42349861 design of liquid propellant engines textbook
TRANSCRIPT
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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,