d

_

'"

_/

:_'_

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,-7{ "i

_';""_"'-7 ;, 77:7> _,. /

i

I

-Ii

Declasslficd

by _ut._or!ty

df NA_A-,,._

i

iI

.!

!ii i :7d ['i

0 (lb/in resulting of the on the cancel AePa. velocity pressure onto the term the

pressure chamber part walls Howof the gases exit have cre-

on the on the pressure

outside gas forces

at an ambient Then,

pressure the net

Pa = 0 (high-altitude force acting on the

inside.

condition).

gas in the chamber is the sum of the reactions from the chamber walls and of the reaction of the absolute reaction ing the to the gas gas forces pressure are at the opposed theorem, to the exit. (fig. the These 1-1). net two Accordforce flux on out

thrust with A e, the to it.

by an amount supersonic pressure force (opposing this thrust ambient ambient The area

Since in the not Pa thus

Pa does

a net

unbalanced

projected of mag-

momentum be equal

chamber Aep a. the

thrust)

must chamber:

momentum

of the

Including rocket

in equation is ob-

general

equation

AtC

Ptc

dA-

AePe

--_-V

e

F =/2: Ve. g

Ae(Pe

- Pc)

(1-6)

Tile acts hicle.

integral on the

describes that force F (Ib) which thrust chamber and thus on the vewrite:

The standing pose movable ber and pressure),

following of the equation cylinder vehicle a piston

model nature (1-6). ,nass),

may of the

extend terms the

the which thrust gas

undercoma gas mass), concham-

We can

Let

us assume

we have

F-AePeor

=_Ve

(1-4)

(representing a spring (representing rack (representing

(representing the

F = W---ve+ AePe g

(1-5)

and

a stationary (fig. 1-2).

ambient

ditions)

INTRODUCTIONTO LIQUID PROPELLANT ROCKET ENGINES

MOVEABLE THRUST

CYLINCER CHAMBER

(REPRESENTING AND VEHICLE)

(g/_/) indicatesthatoptimum ve has not been obtained. Sample Calculation (I-1)

MASS)

-l_:,Ig _YI'iY'_LI -T. _U-The following data are given for a liquid propellant rocket engine: thrust, F : 100 000 lb at sea level; propellant consumption rate, g/= 369.3 Ib/sec; thrust chamber exit area, A e = 760.8 in 2" gas exit static pressure, Pe : 10.7 psia; ambient pressure, Pa : 14.7 psia (sea level); gravitational constant, g: 32.2 ft/sec _. From what we have just learned, we will determine (a_) gas exhaust velocity, (_b_) ngine e thrust in space, and (c__) he effective t exhaust velocities at sea level and in space. Solution (a) From equation velocity (1-6) the gas exhaust

(REPRESENTING GAS PRESSURE)

'_- STATIONA RY RACK (REPRESENTING AMBIENT CONBITION$)

Figure

I-2

The spring is so made that its end slips sideways upon reaching the end of the cylinder and engages the stationary rack. The cylinder is suspended in a suitable manner to move freely. When releasing the spring force ("Pc"), the "gas" is expelled to the rear. If, upon reaching the chamber exit, some spring force remains, the spring engages the rack and continues to act upon the cylinder, but ceases to act upon the "gas." We find that the model works for all cases: underexpanded (as assumed above, where spring free length is longer than cylinder length); overexpanded (spring free length is less than cylinder length and the spring force is exhausted prior to the "gas" reaching the exit, the "gas" therefore being subject to deceleration within the cylinder); and ideal expansion (where spring free length equals cylinder length). The model can also illustrate the case of the overexpanded nozzle without jet separation, which will be further explained below. This situation is equivalent to that of the inertia of piston ("gas") and spring pulling the spring beyond its null point. The negative-loaded spring, in engaging the rack ("ambient"), will pull the cylinder backward. Equation (1-6) is often expressed as

ve : IF - Ae(P e - pa)](g/g/) = [100 000: 9040 ft/sec Our calculation assumes a nozzle somewhat too 760.8(10.714.7)](32.2/369.3)

long for sea-level the fact that Pe is "undershoot" and shoot" occurred. i.e., if the nozzle

conditions, as indicated by smaller than Pa; a pressure an exhaust velocity "overIf no jet separation occurred, remained _filled" to the exit

F:c--

g

(1-7)

plane, the calculation is valid. The "penalty" of incorrect nozzle length simply appears as the negative thrust term Ae(Pe-Pa). If jet separation does occur within the nozzle, or if it is combined with decelerating shock waves, the situation becomes considerably more complicated and requires elaborate mathematical treatment. However, there should be no concern at this point. From equation (1-6), we know that the difference in thrust between space and sea level is AeP a. Since the nozzle selected was too long at sea level, this thrust increase AeP a during rocket ascent will be obtained in two distinct steps. First, by reduction of the negative thrust term Ae(Pe-Pa) to zero. This will occur when Pe = Pa; that is, when the rising vehicle reaches an altitude where Pa = 10.7 psia, in our specific case. As we have learned, this represents ideal expansion. As the vehicle continues to ascend farther

Where c is defined velocity (ft/sec)

as the effective

exhaust

and comprises (1-8)

c= v e + Ae(Pe - Pa) (g./W)

The effective exhaust velocity is not the actual gas velocity except when Pe : Pa where becomes equal to Ve. As explained with equation (1-6), the presence of a term Ae(Pe- Pa)

c

DESIGN OF LIQUID PROPELLANT

ROCKET ENGINES

and eventually reaches Pa---0, the increase of Ae(Pe- Pa) raises the combined effect of the simply the elimination nozzle is filled at all Thus, we obtain

"empty space" where the positive term thrust level farther. The two phases, however, is of paAe, provided the times. thrust in space:

(4) (5) (6) (7)

engine

ible, it is additionally called an isentropic process. No friction Steady flow rate One-dimensional flow (all gas molecules move on parallel lines) Velocity uniformity across any section normal to chamber axis

F= 100000+760.8 (c) From equation velocity at sea level

14.7= 111 183.8 lb (1-8) the effective results exhaust

(8) Chemical equilibrium established within the combustion chamber and not shifting in the nozzle. Certain correction factors, usually empirically obtained, will be applied to the results derived from these ideal assumptions in the actual design of a rocket and for the prediction of its behavior.

c = v e + Ae(Pe - pa)(g/W) =9040-_760.8(10._= 8772, ft/sec and in space c= v e + AePe(g/_l) = 9040 + 760.8 10.7 (32.2,/369.3) = 9750 ft/sec 14.,)_ X

(32.2,' 369.3)

1.2

THE GAS-FLOW PROCESSES IN THE COMBUSTION CHAMBER AND THE NOZZLE

Since the analytical treatment of compressible fluids flowing through cylindrical ducts and nozzles can be found in standard aerodynamics and thermodynamics textbooks, no attempt will be mad'_ here to derive basic equations governing gas flows. Rather, significant applications of those equations used in actual rocket design are presented. The parameters and terms applicable to gas flows in a liquid propellant rocket thrust chamber are shown in figure I-3 and table 1-1. These parameters serve to define the characteristics of gas flow at various points within the thrust chamber. Gas-flow calculations for rocket thrustchamber design ideal conditions: usually assume the following

The Perfect

Gas Law X the peifect 144pxVx = RTx gas law states: (1-9)

At any section

(1) Homogeneous gas composition (2) Perfect gas (3) No heat transfer through the motor walls in either direction; i.e., adiabatic processes. If no increase in entropy occurs, i.e., if the process is considered revers-

The Principle

of Conservation

of Energy

In an adiabatic process, the increase in kinetic energy of the flowing gases between any two points is equal to the decrease in enthalpy.

ix _

/

INTRODUCTION

TO

LIQUID

PROPELLANT

ROCKET

ENGINES

TABLE

l-l.-Terms

Used in the Gas Flows

Calculation

el

The PrincipleV :

of ConservationAIvi 144 Vi Axvx = 144 Vx

of Matter

aC,

a

Local velocity of sound in chamber and at nozzle throat (ft/sec);

=constant

(1-11)

(at =v gy-F/_).mc

Cylindrical Ae, Ax

cross-sectional inlet,

area throat

of and to

The Isentropic Flow Process For any isentropic flow process the following relations hold between any two points:piViY:

Aj, At,

chamber (in2). Flow areas at nozzle exit; axis and at any (in2).

section

X normal

Cp, Cv g J

Specific heats for constant and for constant volume Gravitational sea level). Energy Btu). constant factor

pressure (Btu/lb F). ft/sec ft-lb/ -_ at

PxVxY= constant

(1-12)

(32.2 (778

and TI/Tx:(pI/px)(Y-9"Y=(Vx/VI)Y -1 (1-13)

conversion

Mc, M i, M_, M e , Mx

Flow Mach number (v/a) at chamber; nozzle inlet, throat and exit; and at any section X normal to axis. Molecular products. weight of combustion end

Gas Flow Through Liquid PropellantRocket Combustion Chambers The functionof a liquidrocket combustion chamber is to convertpropellantsintohightemperature, high-pressure gas through combustionwhich releases the chemical energy of the propellant, resulting an increase of internal in energy of the gas. Combustion chambers are generallytubular,as shown in figure1-3. The liquidpropellants are injectedat the injection plane with a small axial velocitywhich is assumed to be zero in gas-flow calculation.The combustion process proceeds throughoutthe lengthof the chamber and is assumed to be completed at the nozzle inlet.As heat is liberated between injection plane and nozzle inlet, the specificvolume of the gas is increased. To satisfythe conditionsof constantmass flow, the gas must be accelerated toward the nozzle inlet with some drop of pressure. In brief, the following takes place: The gas-flow process within the combustion chamber, that is, within the volume upstream of the nozzle entrance, is not entirely isentropic but is a partly irreversible, adiabatic expansion. Although the stagnation temperature or total temperature remains constant, the stagnation pressure or total pressure will decrease. This causes permanent energy losses, which are a function of the gas properties as expressed by y, and of the nozzle contraction area ratio ec or (Ac/At). Wherever the acceleration of gases is largely effected by expansion due to heat release, rather than by a change of area as in a nozzle, the stated losses occur. The greater the

