d
_
'"
_/
:_'_
_'
,-7{ "
_';""_"'-7 ;, _, 77:7>
i
.
/
i
I
-I
Declasslficd
i
by _ut._or!ty
df NA_A-,,._
i
i I
.!
!ii i :7 d
P=
of e PO
Optimum thrust for a given ambient pressure is obtained when the nozzle expansion area ratio e=Ae/At is such that Pe--Pa. This may be seen from figure 1-10. If the divergent nozzle section is extended in the region where Pe > Pa, thrust will increase. Where Pe
uJ 5200 I0
20
30
40
50
CHAMBER CHARACTERISTICLENGTH( Le) IN. Figure
4-7.-Effect 6[ L* on c* value mental thrust chamber.
4-1.-Recommended
Characteristic Length lant Combinations
of experi-
Combustion (L*) for Various
Propellant combination
Chlorine trifluoride/hydrazine-base fuel.. Liquid fluorine/hydrazine ............. Liquid fluorine/liquid hydrogen (GH_ injection) .......................... Liquid fluorine/liquid hydrogen (LH 2 injection_ .......................... Hydrogenperoxide/RP-I (including catalyst bed) ....................... Nitric acid/hydrazine-base fuel ........ Nitrogen tetroxide/hydrazine-hase fuel.. Liquid oxygen/ammonia ............... Liquid oxygen/liquid hydrogen (GH2 injection) .......................... Liquid oxygen/liquid hydrogen (LH 2 injection) .......................... Liquid oxygen/RP-1 ..................
Combustion in
various thrust chamber designs. Typical L* values for different propellants are given in table 4-1. With At and minimum required L* established, the required combustion chamber volume Vc can be calculated by equation (4-4).
NZ041 50-50 O/F MIXTURE
TABLE
Chamber Propel-
Combustion chamber characteristic length (L*), m. 30-35 24-28 22-26 25-30 60-70 30-35 30-35 30-40 22-28 30-40 4@50
Chamber Shape
As can be seen from equation (4-3), the stay time ts is independent c; the combustion chamber geometry. Theoretic:ally, for a given required volume, the chamber can be of any shape. In actual design, however, the choice of the combustion chamber configuration is limited. In a long chamber with a small cross section, higher nonisentropic gas flow pressure losses will result as explained in chapter I. This approach also dictates a longer thrust chamber space envelope and imposes certain space limitation on the injector design to accommodate the necessary number of injector holes. With a short chamber of large cross section, the propellant atomization or vaporization zone occupies a relatively large portion of the chamber volume, while the mixing and combustion zone becomes too short for efficient combustion. Other factors, such as heat transfer, combustion stability, weight, and ease of manufacturing, are to be considered in determining the final combustion chamber configuration. Three geometrical shapes which have been used m combustion chamber design are shown in figure 4-8. While the spherical and the nearspherical chambers were used in earlier European
v
88
v
__
--
DESIGN OF LIQUID PROPELLANT ROCKET ENGINES
designs, the cylindrical chamber has been used most frequently in the United States. The spherical or nearly-spherical chamber, as compared to the cylindrical one of the same volume, offers the advantage of less cooling surface and weight. A sphere has the smallest surfaceto-volume ratio. For equal strength of material and chamber pressure, the structural walls of the spherical chamber are about half the thickness of the walls of a cylindrical chamber. However, the spherical chamber is more difficult to manufacture and has poorer performance under most circumstances. For these practical reasons, the design details of the cylindrical combustion chamber will be treated in this book. Several
THROAT
/NOZZLE
novel thrust chamber designs will also be discussed. In the design layout of the cylindrical combustion chamber of a given At and L*, the value of the contraction area ratio, (ec =(Ac/At)) can be optimized through careful studies of the following factors: (1) Combustion performance in conjunction with the injector design (2) Chamber gas flow pressure drop (3) Chamber wall cooling requirements (4) Combustion stability (5) Weight (6) Space envelope (7) Ease of manufacturing For pressurized-gas propellant feed, lowthrust en_ne systems contraction area ratio values of 2 to 5 have been used. For most turbo-
pump propellant feed, high thrust and high chamengine systems lower ratio values THRUST--CHAMBER ber pressure of 1.3 to 2.5 are employed. The reader is also referred to section 1.2 chapter I, "The Gas-flow Processes in the Combustion Chamber and the AXIS Nozzle."
IN_
The basic elements of a cylindrical combustion chamber are identified in figure 4-9. In design practice, it has been arbitrarily defined that the combustion chamber volume includes the
COMBUSTION CHAMBER
IN_
space between injector face I-I and the nozzle throat plane II-II. The approximate value of the combustion chamber volume can be expressed by the following equation
NOZZLE
Vc = A_ [Lcec + ½_-A-_Cot _-NEAR SPHERICAL COMBUSTION CHAMBER
INJECTOR
(4-5)
THROAT
FACE
[-CHAMBER
I
T_T
O(ec_/3 -1)]
NOZZLE
[
DIA
I
AREA
"
n" Dc
I
Ac
,
,---
NOZZLE
/
INJECTOR
?
HRUSTC.___.HHAMBER CHAMBE:"
AXIS [
[
_
CYLINDRICAL
OIA
[
AREA
Dt A t
SECTION
z_LENGTH
CYLINDRICAL COMBUSTION CHAMBER Figure
4-8.-Frequently used geometrical [or combustion chambers.
Lc
CHAMBER
CONTRACTION AREA
shapes
Figure
RATIO
Ac (¢
= A'-'_T
4-9.-Elements of basic cylindrical bustion chamber.
com-
DESIGNOF THRUST CHAMBERSAND OTHER COMBUSTIONDEVICES
The total
surface
area of the combustion
chamber walls excluding injector face can be approximated by the following expression:
Total
Nozzle
area =2Lc_cAt
Expansion
It was learned
+ csc 9(ec - 1)At (4-6)
Area Ratio earlier
that
with all other
parameters fixed, in particular chamber pressure, there is only one optimum nozzle expansion area ratio for a given altitude or, more specifically, ambient pressure. Except for those systems which start in vacuum, ambient pressure will have to be considered. This is especially true for boosters which start at or near sea-level conditions. It is the ultimate purpose of a rocket engine to lift vehicles to altitudes. Inherently, then, ambient pressure will not be a constant (except for high-altitude starts, as mentioned). It is, therefore, extremely important for the designer to know the trajectory of the vehicle to be propelled or, more specifically, its altitude-versus-time characteristics. With this information, the designer is in a position to make a first, optimizing selection of a nozzle expansion area ratio, for best results throughout the entire trajectory. As shown earlier, area ratio will be truly optimum for only one specific altitude. The optimization for ambient pressure then is essentially an averaging process. Other considerations usually cause the designer to deviate from the "paper optimum" for the nozzle expansion area ratio. Some of the most common are: weight, size, ease of manufacturing, handling, and cooling (heat transfer) considerations.
Nozzle
89
The selection of an optimum nozzle shape for a given expansion area ratio is generally influenced by the following design considerations and goals: (1) Uniform parallel axial gas flow at the nozzle exit for maximum momentum vector (2) Minimum separation and turbulence losses within the nozzle (3) Shortest possible nozzle length for minimum space envelope, weight, wall friction losses, and cooling requirements (4) Ease of manufacturing In actual design practice, any abrupt change or discontinuity in the nozzle wall contour should be avoided to eliminate the possibility of shock waves or turbulence losses. Theoretically, the nozzle throat is simply the unique plane of minimum cross-section area. In practice, a wellrounded throat section is employed. Only at the nozzle exit plane is a sharp edge used because a rounded one would permit overexpansion and flow separation. 1. Conical
Nozzle
In early rocket engine applications, the conical nozzle, which had proved satisfactory in most respects, was used almost exclusively. The advantages of a conical nozzle are ease of manufacturing and flexibility of converting an existing design to higher or lower expansion area ratios without major redesign of the nozzle contour. The configuration of a typical conical nozzle is shown in figure 4-10. The nozzle throat section has the contour of a circular arc with a radius R ranging from 0.5 to 1.5 times the throat radius Rt. The half angle of the nozzle convergent cone section can range from 20 ° to 45 °. The
Shape
Most rocket nozzles are of the convergingdiverging De Laval type. Since the flow velocity of the gases in the converging section of rocket nozzle is relatively low, any smooth and wellrounded convergent nozzle section will have very low energy losses. By contrast, the contour of the diverging nozzle section is very important to performance, because of the very high flow velocities involved.
RI
,. Figure
:4-I O.-Conical
y-os nozzle
contour.
9O
DESIGNOF LIQUID PROPELLANT ROCKET ENGINES
divergent cone half angle a varies from approximately 12 ° to 18 °. The length of the conical nozzle section can be expressed by the equation
Rt(_e - 1) + R(sec Ln= tan a
/ / /
E.
L_E
_-c:,,-_,.
1
(4-7)
-,---__
;_= _ (1 + cos a)
(4-8)
where a = half angle of the conical nozzle. For an ideal nozzle, A would be unity. For a conical nozzle with a = 15 ° and h =0.983, the exit gas momentum or the exit velocity will be 98.3 percent of the ideal nozzle exit velocity calculated by equation (1-18). The value of the vacuum thrust coefficient of a nozzle is in direct proportion to the thrust generated by the nozzle, or to the nozzle exit gas velocity. Therefore, the theoretical vacuum thrust coefficient (neglecting friction and other flow losses) of a conical nozzle with 15 ° half angle will be 98.3 percent of the ideal nozzle thrust coefficient calculated by equation (1-33a). 2. Bell Nozzle For increased performance and shorter length, bell-shaped nozzles have been developed. This nozzle design employs a fast expansion or radial flow section in the initial divergent region, which then leads over to a uniform, axially directed flow at the nozzle exit. The wall con-
zle.
.
/
with uniformly parallel axial gas flow. The value of h can be expressed by the following equation:
enough
PLANE L_
[:
a - 1)
The conical nozzle with a 15 ° divergent half angle has become almost a standard, as it is a good compromise on the basis of weight, length, and performance. Since in a conical nozzle certain performance losses occur as a result of the nonaxial component of the exhaust gas velocity, a correction factor h is applied for the calculation of the exit gas momentum. This factor or thrust efficiency is the ratio between the exit gas momentum of the conical nozzle and that of an ideal nozzle
tour is changed gradually shocks will not form.
EXIT [
so that
oblique
Figure 4-11 shows the contour of a bell nozA circular arc of selected radius R, is
/ _/ _,
1 Figure
....., C_CrERIS_r
ic
._ 4-11.-Bell
nozzle contour.
chosen for the nozzle contour MT upstream of the throat. Contour TNE is the diverging portion of the nozzle. The initial expansion occurs along contour TN; contour NE turns the flow over to a direction nearer to axial. For design convenience, the contour TN is also a circular arc, with a smaller radius R2. For those familiar with compressible flow theories, it is noted that, using transonic flow analyses, a constant-Mach-number line TO can be defined at the throat. Given the flow condition along TO and the solid boundary TN, a kernel flow field TNKO can be generated by the method of characteristics developed in gas dynamics. The kernel of the rocket nozzle contour is defined as that portion of the supersonic flow field determined entirely by throat conditions. The last right characteristic line NK of kernel TNKO, and thus the location of the point N along contour TN, is to be determined by specific design criteria. The location of the end point E along contour NE is defined by the given nozzle expansion area ratio and nozzle length (distance between throat and exit plane). Then the right characteristic line NK can be determined by satisfying the following conditions concurrently: (1) A control surface PE can be generated between the point E and a selected point P along the line NK (2) Mass flow across PE equals the mass flow across NP (3) Maximum thrust by the nozzle is attained. By selecting points P', P", etc., along line NK, a series of control surfaces P'E', P"E", etc., can be generated to define points E I, E", etc., along the contour NE. Calculations for the nozzle contour can be effectively performed by a computer.
91
DESIGN OF THRUST CHAMBERS AND OTHER COMBUSTION DEVICES
8,\
I
I
IO0
99
!
.J
j
-_ 98 pZ _J {J nr bJ O.
/
!
,jo POINT
NOZZLE AX*S
i
////
i I,
Ln
THaT 97
Figure
section
/
9_
with
T to the 60
70
90
80
I_
Lf
exit
%
NOZZLE CONICAL
Figure
LENGTH NOZZLE
4-12.-Thrust
length.
BASED ANY
ON
for
conical
ANGLE
RATIO
versus
comparison:
nozzle,
A 15 = HALF
AREA
efficiency
(Shown
ening
(Lf)
WITH
bell
effect
increasing
lowing
nozzle
Rt from
a parabola
from
the
design
data
are
Commonly, nozzle
nozzles.
used
For
percent exit
an equivalent is
bell
plane)
Throat Axial
length
of the
exit
plane,
Ln,
diameter,
fractional
angle.)
area,
nozzle
the
the
of an
between or 0.8
nozzle
below
to specify
length
(distance
80 percent,
conical
radius
15 ° half-angle
a standard
instance,
is
half-angle
as
having
throat,
the
and
(3)
Expansion
bell
(4)
Initial
(5)
and
of a 15 °
area
shows the thrust nozzle length
nozzle,
the
fol-
Dr, inches nozzle
inches
length area
wall
throat
Nozzle
exit
The
wall
angles,
4-14
as
a function
from
throat
(or the
Lf based
to
desired
on
a 15 °
ratio
angle
e
of the
parabola,
On,
wall On and of the
angle,
0e,
Oe are
degrees
shown
expansion
in figure
area
ratio
E.
expansion
ratio. Figure 4-12 versus fractional
to the
degrees
80-
same
throat
nozzle)
coni-
throat
of that
of a specific
(2)
conical
cal
the there
required:
(1)
of short-
half
of 0.382
N and
E. For
FRACTIONAL
bell
contour.
a radius
point
of
approximation
nozzle
,,,o// / /
96
4-13.-Parabolic
efficiency h LI for conical
!
40
L/= toO% Lf= 70%
and
bell As
nozzles.
may be
seen,
approximately contribute sidering
3.
nozzle
80 percent
weight
with
Approximation
convenient
nozzle
in figure upstream a radius contour
when
con-
penalties.
way
of Bell Nozzles to design
4-13.
The
of the of 1.5
Rt.
is made
2¢
a near-optimum-
is through procedures
gested by G.VR. Rao. The of a parabolic approximation diately
Lf = 80% L_= 90% Lp 100%
_5o
beyond
significantly
especially
thrust bell nozzle contour the parabolic approximation
shown
lengths
do not
to performance,
Parabolic One
bell
the
__
use of as sug-
design configuration bell nozzle is nozzle
throat The
contour
up of a circular
i
i
_ "_ 0
section entrance
EXPANSION
t
30
20
_0
imme-
T is a circular divergent
_ _'5.,c z E
AREA
40 RATIO
Lf"
60=/=
LI"
70%
Lf = 80% .f, 90°/° Lf, 100%
5O
•
arc Figure
4-14.-0n
and area
Oe as ratio
function _.
of expansion
92
DESIGN
OF
LIQUID
PROPELLANT
Optimum nozzle contours can be approximated quite accurately by selecting the proper inputs. Although no allowance is made for different propellant combinations, experience has shown that the effect of specific heat ratio y upon the contour is small. A computer program can be readily set up to perform the calculation. 4. Annular Based
theorem,
for ideal
ex-
pansion the thrust generated by a thrust chamber depends only upon the mass flow conditions (velocity and direction) at the nozzle exit. In some nozzle designs, such as annular nozzles, the gas flow at the throat is not necessarily parallel to the axis, but the exit flow is similar to that of a conical or bell nozzle and thus produces the same thrust results. There are two basic types of annular nozzles: the radial in-flow type (spike nozzle) and the radial out-flow type (expansion-deflection or E-D; reverse-flow or R-F; and horizontal-flow or H-F nozzles). They are shown in figure 4o15, together with conventional conical and bell nozAREA
ENGINES
zles. For comparison of the effect of nozzle type on size, all nozzles shown are scaled to the same thrust level, nozzle expansion area ratio, and theoretical nozzle efficiency. These nozzles show potential of adapting their geometry to space vehicle application, because shortened nozzles reduce interstage structure weight and will permit an increase in payload through increased performance for a given length. The nozzle expansion area ratio ( for an annular nozzle is defined by equation (4-9):
Nozzles on the momentum
ROCKET
Projected area of the contoured nozzle wall Ae-Ap e: Throat area At
(4-9)
where the projected area of the contoured nozzle wall equals nozzle exit plane area Ae, less the centerbody projected area Ap. Another convelent design parameter for annular nozzles is the annular diameter ratio, Dp/Dt, where Dt is the throat diameter of an equivalent circular throat, and Dp the centerbody diameter. Dp/Dt is an index of the annular
RATIO = 36:1 = 9B.3%
The parameter nozzle design
(ALT}
OF EFFICIENCY JECTOR OMBUSTION HAMBER INJECTOR COMBUSTION
HROAT I_
INJECTOR
/
rl ..--"- COMBUSTION JJ'CHAMBER
: [_ _ 'tl X
, T
:i' CONE w.,, '
Dp/D NOZZLE
LENGTH
= 100%
NOZZLE
LENGTH
= 74.2%
OVERALL
LENGTH
= I00%
OVERALL
LENGTH
= 70%
DIAMETER
= 100%
OVERALL
OVERALL
DIAMETER
_
= tO0%
"'THROAT
/
Dp/D
LENGTH
= 41.4%
OVERALL
LENGTH
= 51%
OVERALL
DIAMETER
= 105"/.
COMBUSTION
LENGTH
= 41.4%
OVERALL
LENGTH
= 519=,
OVERALL
DIAMETER
/X_
COMBUSTION
/
CHAMBER
CHAMBER {NJECTOR Ii- I
p---Dp"---'4
;_
R-F Dp/D
Y
H-F Dp/D
T = ,5
i1_
t = t0
NOZZLE
LENGTH
= 24,9
NOZZLE
LENGTH
= 14.5
OVERALL
LENGTH
= 21%
OVERALL
LENGTH
= 12 %
OVERALL
DIAMETER
= 150 %
Figure
4-I 5.-Comparison
OVERALL
of nozzle
DIAMETER
shapes.
= 194
T = 1.3
NOZZLE
INJECTOR-,,
THROAT
_
E-D ' "
I = 1.3
NOZZLE
TH R OAT
j.._D,I._,
5f 'i,!
sPIKE
,
cOM BUSTION CHAMBER
j/"-/pD'_ i
i':44--.. "i
T,'
' BELL
/
INJECTOR
i;;rl_ _../-_l.J Z"
%
%
= 102.5 %
93
DESIGN OF THRUST CHAMBERS AND OTHER COMBUSTION DEVICES
geometry The
as
compared
to a conventional
contour-calculating
nozzles
are
similar
In a conical
well
below
level
or low-altitude the
in chapter
overexpansion
low
altitudes.
characteristics,
losses.
As shown
zle
equally
(and
zles), the
the
back
the
function lower
are
4-16
back
ambient.
base
pressure
expansion the
is reached.
through
the
downstream
by
flow
the
following
(i)
The
(2)
The
two
nozzle
the
gases base
the
Figure
gas CD,
controlled
of the
are
deflected,
and
local
nozzle operation
curved-wall which
of the
turns
inner
shown
the
to some
in wall
distribution in figure
jet
gases
A typical
for low-altitude
4-16.
This
Because
corn-
CONSTANTI_ACH---k
L.NE \ TN"OAT ,NJECTO,
E
performance
AXIS BODY
wall,
as
1
4-16.-E-D
nozzle
at low altitude
that
so low
behind Since
be axial,
the
is
altitude.
of the
separation
case
inner
from
for a conven-
the
the
flow
the
gases
flow
nozzle. under
figure
4-17.
