T system time constant_ sec

12 NACARME51FI5

REFERENCES l, Lazar, James_ and De Rocher, Wilfred L., Jr.: Correlation of Analog Solutions with Experimental Sea-Level Transient Data for Controlled Turbine-Propeller Engine, Including Analog Results at Altitudes. NACA RMESIB08, 1951.

B Taylor, Burt L.; III, and 0ppenheimer, Frank L.: Investigation of Frequency-Response Characteristics of Engine Speed for a Typical Turbine-Propeller Engine. NACA TN 218_, 1950.

TABLEI. - STEADY-STATE ANDTRANSIENT CHARACTERISTICS OF INSTRUMENTS

Transient instrumentation

Steady-state

Measured quantity

instrumentation S ens or

Frequency O] response range H (cycles/see) O] 0 - 40

Fuel flow Rotameter

Aneroid-type pressure sensor with strain-

(static pressure)

gage element connected to give indication on oscillograph 0 - _0 Wire-wound potentiometer

Blade angle Wire-wound potentiometer

connected to give posi- connect to give position

tion indication on indication on

microammeter oscillograph

0 - 1 Three chromel-const antan

Turbine-out let One chromel-alumel

!

thermocouples in series

temperature thermocouple connected

to recorder

connected to give indi- cation on oscillograph 0 - AO

Bourdon-type gage Aneroid-type pressure

Torque

sensor with strain-gage element connected to give indication on oscillograph Limited by Direct-current generator

Three-phase tachometer Engine speed

filter connected to give indi-

generator, mechanical

circiut

differential and

cation on oscillograph 0 - 2.65

synchronous motor to

eliminate sensing of

C_

speeds below desired

range

Bladeangle

(deg)

560 Correctedfuel flow / 29

wf/_/_ (ib/hr ) / / 480 /Z _ "-'_/_.____ _:_/ 27 400 ....._.....___ __-_= j__ ,

_o _____+_ __ _o____ _

_------" "_ "---"- _ 19

_o __----- ___ _ __ _ __

8O 0 II,000 11,500 12,000 12,500 15,000 (J1 Corrected engine speed, Ne/_/_ , rpm Figure I. - Steady-state torque-speed characteristics of turblne-propeller engine.

NAOAI_ESIFI5 15 _0

\

U .3 .2 Time constant = t2-t I t I t2 .i 0 2 _ 6 8 i0 Time, t, sec Figure 2. - Semilogarithmic variation of FN÷-N(t)] with time.

16 I_ACA RM ESIFI5

_Blade angle, _, deg

Uf ....... inthis nvestl

\/ _( ranslent mtasurement (a) Step input in blade angle at constant fuel flow.

tue notre

nnve I

r 4 y1_ec Time--

.... _ """ 1! _1_!1_ ' i ................................................. ' ....................................

_ J_H 'H' , , • in fuel flow at constant blade angle. _C_ (b) Step input Figure 5. - Typical recording of transient data from turbine-propeller engine.

Z ^'m_nr-_l._--' NACARMESIFI5 17 O h ill O tO 4._ .r-I I N

i

kl

o_

gl

III

,'11 .I

N O co l.O ,d

o

@ h k'/, g r_

II I_

4 _ I

I

Iit I/I

tO 4_ O

I

Ill I//i

,:11 IN/

O

" #111 I/I III

._ '_ Io oo_o: -I_ cH r.-I i"'-, ¢0 _ O"J / o li.7 oo I r-t tO aas ¢_ A c_-suoa e_ pa_0e.n_oo I p4 CO Corrected fuel flow wfls-_ 5_ (ibl_) 700 _ 750 __-_.. _ a83 _7__ -----_ 9so :]-'_ _ _ -.------ -----" zo-'_- (a) Constant fuel flow.

J 4_ o Blade angle (deg) ls'°°l 17.1o +_ u 5-- 18.90[ r-._ _'_ _ k o 25. OQZ _ _

g

t ; ll, 000 ii, 500 12,000 12,500 15,000 Corrected engine speed, Ne/%/e , rpm (b) Constant blade angle.

Data Figure 5. - Variation of time constant with engine speed for turbine-propeller engine from transient operation.

£n points shown are averaged values.

Corrected fuel flow wf/8._ _° Transient operation ..... (zb/_ Steady-state performance-- • _--'_d 700 "-700 Corrected fuel flow wf/_ (lb/_) .... ('i126 o 4_ (a) Upper and lower constant fuel flow limits.

o 4_ Blade angle +_ 15.00 z7.03 I 27._&

I

I I ll,O00 12,000 12,500 15,000 Ii, 5 O0 Corrected engine speed, Ne/%/e, rpm (b) Upper and lower constant blade angle limits.

Figure 6. - Variation of time constants from steady-state characteristics and from transient operation with engine speed for turbine- _0 propeller engine. Data points shown are averaged values.

20 NACA RM E51_15

i

\\ t-

,_ " o

_o [] ,\ _ c'%,"

o_ \ \ \ _Corrected fuel flow

ib/hr )

\ "-_ \ _ \ -\ ,,,.j_o-_

_1 _ i lo66

o l_O _. \ .%

\. \ _ "_

_l_o _ k.. "_ _oo

" Z _, _" : 950 150 _ _ "_z _, _ "_ ' i I

4o0 " _" i

90 750 ii, 000 ii, 500 12,000 12,500 13,000 13,500 Corrected engine speed, Ne/_/-_, rpm Figure 8. - Variation of speed-to-blade-angle-gain factor with engine speed for turbine-propeller engine from transient operation at constant fuel flow.

00£ " Tg-g-6 - _eI_ue'I-yOV._ Corrected speed-to-fuel-flow-gain factor, _i-6, rom Zg,/f lb/hr _" I--' !

I CO I r i-1

/

?

i /

i J. / /

_0

///

_P 0

/

/

O_ Q

y//

o /

o 1

"1 I

/

el

g _ I il]:

..... / =_/_ / o

°I> 1

/° "" I "["

4, 0_,0 N o o° o o _D o o_ b Ol o (0 g ,g g O