(Pc)tnj

Chamber (lb/in2).

total pressure at injector Because of the relatively injection flow

low propellant

veloc-

ities vtaj, the measurable static pressure at this station is generally treated as pressure. (Pc)ns equivalent to the total

Nozzle stagnation pressure or chamber total pressure at nozzle inlet (lb/in2 ); (Pc)ha = pi[l + _ (yI)Mi] Y/y'. Flow static throat and pressures at nozzle inlet, exit; and at any section X

Pi, Pt, Pc, Px

R (Tc)ns

normal to axis (lb/in2). Gas constant (1544Dli)(ft/R) Nozzle stagnation :emperature or chamber total temperature (R). (Te)ns = Ti[1 + 'z(y- 1)Mi] Flow temperature at nozzle inlet, throat, and exit; and at any section normal to axis (OR). Injector flow velocity =0 (by assumption). Flow velocities at nozzle inlet, throat, and exit; and at any section X normal to axis (ft/sec).

Ti, T, Te, Tx

Vin/

Vi,

Vt,

re,

V x

V_, Vt, Ve, Vx

Flow specific volumes at nozzle inlet. throat, exit; and at any section X normal to axis (fta/lb). Steady weight flow rate (lb/sec). area ratio (Ae/At). area ratio (Ac/At). Nozzle Nozzle Specific expansion contraction heat

E (c

Y

ratio (Cp/Cv).

Applied to a nozzle, of gas flowing1 2

this

yields

for unit weight

_-2(Vx

- vi:): Cp(Ti - Tx)

(i-10)

DESIGN OF LIQUID PROPELLANT

ROCKET ENGINES

contribution the zle gas

of the acceleration. the

nozzle,

the

more

efficient with

is

of the the at the as the through

converging-diverging area then 1-3. increases then it and increases throat and

De Laval decreasing increasing The flow to sonic further that the the total

type, exit

with area, at

Conversely, losses It will the are thrust

no nozThe design further great bein

cross-sectional

to a minimum to the velocity velocity supersongas flow expantemperature throughout becritical of spethe

attached, apparent. IV.

maximum. chamber

importance comes chapter Figure

of ec to the

shown throat

in figure a nozzle and

be discussed loss of total

1-4 shows

pressure are

ically through sion and the tween pressure cific

in the

diverging nozzle that

section. is an isentropic both remain ratio

for two typical y values nozzle contraction area generally lated from used the in rocket Rayleigh

as a function of the ratio ec. These data design, flow and are calcu-

In practice a rocket process, the total throat ratio ratio heat

is assumed

process.

pressure The and and

constant Pt/(Pc)ns

nozzle.

pressure chamber is solely

is called

a function

09 1.0

08 o.

Pt/(Pc)ns

= [2/(y+

1)] y/(F-0

(1-16)

, i.o( CYLINDER )

l

l 2.0 Figure

I

L 30 1-4

L

3 40 Ao/At

The sonic unit The

static flow, area velocity

pressure where occurs, the is

Pt at a nozzle maximum defined as wave is equal

throat

with flow per of pressure.

weight critical to the within

of sound of a pressure

velocity a medium. disto in-

propagation Neglecting end, i.e., the flow velocity at the (Pc)inj injecting = Pinj, the

assuming

Vin j = 0 and (Pc)inj/(Pc)ns of flow Mach of the

It is, therefore, impossible for a pressure turbance downstream of the nozzle throat fluence throat, create pressure. It is attached the flow at the that throat throat pressure or upstream will the than

total pressure ratio expressed in terms the nozzle inlet and

can also be number Mi at heat ratio y:

of the not critical of an however, is mainpresthe presAs must

provided a higher one

this

disturbance

specific

(Pc)inj/(Pc)ns

= that

of the

characteristic or De Laval in the back exit throat nozzle pressure is greater

features nozzle, thrcat (ambient than (recovery) and the velocity.

diverging velocity if the nozzle at the even at the

(1 + yMi_)/(1

+_'_Mi2)

)''(y-I)

(1-14)

sonic

tained sure) For that small. the the reasons Mach mentioned number value ratio the at the above, nozzle it is desirable be with sure entrance chamber 2 is Mi= ratio, the

required

for sonic

a result, take exit take tropic), ties place

a pressure between through way

adjustment the throat This

A typical area For

for a thrust of Ac/At= static to pressure

nozzle may (isen-

a contraction 0.31(),: expression 1.2).

(ambient place or by

pressure). subsonic

adjustment deceleration

simplifies

of nonisentropic waves, represents that may occur nozzle situations

discontinuiof pos-

called Figure

shock 1-5a

or by a combination several shown which of the in a overexrepresent was

Pinj/Pi

= 1 + y Mi 2

(1-15)

both. sible panded

conditions nozzle. earlier. that

The

Gas

Flow The

Tl_ough

Rocket

Nozzles nozzle of the and gases are thus is to combushigh gas

cases

of an overexpanded

prime

function the kinetic The

of a rocket enthalpy energy nozzle

mentioned We see be obtained ambient the with

convert tion cient

efficiently into velocity. device Rocket

pressures cannot since

lower advance the

tba_

ambient The

may within

gases

in a supersonic

nozzle.

higher

exhaust velocities.

is the

most

effi-

pressure

upstream gases are

for accelerating nozzles

to supersonic

nozzle,

however,

flowing is along

conventionally

supersonic

velocity.

An exception

INTRODUCTION

TO LIQUID

PROPELLANT

ROCKET ENGINES

OrEXF&NS_ON Pe ' Pa JET SEPaRaTION

F

,

*'-

lit

,>%

iPe = ,-; E

._ = r.,.. O

3

,_r,,

,-..1

,..4

... r._ o 3 0,3

o_

o

c_o

I

f,-.1

==r. r,,, r,,,

=_...'Er.=.. _ r,,.

._"-.O_ r,..

._""_

..O

r,.

o"

o_ zco

"=

_

z

_

_

z

e._ o

-

_

_-_

_

-,

0=O

_._.

_=

_;_

_;

._

_

24

DESIGN

OF

LIQUID

PROPELLANT

ROCKET

ENGINES

-_=_=

:E

_.

_

_'_

_

=_r

E_

.-_

5

_

_

..4

;=

,-_ .-

I

r.

.4

E_ _ _ ....

r_

_

_

c_

o

c7

.oO.

-_

_

.=

o =

INTRODUCTION

TO

LIQUID

PROPELLANT

ROCKET

ENGINES

25

TABLE

1-6.-Perlormance

of

Some

Liquid

Rocket

Monopropellants

Specific Propellant impulse lb-sec/lb (H=O2) (95%) . 140 Is, a

Density impulse Id, sec gm/cc 198 Applications Remarks

Hydrogen

peroxide

Gas generators for turbopump and auxiliary drive; small control rockets Gas generators: rockets small control

Difficult

handling

Hydrazine

(N2H ,) ..............

205

207

Difficult compose ature)

handling at high

(can

de-

temper-

Nitromethane

(CH3NO

=) .........

180

204.8

Small

ordnance

rockets

Dangerous detonate

handling unexpectedly)

(can

Methylacetylene

...............

160

108.6

Gas

generators;

small

rockets

Safe handling; very smoky or frozen

dangerous and exhaust fumes equilibrium.

a Theoretical

value

at 300

psia

(Pc)ns,

sea-level

optimum

expansion,

frozen

gas

composition

TABLE 1-7.-Theoretical

Performance

of Some Medium-Energy Combinationsrw 2.99 3.24 rv 1.51 1.63 95 ,99 1.26 1.39 1,70 1.82 2A8 2.65 2.08 2.23 2.16 1.47 138 1,61 2,53 2.64 1.54 1,57 212 2,20 2.83 2.95 4.18 d 1.26 1.27 1.28 1.29 1.27 1 29 1.31 1.32 1.35 136 Tc !5340 !5315 5090 5100 5250 5220 5295 5270 5355 5330

Storable

Liquid

Rocket

Bipropellant

Oxidizer

Fuel UDMH ....................

}_ 23.7 24.2 20.8 211 22.4 23.0 24,1 24.5 25.8 262 25.1 25.5 246 .... .... .... 217 21,3 19.5 19.5 20.5 20,6 21,3 21.4 22,1 22.2 218 21.9

c* 5490 5435 5690 5665 5580 5510 5425 5375 5275 5225 5335 5280 5320

Ct 1619 1630 1.602 1.608 1.610 1.618 1.620 1.630 II.636 !1.646i

Is ilsd 276 275 283 283 279 277 273 272 268 267 270 269 269 259 279 271 348 350 362 365 354 358 358 359 ]362 363 356 358 358 326 357 328

Applications Small air-to-air, air-to-surface rockets and upper stages of space vehicles

IRFNA

(15%

NO 2) .

Hydrazine

................

1.47 1.54

50% UDMH-50%

hydrazine...

2.20 242

Hydyne

...................

3.11 3.33

RP-1

......................

4.80 5.14 4,09 4.37 4.13 2,89 2.47 4.01 4.54 4.74 2.17 2,20

TMB-1,

3-D ...............