The this
ondary
spike
which
flow
secondary
streams. effect
To
describe
of truncating
is
the concept
(radial
in-
amount
nozzle
aerodynamic
flow
in
nozzle
a small
between
of
of sec-
base
spike
nozzle
geometric flow, is
the the
param-
the
manner
introduced, primary flow the
end
distri-
shown
nozzle
of secondary
energy
pressure
concept
nozzle
on
up to the
This
the
must
expansion
is also
into
of the
amount
the
spike
of various
this
relative
depending
nozzle
introduced
is a function
occur
wall
utilizes
in figure
point
nozzle.'
annular
region. Performance
the
nozzle
con-
shown
unaffected
condition
pressure
flow
closure
However,
spike
type),
as
may
may continue
bution
flow
wave
base
nozzle
at the
conditions.
of the
the
the
centerbody,
a shock
ondary
operation.
the
operation
interrelated
Figure
is
flow
becomes
in which I.
at low nature
At high-altitude verges
the
is no
which
is responsible
nozzle.
eters,
PRESSURE_
nozzle,
self-adjusting
there
is a truncated
F,,EE " SURFACE NOZZLE
WALL
altitude
wall,
nozzle
aerodynamic
'"_""_'"_
nozzle
spike
of the
nozzle
tional
at the
An improved NOZZLE WALL _
at high
for the
for improved
Pb
compression
pressure.
turning
typical
jet boundary,
influences
contour,
leads
pressure
is
also
4-17.
increases
wall
pressive
flow.
surface
nozzle operation.
the
which
Pb which
4-17.-E-D
is
boundary. Because
, Essu,
throat,
line
DE
WALL
a
initial
is
to near-axial stream
of
conditions:
contour
pressure
free
the
gases
boundary
wall
noz-
the centerbody until this
constant-Mach of the
.... '------CENTER BODY
generally
of the
After
.OZZkE
in regu-
and
Downstream
_--SNOCK
noz-
face
of Pb is
the expansion of the gases around shoulder C will continue unaffected
°"--_B-_]_
of their
role
pressure
__! FREESTREAMSURFACE
to these
annular
value
_,,/f_-_'_ /_I_
THROAT----x \
at
for an E-D
at the
The
ambient
ratios,
losses
an important
flow.
area
subject
WALL
__/I
sepa-
explained
to other Pb
plays
flow
because
not
in figure
nozzle
than
nozzles,
pressure
of the
large
ex-
(sea-
As
in thrust
applicable
centerbody
lating
with
Annular
special
before
_NOZZLE
MACHLINE_
may
ambient
occurs.
results
CONSTANT_
nozzles. gases
the
wall
I, for nozzles
this
the
operation)
nozzle
nozzle.
for annular
for bell
nozzle,
to pressures from
to those
or bell
pand ration
methods
and and
field
spike
secand
nozzle,
_Source: AIAA Paper No. 66-828, "Liquid Rocket Engines: Their Status and Their Future" By S. F. Iacobellis.
94
DESIGNOF LIQUID PROPELLANT ROCKET ENGINES
base achieved the
pressure through
and the base the secondary
pressure increase flow addition
requires a lengthy, detailed discussion; only the basic operation can be presented here. The primary flow (high-pressure gases) which produces the major portion of the engine thrust is exhausted from an annular-type combustion chamber and expands against the metal surface of the center tru-_ated-spike nozzle (fig. 4-18). The characteriF of the primary flow field upstream of the basv, shown as region 1 in figure 4-18, are determined by the annular throat geometry, the nozzle wall contour, and the ambient pressure. The annular primary flow continues to expand beyond the nozzle surface and encloses a subsonic, recirculating flow field in the base region (region 2). The pressure acting on the nozzle base contributes additional thrust to the nozzle. When a small amount of secondary flow is introduced into the base (added to the recirculating flow), the base pressure is increased further. As the secondary flow is increased, the overall nozzle efficiency (considering the additional flow) increases because of this increase in base pressure. There is a limit to this gain in efficiency, and an optimum secondary flow exists for each configuration. The outer surface of the annular primary flow is a free-jet boundary, which is influenced by ambient pressure. This ambient pressure influence on the primary nozzle flow endows this type of nozzle with altitude compensation. In operation at high-pressure ratios (i.e., altitude conditions), the outer free-jet boundary of the primary flow expands outward, governed by the Prandtl-Meyer turning angle at the throat. At low-pressure ratios (i.e., sea level operation), the relatively higher ambient pressure cornTOR_DJU._Ew
Figure
4-18.-Aerodynamic spike flow [ield i11usSrated under altitude conditions.
IDEAL
NOZZLE
(NO
LOSSE!
HIGH-AREA-RATIO AEROSPIK E NOZZLE
_
i, LL
/" /
L)
/ /
/_
i /
HICa-I-AR
/_
f
BELL
EA-RATIO
NOZZLE
I
I
,'
LU
/
//SEA'LEVEL
/
_
(VACUUM)
/
OPERATING
RANI
/ SEA
LEVEL
_,t_--
IJ
iI
50
100
I 200
IVACUUMI OPERATING
RANGE
] K JlJli{ 300
500
1000
2000
4000
PRESSURE RATIO (pc,/pa) Figure
4-19.-Nozzle
presses the flow field. pressure on the negative sure on the
perlormance
comparison.
outer free-jet boundary of the primary This compression increases the static the nozzle wall and partially offsets effect of the higher ambient presback side of the nozzle. The base
pressure also is increased with the higher ambient, because the compressed primary flow field, which influences the base pressure, has higher static pressures. This combination of flow field effects provides the altitude compensation inherent to the aerodynamic spike nozzle. Figure 4-19 presents the performance comparison of various nozzle designs. The nozzle thrust coefficient Cf for an ideal nozzle (i.e., a variable-area-ratio nozzle having the optimum expansion for each chamber pressure to ambient pressure ratio, pc/Pa) is shown together with those of the high-area-ratio aerodynamic spike and bell nozzle. As is evident, the CI curve of the aerodynamic spike follows the ideal nozzle performance (altitude-compensation), rather than dropping off rapidly like the bell design at low pc/Pa (i.e., sea level) operating points. M1 nozzles have a higher CI at a high Pc/Pa (i.e., vacuum). The development of the annular-nozzle concept may influence the design of rocket vehicles,
DESIGN OF THRUST CHAMBERSAND OTHER COMBUSTIONDEVICES
95
especially in the areas of boattail structure and mission staging optimization. The advantages and disadvantages of annular nozzles are summarized as follows:
4-23. The reader is urged to conduct his own calculations using the first stage as a guide, and to compare his results with those shown.
Advantages (1) Shortened nozzle length for the same performance, or increased performance (higher expansion area ratios) for a given length. (2) Improved performance at sea level or low altitudes. (Annular nozzles with high expansion area ratios can be used for a single-stage sea level to vacuum vehicle mission.) (3) The relatively stagnant region in the center of the nozzle can possibly be used for installation of gas generators, turbopumps, tanks, auxiliary equipment, and turbine gas discharges. (4) A segmented combustion chamber design approach can be used, easing development effort (individual segments can be built and tested during the early phases) and improving combustion stability.
Solution
Disadvantages (1) Relatively because surface
A-1 Stage Engine: From sample calculation Design
sea level
Substitute
Calculation
in some
(4-2)
Lay out the thrust chamber internal configuration (cylindrical combustion chamber with bell nozzle) for the engines on the Alpha vehicle with the data derived from sample calculation (4-1) and the following required chamber thrusts Ftc: engine:
Ftc
=747000
747 000 At - 1.531 x 1000 = 487 in:
Throat
diameter:
Dt = _=
24.9 in
Rt=_= Exit diameter:
De
--'-_V/_ -x
Use a combustion LO2/RP-1 (4-4):
24.9 =93.4
engine:
Ft%= 149500
lb at altitude
(c) A-3 stage
engine:
Ftc3=
Ib at altitude
(d) A-4 stage
engine:
Ftc4=
calculations
16000
chamber
application.
volume:
7500 lb at altitude and their results
are presented in the following for the first-stage engine only. For the other stages, the calculation results are summarized in figures 4-21 to
e= 14
(1-33):
area:
12.45
in
in
93.4 e =---_- = 46.7 in
L* of 45 in for
Substitute
into equation
Vc=487x45=21915cuin
Use a nozzle convergent half angle of 20 °, a contraction area ratio ec = 1.6, and a circular arc of radius R= 1.5Rt, or 18.68 in, for nozzle contour upstream of the throat. Chamber
diameter:
Dc = _'.'.6x
lb at sea level
(b) A-2 stage
The detailed
into equation
= 1000 psia;
Throat
Chamber
(a) A-1 stage
C/= 1.531; (Pc)as
R high cooling requirements, of higher heat fluxes and greater areas to be cooled.
(2) Heavier structural construction applications. (3) Manufacturing difficulties.
Sample
(4-1):
24.9 =31.5 R C
Use equation (4-7) to calculate convergent cone length Convergent
in
31,5 =_----=--=15.75
in
the chamber
cone length _ 12.45 (x/1.6 - 1) + 18.68 (sec tan 20 °
20 °- 1)
4.515 = 0.---3"64= 12.4 in
96
DESIGN OF LIQUID
PROPELLANT
ROCKET ENGINES
INJECTOR FACE
THRUST CHAMBER
AXrS
L n = 102.4"
Figure
4-20.-A-I
stage engine thrust (--14, 80% bell,
chamber L*=45",
internal (o=1.6.
-"-
configuration
INJECTOR THROAT FACE ,d
layout:
EXIT =9.25°
I
b I
8n=33 ° N
THRUST
J
__
_L_
14"R
CHAMBER AXIS
I
N0=5.94.
De=71"
L
I
17.3" - ! _ Figure
4-21.-A-2
stage
Ln =83.6"
engine _=40,
thrust
75% hell,
chamber,
internal
L*=26",
_c=1.6.
configuration
layout:
4mmmal
k.,
DESIGN
OF
THRUST
CHAMBERS
AND
OTHER
COMBUSTION
97
DEVICES
INJECTOR FACE
THRUST CHAMBER
AXIS
Figure
4-22.-A-3
stage
engine _=35,
thrust 70%
INdECTOR FACE
chamber,
bell,
L*=28",
internal
configuration
THROAT
EXIT
I
_1
V
layout:
_c=2.
Et:46.1,
`
THROAT CHAMBER
AXIS
Figure
4-23.-A-4
stage
engine _=35,
thrust 70%
bell,
chamber, L*=32",
internal ec=2.
configuration
layout:
98
DESIGN OF LIQUID PROPELLANT ROCKET ENGINES
Since
Using the frustrum cone volume equation and neglecting the slight rounding of the throat, the approximate convergent cone volume is obtained:
Volume =3 x12.4 [(15.75)2 + (12.45)2 +15.75×12.45
]
the calculations
for the thrust
chamber
configuration are based on the calculated design C[ value which has to be verified by later actual testing, a slight change of chamber pressure is usually allowed to compensate for C! deviations in order to meet the required thrust value.
= 7760 cu in 4.4 Required
volume
for cylindrical =21 915-
chamber section 7760:14 155 cu in
Required
length
for cylindrical chamber section = 14 155/1.6At= 18.17 inches
Distance
from injector face to throat = 18.17+ 12.40= 30.57, say 31 inches
Design an "80-percent bell" nozzle configuration using the parabolic approximation procedure. The nozzle contour downstream of the throat will be a circular arc of radius 0.382 Rt, or 4.75 inches. By definition, the nozzle length Ln will be 80 percent of the length for an equivalent 15 ° half-angle conical nozzle. Substitute into equation (4-7)
Ln=0.8×
[12.45
(VIT-1)+4.75 tan 15 ° (sec
15 °- 1!]
= 0.8 x 128 = 102.4
inches
The parabolic contour wall angles 0, and 0e can be derived from figure 4-14, for e= 14 and L/=0.8; On = 27.4 ° and 0e = 9.8 °. The location of N and E along the nozzle contour, with respect to throat and nozzle axis, can be calculated Nt =0.382
R: sin On = 2.19 inches
Na = Rt + 0.382 Rt(1 - cos 0n) : 12.99 inches Et : Ln = 102.4 Ea= Re=46.7
inches inches
With the aid of the established coordinates for points N and E, and the angles 0_ and 0e, a parabola can be fitted to complete the contour. The general layout of the A-1 stage engine thrust chamber is shown in figure 4-20. With the aid of a computer program, more accurate calculations of the divergent nozzle contour can be made by the method of characteristics.
THRUST
Techniques
CHAMBER and Their
COOLING
Selection
Because of the high combustion temperatures (4000 ° to 6000 ° F) and the high heat transfer rates from the hot gases to the chamber wall (0.5 to 50 Btu/in2-sec), thrust chamber cooling becomes a major design consideration. For shortduration operation (up to a few seconds), uncooled chamber walls can be used. In this case, the heat can be absorbed by the sufficiently heavy chamber wall material which acts as a heat sink, before the wall temperature rises to the failure level. For most longer durationapplications, a steady-state chamber cooling system has to be employed. One or a combination of the following chamber cooling techniques is often used: 1. Regenerative coollng.-Regenerative cooling is the most widely applied method and utilizes one or possibly both of the propellants, fed througt_ passages in the thrust chamber wall for cooling, before they are injected into the combustion chamber. (See par. 4.1 and fig. 4-1.) 2. Dump cooJing.-With this principle, a small percentage of the propellant, such as the hydrogen in a LO2/LH2 engine, is fed through passages in the thrust chamber wall for cooling and subsequently dumped overboard through openings at the rear end of the nozzle skirt. Because of inherent problems, this method has only limited application. 3. Film cooling.-Here, exposed chamber wall surfaces are protected from excessive heat with a thin film of coolant or propellant which is introduced through manifolded orifices in the chamber wall near the injector, and usually in several more planes toward the throat. The method has been widely used, particularly for high heat fluxes, either alone or in combination with regenerative cooling. 4. Transpiration cooling.-Transpiration cooling is accomplished by introducing a coolant
DESIGN OF THRUST CHAMBERSAND OTHER COMBUSTIONDEVICES
(either gaseous or liquid propellants) through porous chamber walls at a rate sufficient to maintain the desired combustion gas side chamber wall temperature. This method is essentially a special type of film cooling and has been widely used. 5. Ablative cooling.-In this process a sacrifice of combustion-chamber gas-side wall material is made by melting and subsequently vaporizing it to dissipate heat. As a result, relatively cool gases flow over the wail surface, thus creating a cooler boundary layer, assisting the cooling process. Ablative cooling has been used in numerous designs, initially mainly for solid propellant systems, but later equally successfully for low Pc, pressure-fed liquid systems. 6. Radiation cooling.-_tith this method, beat is radiated away from the surface of the outer thrust chamber wall. It has been successfully applied to low heat flux regions, such as nozzle extensions. The selection of the best cooling method for a given thrust chamber depends on many design considerations. There are no simple-and-fast rules. However, the following are the main factors which influence the selected design approaches: 1. Propellants.-The properties of the combustion products, such as temperature, specific heat, specific weight, viscosity, etc., have a direct bearing on the heat transfer rate and in turn affect the chamber cooling requirements and methods. The cooling properties of the propellants and their relative flow rate decide whether they are suitable or sufficient for regenerative or film cooling. Therefore, in evaluating a chamber cooling system, the propellants involved will be one of the primary design considerations. 2. Chamber pressure.-High chamber pressure is linked with higher combustion gas mass flow rates per unit area of chamber cross section and thus raises the heat transfer rate. Combined regenerative and film-cooling methods are usually employed for the stringent requirement of higher chamber pressure applications. 3. Propellant feed system.-The type of propellant feed used in an engine system determines the pressure budget for the system. In a turbopump-fed engine system, more pressure drop is usually available for chamber cooling. The
99
availability of this pressure drop permits the use of regenerative cooling which requires propellant pressure sufficient to force the coolant through the cooling passage before entering the injector. A pressurized-gas-fed engine system usually has more stringent pressure limitations and operates on relatively low chamber pressures. This suggests the application of film, ablative, or radiation cooling. 4. Thrust chamber configuration.-The geometric shape of the chamber affects local combustion gas mass flow rates and wall surface areas to be cooled. This influences the choice of cooling method. It can also arrangements for regeneratively wall thrust chambers. 5. Thrust
chamber
limit the design cooled tubular
construction
material.-The
properties of the thrust chamber materials will affect the cooling system design profoundly. Strength at elevated temperature, combined with heat conductivity properties of a metal, will Jetermine suitability for regenerative cooling systems. For film-cooled chambers higher allowable material working temperatures are desired to reduce heat transfer rates and thus film coolant flow rates. The application of radiationcooling to a chamber depends largely on the availability of high temperature (3000 ° F and up) refractory alloys. The success of ablative cooling depends entirely on the availability of suitable composite plastic materials. In practice, the design of thrust chamber cooling systems is a major link in the complete engine system design. It cannot be treated independently, without due consideration of other engine system aspects. For instance, optimization of the chamber pressure value for a highperformance engine system is largely limited by the capacity and efficiency of the chamber cooling system. In turn, chamber pressure will affect other design parameters such as nozzle expansion area ratio, propellant feed pressure, and weight. Because of the complex interrelation between these factors, the complete analysis of chamber cooling systems is a specialized field and requires thorough knowledge of heat transfer, fluid mechanics, thermodynamics, and thermal stresses. The engine system designer, therefore, will enlist the services of heat transfer specialists.
100
DESIGN OF LIQUID PROPELLANT ROCKET ENGINES
Gas-Side
Heat Transfer
One of the primary steps in the design of a thrustchamber cooling system is the analysisof the heat transferfrom the combustion gases to the chamber walls (gas-sideheat transfer).Because of the very high surface velocityof the gases along the chamber walls, the heat transfer occurs mainly through forcedconvection; i.e., throughthe transferof heat energy resultingfrom the relativemotion of different parts of a fluid. Before the gases can transferheat to the wall, the heat energy must pass througha layer of stagnantgas along the wall, calledthe boundary layer. The basic correlationforthiscomplicated convective heat transfercan be expressed by the followingequation: q : hg (Taw - Twg) where q = Heat flux or heat transferred across stagnant gas film per unit surface per unit time, Btu/in2-sec hg
=Gas-side heat transfer in2-sec-deg F
coefficient,
(4-10)
the area
dominantly influenced by the mass wlocity or the mass flow rate per unit area of the gas, subject to the exponent 0.8. In comparison, all other factors are relatively minor. A rough approximation of hg can thus be expressed by the following equation: hg=(p'V)
Twg = Hot-gas-sidelocal chamber-wall temperature,deg R The determination of the gas-side heat transfer coefficient hg is a rather complex problem. The convection phenomenon as it occurs in rocket thrust chambers eludes complete understanding. Attempts to compare analytical results with experimental heat-transfer data obtained on rocket thrust chambers have often shown disagreement. The differences are largely attributed to the initial assumptions for analytical calculations. For example, there is good evidence that oxidizing and reducing atmospheres covering a wide range of temperature exist locally in the combustion product gases within the thrust chamber, because of the imperfect mixing of the propellants at the injector face. This results in deviations from calculations based on the assumption of homogeneous product gases. However, it has been established by experiment _hat the beat-transfer coefficien_ is pre-
(4-11)
where p' = Free stream value of local gas density, lb/cu in = Free stream value of local gas velocity, in/set Thus, under normal circumstances, the heattransfer coefficient varies with the chamber pressure to the 0.8 power and throughout a given chamber inversely with the local chamber diameter to an exponent of 1.8. Based on experience with turbulent boundary layers, some relatively simple correlations for the calculation of the gas-side heat-transfer coefficient have been developed. A much-used form is that credited to Colburn
Btu/
Taw = Adiabatic wall temperature of the gas, deg R= (Tc)ns x turbulent boundary layer recovery factor (ranging from 0.90 to o.9s)
°8
Nu = C Re °8 Pr °_
(4-12)
where Nu = Nusselt number = hg D/k C =Dimensionless constant Re = Reynolds number = p'VD/_ = Free stream velocity,in/set Pr = Prandtlnumber = _Cp/k D =Hydraulic diameter,in k =Gas thermalconductivity,Btu/sec-in2deg F/in _t =Viscosity, Ib/in sec Cp=Specific heat at constantpressure,Btu/Ibdeg F or as Bartz
has shown
'++L+. + ,.'+c+++" It+ ] i+)o. (-+)°'o +,++ where R = l_dius of curvature throat, in
of nozzle
o = Correction factor for property across the boundary layer
contour variations
at
101
DESIGN OF THRUST CHAMBERSAND OTHER COMBUSTIONDEVICES
A = Area under consideration along chamber axis The value of a can be evaluated in terms of nozzle stagnation temperature, local gas-side chamber wall temperature, and local Mach number. 1
values of a for various Twg/(Tc)n s and y, as computed by Bartz, are shown in figure 4-24. If Pr and # data are not available for particular combustion gas mixtures, the following equations can be used for approximate results:
(4-15)
Pr=9__5 /_=(46.6 where T= temperature Equations (4-13),
× 10-_°) _ °ST °'6
(4-16)
of gas mixture, °R (4-14), (4-15), and (4-16)
can be used to calculate the ues along the thrust chamber the calculated values can be lower than the actual ones if ditions exist:
approximate hg valwalls. However, expected to be the following con-
0.6
"'l O -I'z
I J
o.6[ 1 4
3
TI/
I
JI
I
I
I
I
_1
2
I
Z
3
4
Figure 4-24.-Values property variation
The calculated values may be higher than the actual ones, because of the following: (1) The combustion reactions may not be completed in the chamber. (2) The combustion gases may deposit solids on the chamber walls, which act as insulators. In certain propellant combinations, the combustion products contain small amounts of solid particles. These solids tend to deposit on the chamber wails, and form a rather effective insulating layer. A quantitative evaluation of _he insulation effectiveness of this layer, necessary for correct heat transfer calculations, has been accomplished only experimentally. In the case of the LO2/RP-1 combination, carbon solids are deposited on the chamber walls. After a firing, the carbon gives the interior of the thrust chamber the appearance of being freshly painted black. The outer surface of the carbon appears sooty and can easily be removed by light rubbing. Underneath the exterior soot layer is a harder, graphitelike layer which can also be removed, but is more tenacious. This carbon deposit significantly increases the gas-side thermal resistance. The temperature of the carbon deposit at the hot gas-side interface approaches the gas temperature as the carbon thickness increases. The values of the thermal resistance of the carbon deposit based on actual experimental testing results of a thrust chamber burning LO2/RP-1 are shown in figure 4-25. For the heat transfer calculation of the gasside heat transfer with solid deposit on chamber walls, the following equations can be used q = hgc (Taw - Twg)
I
CONTRACTION
(1) A substantial fraction of the combustion gases are strong radiators. (2) There is substantial dissociation, with subsequent recombination near the wall. (3) There are strong high-frequency flow instabilities.