1.32!5325 1.33 5300 1.33,5310 1.26!4935 1.28 1.21 1.24 1.25 1.26 1.26 1.25 1,26 1.27 1.28 1.30 1.31 1.28 1.29 5290 5285 4800 4780 4675 4675 4760 4740 4765 4745 4785 4765 4770 4745

1.632 1.640 1628

JP-X 92.5%

(60%

JP-4,

40% UDMH)

E.A ................

5130_1.626 5550:1.618 5375 5530 5505 5655 5655 1625 ;1.620 !1.620 11.604 1.604

MMH ..................... TMA ..................... UDMH ....................

95% hydrogen peroxide

278 277 282 282 279 279 276 275

345 346 355 '355 349 351 350 352

Manned small

aircraft, air-to-air.

Hydrazine

................

50%

UDMH-50%

Hydrazine

..

3.35 3,47

5580:1.610 5560 5485 5465 5405 5390 1.615 1.'622 '1.619 1.627 1.620

air-to-surface rockets, and upper stages of space vehicles

Hydyne

...................

4,68 4.87

IRP-1 ..................... TMB-1, 3-D ...............

7,35 7.58

273:355 271 274 272 355 351 351

432 J 6,20q3.49 6,45/3.63 i

544011622 5415 1.618

26

DESIGN

OF LIQUID

PROPELLANT

ROCKET

ENGINES

TABLE

1-7.-Theoretical

Performance

of

Some

Medium-Energy (Continued)

Storable

Liquid

Rocket

Bipropellant

Combinations

Oxidizer Nitrogen tetroxide.

Fuel UDMH ................... Hydyne ..................

I

rye

IV

, T.l,lc.lc,1.20 1.22 1.24 1.25 1.27 1 23 1.24 1.19 1.38 1 40 1.43 144 1 41 168 1.40 5685 5650 5655 5745 24.5 124.1 !24,7 25.7 55551632 55801 5525 544011 1631 636 5755265 5715 25.2 5710 5290 6305 6330 6220 6250 5890 5735 6035 25.9 .... 258 26.2 26.1 265 29.1 370 27.6 538511639 5495 1631 5425 5260 5630 5605 5555 5535 5140 4535 5330 1.645 1.635 1.602 1.589 1,599 1.595 1.618 1636 1608

1 Is 282

, I sfl 339 344 347 345 _348 342 344

Applications Manned ICBM, aircraft, IRBM,

I 2.95 I 2.71 295 4.04 4.50 J 3.55 i 3.90 J 2.59 ! 303 328 298 320

1.61 ] 1.61I

626 ! 282 280 276 274 278 277

' RP-1 T_IB-I,

.................... 3-D ..........

1.75 2.26 2.51 196 2.15 1.45 131 1.42 1 40 150 1 42 566 1.39 1.57 1.37

ALBM. smallairto air, surfaceto-air rockets, upper space stages vehicles of

267 rr 318 280 277 386 ICBM, IRBM and small

% E.A .......... Chlorine trifluoride t UDMH .................... I Hydyne ...................

388 I ALBM.

274 276 258 230 266 261

395

RP-1

..................

320 12.80 3 17 3.60 3.35

rockets, upper stages of space 395iL air-launched 364 vehicles 386 373 374 453 Small air-launchec rockets

TMB-I,

3-D ..............

Bromine pentafluoride

Hydrazine

..............

1 43 186

6040 5570

28,1 ....

5280 5000

i1 592 1 565

_ 243

TABLE

1-8.-Theoretical

Performance

o[

Some

High-Energy

Storable

Liquid

Rocket

Bipropellant

Combinations

Oxidizer 95% Hydrogen peroxide Hydrazinel

Fuel ............. ............

rw 201 270 _2.61 1.34 1.42 2.00 2.15 2.16 2.77 2.94 2.89 311 3.00

rv 1.41 1 188 1.42 .93 .99 1.24 1 33 1 31 1.53 1.62 1.42 1.53 1.44 85A

Tc] 1 26 1 037 4775 5390 5685 5390 5415 5590 5570 5635 6550

_ 19.5 19 01 236 20.9 213 22.6 23 0 I ..... [232

C! c* I1 601 11600

Is285

Isd

Applications]CBM, IRBM.

359

Pemaborane Nitrogen tetroxide . . UDMH Hydrazine

6067 5735 15650 5845 5815 5725 5665 5720 5995 590 5795 5770 5763 6402

302 i

313

ALBM

................ ............. Hydra_ine

1.18 1.22 1 23 1.21 1.21 1 20 1.51 1.52 1.45 1.46 1,44 .796

1.624 1 610 1605 1.620 1 636 1.621 1 582 1 572 1 596 1.598 1,591 1644

285 292 290

336 357 357

!FBM, IRBM, upper

ICBM. ALBM. stages

50% UDMH-50% MMH ................. 2hlorine trifluoride ...

288 348 288 348 288:346 t294,444 292:444 287 416 286 285 327 417 410 261

of space vehicles

Hydrazine

.............. Hydrazine

FBM, IRBM, upper

ICBM, ALBM stages

6600'236 6385 24.5 6420124.9 6400 .... 4430 147

50% UDMH-50% MMH ................... Pentaborane

of space vehicles ICBMIRBM

Hydrazine

...........

............

1.4

INTRODUCTION

TO

LIQUID

PROPELLANT

ROCKET

ENGINES

27

TABLE

1-9.-Theoretical

Performance

of

Some

High-Energy

Cryogenic

Liquid

Rocket

Bipropellant

Combinations

Oxidizer RP-1

Fuel .....................

rw 2.00 2.40 2.56 2.73

rv 1.421 1.708 1.82 1.94 .78 .84 1.23 1.28 .80

d 0.998 1.012 1.02 1.03 .88 .89 .99 1.00 1.07 1.02 1.03 1.02 102 .98 .99 1.01 1,01

Tc 5760 6100 6150 6200 5055 5100 5640 5675 5660 5980 5905 5990 6030 6010 6065 6100 6120

_ 211 22.8 23.3 239 19.3 198 24.1 24.4 19,3 20.6 20.9 21.81 22.2 21.3 22.1 22.9 23.2

c* 5898 5953 5920 5865 5920 5865 5605 5585 6235 6160 6155 6035 6010 6115 6040 5945 5915

Ct 1,605 1.620 1.632 1.642 1.608 1.612 1.648 1.644 1618 11,628 '1.622 1,632 1.639 1631 :1.638 11.642 1.650

Is 294

Isd 293

Applications ICBM, [RBM, large and

Liquid

oxygen..

300:303 300306 299 308 296 294 287 285 313 312 310 306 306 310 307 303 303 260 261 2S4 285 335 318 319 312 312 30,t 304 308 306

space-probe space craft boosters

Ammonia 95%

.................

1.30 1.40 1,73 1.80 90

E.A .................. ................. Hydrazine.,

Hydrazine

50% UDMH-50% Hydyne ..................

1.30 1.03 1.37il.08 1.73_1.31 1.80 1.36 1.14 1.65

UDMH .................... TMB-1.3-D ................

1.83 1.27 2.28 ! 1.60 2.37 1.66

TABLE

1-10.-Theoretical

Performance

of pellant

Some

Very-High-Energy Combinations

Cryogenic

Liquid

Rocket

Bipro-

Oxidizer

Fuel

r., ..... 4.02 19.50

rv 0.25 1.20 1.54 1.61 .35 1.10 1.48 1.53

d 0.28 .65 1.31 1.32 .45 .82 1.18 1.18

Tc 4935 4960 7955 7980 6505 8230 7715 7745

,_ 10.0 23,4

c* 7980 5300

CI 1.578 1.610 1615 1.614 1.578 1.592 1.605 1612

Is 391 265 363 362 410 372 357 357

Isd 109 172 476 478 185 305 421 422

Applications Space space stage Space stage probe and

Liquid

oxygen

..........

Liquid

hydrogen

craft upper and booster probe upper

Liquid

fluorine

..........

Hydrazine Liquid Ammonia

.......... hydrogen ........... .....

2.30 2.40 7.60 23.70 3.29 3.40

19,4'7245 19,6 18.5 19,3 19.5 7225 7515 7155 7140 11.818365

NOTES (1) Conditions are based (a) (b) upon = chamber pressure pressure = ambient ratio = 1000 which the performance

FOR calculations

TABLES

I-7

THROUGH tw = Propellant fuel)

I-i0 weight mixture ratio (wt. oxidizer/wt.

Combustion Nozzle (optimum ation) exit

psia = 14,7 psia oper-

tv

pressure

= Propellant fuel)

volume

mixture

ratio

(vol.

oxidizer/vol.

nozzle

expansion

at sea-level

d

(c)

Chamber contraction throat area) = infinity Adiabatic Isentropic composition combustion expansion or shifting

ratio

(chamber

area/nozzle

= Bulk density of propellant combination (gm/cc). (The density at boiling point was used for those oxidizers or foels which boil below 68 F at one atmosphere pressure) chamber molecular temperature, weight _F products

(d} (e)

Tc =Theoretical of ideal gas with shifting = Average at Tc c* =Theoretical

of combustion

equilibrium

in the nozzle

(2)

Symbols:

characteristic

velocity

(ft/sec)

28

DESIGN OF LIQUID PROPELLANT ROCKET ENGINES

NOTES C[ :Theoretica] thrust coefficient

FOR

TABLES

i-7

THROUGH

I-i0

(Continued) 99 98 97 95 93 91 88

900..................................... 800 ................................. 700................................ 600 .................................. 500 ................................. 400 ............................... 300................................

Is : Theoretical maximum specific impulse, lb-sec/lb lsd= Theoretical maximumdensity impulse, sec-gm/cc (3) To approximate Is and lsd at other chamber pressures. Pressure (psia): I000 ............................... Multiply byi00

further define that the engine system shall comprise all parts without which the propulsive force cannot be generated. Thus, we will include the propellant tanks and their accessories. A system thus defined frequently is called a propulsion system. We know, from the above, that by including the tanks, we may be "infringing" on the vehicle structure by other definitions. Thus prepared, we may now proceed to subdivide the engine system further into major components or subassemblies as follows: (I) Thrust chamber assembly (2) Propellant feed system: One of the following two is generally used: Pressurized gas propellant feed system and turbopump propellant feed system. The latter includes some type of tank pressurization system (3) Valves and control systems (4) Propellant tankage (5) Interconnect components and mounts Depending on the engine system selected, one or another subsystem may not be required or may be integrated with another one. Typical liquid propellant rocker engine systems are shown in figures 1-12 and 1-13. The rocket has occasionally been called the simplest propulsion system known. The simplest form of a solid propellant rocket or of a pressurized gas-fed storable liquid propellant rocket appears to come close to this ideal. Unfortunately, simplicity frequently is synonymous with inflexibility. Due to vehicle requirements, substantial departures from the basic simplicity may become necessary to meet requirements such as: light weight, high performance, thrust control, thrust vector control, restartability, cutoff ira-

pulse control, propellant utilization control (sometimes called propellant management), storability, ease of handling, etc. Thus, modern rocket engines contain more subsystems than their basic principle of operation may suggest, to meet the often stringent vehicle requirements. This is true for both liquid as well as solid propellant systems. In general however, the liquid propellant engine is the more flexible one, particularly where large systems are considered.

A Check valve B Pressurizing diffuser C Fuel tank D Pressurizing diffuser E

gas

K High-pressure helium bottle L Pressure regulator M Heat exchanger N Fuel tank vent and relief valve O Oxidizer tank vent and relief valve P Oxidizer tank fill and drain valve Q Oxidizer duct R Main oxidizer valve S Thrust chamber assembly gas feed liquid system.

gas

Pressurizing gas line F Check valve G Oxidizer tank H Fuel duct I Fuel tank fill and drain valve J Main fuel valve

Figure 1-12.-Typical pressurized propellant rocket engine

INTRODUCTION

TO LIQUID

PROPELLANT

ROCKET

ENGINES

A B C D E lr G H I J K

Check Fuel Check

valve tank valve gas tank line

L M N O P

Pressure Heat Turbine Thrust Fuel valve

regulator exhaust chamber tank vent duct assembly and relief V U

cryogenic nation) Fuel valve Oxidizer valve tank

propellant fill and

combidrain

exchanger

Pressurizing Oxidizer Fuel High Gas duct pressure generator starting

tank

fill

and

drain

helium and

bottle

Q R S

Pressurizing Pressurizing Oxidizer valve Inter-tank quired tank

gas gas vent

diffuser diffuser and relief

W Oxidizer X Y Z Oxidizer Fuel Gear pump box

duct pump

valve spinner

assembly Turbine Gas Main turbine fuel valve Figure 1-13.-Typical

T

insulation for cryogenic feed liquid

(reand nonpropellant

AA Main

oxidizer

valve

turbopump

rocket

engine

system.

Chapter Rocket2,1 THE MAJOR ROCKET PARAMETERS ENGINE

II

EngineDESIGN

Design

Implements

To fit the engine system properly into a vehicle system, engine systems design and development specifications will have to cover the following parameters above all: (1) Thrust level (2) Performance (specific impulse) (3) Run duration (4) Propellant mixture ratio (5) Weight of engine system at burnout (6) Envelope (size) (7) Reliability (8) Cost (9) Availability (time table-schedule) As the design progresses, numerous additional parameters will have to be considered. Before turning to the latter, let us briefly review and discuss those listed above. It should be noted that the last five items are closely interdependent. For instance, making an engine available in the shortest possible time ("crash program _) will raise the cost and will unfavorably affect reliability. A longer design and development period may not necessarily reduce cost, but it will offer higher values in exchange for the dollar; higher reliability, refined (lower) weight, and an optimized (smaller) envelope.

results from the decision whether a single- or a multiple-engine system is to be used. This decision is often strongly influenced by the availability of already existing engines, which would eliminate, or at least drastically reduce, the design and development cost for the propulsion system. The selection of individual engine thrust level also is-or at least should beinfluenced by the general state of the art, particularly if sizes substantially larger than previously developed are considered. More recently, largely as a result of the advent of manned rocket flight and of the high cost of very large vehicle systems, the decision to use a multiple (clustered) propulsion system consisting of several engines rather than a single one has been additionally affected by safety considerations, to permit mission completion, or at least safe return of the crew, in case of an engine failure. This "engine out" principle is analogous to the consideration of multipleversus single-engine airplanes. Extensive studies have been conducted in this field for rocket vehicles to establish the "break-even" point regarding the minimum and maximum number of engines profitably employed in a cluster. Failure of single-engined rocket vehicles not only might destroy the vehicles themselves but also could cause severe damage to expensive ground facilities. This explains the great emphasis placed on thrust subdivision. Thrust levels for first-stage booster engines, which start at or near sea-level altitude and stop at a specified higher altitude, are usually quoted for sea-level conditions. Additionally, the specifications may contain information on thrust level at altitudes above sea level, frequently form of a graph (see fig. 2-1). in the

Thrust

Level

This engine parameter is a basic one, similar to the power rating of a gasoline engine or electric motor. It will affect most of the other engine parameters and many of the development considerations. The total thrust requirement of a rocketpropelled vehicle is predominantly governed by1. The total takeoff weight of the vehicle (including engine!) 2. Minimum and maximum accelerations permissible Selection of the proper engine thrust level

The nominal thrust of engines in stages starting and operating at or near-vacuum conditions is quoted for that environment. Most engines are designed for a single nominal thrust (sea level or altitude), for which they are calibrated by 31

32

DESIGN OF LIQUID PROPELLANT

ROCKET ENGINES

I SlEC S_C_FE q_PUL_ m CUTO=r

,oo Tzr_* F_ IZSO'

its true Kgrmgn

significance. observed:

In June

1959,

Dr. von

1

L_Crr

]t is my personal belief that the length of the period of attaining reasonable reliability in the development process could be essentially reduced if simple design were emphasized as a leading principle, even if we had to make some sacrifice in the quantitative measure of "efficiency." Essential elements have to be designed as simply as possible, even if this means a reduction in quantitative efficiency and a certain increase of bulkiness andsor weight. Undoubtedly, these a noticeable builder as or at least capabilities observations trend well as were on the the part of customer, nearly sysamounted

so

s

go ALTITUDE

L2o (FT

_r_ X I0 $)

prompted both engine perthe to sacrifice, all other tem

by

engine

Figure

2-I.-Typical lormance as

graph function

o[ rocket of altitude.

to compromise, of a rocket which sometimes

propulsion

for Is increases, than 1 percent.

means quently, designed require discussed Control."

of propellant with some the type aid for variable in section

line

orifices

or,

less Engines

frealways

to less the life

of regulators. thrust (throttling) This "Engine

Frequently, engineering especially capacities. may have

increasing can reserves with The weight need in the

emphasis be traced initial assumptions for competitive

on Is during to marginal vehicle and design tank

of a project

of regulator. 7.3,

will

be Level

Thrust

bidding

contributed other hand,

to this the

situation. Is which will case pay can off sub-

Performance Although rocket ber impulse parameter cific is the impulse, dimension measured engine (Is) is As the general strict c*, term _performance" covers prime of a a num-

On the be obtained stantially. medium-range 1 second approximately

highest

without For

compromise in the missile, effect a range miles.

instance,

of a typical of of terms, As flight those whether be corn-

in the (Is,

sense Cf, the

ballistic in Is will 15 nautical of less as these

an increase increase In other percent

of parameters was also

etc.),

specific performance I, the specific spethrust, is not of the lb/(lb/ It is imporof Is or to the a of Is value

considered seen referred but (specific

in chapter to as which

an Is increase results impressive range engine the are, vehicle

than figures be kept

one-half

in a range

increase

of I percent. for increased in mind determine not that

in seconds, of time,

obviously

an abbreviation impulse), value system,

it should will fly

dimension sec) tant refers thrust is to state

lb-sec/lb thrust), whether complete only. "actual" an to the The propellant and as quite

properties

which at all

will

(specific

respectively. a specified engine Frequently, value values are With less have

should

to the chamber

Duration Because, carries its the cluding as takeoff mum and by definition, own complete its oxidizer, a rocket propellant run duration balance thrust level, vehicle supply, inis limited, between and miniConsequently, liquid-propellant narrow band,

by stating theoretically for the well

percentage linked possible. known lished become

or "practical"

maximum theoretical

better estab-

combinations a result predictable. disappointments practical

a result

of an optimized trajectory, maximum times

values

have well-known often rein

weight,

accelerations. of most large

combinations, sulted. the use been

run-duration rocket about

Therefore, of theoretical

great caution is advisable values which have not test. of a rocket impulse, far beyond

engines fall into 50 to 400 seconds. specifications (such and duration as qualification times,

a relatively include

verified

in an actual years, expressed considerable the

User stration (PFRT) mulated

a formal flight rating requiring breakdown,

demontests accuof

In recent engine, has as received

performance by its specific attention,

preliminary tests) without

ROCKET ENGINE

DESIGN IMPLEMENTS

33

many duration PFRT

times

the

comparatively six full

short duration

rated tests

flight for

This exit tude,

is analogous velocity and of the

to a cannon, projectile, of the such gun not gun as barrel system, only

where gun-barrel emplacement (neglecting wind). the

muzzle attiwill enviWith intricate the have of trajecsteep, a re-

(typical: of an ICBM).