5 6
I 78510
20
30
40
where hgc = overall gas-side Btu/in2-sec-deg F
I[XP&NSION
of correction factor a for across boundary layer.
thermal
1 hgc-
conductance,
(4-18)
i hg +
(4-17)
Rd
102
DESIGN
!,!
2400
OF
LIQUID
PROPELLANT
,;
ROCKET
ENGINES
= 6460 × (0.975) 2 : 6140 ° R (See eq. 1-32a and 1-41). From sample calculation
(4-1):
22(311 _
Design I_ u? ,8o0
From sample
c* = 5660 ft/sec
calculation
(4-2):
i
Dc=24.9 Mean radius fzoo
of the throat
I
2 CONTRI.CllON _
I
2
4 t _
_¢ AREA
I ,
6 8 EXPANSION
_
,
i
12
- 11.71 in
e 44)
yR 1.222 x Cp - (),_ I),I - (i. 222 - I) × 778 = 0.485 Btu/lb-deg
From equation where Rd thermal resistance caused by the solid deposit, in2-sec-deg F/Btu When there is no solid deposit, Rd =0 and hgc = hg, and equation (4-10) is used for heat transfer calculations.
Calculation
contour 18.68+4.75 2
_4
RATIO
Figure 4-25.-Thermal resistance el carbon deposit on chamber walls LO2/RP-1, mixture ratio = 2.35, (Pc)n s = 1000 psia.
Sample
in
(4-15):
4 × 1.222 Pr : (9 × 1.222) - 5 =0.816
From equation
(4-16):
: (46.6 × 10 -1°) × (22.5) 05 x (6140) 0.6
(4-3)
Determine the approximate design gas-side overall thermal conductance hgc in the combustion chamber, at the throat, and at the exit nozzle point of e=5, for the regeneratively cooled thrust chambers on the A-1 and A-2 stage engines.
= 46.6 × 10-1° × 4.76 × 188 - 4.18 x 10 -6 lb/in-sec From equation
h -V0"026
g-L
(4-13):
x((4"18×10-_)°2x0'485) 0.8160.6
Solution
0.9
(_.) A-I Stage Engine First, let us consider equation (4-13). The combustion reactions are assumed to be homogeneous and complete. From figure 4-3 the following values are derived for the chamber product gases, for LO2/RP-1 mixture ratio of 2.35: (Tc)ns
F
at (Pc)ns = 1000 psia
and a
lb/mol,
y= 1.222
(Tc)ns
=Theoretical
(Tz)ns
: 0.01366
× (c* correction
factor) 2
7
At\ 0.9 × 0.046 × 4.02 × 1.078 × k-_} o
"At_O.9
= 0.0027 x ("_')
= 6000° F or 6460 ° R, =22.5
The design
×\-g-6-65
a
Since the carbon deposit temperature approaches the gas temperature, a (Twg/(Tc)ns) value of 0.8 is used to determine the a values from figure 4-24 (),_1.2). At the combustion chamber:
J
(7
DESIGN OF THRUST CHAMBERS AND OTHER
COMBUSTION DEVICES
b(b_)A-2 (__)
°9:(1_16) " 1" 0.9 :0,655,
a=l,05
Again,
Stage the
Engine
combustion
to be homegeneous hg : 0.0027
4-4,
× 1.05 = 0.00185
x 0.655
Btu/in2-sec-deg
F
the
= 800 At the
following
chamber
product
psia
and
103
reactions
and
complete.
values
are
gases,
assumed figure
derived
for
for LO;/LH2
a mixture
ratio
the
at (Pc)as
of 5.22:
throat: (Tc)ns
= 5580 ° F or 6040
° R, =12
-_)°'9=l,a=
hg = 0.0027
x 1 x 1 : 0.0027
Btu/in
2-sec-deg
design
exit
nozzle
point
(Tc)ns
=
(Tc)ns
x (c*
From
sample
calculation
× 0.8 : 0.000507
The experimental used to determine Rd,
for the
resistances
Btu/in2-sec-deg
data of figure 4-25 the values of thermal carbon
factor)
× (0.975)
2
2 = 5740 ° R
(4-1):
a=0.8 Design
× 0.235
correction = 6040
of
e=5,(_-)°'9=(1)°9:O.235,
hg = 0.0027
y= 1.213
F Theoretical
At the
lb/mol,
1 The
ance
are From
deposit.
The
F
From
figure
c* = 74S0
ft/sec
4-21:
Dt = 11.2 in
can be resistMean
thermal
radius of the throat contour =
are 8.4+2.14 - 5.27 in
in2-sec-deg 1670
F
in:-sec-deg
Btu
,
1125
2
F
Btu
' in2-sec-deg
and
for points and
the
at the exit
Substitute combustion
combustion
nozzle into
area the
chamber, ratio
equation
Cp = (y_
Btu
the
yR
From
throat,
1.213
equation
(4-18);
Btu/in2-sec-deg
F
1.21a
equation
- 5 = 0.820
(4-16):
F
1670
= (46.6
x 10-lo)
(12) o.s (5740)o6
x 10- ,o × 3.47
x 180
throat =2.92x
hg c -
At the
1 --+ 0.0027 exit
= 0.00067
Btu/in2-sec-deg
nozzle
1 -0.000507
From
lb/in-sec
equation
(4-13):
of e= 5.
= 0.000276 e1645
10 -6
F
1125
hg=L [ 0.026 hg c-
Btu/lb-deg
(4-15): 4x
at the
From = 0.00045
0.943
of e = 5.
= 46.6 at the
- 1) × 778-
Pr = (9 x 1.213)
1 --+ 0.00185
1544 i----_
x
1)g = (1.213
chamber
1 hgc -
1645
F
Btu/in2-sec-deg
x ((2.92x,
_10-6)°2×0.943)
.
F x\
7480
x\5--._
]
j\-_--]
a
104
DESIGN OF LIQUID PROPELLANT
(A_
ROCKET ENGINES
t.,4_CHAMBER
09
:0.01605 ×0.0828 ×2.69×1.078×\--X-J ° GAS SIDE BOUNDARY
I INNER WALL ['_qI.--COOLANT SIDE BOUNDARY LAYER
LAYER
I A_ x°9 _At = 0.00385
Since wails,
x _---_-)
there
is
no solid
an average
and
(1500/5740)
or 0.26
values
figure
At the
--
0.9
on the
wall
temperature
of
a (Twg/(Tc)ns)
is used
the
a
Tw_
chamber:
G.__16
)
0.9
= 0.655,
RADIAL
a= 1.38
At the
x 0.655 x 1.38 = 0.00348 Btu/in2-sec-deg
Figure
--Twc
DISTANCE
CENTER hgc = hg : 0.00385
COOLANT
°1 It
valueof
to determine
\
To. COM__
chamber
4-24.
combustion
(__)
deposit
gas-side
1500 ° R is assumed, from
Z
a
OF
4-26.-Heat
FROM
CHAMBER
trans[er
F
erative
Tco
schematic
for regen-
cooling.
throat: =hc(Twc-Teo)
_)°9
fig c :hg=0.00385
Btu/in2-sec-deg
(4-21)
1
H-
× 1 x 1.35 = 0.00520
-Tco)
= H (Taw
= 1, o=1.35
(4-20)
1
t
(4-22)
1
F where
At the
exit
nozzle
point
of e = 5:
(-_)°9=(1)°9=0.235,
q
= Heat
hgc
= Overall
Btu/in2-sec
gas-side
thermal
Btu/in2-sec-deg
a=1.16 hc
hgc = hg = 0.00385
flux,
× 0.235 × 1.16 =0.00105 Btu/in2-sec-deg
out deposits, =Coolant side
k
= Thermal
t
Cooling
conductivity
= Chamber
wall
Taw =Adiabatic The
heat
chamber tween
transfer
can two
partition. matically.
be described fluids,
Figure
4-26
The transfer
through
the
by the
as
moving
of heat
chamber
in a regeneratively
layers,
walls, following
shows
general from
this
heat
which
process
include
equations:
can
be-
sche-
correlation
combustion
coolant
flow
a multilayer
steady-state the
to the
the
through
cooled
deg
metal
be expressed
with-
coefficient,
of chamber
wall,
F/in thickness,
in
temperature
of the
gas,
R
Twg= Gas-side Two = Coolant
wall temperature, deg R side wall temperature, deg
Teo H
bulk temperature, deg heat-transfer coefficient,
= Coolant = Overall
gases the
wall
4-18;
F
Btu/in2-sec-deg Regenerative
eq.
hg c = hg) heat-transfer
Btu/in2-sec-deg F
conductance,
F (see
sec-deg The
bulk from
cooling
passages,
absorbed,
the
and
balance
of these
chamber
walls
Btu/in:-
F
temperature
creases
R
R
Too
of the
point
of entry
as
a function
of the
coolant
parameters, at temperatures
coolant
until
of the
flow
the
heat
rate.
Proper
to maintain below
in-
it leaves
those
the at
DESIGN
OF THRUST
CHAMBERS
which failure might occur because of melting or stress, is one of the major criteria for the design of regeneratively cooled thrust chambers. For metals commonly used in thrust-chamber walls, such as stainless steel, nickel, and Inconel, the limiting hot-gas-side wall temperature is around 1500°-1800 ° F. The resultant differences between combustion gas temperature and wall temperature range from 2500 ° to 6000 ° F. Assume a station in the thrust chamber with gas temperature Taw and coolant bulk temperature Tco. Referring to equation 4-21, it is seen that the heat flux q, which must be the same through all layers, is a function of the temperatures, and of overall heat transfer coefficient H. The value of H is composed of the individual coefficients for the boundary layers and the chamber metal wall (eq. 4-22). The smaller H, the smaller is q. However, it is one of the major design goals heat transfer
to keep coefficient hgc low, but coefficient hc and conductivity t/k
high, in relation to hgc. Since the temperature differentials are inversely proportional to the heat-transfer coefficients of the heat flow paths, the temperature drop will then be steepest between hot gas and inner chamber wall. The effect is analogous to voltage drops along resistors in electrical circuits. It is noted that the heat absorbed by the propellant used for regenerative cooling raises temperature of the propellant, and thus the energy level before it is injected into the combustion chamber. However, this effect on overall engine performance is slight, the gain usually being less than 1 percent. On the other hand, regenerative cooling with attendant pressure losses requiring additional turbopump power or higher gas pressurization levels imposes a performance penalty.
AND
OTHER
COMBUSTION
105
DEVICES
The characteristics
of coolant
side
heat
transfer depend largely on the coolant pressure and coolant side wall temperature. In figure 4-27, the heat flux is plotted versus wall temperature for a constant coolant pressure, bulk temperature, and flow velocity. Curve A indicates the behavior of heat transfer at coolant presst, res below critical. Line segment At-A2 represents the heat transfer without boiling when the wall temperature is below the saturation temperature of the coolant corresponding to the fluid pressure. As the wall temperature at A: exceeds the saturation temperature by a certain margin (50 ° to 100 ° F), bubbles will form within the coolant layer close to the wall. The bubbles grow continuously out into the colder liquid stream until condensation at the vapor to liquid surface begins to exceed the rate of vaporization at the base of the vapor bubble, whereupon the bubbles start to collapse. This process, which occurs at high frequencies, is described as "nucleate boiling." It substantially increases the heat-transfer coefficient, resulting in little increase in wall temperature for a wide range of heat fluxes. The heat transfer with nucleate boiling is represented by line A2-A 3. At A 3, further increase in the heat flux abruptly leads to such'a dense bubble population that the bubbles combine into a vapor film with an attendant large decrease in heat-transfer coefficient. The region of heat transfer with film boiling is represented by line A3-A 4. The resulting increase in
_6
m
.A 3
-w,.
....
° .........
¢o P"_
x
_
C U RVE
A
(Pco =I/2
N
Pc_,r,cAO
z4
Coolant Side Heat Transfer The coolant side heat-transfer coefficient hc is influenced by many factors. At the high heat fluxes and temperatures encountered in thrust chamber operation, the propellants used for cooling may become corrosive, may decompose or deposit impurities upon the heated surface, thereby reducing cooling effectiveness. It is impossible to calculate the hc values under these conditions without experimental data.
Mr At _
_"
O B_2
I
I I
4
6
,"--CURVE ( P"OI
e
I0
> I PCmTICALI
12
14
I)
16
is
20
COOLANT SIDE WALL TEMP. TWC (°F) X I0 -z Figure 4-27.-Heat flux versus coolant side wall temperature of typical propellant in various heat trans/er regions.
106
DESIGN OF LIQUID PROPELLANT ROCKET ENGINES
wall temperature is so high that failure of the wall material often occurs. The heat flux at A_ is defined as the upper limit of nucleate boiling of the coolant qul, which therefore should be used as the design limit for a regenerative cooling system. Curve B indicates the heat transfer behavior of a coolant above critical pressure. Since no boiling can occur, the wall temperature continually increases with increasing heat flux. Line B1-B2 represents the heat-transfer region, when the wall temperature is below the coolant critical temperature. The heat-transfer coefficient remains essentially constant. As the wall temperature reaches the critical temperature B2 and higher, a gradual transition to a stable supercritical vapor-film boundary layer begins, which results in somewhat lower heat-transfer coefficients. Line B2-B 3 represents the heat transfer in this region. Wall failure temperatures are usually reached at lower temperatures when the coolant is above the critical presstire than when it is below it. Where possible, a coolant operating pressure between 0.3 to 0.7 of critical pressure should be used to take advantage of the high heat-transfer coefficients available with nucleate boiling. However, in most systems, particularly those which are fed from a turbopump, the cooling jacket pressure, which is equal to or larger than the sum of chamber pressure and injection pressure, is supercritical. For the nonboiling subcritical temperature regions of both, subcritical and supercritical coolant pressures (AI-A2 and B_-B 2 in fig. 4-27), the relationship between wall temperature and heat flux, which depends on the heat transfer coefficient hc, can be predicted with sufficient accuracy for design purposes with the help of the Sieder-Tate equation (eq. 4-23) for turbulent heat transfer to liquids flowing in channels:
gw =coolant viscosity at coolant sidewall temperature d = coolant passage hydraulic diameter, in k = coolant thermal conductivity, Btu/sec-in deg F/in p =coolant density, ib/in 3 Vco = coolant velocity, in/sec Cp = coolant specific heat at constant pressure, Btu/ib-deg F The heat flux at the upper limit of nucleate boiling qul can be estimated from qul qnonboiling
Nu=C 1 Re °SPr°4
(4-23)
(ju+)
where C I =a constant (different values coolants) Nu =Nusselt number= hcd/k
for various
Re = Reynolds number = pVcod/_ Pr = Prandtl number = i_Cp/k /_ =coolant viscosity at bulk temperature
C 2 x 10* (4-24)
PcoG
where C2
= constant, coolant
qnonboiling
-- heat
Pco G
= coolant pressure, psia = coolant maximum flow rate unit area, lb/in2-sec
its value used
flux without Btu/in2-sec
depending nucleate
on
boiling,
per
When the heat is transferred through a vaporfilm boundary layer (coolant at supercritical pressure and temperature, region B2-B 3 in fig. 4-27), the coolant-side heat-transfer coefficient hc can be estimated from
hc: 0.029 Cpp °2 (.GO*,_.2._, _ oss pr2/3 \--d'_] \Twc!
(4-25)
where Cp
Pr G
= coolant specific heat at constant pressure, Btu/Ib-deg F coolant viscosity, Ib/in-sec = Prandtl number = coolant weight flow rate per unit area, Ib/in2-sec
coolant passage hydraulic diameter, in = coolant bulk temperature, deg R Twc--coolant side wall temperature, deg R The bulk temperature of most coolants should be kept below the critical temperature, since the vapor-film heat-transfer coefficient would be too d
014
2-
z
Tco
low to cool the wall effectively. The cooling capacity of the liquid-state regenerative coolant system can be estimated by Qc
= #cCp
(Tcc - Tci)
(4-26)
DESIGN OF THRUST CHAMBERSAND OTHER COMBUSTIONDEVICES
k._.._,
_f.._
transfer calculation. There are several basic design approaches for regenerative-cooled thrust chambers. Axial-flow cooling jackets, made up of tubes, are used in the design of large thrust chambers (3000 pounds of thrust and up); coaxial shells separated by helical ribs or wires are typical of the smaller thrust chamber designs. Figure 4-1 shows a large regenerative cooled tubular wall thrust chamber. Figure 4-28 represents a typical coaxial shell design for a smaller thrust chamber.
L
i
In this design, the coolant passage is defined as the rectangular area between inner and outer shell and two adjacent ribs, which are wrapped helically around the inner shell or liner.
i
/ Figure
4-28.-Coaxial
shell
way. Note overheated on chamber wall.
thrust and
Tubular
chamber
cuta-
burnt-through
spot
where Qc =coolant We = coolant
107
capacity, Btu/sec mass flow rate, lb/sec
Cp
=coolant specific heat at constant pressure, Btu/lb-deg F Tcc =coolant critical temperature, deg R Tci = coolant inlet temperature, deg R The allowed value of the total chamber wall gas heat-transfer rate Q should be kept below Qc by a safe margin (Q V2, due to friction losses. Ideally, the gas should leave the blades at very low absolute velocity C 2 and in a direction close to axial for optimum energy conversion in the blades. The forces generated at the rotor blades are a function of the change of momentum of the flowing gases. The following correlations may be established for design calculations of the rotor blades of a single-stage, single-rotor turbine.
(6-129)
For subsequent calculations, relation will be useful:
Axial
(6-128)
,TdmN 720
and
The velocity vector diagram shown in figure 6-56 describes graphically the flow conditions at the rotor blades of a single-stage, single-rotor turbine, based on tile mean diameter din. The gases enter the rotor blades with an absolute velocity C_, and at an angle a, with the plane of rotation. The tangential or peripheral speed of the rotor blades at the mean diameter is U. V 1
Tangential force gas flow/sec):
cos E1 +V2 cos/_2)
_b =
cos22a_(1
is some reaction
component
of C_.
' cos_ + _b co--_-_-_fll)(6-134)
or expansion
gas flowing through the blades, flow velocity at the rotor blade calculated as
of the
the relative gas outlet can be
of gas V 2=\/kb2Vl2 + 2gJ_?nAHi-2'
(6-135)
DESIGN OF TURBOPU_P PROPELLANT-FEED SYSTEMS
Amount of reheat gas flow:
qbr=(1
-kb
in the rotor
v?,
)2g j-r(1-
blades,
Btu/lb
r]n)A/-/l-2'
of
(6-136)
where al,
a2 =absolute gas flow angles at the inlet and outlet of the rotor blades, dog ill, fi2 = relative gas flow angles at the inlet and outlet of the rotor blades, dog C,, C: =absolute gas flow velocities at tile inlet and outlet of the rotor blades, ft/sec V,, U dm _?n
V 2 =relative
gas flow velocity
at the inlet
and outlet of the rotor blades, ft/sec = peripheral speed of the rotor, ft/sec = mean diameter of the rotor, in = equivalent nozzle efficiency applicable to the expansion process in the blades
AH,_2,=isentropic enthalpy drop of the gases flowing through the rotor blades due to expansion or reaction, Btu/lb; AH1-2' = 0 if only impulse is exchanged All parameters refer to the mean diameter d m, unless specified otherwise, The turbine overall efficiency Ut defined by equation (6-19) can be established for a single-stage, single-rotor impulse turbine as y_: _?n_b _rn
(6-137)
where rl_ =nozzle efficiency )7b =rotor blade efficiency fir. =machine efficiency indicating the mechanical, leakage, and disk-friction losses in the machine. Equation
(6-134)
shows
that
the blade
effi-
ciency ;?b improves when/32 becomes much smaller than I3L. Reduction of/32 without decreasing the flow area at the blade exit can be achieved through an unsymmetrical blade design (fig. 6-56), where the radial blade height increases toward the exit. In actual designs, the amount of decrease of fi2, or the increase of radial height, is limited considering incipient flow separation and centrifugal stresses. Generally, the _2 of an unsymmetrical blade will be approximately f3_-(5 ° to 15°). Equation (6-134) also indicates that _b improves as a_ is reduced.
1L
243
Design values of kb vary from 0.80 to 0.90. Design values of _b range from 0.7 to 0.92. Referring to figure 6-56, the radial height at the rotor inlet, hb, is usually slightly larger (5 to 10 percent) than the nozzle radial height hn. This height, together with the blade peripheral speed U, will determine the centrifugal stress in the blades. The mean diameter of the rotor blades is defined as dm= d_- hb, where d t is the rotor tip diameter. Pitch or blade spacing, Pb, is measured at the mean diameter dm. There is no critical relationship between blade pitch Pb and nozzle pitch Pn. There just should be a sufficient number of blades in the rotor to direct the gas flow. The number of blades zb to be employed is established by the blade aspect ratio, hb/Cb and the solidity Cb/Pb, where Cbis the chord length of the rotor blades. The magnitude of the blade aspect ratio ranges from 1.3 to 2.5. Design values of blade solidity vary from 1.4 to 2. Best results will be determined by experiment. The number of rotor blades should have no cdmmon factor with the number of nozzles or of stator blades. The blade face is concave, with radius rt. The back is convex, with a circular arc of small radius rr concentric with the face of the adjoining blade ahead. Two tangents to this arc to form the inlet and outlet blade angles 0b_ and Oh2 complete the blade back. The leading and trailing edges may have a small thickness tb. The inlet blade angle 0b_ should be slightly larger than the inlet relative flow angle fl_. If Ob_ fi_, the stream will strike the concave faces of the blades and tend to increase the impulse. The outlet blade angle Oh2 is generally made equal to the outlet relative flow angle /32. The mass flow rate _'t through the various nozzle and blade sections of a turbine is assumed constant. The required blade flow areas can be calculated by the following correlations. Note that the temperature values used in calculating the gas densities at various sections must be corrected for reheating effects from friction and turbulence.
Wt =
p1VlAblebl 144
_p2V2Ab2eb2 144
(6-138)
DESIGN OF LIQUID PROPELLANT ROCKET ENGINES
244
Total
blade
inlet area,
Abi =Zbbbzhbz
in2:
=Zbhbi (Pb sin Obl -tb)
(6-139)
Total blade exitarea,in2: Ab2=Zbbb2hb2=Zbhb2(Pb
sin Ob2-tb) (6-140)
where Pb
= pitch
P,, P2
=density outlet
V z, V 2
=relative gas flow velocities at the inlet and outlet of the rotor blades, ft/sec
ebl, (b2
=
area coefficients at inlet of the rotor blades --number of blades
and outlet
and outlet
Zb
or rotor blade spacing = rrdm/zb, in
(6-140a)
of the gases at the inlet and of the rotor blades, lb/ft _
hb_,
bb2
:radial height at the inlet of the rotor blades, in
bbl,
bb2
:
passage widths (normal to flow) at the inlet and outlet of the rotor blades,
in
0b_, 062 :rotor blade angles at inlet and outlet, deg tb = thickness of blade edge at inletand outlet,in Typical constructionsof rocketturbinerotor blades and disks are shown in figures6-53,6-55, 6-56,and 6-57. Usually,blades are designed with a shroud, to preventleakage over the blade tips and to reduce turbulenceand thus improve efficiency.Frequentlythe shroud forms an integralportionof the blade, the shroud sections fittingcloselytogetherwhen assembled. In otherdesigns the shroud may form a continuous ring (fig.6-55)which is attachedto the blades by means of tongues at the blade tip,by rivets, or is welded to the shrouds. The blades may be eitherwelded to the disk, or attached to itusing "fir-tree" or otherdovetailshapes. The main loads to which a rotorblade is
of various blade sections at different radii generally do not fall on a true radial line. Thus the centrifugal forces acting upon the offset centroids will produce bending stresses which also are a maximum at the root section. 2. Bending due to gas loading.-The tangential driving force and the axial thrust produced by the momentum change of the gases passing over the blades may be treated as acting at the midheight of the blade to determine the amount of bending induced. 3. Bending due to vibration loads.-The gas flow in the blade passages is not a uniform flow as assumed in theory, but varies cyclically from minimum to maximum. The resultant loads represent a dynamic force on the blades, having a corresponding cyclic variation. If the frequency of this force should become equal to the natural frequency of the blades, deflections may result which will induce bending stresses of considerable magnitude. Detail stress analyses for rotor blades can be rather complex. A basic approach is to counteract a major portion of the bending moments from gas loading with the bending moments induced by the centrifugal forces at nominal operating speeds. This can be accomplished by careful
i-
INTEGRAL
_
TYPE
SHROUD
gLADE _
ROOT A-A
S.HROUDED BLADES CASTING PROCESS
FABRICATED
BY PRECISION
exposed can be dividedintothreetypes: _ BLADE
1. Tension and bending due to centri[ugal [orces.-The radial component of the centrifugal forces acting on the blade body produces a centrifugal tensile stress which is a maximum at the root section. As a remedy, blades are often tapered, with the thinner section at the tip, for lower centrifugal root stresses. The centroids
JOINT
L.,_
!_
z
DISK
BLADES WELDED THE DISK
TO
8LADES TO THE
ATTACHED DiSK BY
TYPICAL "FIR TYPE TANG
TREE"
"FIR TREE"TYPE TANG
Figure
6-57.-Typical
rotor blade
constructions.
DESIGN OF TURBOPUMP
blade
design.
stresses
Thus
become
design,
while
location
and
later ing
the
other root
details
to fulfill
design are
where
of blade
such
as
centroid
The
tensile
stress
of uniform
cross
at the
most
duced
section,
follow-
blade
root
from the torque. As seen in figure 6-55, turbine disks are generally held quite thick at the axis, but taper off to a thinner disk rim to which
root
section
psi:
blades tions, both
Sc = 0.0004572
stresses in a turbine rotor disk are inby (1) the blades, and (2) the centrifugal
addition, there will be shear stresses resulting
critical.
at the
245
SYSTEMS
forces acting on the disk material itself. In
established
requirements. are
The
in blade
are
established
stresses
Centrifugal
tensile
consideration
configuration
correlations
section
centrifugal
a first
PROPELLANT-FEED
1pbhbdmN2 g
(6-141)
are
attached.
it is
possible
radial
at all
and
points,
rotor
In single-rotor to design
tangential
shear
applications,
cause
of the
it is
greatly
a disk
stresses
being
the
applicaso that are
neglected. difficult
uniform In multi-
to do this
increased
axial
be-
length
and
Centrifugal tensile stress at the root section of the resulting disks.
a tapered blade, psi:
large
Equation Sct=
O.O0045721pbhbdmN
2
(6-144) in a uniform
ing
blade
rotor
moment
section,
in-lb:
due
to gas
loading
at the
root
(6-143)
tensile turbine
=turbine
tr of the
blade
hb
blade
height,
=average
din =mean
diameter
=turbine
speed,
ar
= sectional
area
sectional
area
_i,t = turbine
gas
=number
of blades
Ft
= tangential
force
lb/lb/sec
(eq.
The culated
bending from
vibration design rate
data.
stresses forces
blade
root,
at the
blade
tip,
rate,
lb/in
s
in
rpm
of the disk at the axis, in
= thickness of the disk rim at d d, in (6-144a) permits estimation of the
in 2
Sd = O.O0044251W
on
the
blades,
Sd
= centrifugal
(6-127)) on
disk, the
blades,
lb/lb/
(6-144a)
at the be
blade root.
obtained caused blades.
root
can
bending
moment. from
is
fitted force The
with
The past
total
stress
by adding
these
by the
disk ad =disk N
centrifugal
from
the
of gravity
axis,
speed,
good
turbine
that
at maximum
at
the
S d calculated 0.75
of the
turbine
lb
center
to 0.8
Turbine high-temperature
rotor
of tile half
in
cross-sectional
addi-
about
stress
disk,
of the
=turbine For
a sepa-
produces
of the
=distance
be cal-
estimated
tensile psi
Wd = weight ri
centrifugal
on the
dri N2 ad
g
in 2
lb/sec
acting
can
is
to those
material,
where
resultant
at the
section acting
at the
acting
If the its
stresses root
in
stresses
the
of a constant
psi
disk,
speed,
Equation
3
(6-131))
stresses
shroud,
tional the
(eq.
(6-144)
stresses in any turbine disk, neglecting effects of the rotor blades:
rotor,
flow
thrust
sec
the
neglect-
rpm
zb
Fa = axial
lb/in
in
of the
N at'=
material,
stress
disk
of the
to =thickness
pb =density
disk,
stator
dd 2N2 log ___o_
disk,
of the
d d = diameter N
where
to estimate
turbine
and
where
Pd= density 2
be used
stress
Sd=O.OOOll41pd
stress _ hbcct /F,_+Fa S-2Zb _
rotor
effects:
Sd =centrifugal
M
between
may
stresses
(6-142)
Bending
gaps
area,
in 2
rpm design,
it is
allowable
design
by equation material
recommended rotating
(6-144a)
yield
blades
and
alloys
of three
disks
speed,
should
be
strength. are different
made
of
base
246
DESIGN OF LIQUID PROPELLANT ROCKET ENGINES
materials: iron, nickel, and cobalt, with chromium forming one of the major alloying elements. Tensile yield strength of 30 000 psi minimum at a working temperature of 1800°F is an important criterion for selection. Other required properties include low creep rate, oxidation and erosion resistance, and endurance under fluctuating loads. Haynes Stellite, Vascojet, and Inconel X are alloys frequently used. The rotor blades are fabricated either by precision casting or by precision forging methods. Rotor disks are best made of forgings for optimum strength.
Design of Single-Stage, Two-Rotor VelocityCompounded Impulse Turbines (figs. 6-9, 6-55, and 6-58) In most impulse turbines, the number of rotors is limited to two. It is assumed that in a singlestage, two-rotor, velocity-compounded impulse turbine, expansion of the gases is completed in the nozzle, and that no further pressure change occurs during gas flow through the moving blades. As mentioned earlier, the two-rotor, velocity-compounded arrangement is best suited for low-speed turbines. In this ease, the gases ejected from the first rotor blades still possess considerable kinetic energy. They are, therefore, redirected by a row of stationary blades into a second row of rotor blades, where additional work is extracted from the gases, which usually leave the second rotor blade row at a moderate velocity and in a direction close to the axial. The velocity diagrams of a single-stage, tworotor, velocity-compounded impulse turbine are shown in figure 6-58, based on the mean rotor diameter. The peripheral speed of the rotor blades at this diameter is represented by U. The gases leave the nozzles and enter the first rotor blades with an absolute velocity Cx, at an angle a_ with the plane of rotation. V_ and V2 are the relative flow velocities in ft/sec at the inlet and outlet of the first rotor blades, The gases leave the first rotor blades and enter the stationary blades at an absolute flow velocity C 2, and at an angle a2. After passing over the stationary blades, the gases depart and enter the second rotor blades at an absolute flow velocity C 3, and at an angle as. V3 and V4 are the relative inlet and outlet flow velocities at the second rotor
blades. Angles ]3,, f12, /33, and /34 represent the flow directions of V,, V 2, V 3, and V 4. As with single-rotor turbines, the exit velocity from any row of blades (rotary or stationary) is less than the inlet velocity, because of friction losses. It can be assumed that the blade velocity coefficient any row of blades:
k b has the same value
V2 _Ca _V4 kb- v 1 C: V 3
for
(6-145)
In a multirotor turbine, the total work transferred is the sum of that of the individual rotors:
C]
Vl
NOZZLE _lI
ROTA --
-_
....
FIRST
ROTOR
C2
ROT.T,ONOX "_'_
_/,,_,=
SECOND ROTOR
4
S_a4 _¥4 U
Figure 6-58.-Velocity diagrams o{ a typical single-stage, two-rotor, velocity-compounded impulse turbine.
Total
work transferred
rotor turbine, U E2b=-_(Cl
ft-lb/lb
to the blades
of a two-
of gas flow/see
cos al +C2 cos a2 +C
a
COS
a3+C
4
C0S
a4)
H
=g(V,
cos/31 +V2 cos/32 +V 3 cos /3a +V4 cos /34)
(6-146)
DESIGN OF TURBOPUMPPROPELLANT-FEED SYSTEMS
Combined nozzle and blade efficiencyof a tworotorturbine: E2b T]nb= JAH
(6-147)
where AH =overall isentropicenthalpydrop of the turbinegases, Btu/Ib = totalavailableenergy contentof the turbine gases (eq.6-17) Equation (6-137)can be rewrittenforthe turbine overallefficiencyqt of a two-rotorturbine as
7It = T/nbT/m
(6-148)
Ideally,tin b is a maximum forthe singlestage,two-rotor,velocity-compoundedimpulse turbinevelocityratio
U
C,
cos
a
I
4
i.e.,when U= ¼C,t. The workload forthe second rotorof a two-rotor, velocity-compounded turbineis designed at about one-fourthof the totalwork.
The design procedures for the gas flow passages of the rotor and stationary blades of a single-stage, two-rotor turbine are exactly the same as those for a single-rotor turbine. However, velocities and angles of flow change with each row of blades. As a result, the radial height of symmetrical blades increases with each row, roughly as shown in figure 6-55. The effects of reheating (increase of gas specific volume) in the flow passages must be taken into account when calculating the gas densities at various sections. Equation (6-136) may be used to estimate the amount of reheat at each row of blades. Also see sample calculation (6-11) and figure 6-60 for additional detail. In the calculations for multirow unsymmetrical blades, the radial heights at the exit side of each row are determined first by equation (6-140). The radial heights at the blade inlets are then made slightly larger, approximately 8 percent, than those at the exit of the preceding row.
Design of Two-Stage, Compounded Impulse and 6-59)
247
Two-Rotor PressureTurbines (figs. 6-10,
6-14
An operational schematic of a typical twostage, two-rotor, pressure-compounded impulse turbine and its velocity diagrams at the mean diameter are shown in figures 6-10 and 6-59. Each stage of a pressure-compounded impulse turbine may be regarded as a single-stage impulse turbine rotating in its own individual housing. Most of the design characteristics of a single-stage turbine are applicable to the individual stages. The gas-spouting velocities Cz and C3, at flow angles a, and a3, of the firstand second-stage nozzles, are designed to be approximately the same. Vz, V 2, V 3, and V 4 represent the relative flow velocities at inlets and outlets of the rotor blades, fiz, fi2, f13, and f14 are the corresponding flow angles for Vz, V2, V 3, and V 4. The second-stage nozzles are designed to receive the gas flow discharged from the first-stage rotor blades at an absolute velocity C2, and to turn it efficiently to a desired angle a 3. Simultaneously, the gases are accelerated to a desired velocity C3, through expansion to a lower pressure. The flow at the outlet of the second rotor has an absolute velocity C4 and a flow angle a4. U is the rotor peripheral speed at the mean effective diameter din. The totalwork performedin the turbineis the sum of thatof the separate stages. These may be designed to divide the load equally (i.e.,the
FIRST
STAGE
FIRST
STAGE
C1 V1
01 "_l
ROTOR NOZZLE
_
_'
'= 2
SECOND
U _
V3
a 3 C3
Figure
6-59.-Velocity
stage, two-rotor, turbine.
STAGE
NOZZLE
diagrams
SECOND ROTOR
of a typical
pressure-compounded
STAGE
two-
impulse
DESIGN OF LIQUID
248
velocity
diagrams
Cl=C
of each
3, C2=C
4, al=a
friction
losses
occurring
passed
on in the
thalpy
and increases
second
stage.
gases not
leaving
The
the lost
carryover
kinetic
gas
ratio
energy
kinetic
stage
rc,
second-stage
nozzles
energy
of the
leaving
from
tance
0.4
to close
between
the
second-stage through should
resulting quire
in equal
drop
may data.
zles
and
With
be used
blades
from
designs
coefficients
(6-122)
and
amount
of reheating.
additional
stage
are
rc
= second-stage
= turbine
ratio
of kinetic
specific specific
through due total in 2
k_
: nozzle
velocity
ent
:nozzle
throat
Sample
Calculation
at constant
F heat
enthalpy
nozzles
can
heat
Btu/lb-deg
ratio
drop the
of the
gases
second-stage
to expansion,
Btu/lb
second-stage
nozzle
coefficient area
coefficient
design
The
available
followfor the
data
2
T2 t = T2 + rc _ gJCp
(6-149)
From sample have been
Y T2t_ )'-1 k_]
(6-150)
(6-11) calculation (6-5), the following obtained for the turbine of the
stage
engine
Turbine
gas
mixture
ratio,
LO2/RP-1
: 0.408
Turbine
gas
specific
heat
at constant
pres-
sure,
p2(
gas
(Ant) 2 =required area,
A-1
P2t:
at second-stage
carryover
=turbine gas
and
nozzles:
C2
at firstft/sec
single-
in the
turbines.
correlations
of second
outlet,
flowing
(6-136)
for the
may be employed for two-stage
velocity
AH2_ 3, =isentropic
or concurrent
established
flow blade
=gas-spouting velocity nozzle exit, ft/sec
y
for noz-
by past
the
gas rotor
pressure,
re-
previous
at second-
psia
energy
of the
enthalpy
pressure
inlet,
C3
Cp
may
in view
at second-
stage
drop
given
turbines
design
stage
°R
psia
=absolute
stages,
equations equations
calculations
leakages
proper
velocity
to estimate
Most stage
the
dis-
the
enthalpy
for each Or, the
C2
pressure
static
at
inlet,
inlet,
nozzle
inlet,
temperature
total
gas
temper-
nozzle
nozzle
nozzle
stage
carryover.
right
approach,
be estimated
experiments,
ing
work
of reheating.
test
the
(stagnation)
static
gas
= turbine
can
axial and
between
of the
a trial-and-error
effects
The
for optimum
determination
stage,
total
gas
= turbine
P2
kinetic
as
P2 t
of the total
well
= turbine
stage
to the
diaphragm
be minimized
The
and
energy
rotor
T 2
turbine.
first
gas
at second-stage
second-stage
inlet
to unity. as
sealing
for the used
ratio
the
= turbine ature °R
as
first-stage
nozzle,
the
T2t
of the
largely
the
where
is
energy
is
ROCKET ENGINES
en-
energy
utilized
by the
vary
stage
a single-stage i.e.,
or
The
additional
available
actually gases
as
the with
identical
first
the first
as
are
4, etc.).
in the stream
Also,
entirely
stage
3, a2=a
PROPELLANT
turbopump.
Cp=0.653
Btu/lb-deg
Turbine
gas
specific
Turbine
gas
constant,
heat
total
ratio,
R = 53.6
Gas total temperature = 1860OR Gas
F
at turbine
pressure
at turbine
y= 1.124 ft/°R inlet,
inlet,
T o
Po = 640
psia C3=kn
gJCpT2t
_
P3
Y
Gas
static
pressure
at turbine
exhaust,
pc=27
psia = kn ,(_-cC22 + 2 gJAH2_
s,
Total
(6-151)
available
gases, (Ant)2
(6-152)
= l /
r27
Y+l _-zT
4/ ,,'LT-qj
content
Btu/lb
Turbine
gas
rate,
Turbine
shaft
Overall
turbine
compounded In addition, forth:
L-
energy
AH = 359 flow
speed,
turbine
_i,_= 92 lb/sec N= 7000
efficiency wheels), the
of the
following
rpm
(when _t= 58.2 design
using
velocity-
percent data
are
set
DESIGN OF TURBOPUMP
Nozzle
aspect
Nozzle
velocity
Nozzle
throat
Nozzle
exit
Rotor
and
ratio
area
kn = 0.96
coefficient,
ent:
coefficient,
stator
blade
(a._) Single-stage,
0.97
compounded
ene = 0.95
velocity
and
stator
blade
exit
area
turbine
length
Cb=l.4 Partition
of rotor
and
coefficient,
at the
tn = tb = 0.05
Solidity
of first
Solidity
of stator
Solidity
of second
blades,
exit
of nozzles
for the
ation
of this
blades
= 1.82
tions
= 1.94
rotor
= 1.67
velocity-compounded,
impulse-type
A-1
stream
stage
engine
reaction of the
and
with stator
compounded,
impulse-type
stage
engine
turbopump,
stage
and
about
turbine with
3 percent
downstream
of the
about
6
of an
reaction
in the
nozzles
of each
3',
oper-
subscripts
processes
listed:
representing
inlet
first
blades;
second
first second
and
rotor
representing
and
condi-
blades;
second
nozzles;
blades;
rotor
rotor
of the
4' =Points
at the
expansion
zles;
rotor
first
second
rotor
the
blades. exit
condi-
rotor
blades;
rotor
blades,
for
1-2,
2-3, nozzles;
in each
blades;
and
1'-1,
stage.
2'-2,
stant
second
3'-3,
4'-4
rotor
blades;
rotor
blades.
and
due in the
stator
along
between
ideal
processes
and
actual
losses
and
and
first
second
rotor rotor
con-
isen-
to friction nozzles,
blades,
processes
= Differences
lines,
expansion
stator
noz-
blades;
of actual
first
pressure
heating
a_ PO
in the
stator
3-4=Path
in the
rotor
process
blades;
blades.
A-1
processes,
'_k_-
diain the
following and
nozzles;
isentropic
0-1,
work
6-60
an ideal isentropic expansion process. 0-1', 1-2', 2-3', 3-4' =Path of an ideal
down-
for the
equal
2',
tropic
0
The
blades;
stator
for
blades
diagrams pressure-
for this
Figure
involved
points
conditions
tions
nozzles.