location the rocket, point influences

These engine of the erations (1)

specifications, design considerations, areas,

therefore, with flight-run which to the

govern the

most consid-

determine ronmental ballistic placed components three the any basic capability or all angle guidance

of impact

exception

following are which supply

for weight

the guidance

is literally predetermine but also the is too for deviations

by the

tailored tank employ

duration: power

of which parameters of them. near the If,

Auxiliary

capacity, a separate

for systems turbine

mentioned for instance, of cutoff compensate final signal,

to compensate

(2)

Propellant-tank it is part of the

pressurization engine system

supply,

if

tory the

point will

system the the that cutoff several

accordvelocity, simultaneground repeatable impossible cessation: transmit considerapropellants Figure 2-2 the a finite to by

(3)

Lube

oil tank

capacity, nozzles

if applicable

ingly, slightly ously

by calling delaying considering covered.

for a higher cutoff distance a prompt signal reasons,

(4) Temperature of uncooled

nonequilibria, such as those

over and it is thrust

Closely related to the run duration are the start and shutdown characteristics of an engine for both of which the quality may system, the requirements The "start," engine (l) characteristics or "thrust are judged Compliance time

already execution However, effect time cutoff time; tions below shows is

It is obvious of the for a truly required signal; structural are the valves

is imperative.

be very stringent in a given vehicle system. and buildup," bywith specified thrust versus of the rocket of a liquid

instantaneous to sense closing (hydraulic have thrust an and

then

of valves residual effect. decay

requires

hammer)

characteristics rate buildup from surges and thrust overoscilof increase at any time

superimposed;

(2) Maximum during (3) Freedom shoots

a typical us recall:

diagram.

Let

(4) Smoothness lations)

(freedom from damaging

Ft = may

(5) Repeatability from run to run and from engine to engine These characteristics will be discussed greater detail in chapter X, "Engine Design Systems in

Thrust multiplied by time equals mass velocity increase, or Ft m

times

Integration." Suffice it to state, at this Difficu_rr ro ca.as[ F.Y. IOO

Av=

point that a rocket engine is not easy to adapt with special thrust buildup requirements. communication and ing the engine between contractor. by both the vehicle Thorough contractors culties in this area can arise from inadequate contractor understandis vital, or by this the term to in aTIWE F_OI, I CUTOFF S_ONAL {SEC ) 0

of the The

problems

characteristics decay" are considerations. let us consider implies, a desired direction the payload the speed from coasts

of engine predominantly To the case missile. missile

"shutdown" influenced

"thrust guidance better, "ballistic" impart desired which

understand As

of a single-stage, is designed payload, after target. Figure to the

ground-to-ground,

ballistic

to a known a desired freely

point,

2-2.-Typical

thrust

decay

diagram.

34

DESIGN OF LIQUID PROPELLANT ROCKET ENGINES

The velocity increase following cutoff signal is a function of the residual thrust acting on the vehicle mass m, and is integrated over the time from cutoff signal to final thrust cessation; this integral is commonly referred to as the "cutoff impulse." A typical value for a well-known earlier rocket (Redstone) was 16 000 lb-sec z2500. Note the tolerance. This deviation will obviously influence missile accuracy. Reduction of the tolerance is thus an important design and development goal. It might be concluded that a substantial reduction of the tolerance is the principal task, zero deviation being the optimum. This is unfortunately not so because the final vehicle mass m, on which the decaying thrust force acts, is unpredictable within certain limits, due to weighing tolerances of the initial vehicle mass, and to flow rate and mixture ratio tolerances. The engine designer and developer will have to concentrate on reducing both: base value and tolerance. A glance at figure 2-2 shows that the area under the thrust curve is a function of not only decay time but also of main-stage thrust level. In fact, the major portion of the shaded area is accumulated prior to the beginning of thrust decay. This observation has led to the utilization of vernier thrust systems. A vernier cutoff system is characterized by a substantial thrust reduction before final cutoff. This can be accomplished by thrust reduction, for a few seconds, of the main engine itself (V-2 fashion) or by shutdown of the main engines, while much smaller engines continue for a brief period (typical: 0-25 seconds, depending on final __v required). It should be emphasized that any components that must be added to improve cutoff characteristics are basically undesirable, since engine complexity is drastically increased. The addition of such components should be avoided at all costs. Here again, close coordination between the vehicle (guidance) designer and engine designer, and thorough understanding of their common problems, is vital. Mixture Ratio

amount

of oxidizer.

That

mixture

ratio

which

effects complete combustion, with no leftover of either fuel or oxidizer, is called the stoichiometric mixture ratio. This ratio depends on the type of propellants used. Tbeoretical temperature and heat release are maximum at this ratio. In rocket engines, however, where the highest possible exhaust velocity is desired, optimum conditions often prevail at other than stoichiometric ratios. Equation 1-18 indicates that the gas properties strongly affect exhaust velocity. The expression for the specific gas constant, R, in equation 1-18 may be rewritten as-

where R' is the universal gas constant and is the molecular weight of the gas (see table 1-1). The lower tile molecular weight, the higher the exhaust velocity, other things being equal. Analytical and experimental investigations will determine the optimum point of balance between energy release (heat) and composition (molecular weight) of the gas, a portion of which will consist of gasified but unburnt propellants. The optimum point may also be affected by(l) Stay time of the burning gas in the combustion chamber.-Stay time is a function of combustion chamber volume and of gas volumetric flow rate. Complete combustion, even though desirable, requires a finite time which is not available unless the chamber is relatively large, and correspondingly heavy. A compromise in chamber size, therefore, is often made. This leaves unburned a small percentage even of those propellants entering the nozzle, which could have burned given sufficient time (chamber volume). This percentage must be considered for accurate determination and optimization of the composition of the combustion gases and when optimizing the gas properties with energy release and system weight. (2) Cooling conslderations.-The temperatures resulting from stoiehiometric or nearstoichiometric mixture ratios, dependent on propellant type, may impose severe demands on the chamber-wall cooling

As is well known, complete combustion of a given amount of fuel requires a corresponding

ROCKET ENGINE DESIGN IMPLEMENTS

35

system. A lower temperature, therefore, may be desired and obtained by selecting a suitable ratio. Once the optimum mixture ratio has been determined for a given engine system, based on the major factors just discussed, it is obvious that deviations from it would result in engine performance penalties. Since the vehicle powered by an engine will have been sized and tanked to conform with the specified engine mixture ratio, it is important to know that deviations will also result in reduced vehicle performance, namely: (1) Reduced engine duration, due to premature exhaustion of one of the propellants (2) Reduced mass ratio, due to excessive residual amounts of the other propellant (increased burnout weight) Since the relationship between engine performance (/s) and mixture ratio for many systems is usually relatively flat near the optimum point (fig. 2-3), the effects from duration and burnout weight may well be the most influential ones for vehicle range. The effects of even minor discrepancies in mixture ratio (propellant utilization) are substantial. For instance, in a typical single-stage medium-range ballistic missile, each pound of excess burnout weight will result in a range decrease of approximately 0.2 nautical miles. For long-range vehicles, the penalty is still higher. The close target tolerances that have occasionally been reported for test flights illustrate the remarkable degree of accuracy which can be achieved from all contributing subsystems.

Weight The parameter of weight, as no other, dominates the thinking of those employed in rocketry. Weight of payload flown over a distance, or placed into orbit, is the ultimate accomplishment. Success is often gaged directly in pounds of payload flown per dollar spent. The importance weight rightfully carries does not necessarily mean that it is all important. For instance, a somewhat smaller payload placed into orbit more reliably, or at a lower cost per pound, may be preferred. By and large however, weight is a most important consideration. As we have seen earlier, a vehicle's final velocity is a function eters, its mass ratio. of, among other paramThe smaller the final velocity. However, be as high as possiapplied to all those are not payload. This of vehicle-structures

mass, the higher the final since payload mass should ble, the weight squeeze is vehicle components which includes the engine. To isolate the influence

320

weight, a parameter called "propellant fraction" has come into increased usage. This factor expresses the ratio of the total propellant weight to the fueled vehicle weight without payload. Typical values are 0.94 for turbopump-fed systems, and 0.89 for pressure-fed systems. For turbopump-fed engines, the ratio of thrust to engine weight is a useful additional yardstick. Larger modern liquid rocket engines may fall into a range from 75 to 125 pounds of thrust/lb of engine weight. These figures represent asubstantial progress over the past (see fig. 2-4). As was seen with residual propellants, excessive dead weight at burnout imposes penalties. Therefore, whenever rocket engines can be made lighter without compromising reliability and structural integrity, the payoff in range and payload will be sizable. Engine and vehicle builders usually distinguish several types of engine weight: (1) Dry weight.-The net weight of the engine as it leaves the factory. (2) Burnout weight.-The engine dry weight plus residual, measurable propellants remaining in the engine at cutoff. In a typical engine design, burnout weight may be 4 percent higher than dry weight. Burnout weight is significant for vehicle mass ratios (eq. 1-30).

,.-zao 0Z60G e 0 I

/LO O/F I 2 MIXTURE L4 RATIO 1.6 L Jr 2D_

Figure 2-3.-Theoretical thrust chamber performance vs mixture ratio for N204/N2H4 at Pc = 1000 psia shifting equilibrium and optimum sea level expansion.