(b_) Determine the velocity alternate two-stage, two-rotor,
blades
and printwo-rotor,
turbine
turbopump,
in rotor
at the
exit 1',
the velocity diagrams of the single-stage,
percent
turbine. various
stator
blades
(a_) Determine cipal dimensions
the
processes
0, 1, 2, 3, 4 = Points
blades
6-58.
temperature-entropy-enthalpy
gas
the
diagram
in figure
and
in
rotor
the
velocity-
turbine. velocity
shown
gram
denote
in thickness
blades,
stator
is
represents
_b2 =0.95 Chord
two-rotor,
impulse
A representative
coefficient,
kb=0.89 Rotor
249
SYSTEMS
Solution
= 9.7
coefficient, area
PROPELLANT-FEED
re-
blades,
blades
CONSTANT
To A, s
/_PR_LFE
UNES
I
Point :2:
/"
II
_..,"_,'_.,% / p4
>_-
inlet
total bine of the
gram
the
gas
processes
two-rotor, velocity-compounded with small amount of reactions the
nozzles.
drop
available
gases
efficiency
in
about
enthalpy
drop
a single-stage,
rotor
and
stator
impulse turbine downstream o[
drop
in the
6-60.-Temperature-entropy-enthalpy o[
= turbine
= 359
First
of the
energy
tur-
content
Btu/lb
= kn 2 : (0.96) exit=
inlet
psia
enthalpy
= total
"1 "-Nozzle
inlet
2 = 0.92
Rotor
Blade
Inlet
S
Since Figure
pressure = 640
turbine
: turbine
= 1S60°R
isentropic gases
T/n = nozzle Point
temperature
total
pressure
AH = overall
ENTROPY,
total
temperature
= nozzle
-r b==
-._-_/
Inlet
inlet
total
o.
Po
...........
" O"-Nozzle
T O = nozzle
dia-
6 percent AH is blades,
of the
assumed the
overall
to occur isentropic
isentropic in the enthalpy
nozzles
'AH o-1' : A H (1 - 0.06)
-- 359 x 0.94
: 337.5
Btu/lb
250
DESIGN OF LIQUID PROPELLANT ROCKET ENGINES
We can write:
Ideally, the efficiency r/n b of a two-rotor, velocity-compounded impulse turbine is a maximum when the turbine velocity ratio
AHo_p = CpT o I 1-(P-21U y_,] \Po]
U
COS
C1From this, zle exit
the gas static
pressure
COS a I U=C1_=3940xCOS
CpToJ
= 640
E1
9._
=
From equation diameter
640 x 0.053 = 33.94
From equation (6-121), the gas velocity at the nozzle exit
(6-122),
(1 - kn 2) C12 _ 0.08 × 15 524 000 =
kn22gJ
Referring at the nozzle pansion
0.92× 64.4 x 778
of reheat C,cosal-U sinai
_ 3940×0.9063940x0.42390=0.622
/31 =31053 '
= 27 Btu/lb
to figure 6-60, the gas temperature exit, following an isentropic ex-
Referring to figure 6-58, the relative velocity at the first rotor blade inlet
gas
flow
C 1 sin a1._3940× sin 25 ° sin fll sin 31°53 ' AHo_,, Cp -1860
TI, ZTo The actual nozzle exit
gas
static
337.5 0.653-1344°R temperature
27 qn---sr T1 = TI' + Cp -- 1344 +0.---_ The gas
rotor mean
From equation (1-130), the relative gas flow angle/3, at the inlet to the first rotor blade can be calculated:
tanfll=Cl
qnr
the turbine
dm =720 U_0_720 × 89___- 29.1 in 7r N 7rx7000
spouting
the amount
(1-129),
psia
CI = kn V2 gJAHo_l, = 0.96 _/16.9 × 106 = 3940 fps From equation in the nozzles
at the mean diam-
=3940 × 0.226 = 890 fps
337 5 ]o.124 0.65-3x-_s60.J
x (0.722)
speed
425 °
1.124
=640×
1
at the nozFrom this, the peripheral eter of the rotor
Pl =Po
a
4
density
at the nozzle
at the
= 1385° R exit
P, 144 33.94x 144 Pl =-_-T x--_ -1385.4 × 53.6 = 0.0658
lb/ft 3
We will use an angle a_ of 25 ° for the spouting-gas-flow direction at the nozzle exit.
_ 3940 x 0.423 O. 528 Point Inlet
"2"-First
Rotor
Blade
Exit=
3156 fps
Stator
Blade
Assume that the given 6 percent reaction downstream of the nozzles is equally divided between the two rotors and the stator. Then the isentropic enthalpy drop in the first rotor blade can be approximated as
AH,_2, =P-_
x 359 = 7.18
Btu/lb
Using equation (6-135), the relative gas velocity at the exit of the first rotor blades
flow
DESIGN OF TURBOPUMPPROPELLANT-FEED SYSTEMS
V 2 = V'kb 2V l2 + 2 gJTlnAH l_2, = V/(0.89 × 3156) 2 + 64.4 × 778 × 0.92 × 7.18 = 2866
V 2 sin/32 tan a 2 = V cos /32 - U a 2 =35°15
fps
From equation (6-136), in the first rotor blades,
the amount
of reheat
251
2866×sin 25 ° 2866 × cos 25 °- 890 = 0.707
'
The absolute blade exit
flow velocity
at the first
rotor
c2-V
2 sin /32 _ 2866 × sin 252 1210 2080fps sin a 2 sin 35o15 ' =0.57---_=
(3156)2 = [1- (0-89)2] x 64.4 x 778 _(1-099)×7.18 • ,
Point Blade
"3"-Stator Inlet
= 41.975
The isentropic blades
V2 2
1
qbrl =(1 - kb )_-_+
The static blade exit
(1 - r/n) AHI_ 2,
Btu/lb
gas pressure
at the first
Exit : Second
enthalpy
Rotor
drop in the stator
AH2_ 3, = AH 1-2' = 7.18 Btu/lb
rotor
gas
Y
F A.,
Blade
Analogous to equation (6-135), the absolute flow velocity at the stator blade inlets C a = x/kb2C22 +2gJ_nAH2_
a,
= X/(0.89 × 2080) 2 + 64.4 × 778 × 0.92 × 7.18 =33.94x
1
= 1938 fps
0.653×1385
= 33.94 x 0.93 = 31.6 psia
The gas static temperature first rotor blade row following expansion
Reheat
in the stator ,
at the exit of the an isentropic
2_
qbs =(l-Kb
blades 622
)2--_+ (1- rln) AH2_ 2 (Analogous
= [i- (o.89) 2] × (2080)2 T 2, = T 1 - AH,_2,/C p = 1385 - 7.18/0.653=
64.4 × 778
1374 ° R
to eq. (6-136))
+ (1 - 0.92) × 7.18
= 18.53 Btu/lb The actual static rotor blade row exit
gas temperature
The static exits
qbr2 41.975 --1374-+ T2 = T2' + Cp 0.653 Gas density
at the first
at the first gas pressure
- 1438 ° R
rotor blade
144p2 144x31.6 P2 = RT 2 - _ 1--_-_-8 = 0.059
exit
at the stator
Y p3 =p2 [1 -CDT2 _H2-21 j Y-1 =31.6x =29.42
7.18 _9.06 E1 0.653×1438J
psia
lb/ft 3 Gas static temperature at the stator exits following an isentropic expansion
We use an angle/32 of flow direction at the first symmetrical blades). The a 2 at the first rotor blade from
blade
25 ° for the relative gas rotor blade exits (unabsolute flow angle exits can be calculated
T3, = T2 -AH2_2/Cp=
1438-7.18/0.653=
blade
1427 ° R
Actual staticgas temperatureat the stator blade exits
252
DESIGN OF LIQUID PROPELLANT ROCKET ENGINES
qbs 18.53 T3 = T3'+-_--= 1427 + x-_--_. = 1456° R
Gas density
at the stator
blade
}r
exit = 29.42 x
144 P3 _ 144 x 29.42 .= 0.0544 P3 = R T 3 53.6x1456
lb/ft 3
We use an angle a3 of 35 ° for the absolute gas flow direction at the stator blade exit (a s Ta2). The relative flow angle t33 at the stator blade exit can be calculated from
tan/33-C3
C 3 sin a s 1938x 0.574 cos a3- U=1938x0.819-890
= 1.596
f13 = 57°56' The relative
flow velocity
at the stator
blade
= 27.46
is slightly higher sure (underexpansion), effects.
The gas static rotor blade sion
T4' --T3
V3 = C s sin a 3 _ 1938 × 0.574 - 1312 fps sin /33 0,847 "4"-Second
Rotor Blade
The isentropic rotor blades
enthalpy
exits
1 - 0.6537.1s x 1456] -1_°_
psia
P4
exit
Point
=v
r
> 27 psia
than the turbine exit presbecause of the reheating
temperature following
T4
at the second
an isentropic
expan-
7.18 - 1445 Btu/lb -AH3__,/C p = 1456--0.653 -
The actual gas static ond rotor blade exit
Exit
(Pc)
--
T4 '
drop in the second
temperature
qbr2 1445 ' 7.73 + C--_---= +_=
at the sec-
Gas density
at the second
1457 ° R
rotor blade
exits
AH___,= AHa_f --7.18 Btu/Ib The relative gas flow velocity rotor blade exit
g
4
= \/kb
2 V3
2
+
2
at the second
gJ77nAHa.. 4,
= 1306 fps of reheat
in the second
(unsymmetrical blades). The absolute flow angle u 4 at the second rotor blade exits can be calculated from
rotor tan a 4 =y4
V 4 sin /34 1306 × 0.695 cos /34- U=1306x0-719-890
a 4 =86°55 ,,y
= [1 - (0.89):]
flow velocity
at the second
rotor
(1312) 2 , ,. x 64--A x 778" Ll - 0.92) x 7.18 C4 =V 4 sin/34_ sin a 4 Nozzle
exit
'
The absolute blade exits
(1- 9n) AH_-4'
Btu/sec
Gas static
-18"5
2
qbr2 = (1 - kb2)-_gj+
= 7.73
lb/ft a
We use an angle/34 of 44 ° for the relative gas flow direction at the second rotor blade exits
= V'(0.89 × 1312) 2 + 64.4 x 778x 0.92 x 7.18
The amount blades
144 P4 _ 144 x 27.46 = 0.0506 P4 - RT 4 53.6 x 1457
pressure
at the second
rotor blade
1306x0'695=908 0.9985
fps
Dimensions
From equation zle throat area
(6-123),
the required
total
noz-
DESIGN OF TURBOPUMP
wt
PROPELLANT-FEED
First
Ant = /
Rotor
The
y+l
253
SYSTEMS
Blade
pitch
Dimensions
or blade
(at
dm)
spacing
r 2 i?-_
gyL iJ
Blade Pbrl =
chord
length
Blade
Cb
solidity
1.4
= 0.769
- 1.82
in
92 From 0.97 x 640
= 13.22
We use nozzle
x 1.124(0.94) 53.6 x 1860
ll/32.2
equation
in2
a radial
throat.
Zbrl height
Thus
the
hnt of 1.5 nozzle
inches
width
atthe
at the
Allow inlet
throat
aspect
number
ratio
- 9.7 - 0.1548
tive
Ant
Pitch
-
bnthnt
0.1548×
_
1.5
57
2 ° between
spouting-gas
From
The
a blade
nozzle angle
-2=25-2=23
(6-125),
the
exit
angle
al;
thus
+2°7'
=3't°
equal
toexit
rela-
=_2
= Pbrl
sin
=25°
radial
height
1.64 x 1.08=
width
Oblrl
at the
at the
- tb = 0.769
inlet
1.77
in
inlet
x 0.559-
0.05
= 0.379
in
From equation blade exit area total
(6-138),
the
required
total
noz144 x 92 --
p2V2Eb2
0.059
x 2866
x 0.95
82.5
in 2
144 x 92
plClene
0.0658×3940×0.95
53'75in2
Combining obtain
equations
radial
and
On and
° required
Ob2rl
144 w_
144 w_
height
(6-125) and
width
and at the
(6-126),
we
nozzle
exit:
the
equations blade
radial
sin
hne = rrd m sin On - Zntn - rrx29.1x
0.391-
and
(1-140a),
at the
we
exit
Ob2rl-Zbtb
53.75
Ane
(1-139) height
Ab2rl hb2rl-_dm
= 1.64
= 31°53'
(1 x 0.08)= passage
area,
Combining
angle _)b_ri
thus
/_2
=
obtain
-119
blade
fl_;
bladeangle
blade
Ab2rl
Ane
inlet
angle +2°7'
angle
hb,rl =hne
flow
equation
exit
--_1
We select
spacing
On=a1
zle
0.769
flow
exit
flow
bblrl nozzle
,Tx 29.1
Ob2rl
Pn - ,din _ _ x 29.1 = 1.604 in zn 57 We allow
,,dm
13.22
or nozzle
of blades
in
of nozzles
Z/l=
number
1.5 Make
The
the
= Pbr 1
2°7 ' between
relative Obxrl
hnt bnt =Nozzle
(6-140a),
lTns
82.5
57 x 0.05
x 29.1
x 0.423
- 119 x 0.05
= 2.52
in
in The
blade
passage
width
at the
exit
Ane
zn bne = hne
bb2rl
53.75 - 57 x 1.6_-
0.576
in
= Pbrl
sin
= 0.291
in
Ob2rl
- to = 0.769
x 0,443
- 0.05
DESIGN OF LIQUID
254
The
mean
PROPELLANT
blade radial height total
hbr,
-
1.77+2.52 2
ROCKET ENGINES
Using equation (6-138), blade exit area
- 2.145 in
144 w_
required
0.0544
x 1938
x 0.95
= 132.5
in s
(6-139)
and
(6-140a),
we
a tapered blade with shroud, and that
it is subject to approximately
the same
tensile
stresses from centrifugal forces, as would uniform blade without shroud. be made
the
144 x 92
Ab2 s = P3 C3eb2 Assume
we obtain
of Timken
lb/in _. Cheek
The
be a
Combining calculate
equations
the
blade
radial
height
at the
exit
blades shall
alloy, with a density pb =0.3
Ab2s
the centrifugal tensile stresses
sin
hb2s=rtdm
Ob2s-Zbstb
at the root section using equation (6-141). 132.5 x 0.574 - 127x
- _x 29.1 Scr I = O.O0045721pbhbrldm
The 0.0004572 × _-0_-X, × 2.145 × 29. i X
blade
passage
bb2 s = Pbs
Second
From
chord length Cb solidity
ndm_
Allowing 0b, s and
Obls=a2
of blades
absolute
inlet flow
angle
blade
exit
angle
a 2
length
(6-140a),
2o4 ' between
and
the
Cb
solidity
equation
Allow 0blr2
x 0.574-
0.05
Dimensions
chord
Blade
From blades
inlet
1.4 1.67
the
0.888
number
in
of the
_ v×29.1=i09 0.838
the
relative
inlet flow
blade
angle
angle
f13;
thus
Oblr2 =f13 +2_4' = 57_56' +2°4' =60o
+2024 `= 34°36 '+2o24 ' =37 °
8b2s=a3
at the
spacing
vdm Zbr2 - Pbr2
We hold exit.blade angle 0b2s equal to exit
We make
the exit blade angle 062r2 equal to
the exit relative flow angle /94 Ob2r2 =/_4 =44°
=35 °
equation (6-149), blade radial height at
From
equation (6-149), the blade radial height
at the inlet is
the inlet
hb,s= The
=
- 127
absolute flow angle a3:
From
Pbr2
0.721
2024 ' between inlet
Blade
Blade
- 1.94 - 0.721 in
_× 29.1
width
062 s - Ib = 0.721
or blade
1.4
equation (6-140a), the number
Zbs = Pbs
in
in
Rotor
Pitch
Pitch or blade spacing
Blade
x sin
= 0.364
Stator Blade Dimensions
Pbs -
-2.87
(7000)2
= 13 050 psi
Blade
0.05
N2
l.08×2.52=2.72
blade passage
bbls= Pbs =0.384
width at the inlet
sin Ob,s-tb=O.721xO.602-O.05 in
hbir
in The
blade
2 = 1.08× 2.87= 3.10 in passage
bb 1r2 = Pbr2 sin = 0.677
in
width
at the
Ob l r2 - tb = 0.838
inlet x 0.866-
0.05
DESIGN OF TURBOPUMP
From blade
equation
exit
(6-138),
the
-P4
_:
total
the
A-1
144 × 92
V4eb2
Combining obtain
-
x 1306
0.0506
equations blade
x 0.95 = 211
(1-139)
radial
and
height
in 2
(1-140a),
at the
we
exit
Stage
Rotor, Design
hbsr2-_d
m sin
velocity
figure
fps; 119×
0.05
diagrams
exit
passage
sin
= 0.533
in
mean
blade
Obsr:
=3"66
in
V 2=2866
x 0.695-
_4=44_;
C4:908fps;
height
3.10+ 2
root
the
- 3.38
section
centrifugal using
tensile
equation
Nozzle
ratio
(at
= 9.7;
=0.1548
in;
rotor
2
× 29.1
Efficiencies
From bined
equations
nozzle
and
blade
and
(6-147),
the
com-
efficiency
in;
t)blrl
=34°;
hb2rl
=2.52
=0.291
blade
a 1 +C:
cos
bb28=0.364
Second
rotor
Pbr2
tinb --
a 3 +C 4 cos
a4)
890 (3940
× 0.906
+ 2080
x 0.817
+ 1938
x 0.819
32.2
x 778x
359
equation
the
turbine
machine
(at
in;
din):
Zbr2 = 109;
in;
Oblr2
=600;
0b2t2
hbsb2
=3.66
in;
compounded grams, following
(6-148),
dimensions Cb = 1.4
in;
=0.533
see
fig.
prior
obtained. rc = 0.91.
=44°;
bblrs=0.677
in
two-rotor,
impulse
turbine.
equal-work, (For
pressure-
velocity
dia-
6-59.) trial-and-error
isentropic
(approximately) From
bbls=0.384
=0.838
From
= 0. 683
efficiency
blade
(_b) Two-stage, + 908 × 0.055)
Zbs = 1.27; 0b28=35°;
in
= 1.67;
bbsr2
=25¢;
bblrl=0.379
hblr 2 =3.10 in;
gJAH
in;
0bls=37°; bb:s=2.87in;
in;
a2
÷C 3 cos
Obsri in;
(at din):
Cb = 1.4
in;
din):
in
dimensions
= 1.94;
Solidity U(C 1 cos
Zbr_=llg;
in;
hbls=2.72in; (6-146)
(at
Cb=l.4in;
= l.77 bbsrl
in; bnt
dimensions
=0.769
Solidity
psi
Pn = 1.604
nne=l.64in;
bblrl in;
x (7000):
din):
bne=0.576in
blade
Pbs=0.721 Turbine
Btu/lb
Pbrl
Stator = 20 550
Btu/lb
Btu/lb
z n = 57;
hnt=l.5in;
Solidity=l.82;
3.38
AHI_ 2, = 7.18
AHs. _, = 7.18
in
0n=23°;
at the
(6-141)
x_x
fps
drops:
dimensions
First
= 0.0004572
a4 =86°55';
V4=1306
efficiencies:
dm= 29.1
in
stress
Scr 2 = O.O0045721pbhbrsdmN
fl3=57°56';
fps;
rotor, AH3. _, = 7.18 5H = 359 Btu/lb
Aspect Check
V1 C 2=2080
7/t=58.2%; ;7n=92%; _7nb=68.3%; qm=85.2% Mean diameter of nozzles and blades:
3.66
hbr2 -
a3=35°;
blades,
blades,
Second Total radial
din,
AHo_ I,= 337.5 gtu/lb
rotor
Working The
diameter
fl_=25:;
V 3 =1312
enthalpy
Stator
0.05
fps;
fps;
Nozzles,
width
- tb = 0.838
Type)
C_=3940fps;
a:=35°15';
C 3 =1938
First = Pbr2
at mean
fl_=31°53';
Isentropic blade
Two-
Impulse
6-58.
=3156fps;
211 x 0.695-
(Single-Stage,
U = 890:
Obsr2-Zbtb
=_x29.1
Turbine
Summary
For see
Engine
a 1=25°;
bbsr2
0.582
Velocity-Compounded
Absr2
The
255
SYSTF.j_,S
area
144 #t Ab2r2
required
PROPELLANT-FEED
equal We assume
enthalpy work a stage
calculations, drops
the
resulting
for each carryover
stage
in were
ratio
256
DESIGN OF LIQUID PROPELLANT
First-stage
nozzles:
AHo_I, = 50%;
AH = 0.5 × 359=
179.5
ROCKET ENGINES
Point
"2"-First-Stage
Stage
Nozzle
Btu/lb
From
equation
velocity First-stage
rotor
(6-135),
at the
V 2 : \/kb AH : 0.03
× 359 = 10.75
Btu/lb
AH2_ 3, = 44%;
= 1736
AH = 0.44
rotor
AH3_4, = 3%;
× 359 = 158
We chose
Btu/lb
blades:
absolute lated as
AH = 0.03
× 359 = 10.75
" O'-First-Stage
Nozzle
tan
Inlet
a s-
a relative
gas
flow
a2= 86040
"1 "-Firs$-Stage equation
Nozzle (6-121),
first-stage
= 2880
Exit
the
nozzle
C 1 = kn \/2 gJAHo_
flow
= Rotor
Using /3_ at the calculated
a l.
For
× 223.8
optimum
--
equation
flow
angle
blades.
can
then
The be calcu-
1736 1736
×0.616
x 0.788-
1308
17.25
0.906×2880 2
sin
rotor
the blade
sin
al
Blade
inlet
equation
gas
Nozzle
(6-151),
the
can
be
stage
V'0.91
: 2880
fps
C 3 = C_,
velocity stage,
C 4:C
+ 2 gJAH2_
= 0.96
Since
flow
Exit
= Second
second-stage
noz-
× (1070)
the
a3:a fps;
2=1070fps;
2 + 64.4 × 778 x 158
remainder
diagram i.e.,
3'
is
the
I =25°;
of the same
as
secondthat
of the
J33 =]31 =43°8';
a4:a2=86°40';
/_4=/_2=38°;
V 4=V_=1736fps.
- 1308 = 0.936
'
The relative blade inlet
fps
velocity
C a = k n \/rcC22
From 131 =43°8
- 1070
Inlet
gas-spouting
1308fps
relative
× 0.906
first-
tile
2880×0.423 U - 2880
at the
0.998
"3"-Second-Stage
first
al-
velocity
1736×0.616
a2
Rotor
diameter
_
flow
exits
Point
zle
spouting-gas
mean
gas
× vJl-7-9_5.5
efficiency,
rotor
(6-130),
first-stage as
/31 = C1 cos
Yl
a2,
f_2
blade
C2 :
exit
f = 0.96
at the
cosalC1 2
C,
rotor
× 10.75
'
V3=Vl=1784
tan
gas rotor
angle,
V 2 sinfl2
gas-spoutingveloc-
of 25 ° for the
speed
--
flow
Blade
fps
a value
angle
peripheral
exit
/32- U
absolute rotor
From We use
× 778 × 0.92
first-stage
i,,2 cos
The
ity at the
exit
psia
stage
From
gas
blade
Btu/lb
T O-- 1860oR
Point Inlet
relative
rotor
fps
V 2 sin
Po = 640
Exit=Second-
2V12 + 2 gJT?n'_H1_ 2,
/3 2 --38 ° for the
Point
the
first-stage
: V_(0.89 × 1784) 2 + 64.4
nozzles:
Second-stage
Blade
blades:
AH__ 2, = 3%; Second-stage
Rotor
Inlet
equation
(6-129),
the
turbine
rotor
mean
diameter gas
C1 sinai sin 131
flow
velocity
at first-stage dm=720U-720x1308 _N _r × 7000
2880×0.423 0.683
1784
From
fps and
blade
equation efficiency
(6-147),
the
42.7
combined
in
nozzle
257
DESIGN OF TURBOPUMP PROPELLANT-FEED SYSTEMS
result
U(C x cos a_ +C 2 cos a 2 +C 3 cos a3+C 4 cos a4) r/nb =
g JAil
right angles those which loads).
1308 (2880 × 0.906 + 1070 x 0.058 + 2880 × 0.906 + 1070 × 0.058) 32.2 × 778 × 359 =0.78
sult The turbine machine efficiency is assumed be the same as that used in design (a._):
to
qm = 0.852 From equation efficiency
(6-148),
the overall
turbine
r/¢ = rlnbr/m = 0.78 x 0.852 = 0.664 A-I Stage Engine Alternate Turbine Design Summary (Two-Stage, Two-Rotor, PressureCompounded, Impulse Type) For velocity diagrams at mean diameter din, see figure 6-59. U = 1308 fps: a1=25°; _1=43°8 '' C1=2880fps; V 1=1784 fps; a_=86°40'; _2=38°; C2=1070 fps; V 2 = 1736 fps; a3 =25°; f13 =43°8'; C3=2880 fps; Va=1784 fps; a4=86°40'; _4=38°; C4=1070fps; V 4=1736fps Isentropic enthalpy drops:
6.6 DESIGN SEALS, Turbopump
a relatively
OF TURBOPUMP AND GEARS Bearing
large
or on the
These forces may those which act at
axis (radial to the shaft
forces), and axis (thrus:
Radial loads on turbopump bearings may refrom one or more of the following sources: (1) Weights of parts such as shafts, pump impellers, turbinerotors, gears (2) Centrifugal forces du_:, to unbalance of these rotating parts (3) Forces due to inertia, resulting from rapid acceleration (4) Resultant radial forces on the impeller due to nonuniform pressure distribution in the discharge volute of the pump (5) Tangential or torque forces induced by the gears on turbopump bearings may remore of the following sources: rotating parts mounted on a shaft
For the turbopumps of liquid rocket engines, high-speed ball and roller bearings are used almost exclusively. A typical two-bearing design is shown in figure 6-7. A ball bearing carries both radial and thrust loads. It is paired with a roller bearing which carries only radial loads, however, of a higher magnitude. A typical three-bearing arrangement is shown in figure 6-63. The shaft radial loads are carried by a single roller bearing at the turbine end and by a roller and a ball bearing on the pump side. The ball bearing also absorbs the thrust loads. As a rule, the shaft thrust loads in a turbopump are carried by a single or dual bearing located at one end of the shaft. Thus loads from thermal expansion or contraction of the shaft are avoided. Bearing design data with regard to loadcarrying capacity, operating speed, and service life are usually furnished by the manufacturers. The useful life of a bearing is dependent upon its speed and load, and may be expressed by the correlation:
that dm is
BEARINGS,
Design
A turbopump shaft is supported by two or more bearings. The loads on the bearings are the
-
act on the shaft
(2) Unbalanced axial thrust of the pumps (3) Resultant axial thrust on the turbine rotor blades
Working efficiencies: r/t= 66.4%; r/n = 92%; rlnb= 78%; _?m= 85.2% Mean diameter of nozzles and blades:
of design (a). However, required (weight, size).
which
to the shaft act parallel
Thrust loads sult from one or (1) Weight of vertical
First-stage nozzles, AH__,, = 179.5 Btu/lb First-stage rotor blades, AH,_ 2, = 10.75 Btu/lb Second-stage nozzles, AH2_2 -- 158 Btu/lb Second-stage rotor blades, AHz._4, = 10.75 Btu/lb
dm= 42.7 in Comment: The overall efficiency of the pressure compounded turbine is higher than
of forces
parts supported by the shaft. be divided into two classes:
lira
_
DESIGN OF LIQUID PROPELLANT ROCKET ENGINES
258
{ Rated speed, rpm Life, hours = gb \Actu-a--1o--p-er_p-_'-d,
._ rpm/
[ Rated capacity, ib ,_4 ×_Actual working load, lt)] (6-153) where
Kb = design factor usually manufacturer.
furnished
by
If a bearing is subjected to both thrust and radial loads, the two can be combined into a single
equivalent
radial
load:
P = R + xA
(6-154)
where P = equivalent radial load used for bearing selection, lb R = actual radial load, lb A = actual thrust load, lb x = design coefficient usually furnished by manufacturer Rocket turbopump bearings quite commonly are cooled and lubricated by the propellants pumped. They are usually operated at very high "DN" values, a parameter which is the product of the bearing bore D (millimeters), and the bearing rotative speed N (rpm). Propellant lubrication has the advantage of eliminating an additional lubricant supply system, and of simplifying bearing sealing problems. The following are important design considerations for propellant-lubricated bearings: (1) Characteristics of the propellants, such as thermal stability, operating temperature, chemical inertness, viscosity. (2) Compatibility of the bearing materials with the propellants. The application of certain high-strength alloys is sometimes limited by the propellants used. The "DN" rating is convenient when selecting high-speed ball or roller bearings. As the rotatire speed of a bearing increases, contact fatigue of the outer race caused by centrifugal loads of the balls or rollers may cause failures. In addition, bearing contact speeds will result in nonrolling phenomena with attendant failures caused by overheating. Through proper selection of the bearing geometry, these problems can be minimized, and the DN rating increased. Note that for a given horsepower rating, the shaft size based on allowable stress does not decrease
proportionally with the increase of shaft design speed. Thus the required bearing DN value rapidly increases for high-speed turbopumps. As a result, especially for liquid hydrogen application, the turbopump rpm is often determined by the DN limits of the bearings. A most important bearing design consideration is the expected operating life of the rocket engine. The bearings must have adequate statistical probability of conforming with this requirement. A generally accepted life rating for ball and roller bearings is the "B-10 life." The term denotes the operating life (hours) of a _population" of bearings at a given load and speed, at the expiration of which statistically 10 percent of them will have failed. Of course, in actual rocket engine operation, component reliability must be much higher. Bearing life at a given load and speed varies inversely with reliability. For instance, the B-1 life (99 percent reliability) is one-tenth of the B-10 life (90 percent reliability), or one-fiftieth of the B-50 life (50 percent reliability). Therefore, turbopump bearings are generally designed for a B-10 life of at least 100 hours. This corresponds to a B-1 life of 10 hours, or a B-0.1 life (99.9 percent reliability) of 1 hour, the latter by order of magnitude being the life the bearing most likely will actually see. For critical applications, an even higher life rating may be selected. Figure 6-61 presents the centrifugal load DN limits in terms of 10, 100, and 1000 hours of B-10 life for a typical ball bearing design (extralight series). The stress-limiting DN values of roller bearings are much higher than for ball bearings; however, it is extremely difficult to control the temperature rise in a roller bearing, if the DN value is above 1.5 × 106, due to excessive cage slip. Generally, rocket turbopump bearings have been successfully operated at DN values up to 1.5 × 106. Limited test information indicates possible
satisfactory
Dynamic
Seal Design
operation
at 2.0 x 106 DN.
The principal dynamic, i.e., rotating seal types used in liquid rocket turbopumps are the labyrinth, face-riding, and shaft-riding seals. Satisfactory seal operation depends upon good design which considers many factors, including
DESIGN OF TURBOPUMP
PROPELLANT-FEED
_.:1
I
I I II I
[
I
¢ol
I
J
I
I ]
II -
I
I
It l
•
[
I
I
_.ou_e
&o i
o
i J
$O MRS
i
i
J
[
=,
BALL
BEA
NG
C
. TRt N
IFUGAL
II
r
.55
J
I
_ _ ._ I I I I
",., .c__..c- 2:.':.
1
LIMIT
IOUTE_ =.cE _*FO*=,T. T--SPEC, .58
../---TST'0,
\-T-_
_.o#-------------J_/--\--4_,_.
1
LOAD
(EXTRA L,_,TSE=,ESS,ZEI !
[ '
I
259
SYSTEMS
...
--_-\-q----
-_ _ ---
' _.3u-=_.
't,
,
I .....
o. Io
ZO
3o
40
50
60
70
8090
_
200
_0
400
=X>o
BEARING BORE SIZE, D mrn Figure
fluid
pressure
surges,
contraction between
ties
of the
free
operation
of the
ence
directly
which these seal.
As
The
function
fluid
p
= density
pres-
Cs
= seal
frictionand
Any
improper
of the leakage
6-62,
seal.
The
sealing is
forced
Labyrinth
on
of pump seals
influ-
seals
leakage
to follow
a devious
entirely,
tion
and
wear. seal
is
but level
The can
amount be
seal
throttled is
rather
not
turbine
of leakage
is
Aps/p
are
path.
=leakage
Ac
=seal
rate, clearance
leak-
turn,
of friccorrela-
(6-155)
a
seal
angle 6-62,
welded is
casing.
to the
follow
axial
and
Sometimes
Aps = pressure lb/in 2
differential
across
seal the
seal,
seal the
and
flexibility
seal
is
(fig.
The
segments
held
against
to the and
permitting
movement used washer,
6-62)
is in
housing
provides face,
As
washer
bellows,
seal
retaining
are
seal
The
floating
faces
of rotation.
floatin£
a seal
segments. shaft
seal
mating
sealed
seal
is between
statically
angular
shaft-riding
housing,
axis
contact
a lip
sealing
The
bellows.
bellows
force
The in 2
between
of a floating
the
and
spring age.
rings
rotating
contact
to a stationary
secured The
the
ring. to the
to a metal
is
wearing
for the diaphragm
faces
in figure
which
for the as
rubbing
a shoulder
at a right
attached
in3/sec area,
3 established
to tim sealing
with a spring-loaded a bellows.
Qe
used well
through
and
shown
to prevent
where
lb/in
stages.
precision-lapped
many
tion Qe=CsAcV'24g
the
washer
through
by the
as
In a face-riding-type
to pass
to reduce
at a minimum
estimated
seal
tending
are
impellers,
attached
two
operation
labyrinth
fluid
interface
of a labyrinth
to a reasonable
the
fluid
coefficient,
experimentally
subsequently
cause
in figure
age
labyrinth
can
and
DN limits.
accomplished
the and
and
surfaces.
load
veloci-
parts,
or indirectly
factors
shown
times
smooth sealing
sealing
a clearance-type through
rubbing
surfaces,
of internal
centrifugal
contact
surfaces,
sealing
bearing
expansion
components,
sealing
squareness alters of the
vibration,
of sealing
sure
6-61.-Bali
it to
without
leak-
in conjunction instead
consists
plate,
and
form
a ring
it by garter
of
of a several around springs.
260
DESIGN OF LIQUID PROPELLANT
ROCKET
ENGINES
-PUMP CASING WEARING RING
....,..\\_
HOUSING
/-- PUMP IMPELLER
___
-_-_-
_SHAFT
CC SHAFT LABYRINTH
SEALS
_
_-TURBOPUMP FLOATING .\'..x>,_" SEAL WASHER_\_\_/ST
,.AL
RETAINING
PLATE /-_
CASING
TURBOPUMP
/CASING
P- SE;TL HO_SING ICSE L
____GARTER
SPR,NGS
_HER_/SEAL SHOULDER
RING_
HOUSING
BELLOWS ....._/,/_ _
_
___cu-_L_L
FACE-RIDING
- --
SEAL
SHAFT-
Figure
Thus
self-adjusted
plished
dynamic
between
ment
inside
forced
shaft
diameter.
against
a static
to occupy
less
A wide floating seal
variety
is
hardened
The 300
assures such
face
rubbing
sealing
interpropellant
tend seals. for
speed
smooth
two
in series.
for critical
held
as
not
gears must
or
sistance
The
gear
pumps
(fig.
tween
turbine,
also
sometimes
trains 6-16)
used afford
pumps between
in liquid speed
and
turbo-
differentials
accessory a pump
rocket
very
impeller
and and
a
often
internally
gears
designer,
steel,
the
with
tooth
surfaces
or induction surface
very
should
process.
tolerances under
re-
usually
tooth
by a grinding
be held
high are
carburizing
dimensional
on bear-
therefore, and
gears
the
most
in turbopump
strength
case
are thrust
Turbopump
finished must
are
of turboclose
control
manufacturing. improve
certain
practices
The
If possible, and
sections
speeds
or
are
cross
minimize
tooth
by either
gears
To ity,
high. high
webs
are
Spur
and
of high-alloy
during
be-
drives,
results.
to wear.
pump
hubs
loads
hardening.
Design
The
oil,
in an aluminum
further,
as
Tooth
Materials Gear
possible
geom-
operation,
with
housed
weight
they
be accurately Turbopump
pumped.
since
hardened
applications
being
used,
are
and
propellants,
During
lubricated
usually
hub.
achieve
made
seals.
as
for best
ings.
factors. and
minimize
thin
rim and
lines This
are
To
widely
should
between
gears
splined
be
or purge
The
arrangement transmitted,
other
cooled
propellant
casing.
the
rubbing must
to a very
vent
installed
the
segments.
The
lapped
cavities
seals
positive as
ring
or shaft
Frequently, to the
dynamic
seal
ring
with
Gear power
and are
SEAL
types.
upon
ratio,
thus
available
frequently. and
seal fps.
connected
more
most
or plated,
exceed are
and
speed
RIDING
inducer.
gears
seals
seal
depend
the
face-riding is
are
etry
housing
washer,
of materials
on shoulder
finish.
the
seg-
segments seal
dynamic
low-speed
and
Shaft-riding than
washers
used
faces
the of the
a spring
seal. space
seal
Carbon
and
turbopump
is accom-
diameter
surface
plate
providing
sealing
Axially,
a flat
by a retaining
6-62.-Principal
outside
SEGMENTS
.....
_ SHAFT
gear
life
modifications can
be applied.
and load-carrying to standard Pinions
stabildesign
are
frequently
at
DESIGN OF TURBOPUMP
made
with long addendum
addendum
PROPELLANT.FEED
considerations
and gears with short
to adjust tip-sliding velocities and to
strengthen the pinion. thicknesses
Furthermore,
pinion tooth
are often increased, at the expense
of gear tooth thickness.
High pressure angles
as high as 22_ °,25 _j,or 271/: ° may be applied to reduce contact stresses on filetooth surface and to increase the width of the tooth at the base,
to compensate
tips
from
cutting
the
The
DESIGN LAYOUT ASSEMBLIES
OF
is
layout aging
a list
Figure 6-63 presents the design layout of the A-1 stage engine turbopump assembly. Logical packaging and arranging of the basic mechanical elements of tim turbopump are among the
For
of important
Positive
systems
pack-
integrity interpropellant
sealing
for thermal
(5) Ease of development (6) Ease of assembly (7) Ease of manufacturing Considerable experience in turbopump
turbopump
plumbing
(4) Compensation contraction
TURBOPUMP
layout.
with engine
and
(2) Structural
part.
the
considerations:
(1) Compatibility
(3)
6.7
in preparing
following
for bending and to keep the mating
261
instance, one of the more important criteria which influences the selection or arranging of the turbopump mechanical elements is the ease of development. Standard or proven mechanical detail should be extensively adopted in the layouts. design
Involute-profile modifications are often also made
SYSTEMS
design
layout
expansion
and
and skill are required work
for best
results.
iNLET PUMP PUMP VOLUTE AND DISCHARGE
i _-FUEL
PUMP
VOLUTE AND DISCHARGE MANIFOLD i
FUEL
PUMP
-TURBINE
NOZZLES ROW
ROTATING
BLADES IMPELLER-_
OXIDIZER PUMP
ROTATION
/
OXIDIZER PUMP
OXIDIZER PUMP IMPELLER
ROTATING BLADES SEAL
INDUCER
HYDRAULIC
3TATIONARY PUMP
IMPELLER
BLAOES
AUXILIARY POWER P1CKUP SHAFT
Figure
6-63.-Assembly
design
layout
of the
hypothetical
A-1
stage
engine
turbopump.
Chapter Design 7.1
CONTROL The
Controls
of
METHODS
opening
foremost design requirements for any
and
deviations pellant
control system ability. Two able:
closing from
flow
the
the
and
Valves
propellant
valves.
design
rates,
VII
mixture
such
as
from
Minor
ratio
or pro-
fabrication
are accuracy, stability, and relibasic control methods
open-loop
are avail-
(no feedback) and closed-loop
tolerances
of engine
beforehand
by insertion
orifices (feedback) control systems.
Both have
into
the
components,
are
corrected
of accurately
propellant
sized
flow
lines
(also
see
to effect
found the
desired
pressure
drops
ch.
II).
The
wide application in liquid propellant rocket proextent pulsion systems.
Open-loop
to those systems
which
of correction
to operate
preflight has
calibration
the
conditions.
Most other applica-
tions require one of the many can be constructed with which
and
is unable
tions
during
models
such as gain factors and stability of a then
system
such
characteristics of the
being controlled, and by allowable Once
elements
the method
time-
is determined, the basic
for the proposed
system must
lected, such as type of components
locks. their
It will be influenced by the required
accuracy, the dynamic lags.
be se-
to compensate
the specific control, which specific application.
of an open-loop
control
for engine
and
of the power
lant
valves
ators
are
with
fuel
and
the
relative
pets,
development
all depend
start
the
aid
are
preferred
stop
of inter-
for
other
of many
positions
with
work.
However,
some
work with attendant redesign will
requirements
Control
off command
means
control
means, devices. is
calibrated
propellant
achieved valve also
between by adjusting
gates
mechanical
can
(electric,
or pop-
linkage.
be
such
is accomplished as
orifices,
A typical an engine to a fixed
flows
hydraulic,
engines, valves
interlock
furnished
by
or pneumatic).
sequencing
and
by the
quence
designs. engine,
ignition
between
system
combination
and
are
propellant
controlled
by
and
example
set
A typical
for which their
the
interlocks
in chapter
Closed-Loop
system,
control
gener-
operated
main
is often
of various example
is the
start
and
stop
were
described
A-1
sein
of perfecting a
system.
this
to the
are
sequencing
is of the
respect
for propel-
or gas
and
Proper valves
the
engines
linked
actuator.
oxidizer
instance,
small
mechanically
In high-thrust
on the
detail
control
For
Ideally, the basic theories
always be required in the process
Open-Loop
interlocks
reliability.
by a single
stage
The
is used
should permit design without
experiment or development
system,
condi-
as
accomplished and past experience
open-loop
for variable
sequencing
Mechanical high
propellant
With
it is
parameters,
fluid (electric,hydraulic, or
pneumatic), and of the operating mechanism
preset
of operating
accomplished
Interlock supply or working
new
set
control
However,
system, can be analyzed.
is an important firststep in control systems
system
Open-loop
operation.