36

DESIGN OF LIQUID

PROPELLANT

ROCKET ENGINES

O

(a) (b) _arly Navaho Engine 1953) Early I Engine 1952) German (c) l Engine lb lb

Redstone

V-2

(Rocketdyne

(Rocketdyme

(1942) Tb_ustsL: 56,000 Dry _elght: 2484 Iss L = 199 sec

ThrustsL: 120,000 ib Dry Weight: 1230 lbs Is3 L = 230 sec

ThrustsL: 75,(>00 ib _ry Wei___ht: 1475 lb Iss L = 215 sec in ratio lb, dry 1475 o[ thrust weight: Ib, sec.

Figure by: war (I942),

2-4.-Substantial (a) postwar (1952), thrust: engine 56 000

progress (1953), Ib,

has

been

made 120000

to engine 1230 Ib, sec;

weight IssL (c) =230

as

demonstrated sec; (b) postV-2 engine

thrustsL: 75 000 lb, 2484

engine

thrustSL:

dr}, weight:

lss L =215

German

dry weight:

lb, lss L --199

ROCKET ENGINE

DESIGN IMPLEMENTS

37

(3)

Wet all

weight.-The propellant

engine within it,

dry

weight

plus

during

main wet dry for loca-

ing and location

routing of lines, of valves. of the

avoidance

of traps,

and

stage. weight weight.

In a typical Wet weight

design, is

engine higher than

Because rocket shows engine

importance

of weight employ

control,

may be 6 percent

manufacturers

engineers Table 2-i

significant

specifically in charge of this area. used by the Rocketdyne can Aviation.

vehicle in-flight tion and moments (4) Wet gimbaled weight earlier the

center-of-gravity of inertia. portion mass

a typical weight progress form, as it is Division of North Amera useful tool to raise In our arbitrary example However, based the almost the data are Itis revised and reissued periodit becomes

weight.-That engine this meant and designs less

of wet which In wet refers This actuator re-

ically. Thus

representing designs

early danger warnings. a slight underweight table also shows that

is gimbaled thrust

for steering chamber In later

purposes. essentially injector it often parts.

is shown.

entirely on estimated

and calculated figures, results. This of design More often is

weight. to the small weight loads sponse Ideally, equal: in the not dry that engine be can 2600

rather than on actual weighing

entire amount is and

engine

a relatively

characteristic for the earlier phases and development of a rocket engine. than not, the weight advantage

of stationary

significant guidance

for gimbal control loop

will disappear

gradually as the design firms up; then the squeeze will be on. For convenient display of the weight tendencies shown The over time, a graph such as

characteristics. and burnout weight should In practice, However, through proper the should be trapped this engine design, sizwill be

weight is,

no propellants at shutdown. possible. do much

in figure 2-5 will be useful. weight changes of the various compo-

always

nents as well as of the entire engine affect centers of gravity and moments of inertia. Through

designer

2450 REV SPEC BURNOUt 2300

2150

BURNOUT 2000 _" ......_ /

//19 I0 II 12

REV SPEC DRY

_

)85o

/1700 / ENGINE ACCESS BURNOUT ..................... ENGINE ACCESS DRYORIGINAL

IS PEc 'r...........................ORIGINAL

................1400 I 2 3

i SPEC I.......................4 5 6 7 8 13 14 15 16

GO AHEAD

MONTH , weight history.

Figure 2-5.-A-2 stage rocket engine and accessory

38

DESIGN

OF

LIQUID

PROPELLANT

ROCKET

ENGINES

z

_= E;oj

4. + _4-

+

-_-

b

I

"7,c_L_.

E_

+

=

ROCKET

ENGINE DESIGN IMPLEMENTS

A-2

STAGE

ROCKET

ENGINE

CENTER

OF

GRAVITY

AND

MOMENT

OF

INERTIA

DATA

ISSUE DATE

ENCLOSURE PAGE I OF r

,

Z

(NOTE: (_erns about (I) thru specified U_e moment

(_"'_

LOX

Pump

I y

(

F uet

Pump

I_ GIHBAL ( Y 0 )

I(31 Tepcesent C.G,'s. the items about the rnorr_t o( iner',ia (41 and (S) represent referenced gJmbal axis. of inerti_

WEIGHT DESCRIPTION LBS. t, Y - CENTER(OF ARH X GRAVITY - ARM INCHES ARM Z -

MOMENT

OF

INERTIA

- SLUG

FT 2

Y-Y t76

(

X-X 391 4tl 408 672 688

IZ-Z 362 379 375 649 662

(I) (2) (3) {4) (5)

RocketEnsine Rocket Rocket Gimb_lled Gimballed Engine En|ine Mass Mass

_ Ace;_ Act. . Ace. Dry Wet -

DrX Wet Burnout

2181 2317 2292 2061 2086

.233 -225 -227 -25.2 -246

. IS .15 .I -I 6 5

07 --0 -0 I 2

185 184 I_ 177

0.2 -02

. I S

Figure

2-6.-Typical

data

sheet

for

center

of gravity

and

moment

of inertia.

issue parties changes

of a data concerned as they

sheet can occur.

as be

shown kept

in figure informed

2-6, on

all

Vbo

-- Cvc

g" (Is)on Stage

in Stage +payload+ weight + weight Stage inert weight.) / \

usable

Note that the data presentedfigures engine multistage later 2-5 and system space chapters. Let weight weight magnitude us has now on varies will explore the the 2-6 are which vehicle for the is a part

in table 2-1 and150K A-2 stage treated in where of an assumed

propellant weight weight

(2-1)

configuration

influence system, design

structural takeoff how its of Stage for Stage system engine weight . guidance T weights, not structure, and other which are payload equations is an even system that (2-2) Stage inert_ Stage residual weight propellant and

performance vehicle with the

and gross parameters individually

of a rocket

weight

at burnout

differentrelationships each case. Equation burnout stage

vehicle systems.be evaluated

The quantitative

(1-30)

can

be rewritten of any system

for the vehicle, individual

stage or the stage It can for a given weight trade be concluded burnout off between from velocity, stage these there

velocity velocity

of a single-stage increment, vehicle as:

of a multistage

engine

4Oweight of all decrease increase For except between and other the a fixed engine the stage items in the stage payload were stage

DESIGN OF LIQUID

PROPELLANT

ROCKET ENGINES

weight. kept constant, system capacity assuming increment,

If the

weight will

vehicle vehicle 1 pound, weight tional fined load) causal weight. value, as

trajectory. system

Therefore, exceeds its of the by a certain result. vehicle of added

if one weight total Growth

part

of the by system is depayby the

a pound weight by 1 pound. other the Vbo, items and

allotment vehicle factor (including divided

engine

an increase at takeoff pounds the will total increase

payload and

number

of addi-

payload, weight stage system as velocity

to be constant, weight for a given

relation system

system inert that is a band.

weight It is but weight system

at takeoff, the not

stage engine can be written

increment

and/or growth

payload factor, a

emphasized system, within

for a given

vehicle varies

a precise For instance, in an exaddition of a but etc. In

Vbo = k 1 In where

k(__. Stagestage ++ engineengine system _]

weight._

(2-3)

small isting

increase may only small enlargement the the breaks next The growth

of a component require the amount

corresponding = constant Stage not residual require case, that use like. Accordingly, another straw = constant = constant decrease decreasing an inwhich will the or the

of propellants, tanks, will back," size, will may valves, be small.

k_ = Cvcg(Is)oa

of the factor

k2 = Stage payload weight , Stage lca = Stage Since more engine crease pay rapidly weight. in burnout off in longer For payload, cific system a given the weight impulse usable k 2 < k3, than

+ propellant weight at burnout structure, and other propellant the the guidance weight weight+k: will with payloads, realized orbit. and of stage as for a fixed overall engine spe-

weight the growth

increase

be "the requiring duet size,

camel's valve factor the engine

of the

larger

then factor

be large. of a preit of

In general, vehicle liminary attaches the For then increase weight can system design

however, is of an

growth tool to the system,

denominator numerator, for fixed is

a useful value weight.

during

the

because weight payload." small factor accuracy system

Thus

a tangible may changes,

importance

velocity range burnout

engine-system single-stage

A systems "uninvited and relatively growth of the

or higher velocity stage

be considered vehicles, the value with Total

required (ls)oa can

average

in terms

be expressed

sufficient vehicle

as

be established

weight Growth k3 , + system Stage ('s_oa:k4.'/in k 2 + system weight engine weight ] \ (2-4) For any stage value system as Total Equation engine-system pulse requirements parameter is For the growth instance, Another of weight system. nent (2-4) shows that the with decreasing specific the weight to adjust propellants of other the i.e., composame and Growth factor = Stage imThe vehicle lower growth system stage can factors weight Growth factor = of a multistage of the growth facto[Payload

at takeoff (2-5) weight vehicle, factors the against can be

// total

approximate where Vbo k 4 = C--vcg = constant vehicle

weight

at takeoff

expressed

vehicle

system (2-6)

weight Stage

at takeoff weight against of the the same or

weight,

overall

payload stage

decrease. illustrating factor if the importance vehicle for this Vehicle system weight at same stage or lower ignition (2-7) payload weight of a compoof any at ignition as

of a rocket

be expressed

increases, the thus as

it is possible weight possibly a pump, of the that

by increasing loaded nents, required and such

to maintain

vehicle

performance;

payload

ROCKET ENGINE DESIGN IMPLEMENT5

41

Sample

Calculation

(2-I)

A three-stage rocket vehicle system has the following weight data: Total vehicle system weight at takeoff, 40000 pounds. Vehicle system weight at second-stage ignition, 7500 pounds; vehicle system at third-stage ignition, 2200 pounds; payload weight, 700 pounds. For each pound increase of engine system weight of first, second, and third stages, respectively, determine (at a constant vehicle performance): (a) increases of total vehicle system weight at takeoff; (b.) increases of vehicle system weight at second- and third-stage ignition. Solution Payload weight of first stage = vehicle system weight at second-stage ignition = 7500 pounds Payload weight of second stage =vehicle system weight at third stage ignition = 2200 pounds Payload weight of third stage = actual system payload weight =700 pounds From equation (2-6): (1) Growth factor of first stage against vehicle system takeoff weight = Vehicle system takeoff weight weight 44000 =_=5.86 7500 stage against weight = _^ =gu (a)

For each pound increase of third-stage enginesystem weight, the increase on vehicle system takeoff weight = 62.9 pounds (b) Note that the weight growth of lower stages will not affect the upper stage weight growth. For an increase of first-stage vehicle system weight, there will be no weight changes on second and third stages, and for an increase on second-stage vehicle system weight, no weight change is required for third stage. From equation (2-7): (1) Growth factor of second stage against vehicle system weight at second-stage ignition = Vehicle system weight

at second-stage ignition 7500 3 Sec'-ond-stag------_ayl----oa--d p wei--_ht =2_ = .41 (2) Growth factor of third stage against vehicle system weight at second-stage ignition = Vehicle system at second-stage Third-stage weight ignition weight-

payload

7500 -10.72 700

First-stage

payload

(3) Growth factor of third stage against vehicle system weight at third-stage ignition = Vehicle system weight at third-stage ignition Third-stage payload

(2) Growth factor of second vehicle system takeoff

2200 -_=3.14 weight700

Vehicle system takeoff weight 44000 Second-stage payload weight = _ (3) Growth factor of third stage against vehicle system takeoff weight =

Therefore: For each pound increase of second-stage engine system weight, the increase on vehicle system weight at second-stage ignition = 3.41 pounds For each pound increase of third-stage engine system weight, the increase on vehicle system weight at second-stage ignition = 10.72 pounds, and the increase on vehicle system weight at third-stage ignition = 3.14 pounds The correctness of results can be checked by recombining the individual stage growth factors to obtain the growth factor for the entire vehicle system: 3.14 3.41 5.86 = 62.9

Vehicle system takeoff weight Third-stage payload weight Therefore:

=44 000 = 62.9 700

For each pound increase of first-stage enginesystem weight, the increase on vehicle system takeoff weight = 5.86 pounds For each pound increase of second-stage engine-system weight, the increase on vehicle system takeoff weight = 20 pounds

42

DESIGN

OF

LIQUID

PROPELLANT

ROCKET

ENGINES

Envelope

(Size)

The linear dimensions of liquid propellant rocket engines require relatively elaborate description and frequently cannot be made clear without a drawing. In those cases where only approximate values are required for comparison or for overall estimates, the term "envelope" is preferred. For instance, definition of a hypothetical smallest cylinder, cube, or sphere into which the engine would fit conveys a good feeling of engine size or bulkiness. Obviously, engine size directly affects engine weight, the importance of which was emphasized above (fig. 2-4). Aside from the engine itself, mnnerous other areas are directly affected by increasing engine size: (1) The vehicle structure, which becomes heavier, especially with upper stages. Engine size directly affects the size and thus weight of the aft end and/or interstage structure. (2} Handling equipment and procedures become more costly (3) Servicing becomes more difficult (4) Manufacturing machinery becomes larger (5) Storage and transportation means become more bulky In several of these areas, there is a definite upper limit, such ances on bridges machine tools. as railroad tunnel and underpasses, sizes, clearand available

The selection of the thrust-chamber expansionarea ratio has a very pronounced effect on engine envelope. When optimizing the thrust chamber expansion area ratio, which is also influenced by performance, weight, pressure drop, heat transfer, and other considerations, its effect on envelope, and thus on other vehicle systems, must be considered (section 10.9).

Reliability The subject of reliability has become almost a branch of science by itself. In addition to the designer, to the development engineer, and to the user, mathematicians, statisticians, and "human factor" and "man rating" specialists are involved. Numerous books have been written on the subject and manufacturers maintain entire g['oups to predict, monitor, tabulate, and evaluate

the reliability of their products. This emphasis on reliability is well justified and is of particular significance to rocket engines. The advent of manned space flight has placed even greater emphasis on rocket-engine reliability. Reliability may be defined as the capability of the engine to perform according to specifications, whenever "the button is pushed." The degree to which this is met can be expressed in figures and graphs. If the evaluation is made following a test series, reliability can be simply expressed as the ratio of success to failure, say 98 percent (2 failures and 98 successes in 100 runs). As there is no guarantee, however, that the system under test will perform identically in subsequent tests, reliability predictions are made, the accuracy ("confidence level") of which increases with the amount of previous information available. The interrelation of reliability and its confidence level is something the statisticians have much to say and write about. What can the rocket engine designer do to achieve the highest possible reliability, as early as possible? Below are compiled a few pointers and thoughts which have proven valuable, not only in rocket engine design. They will be followed by specific details for the implementation of a reliability-assurance program. First of all, painstaking execution of all calculations and drawings that are part of a given design is an obvious requirement. This includes the thorough study of previous experience, one's own as well as that of others; familiarity with and correct application of accepted and proven design standards and procedures; clearly written statements and instructions; clear line drawings. It cannot be overemphasized: it pays to spend that extra hour in carefully checking repeatedly every detail of a design and its contemplated mode of operation, before its commitment to manufacture and subsequent use. Neglectmay have to be paid for by many months of toilsome, tearful, embarrassed "corrective action," often causing losses of hundreds of thousands, even millions of dollars. When making these checks, the most pessimistic assumptions of what someone else may do wrong during manufacture, assembly and use, are not out of place. The designer should not rely solely on his own judgement. Careful and independent checking of all calculations and designs by superiors

--..__

_.

T

--

ROCKET ENGINE DESIGN IMPLEMENTS

43

and by independent checkers is important. Early availability of a wooden (or "soft") mockup of the engine under design will be an invaluable tool to avoid costly errors that subsequently may seriously affect schedules and reliability. Specific recommendations for design and checking techniques will be made in section 2.2. "Reliability" is sometimes treated as being synonymous with "simplicity." Undeniably, simplicity of a design contributes significantly to increased reliability. Parts which do not fulfill a truly useful purpose should be omitted. This may include many of the so-called safety features and interlocking devices, which often cause more trouble than they prevent. Early designs of liquid-propellant rocket engines have indeed frequently suffered from such an overdose of sophistication and safety devices. Many of the more recent designs have been substantially improved in this area, to a point where caution must be exercised not to overshoot the target and not to lose that flexibility which only liquidpropellant systems can provide, as compared to solid-propellant systems. Simplifications, like all other design features, must be carefully planned and evaluated. Simplification by elimination of a useful component must not become an excuse for failure to improve that component if its absence could severely penalize other subsystems, or maintenance and servicing procedures. For instance, to avoid a troublesome sealed connection it may be decided to omit flanges and seals and to weld it. However, if one of the lines thus connected were inadvertently pinched in the field, removal of the entire engine from a vehicle under preparation for launch would become necessary. Thus, a simple replacement may be magmfied into a major operation. To be sure, welding or preferably brazing may indeed be the best solution for many problem connections. The point is, this will not be true for all connections. Careful analysis of all aspects including handling and in particular mishandling by the user, is necessary. In another example, tests may have shown that an engine could readily be set up and calibrated to specifications by means of orifices, eliminating previously-used regulators. Engines are delivered accordingly. With rocket engines, it is entirely normal that many months, if not

several years, may elapse between final use. Much can happen during For instance, changes of plans for may have made another thrust level able. In this case, the adjustment orifices, in particular its verification, major operation. While the omission

delivery and this period. the mission more desirby means of becomes a of a stra-

tegic regulator was indeed an engine simplification, for the vehicle system it turned out to be a complication. The point here again is; the careful evaluation of a planned omission must consider all aspects, including changes of plans.

Reliability

Assurance

The emphasis on reliability must not remain an empty slogan. Fortunately, implements are available to the rocket engine designer which can assist him effectively to achieve the highest degree of reliability. One of these, an effective failure reporting and correction system, will be discussed in section 2.2. Equally, if not more important, is a most effective failure prevention system. The numerous activities contributing to the latter may all be considered part of a reliability assurance program. The quality of design, without question, is the program's foundation upon which all subsequent phases rest. The characteristics of a reliability-assurance program, then is that its most significant steps (analyses, design reviews, design improvements) are taken before the design of a component is finalized; before the development test program is initiated; and again before the first vehicle is committed to launch.

Definitions The definitions used in rocket vehicle reli-

ability assurance programs vary widely with individual preferences, with the object under design and development, and with the missions contemplated. The definitions given below are typical, have been used in actual rocket engine and vehicle programs, and can be readily adapted to others. For the sake of clarity, irrelevant jargon and detail have been omitted.

Reliability The probability that a part or system will

44

DESIGN OF LIQUID PROPELLANT ROCKET ENGINES

function properly and if necessary under rated operating conditions, specified load and time limits.

repeatedly within the

Man Rating Design and operational provisionsto assure crew survivaleven in case of mission failure. Thus, man-ratedreliability must be higherthan mission reliability. For instance, overall vehicle reliability to achieve mission success may be 95 percent. By the addition of an escape mechanism, man-rated reliability may be increased to 99.5 percent. Caution is advised not to become entirely "wrapped up" in man rating, at the expense of mission reliability. A single launch of a man-carrying space vehicle costs several hundred million dollars, all told. Investment in means to save the mission as well as the man, therefore, appears to be prudent. Table 2-2 illustrates this clearly. For optimum reliability of spacecraft and launch vehicle including the engines, the need for a crew escape system is minimized. Both, mission and crew survival are assured with high reliability.