Accurate
the functions and
selection of the best-suited method
design.
data.
of simplicity.
to a specific
is usually The
systems
forms of closed-
loop control. For these, mathematical
proposed
test
advantage
limited
dynamics,
from
control is confined
are designed
at a fixed, steady-state level over a narrow range of environmental
is determined
on-
of flow
of conditions. simply
Control
Closed-loop or feedback
III.
control is also called automatic
control. This
accurately sensed by
system usually in-
cludes sensing means, computing means to detect errors, and control means to correct them. An feedback
is compared
with a
fixed or variable reference by a computer, which 263
_mm
264
DESIGN
then generates
signals
to correct
I=
OF LIQUID
PROPELLANT
For rocket engine application, closed-loop control systems usually employ one or a combination of the following modes of operation: 1. Simple "on" and "off" type.-(Example: pressure switch/valve combination for tank pressure control.) 2. Proportional type.-Employs a continuous control signal which is proportional to the error. (Example: transducer output for chamber pressure control.) 3. Derivative type.-Employs a continuous control signal which is a function of the error and its time derivative(s) (rate of change). This is principally used when systems stability is critical. (Example: thrust vector control system with phase lead.) 4. Integral type.-Employs a continuous signal which is proportional to the cumulative integral of one or more errors. (Example: two flowmeter outputs for mixture-ratio control.) Closed-loop or feedback control systems are essentially dynamic systems. Their design characteristics may be analyzed according to the basic laws of physics. Figure 7-1 shows a typical example. Its function is to maintain the variable
Pc equal
_
ROCKET
ENGINES
for any devia-
tions. The main system thus does not require precise calibration for a specific set of conditions. Unlike open-loop control, closed-loop control depends on sensing absence or presence of an error to maintain a desired condition or to bring about a correction. In general, the objective of closed-loop control is to minimize errors during operation and reduce system sensitivity to environmental changes and changes in component characteristics. It is applied to areas such as engine-thrust control and/or throttling, propellant mixture-ratio control, and thrust-vector control.
controlled
mw
to the desired
value
Pr, by manipulating the variable wg. Maintaining Pc equal to Pr is assumed to maintain the indirectly controlled quantity F. In a typical turbopump fed engine control system, Pc would be the combustion chamber pressure, maintained equal to a fixed reference pressure Pr by means of a valve controlling the gas generator propellant flow wg. F then would be engine thrust, which is indirectly maintained at a desired value. In this control system which consists of a sensor (chamber pressure transducer), a computer
Figure
7-1.-Schematic control
of a typical system.
closed-loop
(electric summing junction and amplifier), and a controller (gas generator flow control valve), the command reference input r is compared with the sensor feedback b. The controller then manipulates • g in response to an error signal e from the computer. Ideally, r should be in linear proportion to Pr and b to Pc, save for constants required to convert one physical quantity into the other. However, this ideal condition is difficult to attain because of the dynamic characteristics of the pressure transducers. These characteristics are influenced by physical properties such as mass inertia, fluid compressibility and viscosity, and frictional resistance. Instead of r being directly proportional to Pr, the two parameters are actually related through a differential equation which represents the dynamic behavior of the elements involved. The same is true for the feedback b and the controlled variable Pc. It is also applicable to other systems components. Hence, the analysis of a closed-loop control system usually involves the solution of sets of often complicated differential equations. Refer again to figure 7-1, where Pc is the controlled variable, _¢g the manipulated variable, e the error signal, b the feedback, r the reference input, and Pr the desired value. A, B, C, and D symbolically represent the dynamic relation between input and output of the respective components. The following terms representative of the differential equations for this closed-loop control system can be written: r =Apt
e =r- b
Pc =C_vg (7-1)
b = Dpc
¢¢g = Be
The solution of these equations in combination with a systematic experimental program will suffice to analyze the dynamic performance of the system. The continuous corrective action of a closedloop control
system
may promote
dangerously
DESIGN OF CONTROLS AND VALVES
unstable
operation
components significant
response one
is
taining
a variable
is
no longer
for control
ity
difficult
often
The
high
ing
high
degrees
of system
results
possible
Higher
However,
leads
to obtain
satisfactory
dur-
various
such
(time
a high
tion on compensation will nection with thrust-vector
as
derivatives),
gain
stability.
through
control
it
system
Additional
informa-
be presented control.
in con-
safe as
The
engine well
cutoff
shutoff
and
As
sequence
is
a rule,
off in the
main
damaging
in smooth
Engine
(gas
generator,
propellant
rapid
LIQUID
ENGINE Most of the
basic
found A-4
CONTROL
engine
following
PROPELLANT
spikes
paragraphs.
in chapter
Ill,
propulsion
for the
systems
several
or all
summarized
Typical
in the
applications A-I,
(figs.
results
governing engine
been discussed
in section 2.i.
is the result of a malfunction, will be supplied
require
systems
and
pre-
The signal for engine in-flightcutoff, unless it
SYSTEMS
systems
control
ROCKET
cut-
This
termination.
Important consideratious BASIC
valve-closing a fuel-rich
Main Stage Duration Control
duration have 7.2
in
(purges,
chamber.
thrust
of
and,
securing
temperature
and
power;
to provide
combustion
opera-
consists
chamber the
cutoff
systems
postfiring
adjusted
noris
usually
power
of main
flushes).
repeatable
reliable
sequence
firings,
during
in an emergency,
to enhance
of test
vents
shutdown,
as
of subsystems
etc.); case
Control
for minimum and
shutoff
gain.
in overshoot
and
desirable
tion.
accu-
high
promoting
of compensation,
phase
The
Cutoff
operation
impulse,
for stabil-
i.e.,
instability.
means
"anticipatory"
with
to combine.
thus
in main-
in.
System
Rapid mal
Instead,
and
amplification;
action,
appropriate is
accuracy
amplification
corrective
set
and
control
value.
may
Engine
or gain
effective
desired
oscillations
requires
high
An unstable
at its
requirements are
elements
having
lags.
that
divergent
racy
control
employed
system large
when
are
265
A-2,
2-10,
are
A-3, 3-3,
and
3-6,
and
by the vehicle and fed directly into the cutoff control system discussed graph.
optimum
utiliza-
tion of the propellants is desired, a tank lowlevel sensor is often employed. where
3-9).
in a preceding para-
For lower stages, where
In final stages,
precise cutoff velocity is essential, an
integrating aceelerometer
or equivalent device
will signal cutoff. Engine
System
The trol
Start
prime
objective
is to bring
start
signal
the
may
(purging,
chilldown);
if required
consist
(start
introduction
and
required
the
generator
and
application
ignition
sequence
This
2-11, system
3-8,
start
of start
energy,
instability,
and
sors,
propellants
Secondary
in the
sequences
of engine
interlocks
control
maintained the
through
functional start
step
transient.
and and
and
by propellant cooling
3-11
cutoff
methods.
present sequences.
typical
fail-safe
of engine
tion
The
system
opening sequence is set to an oxidizer-lead or a fuel-lead start. dictated
ous,
type
and
system
systems
to shutdown
designed
during
it may
be desirable
gency
power
source,
will
Figures
latching, for continued and electrical interlock
engine
extensively
used
the
reliability
in the
of the
control
safety
an interrupcause
to an emerby
operation.) devices
system
control
the mis-
shutdown
mec_Janical Mechanical
phases
engine
certain
to switch
or prevent
all
most
(For
condi-
nonhazard-
so that
supply
safely.
sions
frequently
or unsafe
automatic,
shutdown
power
combussen--
are
In addition,
are
of electrical
trips,
undesired prompt,
operation.
as
combustion
overtemperature
overspeed
to prevent
such
such
for detecting
generator
by effecting
engine-
devices,
monitors gas
employed
Controls
monitoring
or turbopump
tions as
Safety
stability
subsystems
each
ignition 3-5,
Special tion
A reliable
is
is usually
chamber
A typical
System
preconditioning spinner);
of the
Engine
system.
during
propellant-valve effect either
from
for certain
by monitoring
operation
turbine
con-
safely
operation.
chamber.
may be start
system
of systems
tanks,
combustion gas
of a start-sequence
engine
to main-stage
sequence
main
Control
are
to assure
systems.
266
DESIGN OF LIQUID
Propellant
Tank Pressurization
Various tems
propellant
have
been
tank
design requirements tems must consider(1)
Means sure
(2)
within
an allowable
all
phases
of vehicle
(3)
operation,
transients;
periods
between safety
control
and
to prevent of the
with
such
as
pres-
range and
engine
steady-
tank
are
closed-loop
Engine
System
or dynamic
vehicle
coasting
other
as
pressure
overpressurizapropellant subsystem
tanks. con-
propellant-utilization-
and
thrust-control
Figure
7-2.-Control
for desired
and
ori[ice
for each
some
are
parameter
pneumatic stricting
sizes
switches,
are
checkout
ance
and
includes
of orifices.
of these and
cussed
locations
sizing
placed
the
and of timing
switches,
correct
values
during
engine
firings.
Of the
orifices,
Specific ratio 7.3
lines Others
lines
mixture
o[ a typical
setting
position
in propellant
in sections
para-
calibration
characteristics
The
calibration.
devices.
preceding and
verified
or hydraulic and
in the
adjustment
operating
This pressure
the
for thrust
systems.
described
engine
control
type.
Calibration
proper
performance.
pressurization
Control
require
bration such
of the
systems
graphs
devices,
start
restarts.
rupture
Compatibility trols,
sys-
tank
including
devices
valves and
required
mainstage;
throttle
tion
of these
level
Effective
The
propellant
systems
The
engine
relief
control
the
systems
sysV.
for the
ROCKET ENGINES
Most
in chapter
to maintain
during
state
Control
pressurization
discussed
PROPELLANT
and
engine
as
are
used and
in re-
applications
control 7.4;
for perform-
timing
orifice
cali-
will orifice
system.
be disdesign
DESIGN OF CONTROLS AND VALVES
elements
will
be presented
Following
sizing,
identified,
by stamping
actual Control sizes
sizes and
To
verify
means
are
firing
Checkout
its
components, system.
without
and
Provisions
of all
for verifying
voltage
monitors; position flowmeters;
checkout
to tile
ground-support
The
rocket
been
explained
specified
of the
include firings.
It is possible,
orifice
of the
fed
level
in section
2.1.
and
Main
(3)
Variation
for
tems,
engine to
often
of a has
usually
The trate
of the
engine,
various
propellant
without
resort
to regu-
of turbopump
regulation
of gas
rate
or hot
gas
method). rate
tank
pressures
(in
the
systems). (clustered)
reduction
or more
example
chosen
a closed-loop
engine can
engines
be
sys-
effected
of the
power
variation.
control
system
which
relies
Here,
the
thrust Figure
on
main
7.1
system
is
control
sub-
for our
the
flow system
for
turbine' thrust
A-4 stage
propellant control
to illustypical
through
7-3 shows
proposed
closed-loop
the principle main oxidizer
engine,
variation. operates
on
of variable fluid resistances in the and fuel feed lines to achieve
flow-rate by
parameter
most
comparing
the
reference
in section
control
effecting
is determined
simple
thrust
of one
propellant
in the
control
systems.
"_+3%."
calibrations
pro-
pressure,
by
case flow
flow
in multiple
level"
with
the
of pressure-fed
stepwise
"fixed band
the
basic
of Pc
through
of main
Additionally,
with
this
(in
propellant
case
for instance, thrust
rate
(2)
a tolerance; modern
power systems),
(preferred
or vacuum)
Two
be accomplished
flow
flow
CONTROL
It is
reduction can
as
level
is for a planned
of chamber
propellant
equipment
thrust
require range.
during
flight.
generator
This
need
or "throttling,"
reduction
Turbine
a system
LEVEL
(sea
to guarantee
subsystems
(1)
instrumentation.
THRUST
the
will
a wider
possible:
by shutoff
test
cases,
of them
func-
the
predict-
of-
for start
equipment,
missions over
Continuous
Each
system
as
to cham-
is
Pc (b)
signals
engine
such
same
at sea
of altitude
of propelled
are
is
The
of thrust
of thrust,
portion
ratio
relationship
control
(a._) Stepwise
devices.
vehicle
must
engine
in such
last
mixture pressure. starting
vehicle
Usually,
as
regulators,
system
with
engines,
entire
is
accuracy.
thrust
reduction
effect
at altitude
for systems
control
control
of static
significance
liquid
proper
high
and
pressure
their
since
a function
Occasionally,
firing
of all
ratio
checkout
additional
ENGINE
and
the as
in-flight
transducers.
pressure
operating sequence, and cutoff.
7.3
with
continuous
such
to simulate
"cold"
requires
able
propellant
the
subsystems,
mixture
Provisions
control
engine system
true
because pressure
equip-
plug and
range
valves, and
level, ber
such
pressure
operating and
thrust
permit
of the control
of the
for valves;
and
and
control
In addition
is essentially
operation
for verifying
devices
(4)
and
proper
spark
regulation, engine
pre-
at sea system.
chamber
(vacuum),
of chamber
pickups,
closed,
signals
Provisions tion
and
open,
actually
a function
cedures
instrumentation
dc bus
are
At altitude
for a given
system.
Provisions
regulators
solely
checks
checks
Thrust
a
starting
of a multistage
thrust
the
leak
stages
are
require
and repeatability, vehicles
or in final
to thrust
"controllers"
which
of precision
level,
identical
or
systems
in single-stage
regulators.
engine
control
to conduct
7-2.
as
of calibration firings.
regulators
control
critical firing
degree
such
Controls of the
checkout
higher
in figure
ground-support
electrical-continuity
(3)
their
simulation
its
actually
ment (GSE), an engine should include-
(2)
in vehicle
suitable
suitable
engine
employed
shown
permit
engine
Utilizing
(l)
and
readiness
These
of the
"thrust"
for postassembly
checkouts.
lators, and with a minimum However,
and Test
subsystems,
required
operation
are
operational
and
7.10.
be properly
in the engine logbook. orifice locations and
system
Systems
system
must or banding,
recorded calibration
of a typical
Engine
in section
orifices
267
modulation. sensing
indicative feedback
pressure
input
Engine
chamber of thrust b with r.
the
reaction
pressure, level,
the and
by
command
Any resultant
error
e,
268
DESIGN OF LIQUID PROPELLANT ROCKET ENGINES
7.4
C_lu_m _¢_E
,
_
o
_mu
,NPUT
[_
Figure
7-3.-Main-stage thrust loop Ior the ,4-4 stage
C_EC_m_
The significance of propellant mixture ratio and its control have been discussed in section 2.1. The principal reasons for mixture-ratio control are recalled:
control Open-Loop
following amplification and compensation as required, is used to drive the thrust throttle control actuator of the main propellant control valves in a direction which reduces the error. Ideally, the system operates over the entire thrust throttle range with minimal disturbances to other critical engine parameters; in particular, the propellant mixture ratio. In practice, these disturbances are not entirely avoidable, but can be minimized by maintaining a given resistance ratio between the two main propellant control valves throughout the control range. A most reliable method toward this objective would be mechanical coupling of the two propellant valves (fig. 7-4). Orifices, propellant valves, and servovalves required for thrust control will be described in subsequent chapters.
ENGINE
FROM
ST_.RT,
THROTTLE
CUTOFF
CONTROL
{I TPiRUST
_II£TL_TO_
7
FI_:_I
OXIDIZER TANK
._,
N OXIDIZER T _ CO_ ROL LVE
TO THRUST
NO.
I
CHAMBER
/
_
FUEL _'ANK
/
i
MECHAN ICdI, L COOPLING
TO THRUST
NO
Z
CH*_*M_R
TO THCtUST
NO.
I
CHC_MBER
TO THRUST
Figure 7-4.-Schematic of the propellant system for A-4 stage engine start, throttle and mixture ratio control.
AND CONTROL
Optimum engine performance (important) Complete propellant utilization; i.e., minimum residuals (most important) Both goals are closely interrelated and essentially inseparable.
i,,_._,_
throttle engine.
T
PROPELLANT-MIXTURE-RATIO PROPELLANT-UTILIZATION
NO
Z
CHAMBER
control cutoff,
Mixture
Ratio
Control
The simplest form of engine mixture ratio control is obtained by the installation of properly sized calibration orifices in the main propellant lines. Acceleration effects during flight are usually accurately predictable as a function of trajectory and flight time. Thus, simple averaging of flight mixture ratio and selection of the corresponding orifice size reduces mixture ratio deviations over the duration of flight to a level acceptable for optimum total propellant utilization in many missions. Open-loop mixture-ratio control can often be further refined by the following procedures: 1. Weighing ot the propellants loaded; i.e., accurate determination oI the tanked propellant mixture ratio.-The vehicle to be launched rests on load cells, thus permitting weighing of the propellants actually loaded. In mixed systems, the noncryogenic component is loaded and weighed first. The cryogenic component follows and is subsequently maintained at level through a topping line. The mass of both propellants is determined from on-the-spot temperature and ambient pressure readings while the tanking procedure is progressing. 2. Use o[ adjustable, rather than [ixed, ori[ices in one or both propellant lines.-As close to vehicle takeoff as possible, and as a function of tanked weight and temperature readings, a hand or remotely ground-controlled prestart-oriflee adjustment is made. This method is usually confined to noncryogenic fluids. For systems where engine operation closely follows that obtained during final calibration, remarkable accuracy of targeted mixture ratio and thus propellant utilization can be obtained
DESIGN OF CONTROLSAND VALVES
with the open-loop method, closed-loop system (single In certain applications,
approaching that of a stages; first stages). however, the varia-
tion of mixture ratio as a function of increasing acceleration may exceed tolerable limits. Acceleration in most vehicle tank arrangements affects predominantly the propellant in the forward tank. Because of the long supply line, acceleration continues to act upon a relatively large fluid column, even near the end of powered flight (tank depletion). By comparison, the effect on the fluid in the rear tank is often nearly completely offset by the simultaneous decrease in fluid head (short liquid column). To offset excessive acceleration effects on the fluid from the forward tank and thus on mixture ratio, head-suppression valves are sometimes used at the pump inlet of turbopump fed systems. Here, pump inlet pressure increase is sensed as a function of acceleration. Corresponding signals are fed through a logic device to the head-suppression valve which will gradually close, thus acting as a throttling device. This valve also protects the pump structurally.
Closed-Loop
Mixture
Ratio
Control
In certain cases, such as in last stages, or in missions requiring engine restart following extensive cruising periods involving propellant boiloff, a closed-loop system may be required. In figure 7-5 we see the A-4 stage engine mixture ratio control loop which operates on the basis of continuous propellant mass flow sensing. Both fuel and oxidizer mass flow rates are monitored and integrated to establish the ratio of either the propellants consumed or the propellants remaining. The mixture ratio feedback, (MR)b, is then compared with a command reference mixture ratio input, (MR)r, in the propellant utilization control computer. The resulting error signal, (MR)e, is fed to the mixture ratio control oxidizer valve
_9
oxidizer flow in a similar manner. For instance, a propellant-utilization servo control valve, which regulates the pneumatic pressure to the main oxidizer valve actuator, may control the oxidizer flow by adjusting the angular position of the oxidizer valve gate during engine mainstage operation. In certain applications it may be desirable to integrate the propellant flow rates and to compare the masses consumed to one another and to those tanked for optimum propellant utilization. It is readily seen that control systems, based on propellant flow-rate measurements, are a refinement of open-loop systems using fixed orifices. They are basically still mixture-ratio controls and thus merely "assume," but do not measure directly, the amount of propellants actually remaining in the tanks and their unbalance. To accomplish this function, usually referred to as "propellant utilization" (PU), additional control elements must be employed in the form of vehicle tank-level sensors. Numerous principles are known: point sensing, sonar, acoustic, radiation sensing, differential pressure, and capacitance probes. Figure 7-6 presents the propellant utilization control system for the A-4 stage propulsion system. The residual propellant quantities in the main tanks are continuously monitored, summed, and compared with a PU control reference in the propellant utilization control computer. Any error detected is used to modify the command reference mixture ratio input, (MR)r, to tl_e mixture-ratio control computer. This method isolates the mixture ratio control from the propellant utilization control, and thus prevents interaction between them. The bandwidth of the
ilXTU_E
mXTU_f
_*TIO
_A_
vernier position actuator, which forms a link in the mechanical coupling between the two main propellant control valves, as shown in figure 7-4. The oxidizer flow rate is thus modified to eliminate the error. In high-thrust turbopump-fed engine systems such as the A-2 stage engine, where the propellant valves are independently actuated, the system propellant mixture ratio control can be accomplished by varying the main
[CEC_e,( _UV.C'nON _'
Figure
eLecrllc
SUVltNG lm_t.,1,1Ei
7-5.-Propellant mixture ratio loop for the A-4 stage engine.
control
270
DESIGN OF LIQUID PROPELLANT ROCKET ENGINES
°°
]
ELECT't;
Figure
7-6.-Propellant [or the A-4 stage
utilization propulsion
AMPL=FI(R
control system system.
propellant utilization control system is made narrow as compared to that of the mixture-ratio control system, because propellant residual errors may be expected to develop slowly; i.e., initial tanking errors can be corrected over the entire duration of engine operation. The sensors used in the vehicle tanks may serve additional purposes. In combination with suitable ground equipment, they may permit an automatically controlled loading, high-level limiting and topping procedure. In static firings and flight, they may serve as redundant low-level sensors to initiate engine cutoff. For such a complete system, the term "propellant management system" has come into increased usage. Apart from throttle valves placed in the main propellant lines, bypass lines have been successfully applied to vary mixture ratio. Here, a line is tapped off the pump outlet and ducted back to the pump inlet. A servo valve, possibly supported by an orifice, can be varied so that the bypass flow is adjusted from no flow to full bypass flow. The implementation of closed-loop propellantutilization control through mixture-ratio control is a major vehicle-to-engine interface area. The requirements or criteria will usually be established by the vehicle builder and/or user. Close coordination between engine and vehicle designer is essential. A closed-loop mixture-ratioand propellantutilization-control system may not only be used for accurate maintenance of a fixed mixture ratio but it also has the potential for programed mixture ratio control (PMR). Here, the mixture ratio is varied during flight, either continuously or in steps. It must be kept in mind that the average mixture ratio still must be equal to the tanked
mixture ratio to assure simultaneous propellant depletion. However, by programing a mixture ratio in favor of the heavier component during the early portion of flight, and then switching it in favor of the lighter one, the accelerated vehicle mass is reduced faster. Also, mixture ratio may be programed to provide a higher thrust level during the steeper portion of a trajectory. This provides a better thrust-to-weight ratio in the presence of gravitation, with attendant velocity increase benefits. These methods, possibly in combination, may substantially increase stage payload capacity, since the effects of mixture ratio on performance (Is) are usually small within a reasonable range (see table 7-1). Optimization can readily be made with the aid of an electronic computer program. In a number of applications, programed mixture ratio control without PU control, i.e., open loop mixture ratio control with PMR, may give best results, simultaneously reducing complexity. Valves suitable for mixture ratio control will be discussed in section 7.8.