Mission

Success

Completion of the rocket vehicle mission objectives within specified tolerances. All subsystems, including the engine, contribute to the success. It is an inherent characteristic of mission-success analysis and assurance that they anticipate the probability of certain part and subsystem malfunctions, offsetting them with appropriate countermeasures (such as redundancies, emergency power sources, power and propellant reserves, and others).

Mission

Failure

Failure of the rocket vehicle to complete the mission objectives. Mission failures can be classified as: a) Catastrophic, b) Critical, and c) Deferred.

TABLE

2-2.-Relationship to Flight Reliability

of Vehicle Safety

Reliability

Catastrophic A failure

Failure in which the time between the failis less must be

Flight safety Probability of crew survival

ure event and a subsequent crew hazard than 500 milliseconds. Abort sequence automatically initiated.

Spacecraft and launch vehicle 0.50 090 0.999 Engine Out

Escape system 0.998 0.99 0.00

0.999

Critical

Failure

A failure in which the time between the failure event and the hazard ranges from 500 milliseconds to five seconds. Abort sequence may be initiated automatically or manually. Deferred Failure

Design and operational provisions to permit limited or complete mission continuance in case one engine fails to fire, or malfunctions and is shut down. Possible only with vehicles having engine clusters. See airplane analogy under "Deferred Failure," above.

A failure in which the time between the failure event and the hazard is five seconds or greater. Action to cope with the failure is deferred to allow analysis by the pilot or an automatic logic, to decide whether corrective action can be taken or an abort sequence should be initiated. Typical example: shutting off an engine with a feathered propeller in a four engine airplane and reaching destination safely though with a delay. Analogous provisions are anticipated for manned rocket flight.

Failure

Mode

The manner in which a part or system malfunctions. This may be a "short" or "open" circuit, an incorrectly "closed" or "open" valve, an engine out, or similar malfunction. Order of Failure The number of components in a system which

ROCKET ENGINE DESIGN IMPLEMENTS

45

would have to fail, regardless of their failure mode, to cause systems or mission failure. First-order failures are failures caused by a malfunction of a single component or part. Secondand higher-order failures are defined in a like manner. Typical example: a stuck pressurizing valve causing overpressure in a vessel would rupture it only if the safety valve failed to open; this would be second-order failure. However, continuous venting of a properly opening vent valve may prematurely deplete gas supply. A thorough failure-effect analysis will reveal all ramifications. In the example, depletion would not occur instantaneously, this would be deferred failure. The designer can do something about it in advance: provide an overriding closing valve for the pilot, which remains completely inactive when not needed, but adds weight.

Failure

Modes of Engine

Components

The failures of rocket engine components may be attributed to one or a combination of several of the following principal modes: (1) Functional failures (2) Fatigue failures (3) Over-stress and over-strain (4) Failures pertaining to combustion devices (5) Failures pertaining to electrical devices (6) Manufacturing and material defects (7) Unexplained failures (8) Human errors

Functional Failures These are malfunctionsof parts or components due to reasons other than structural failures. For instance,an "0" ringmay failto seal due to impropergroove depth specifiedin the design. Or, a plunger may freeze in the bore of a guiding bushing,because of improper surface finishand/or noncompatibility materials. To of minimize possible functionfailures the design in of engine components the followingprecautions are recommended: (I) Choose proven designs with an established servicerecord. (2) Use standardmechanical elements (bolts, nuts, threads,gears, pins, rivets, springs,seals, tube fittings,istons, p keys, shafts, bearings)wherever possible. (3) Select simple designs, but without impairing flexibility.n particular, I minimize the number of moving parts and sealing surfaces. (4) Allow adequate functional margins in the design of components (spring forces, actuating powers, supply of lubricants, supply of coolants). (5) Subject newly-designed parts to extensive functional testing, under simulated working and environmental conditions, before "freezing" the final configuration. (6) Provide redundancy. This is a "buddy plan": where one component would be sufficient, two of the same type are actually provided. If one fails, the other takes over. This can be achieved in two ways: by noncomplex and by complex redundancy. Intelligently applied,

Failure-Mode-Effect

Analysis

An orderly and qualitative listing of the modes in which components or parts of a system can fail; the effects of the failures on the engine's or vehicle's ability to complete the mission; and the order of the failures. Such an analysis should distinguish between the prelaunch, launch, and cutoff phases. Also, all identified failures should be classified as catastrophic, critical, or deferred.

Failure

Mode Cause

Analysis

An analysis listing all the conceivable reasons why each mode of failure could occur. Likewise, reasons for each potential cause not occurring should be explained in detail.

Emergency

Detection

System

(EDS)

The EDS comprises the electromechanical devices, including sensors and discriminators, to detect an imminent malfunction. Depending on the type of failure (catastrophic, critical or deferred) it may initiate immediate action, or defer but store and/or display it in a suitable manner (timer; visual gage or light). Inputs to the EDS must be analyzed, selected and provided by the designer, in particular the engine designer, at the outset.

4G

DESIGN OF LIQUID

PROPELLANT

ROCKET ENGINES

redundancy reliability. (7) At all times,

can pursue

significantly a rigorous

increase program of

A typical gency circuitry. battery

example with

is voltage

an electric sensor

power and

emer-

switchover

product

improvement. Fatigue Failures failures than those They failure the part. destructive samples failures surface there. gradual The start because actual are fractures at stresses causing are the The be Checking failure. failures most ability checked is tests at random. a crack stresses failure of these will part start and at or are will cracks. will on stress concentrathreads, irregularifailure. of apt caused by rein a single common of a part withpossible,

Noncomplex The ment. failure typical examples valves.

Redundancy Fatigue function of identical equippeated ably load type out load lower applications consider-

simultaneous Application mode wh example, are:

depends upon the - is to be eliminated. _ve dual figures (series) 2-7 and seals,

particular For a 2-8. parallel Other

application. of mechanical fatigue through destroying

to resist however, with

cannot

endurance selected with

representative Most fatigue

PRESSURE SWITCH :IS I POWER

SOLENOID VALVE_

near result

an outside from point upon

to be greatest

propagation the Any crack of the notch

PRESSURE 2 SWITCH = Figure (This 2-7.-Noncomplex type of redundancy called

1 paraI1el guards upon redundancy. against fail-

The depend surface raiser, tion, cracks. SOLENOID VALVE oil ties is holes, are

at which the

geometry

conditions. being Fillet all a point radii

or other stress too small, surface of fatigue

ure to close

when

to close.)

of highest starting that and are similar point

a potential keyways potential a part or the of minute or various itself, and

for fatigue

POWE R

sources

Although SWITCH Figure (This vertent upon =1_" I s e tie guards closing SWITCH s _ 2 geometric grooves 2-8.-Noncomplex type of redundancy i.e., redundancy. against when not inadcalled number tool marks, material matter neer Complex The ponent. switching component, tained The from can potential the Redundancy original Failure devices when function sensors, energize needed. carried logic out by one and standby obadditional circuitry. merely shifted commay are it may equipject and joints subject welding design. com-

may be designed having it may still raisers. identification like,

to be free no shoulders, contain These

irregularities, stress inherent such as

a great may be in the stamp

marks,

scratches,

closing, to close.)

discontinuities inclusions The effort

of foreign design part In the out engisubject for stress

quenching make every

cracks.

should

to avoid

concentrations to repeated rigid surface forgings load specifications finishes. are

in a highly-stressed applications. should For repeated preferred preferred be called load

design, services,

circuits

an identical The offset advantages by the be

generally are

to castings. to material prone

be completely of sensing problem this when days to also and area to the

complexity

switching may failure-detection

Ductile materials to become brittle. In welded to almost fatigue should and

constructions, all types failure. be minimized loads. must Wherever

the of stress

joints

are

sub-

equipment However, (e.g.,

concentration welded of parts for in the out design procedures

ponents. involved

standby long subject mission

redundancy times where backup and the

possible, in the Rigid

be advantageous be undesirable ment to prolonged

or weeks)

to repeated inspection

be called

operation.

tli_.

7,

-,

ROCKET ENGINE DESIGN IMPLEMENTS

47

Over-Stress

and Over-Strain design to prewill be disof

Failures

of Combustion

Devices

vent

Stress analysis in mechanical over-stress and over-strain

cussed in section 2-4. The interrelationship stress and reliability of mechanical parts is illustrated in figure 2-9.

z

_z m

Under steady-state operating conditions, combustion devices in liquid-propellant rocket engines are exposed to hot gases with temperatures ranging from 1000 F to 6000 F. The walls of these devices are either made from hightemperature-resisting (refractory) materials, or are provided with effective cooling, through heatabsorbing effects, ablative cooling, propellant film and/or regenerative cooling. Structural failure may occur because of erosion, from wall temperatures exceeding the values assumed during design. Or failure may occur from a combina-

-ID WORKING STRESS _-_ _

RELIABILITY MARGIN . /-.I_

iV\STRESS

y

f

tion of excessive temperatures and pressures. Under certain transient or unstable conditions, STRESS such as during engine start or stop, combustion O,ST.,BOT,ON instability or abrupt pressure surges may occur and cause a failure. See chapter IV, "Design of Thrust Chambers and Combustion Devices."DAMAGING

Electflcal

Failures

Figure 2-9.-Interrelationship of stress and reliability as related to mechanical parts. Two stress levels exist for every part in a given engine component: the working stress, and the damaging stress at which failure occurs. The failure may be either a fracture, or a deformation beyond allowable tolerances. Each of the two stresses are mean values of a distribution about a mean. The difference between the working and the damaging stress mean values is indicative of the stress reliability margin of the part. The deviations from the mean working stress result mainly from variations in the dimensions of the part, and from operational and environmental conditions. The distribution about the mean damaging stress results from variations in material properties,