TABLE
7-1
Mixture i ratio, Thrust O/F 3hange, percent
+10 -10
General
Considerations
Design
The precision ratio is obtained
+11 -11
Flow rates NPSH
Is
+12 -12
-1.3 +I.3
OxiFuel dizer +4 -4
+14 -14
with which a desired mixture or maintained is affected con-
siderably in open-loop systems, and to some extent in closed-loop systems, by the following: (1) Instrumentation accuracies (in particular, flow and tank-level metering) (2) Machining tolerances of orifices (3) Operating tolerances of regulators (4) Temperature influences on orifices and regulators (5) Density tolerances of the propellants, as a function of temperature and of purity (composition according to specifications; contamination and dilution)
DESIGN OF CONTROLSAND VALVES
(6) (7) (8) (9)
(10)
Acceleration effects during flight Propellant tank pressure deviations Turbopump speed deviations Differences between fuel and oxidizer pump characteristics as a function of speed Line resistance changes as a function of temperature and for miscellaneous mechanical reasons
(11) Temperature effects in rotating machinery In the following we will discuss important steps toward maintenance of high quality, and toward further improvement in the listed areas, for highest accuracy of mixture-ratio (and propellant-utilization) control. First, continued improvement of propellant flow-metering devices is imperative. Here, turbine-type flowmeters have achieved a high degree of accuracy (conformance with truth) and precision (repeatability). The accurate calibration of these meters to most reliable standards engine inlet pressures
is important. Since also affect the mixture
ratio, pressure measurements of the highest reliability are equally necessary. Wherever possible, the rocket engine design should include vital metering and measuring elements from the outset. Dynamic sensing devices, in particular flow meters, are drastically influenced by their installation configuration. If these end organs, following accurate calibration, remain with the engine through its entire life cycle, including flight, a maximum degree of accuracy is obtained. The design and machining of all calibration orifices should closely follow accepted standards (see section 7.10). Selection of suitable materials to eliminate or at least to reduce to a minimum, temperature influences and corrosion, is important. The design of orifice holders must prevent the possibility of incorrect (upside down) installation and of distortion of the orifices. Regulators, if any are used, must be designed for highest accuracy and precision with particular consideration of the medium to be controlled. More detail will be presented in section 7.12. The purity and composition of the better known propellants are regulated by official government specifications. The designer can expect that approved sources will deliver the propellants in conformance with these. However, subsequent contamination, dilution or alteration is
271
always a possibility and must be prevented by proper design and handling procedures. Many of these, such as cleaning procedures, will be called out in the shop drawings. Furthermore, the design, where applicable, will have to include filters, check valves, and suitable line routing in order to prevent contamination and/or contact with incompatible materials. Note that some propellants may change their properties merely as a function of time, such as hydrogenperoxide, which loses its concentration due to (very slow) decomposition (with attendant gas development), even if absolute cleanliness has been maintained. This affects design conditions in addition to contamination considerations since proper venting devices must be provided. The latter, in turn, have to be designed in such a way that no contaminants, including moisture, can enter the propellant system. Since mass flow rates delivered by pumps and/or regulated by orifices will be a function of the fluid densities, mixture ratio may be affected accordingly. The densities, in turn, aside from conformance with specifications, will be affected by temperature (noncryogenic fluids) or ambient pressure; i.e., boiling point (cryogenic fluids). To overcome these effects, it may be necessary to temperature-condition the propellants. This may be done by heating or cooling. Or, it may be accomplished by suitable storage, such as shielding against solar radiation. For cryogenic propellants, it is usually sufficient to keep the containers vented to atmosphere until immediately prior to use, since the possible changes of atmospheric pressure at a given altitude can only introduce relatively minor temperature changes. The designer, through a suitable operating sequence (engine schematic) and through provision of vent valves, recirculators, heaters, and other components, can minimize temperature effects. The actuation
of mixture
ratio
control
devices
affects the nominal engine performance parameters. Depending on the type of engine, in particular its turbopump characteristics, these effects may be significant. In an actual case, the effects shown in table 7-1 were observed. It is clear that the vehicle thrust structure must be capable of absorbing the higher thrust loads. Also, the vehicle tanks and their operating pressures must be capable of meeting the
272
DESIGN OF LIQUID PROPELLANT ROCKET ENGINES
NPSH requirements for extreme mixture ratio excursions. Furthermore, chamber cooling may be affected. During sea-level testing, nozzles with high expansion area ratios may experience jet separation at the lower thrust levels (low Pc), resulting in vibration, destructive to engine as well as vehicle structure. Since vehicles are tanked for their nominal mixture ratio, and since engines are calibrated to this ratio, mixture-ratio valve excursions should be small for vehicles which are expended within a few minutes after takeoff. For stages, with long cruising periods prior to operation or reignition, and which use one or two cryogenic propellants, boiloff may have altered the ratio of the propellants in the tanks to such a degree that the PU system may be called upon to operate at or near its maximum excursion. It is, therefore, vital that the engine designer appraise the vehicle builder of all performance variations as a result of mixture-ratio adjustments, beyond the standard tolerances of the nominal performance values. Also, engine turbopumps must be capable of operating for extended periods with the valve in either extreme position. A propellant utilization system is a complex system. If required, it must be of the highest quality. Otherwise, it will do more harm than good. Only closest cooperation between vehicle and engine designer will assure optimum quality. Areas of particular significance to teamwork are: Selection of the mixture ratiocontrol method.For instance, should the PU system be active during the entire flight duration, or only for the last, say, 30 percent. (Both methods have been successfully used.) Selection of the mixture ratio control valve specilications.-Should it be a variable orifice, or a bypass valve? What should be the permissible pressure drops, required response rates, and accuracies? In case of sensor failure, should the valve return to the neutral position or remain in its last working position? (Self-locking.) Selection of the sensors.-Should it be one of several available continously reading types, such as capacitance gages or differential pressure (tank top to bottom) gages? Or should point sensors be employed, such as hot wires (change of heat loss as a function of being immersed in fluid or exposed); switches triggered magnetically by floats; voltage pips induced in station-
ary coils by a passing magnet, or others? (The engine designer will be involved in this selection only if the generated signals affect engine components.) Selection of the best-suimd electronic control system.-This will be largely influenced by sensors and control-valve selections. A propellant utilization system is not a malfunction prevention system. It does not add to vehicle reliability, possibly subtracts from it. Rather, it is a system required to live with a marginal preliminary vehicle design. It is a safe assumption, however, that the first flights of a new vehicle will not be for its ultimate mission. PU, therefore, will not be a vital necessity for these flights. Thus, enough time is available to thoroughly investigate, analyze, select, and develop the PU system. This time should be utilized. Both engine and vehicle builder have facilities and test programs to permit mutual exposure of their selected systems to flight and simulated-flight environment.
7.5 THRUST-VECTOR
CONTROL
To steer a vehicle over its trajectory, thrustvector control is applied. The following methods have found application: (1) Gimbaled thrust chamber or engine assembly (widely used) (2) Jet vanes (obsolescent) (3) Jetevator (4) Gimbaled thrust chamber nozzle (rare with liquid propellants) (5) Secondary injection (into the thrust chamber) (6) Auxiliary jets The first method is used most frequently, due to its inherent reliability and performance. The first four systems require actuators which may be operated by hydraulic, pneumatic, or electric means. The remaining systems are controlled by flow regulation.
Thrust
Vector
Control Systems
Using
Actuators
Figure 7-7 presents a simplified schematic for a thrust vector control system, employing hydraulic or pneumatic actuators. It may serve to explain the fundamentals of closed-loop thrust
DESIGNOF CONTROLSAND VALVES
toward the same end. Malfunction safety circuits are included to effect engine cutoff in the event of erratic operation. A typical schematic for a thrust vector control system using electromechanical actuators is shown in figure 7-8. Here, the actuator is powered by a continuously operating, constantspeed, 28 volt de motor, fitted with dry-powder metal bidirectional clutches. The control com-
V_HOJ C_OANCE CO_MANO _FE_ENC_
II
=° (_
ELeCTRiC #U_N
9,JMMPNG
_,.ECT RIC
Figure 7-7.-Typical control system actuators.
_PLIFJER
schematic o{ a thrust vector using hydraulic or pneumatic
vector control, even though the systems used in practice may differ significantly in detail. The actuators are controlled by commands, originating in the vehicle guidance system, which are a function of the vehicle's deviations from a prescribed path and of its response to corrective steering action. These signals are fed through an electronic thrust vector control logic to servo valves. In the system shown in figure 7-7, each servovalve modulates the fluid flow to its respective actuator assembly in response to an electrical error signal which is proportional to the difference between desired actuator position and its actual position. Feedback of the actual position is obtained through a transducer attached to the actuator. Additionally, tim actuating speed is sensed by a rate transducer and applied tO the control computer to stabilize the closedloop control through adequate damping. Instead of a rate transducer, electronic differentiation of the position
transducer
output
may be applied
r.lc
Figure 7-8.-Typical schematic tor control system using actuators.
273
_m,¢
lU_W,.G
for a thrust vecelectromechanical
puter consists of summing junctions and an amplifier as in the case of hydraulic actuators. The dc motor drives the actuator through the bidirectional clutches which are controlled by the error signal generated through comparing guidance command reference input with systems position feedback. To provide adequate systems damping, the actuating speed is sensed by a rate generator or through differentiation of the position signal. Apart from electrical feedback and compensation systems, mechanical feedback systems coupled with hydromechanical compensation "networks" are coming into increased usage. They are inherently simpler and thus offer higher reliability. Two basic types of hydromechanical compensating devices may be distinguished: piston-bypass devices and load-pressure-sensing devices. Piston-bypass devices utilize leakages past the actuator piston to introduce system damping and may make use of dynamic relationships to control time constants (a hole drilled through the piston is an example). Load-pressure-sensing devices, commonly called "pressure feedback" (PQ) valves or "derivative pressure feedback" (DPQ) valves, are widely used. Figure 7-9 shows a typical servovalve and actuator schematic with derivative pressure feedback (DPQ) and mechanical feedback. The only electrical signal required is the input to the "torque motor" (an electromagnetic actuator) resulting in deflection of the flapper of a differential valve, which drains to the sump. If the flapper is deflected, as indicated in figure 7-9 by the arrow, nozzle flow on side B decreases, with an attendant pressure rise. The reverse is true for side A. The resulting pressure differential forces the power-stage spool to the left, blocking the return line on side B, and opening it on side A. As a result, pressure Pb increases,
DESIGN OF LIQUID PROPELLANT ROCKET ENGINES
274
N"I
NOZZLE D4ERJVATIV_ FEEDBACK
IS, OL AT _0_
MOTOe
B
PlES$_RE LEAF
DERIV&TIVE PE'E$ SURE
•
TO_OU[
_TE_
-
SPRING
LO_D P_STON
DIRECTNDN FEEDBACK
P'_ST_ON
i_OT _',J
O$"
_ _WER
ST_
I, IEc:,I
_&
FEEDB, ACI( S_4mNG
_'OOL
RETURN
_IECH FEEDBACX
--
m[TUml
O_IFICE
ORF_.J[ _'N.TER
Figure
7-9.-DPQ
valve
wiLh actuator.
and Pa decreases, forcing the actuator piston to the left to apply the desired load force. Attached to the actuator piston rod is a tapered extension which acts upon the mechanical feedback linkage, including a roller and a spring. The mechanical feedback attaches to the torque motor. The pivot point of the valve flapper becomes the error torque summing junction. Note that the nozzle jets also have a feedback effect. The time derivative of the actuator motion, i.e., the hydromechanical compensation, is obtained through action of a derivative load pressure piston. This piston is affected by the same pressure differential that acts upon the actuator piston; i.e., by the load pressure. However, by inserting an isolation piston and permitting flow through an orifice bypassing the derivative pressure piston, the pressures affecting the latter can equalize. The degree of this effect is a function of the actuator pressure differential and its rate of change and of the bypass orifice size (shock absorber principle). As seen in figure 7-9, the derivative load pressure piston acts upon the valve flapper when displaced. Thus it provides the required time derivative of the actuator motion for compensation. As has been seen, it is possible to provide compensation in thrust-vector-control systems by either electrical or hydromechanical means, the latter now being often preferred for actuators. Conceivably, other control systems could be converted from electrical to hydromechanical networks. The analogies between the differential equations of the two network types often permit the use of existing electrical networks
and transfer functions by substituting the equivalent hydromechanical time constants. Table 7-2 may be found valuable by those who wish to familiarize themselves with some fundamentals in this field. Detail on the design of servovalves will be found in section 7.11. Demonstration
Example
Two basic types of electrical compensation networks exist: current output for voltage input, and voltage output for voltage input networks. Figure 7-10 shows a simple form of a current output for voltage input network. Find the analogous hydromechanical network. Solution The transfer work is
function
for the electrical
i I+RCS --:-V R
net-
Amp/volt
where i = electrical current (amps) V = voltage (volts) R : resistance (ohms) C : capacitance (farads) S : LaPlace transform operator (= j_o for sinusoidal forcing functions) From table 7-2, we obtain the equivalent hydromechanical parameters for i, V, R, and C. The new transfer function then is A
2
Q _1+ C_xPK)S AP
1 Cx
o V
1 Figure
G 7-10.-Current
output network.
for
voltage
input
DESIGN
TABLE
drop,
i, current
volts
coulombs/sec
component
' V = V A - VB
.......
AP,
Component
Q, flow,
dq _ =-_
Analogies
Describing
or quantity
pressure
275
VALVES
Hydromechanical
Describing equation
.........
AND
7-2.-Electrical-Hydromechanical
Electrical quantity or component V, voltage
OF: CONTROLS
drop,
psi
AP:
in3/sec
V _AP
PA - PB
dV Q = d--t V:
q = coulomb
Remarks
Analogy
equation
i_Q
volume
charge
_I_-------
V
Capacitor,
-------_
dv
....
[_----
i=C_-
Q
A p ----_
(Ap)2d(,_p)
= -g
Ap 2 ! Massless C _ --_ sumed
-_
piston
as-
--.._Q
farads
Ap : piston K :spring
area, in 2 constant, lb/in
V _=_-
Ap
Q_Cx_,A-'_-_
CSIIE3
_CxA
R _
P
1._
Parabolic linearized
CX
flow curve about
operation
point
Q ---...,lllb Resistor.
ohms
inS/sec --
Orifice,
V -----_
Piston
,, p
....
AP2 y(AP)dt Q:"M-
b
"Ap"
mass
not
negligible
t ------DInductor.
henries
Source:
Ap= piston M =piston
D. h. Engels, mechanisms,"
"A Method Proceedings
of Synthesizing of the IEEE,
Q area, mass
in 2
Electro-Mechanical PTGAC, October
The correct hydromechanical network, which is of the piston-bypass type, is shown in figure 7-11.
Compensation 1964. The
be
significance
seen
from
would Interfaces
With
Actuator
the
at the randomly tolerances,
Engine-to-Vehicle
Networks
be
for Hydraulic
of good
thrust
Servo-
alinement
fact that in an engine distributed
maximum
a trim deflection required
from
can
cluster, of these
of close
all engines
to 0.5 °
to offset
the
misalinement.
Systems For
larger
(looser)
trim deflection Engine For ance that
minimum and
the
alined point
engine engine
with in
tolerances cally.
Installation
all
and
demands
respect three are:
on
actuation thrust
the
planes. t0.25
the
vehicle
systems, vector
to
Alinement
inch
be
it
guid-
trim deflections
thrust
and
is required pre-
ered
properly
vehicle
attachment
Typical
specified
laterally,
if the
need
_*0.5 ° verti-
to
guidance
apply
flight
alinement
would
them
results
be
seem
to reduce
capability for
tolerances,
the
further increased.
the
full
in
appreciable
to
aline
only
Even
effective slightly,
duration
of
payload
re-
ductions. It
is
vector prior
customary to
to
the
upper
shipment•
the
engine
the
gimbal
face
of
Both
optical
and
thrust bearing dynamic
the
pow-
DESIGN OF LIQUID
276
PROPELLANT
ROCKET ENGINES
Q _C-_
/--VECHICLE
//,4i7///
_7
THRUST
MOUNT
CENTERLINE
/
._//
/
/-_..,_ cE.TE_ ,
-/- ,'.t-_.._q EAANCDH yIA_/
Pt:CAHE
)
F_
__
_
GIMBAL
"ARING
to T_IJ_
P_llel
\
\
\
[
Actu_
v_14m
• B * COITe_I_
L.el_gl.h :A
_tCCD
\.\\
AP
\
\
I
"
\
),4 Cx
-, \ "
_--,.,UST ,,c,o,
I,=, Figure
7-12.-Engine
/l\
alignment.
"o "_
x'x-
S
_L_ Figure
7-11.-Piston
methods
(load
cold
alinement
tion
of the
finding exit, dicular
actuators.
have
been
As
meeting
alone.
The
actuator index
can
be marked
gimbal had
(fig.
or as 7-12).
in a suitable
bearing
been
eye-to-eye
points,
points
properly
can
face.
alined
distance the
Lateral
mating
to the
means
engine
usually
vehicle.
produced,
it
of engine to the
launch-
of the
hydraulic-piston
electromechanical, types
other
(fig.
vehicle must ing
and
have
They
also
been
reserve.
end
As a rule,
tant
to note
that
dimensions
effected
by an
deflection") ducts,
flex
builder,
must two
actuators they
if the
maximum
individual
of absorbare
of a pair
is
gimbal
deflec-
It is impordeflection
angle
for instance, ("corner
approximately bearing,
required
permit
actuator,
maximum
and
an adequate
in all directions.
combined
lines,
with
by the
attachment
be capable
Together,
through
is 7 ° , the
procured
engine
The
to the at the
may be
encountered
engine.
attached
vehicle
dimensioned.
at either forces
are
to the
or by the
be properly the
and
7-13).
builder
engine
face
actuators
end,
of the
axes,
type
transportation
gimbal
at one
tion
at or on the
vehicle
the
verification
turbine-driven
for each
simply
vehicle
installation
into
of a new
Hydraulic-rotary,
points will
of the
line
manner
If the
of gim-
engines
be
shows
Loads are
Engine in
experience
by optical
alinement
the
attach
a few
manner,
specification as
two
after
vehicles
consists logbook
investigated.
confirmed
in lieu
7-12 engine
following
pneumatic
during
may be cells
type.
used
simply engine
site.
Actuators
plumb
may be
the
to specify
Actuators,
perpen-
A simple
load
first
or
nozzle
Subsequently,
in this
vertical
documented
line
center
a rule,
alined
permit
plane.
and
then
Figure
loca-
through
throat
connecting
side
the
alinement
optical
engine
of a prealined
is advisable
shop,
measurement
using
For
geometrical
in the
operation. this
methods
Tile
the
injector
of this firing,
dynamically bal
gimbal
to the
it, observing
ing
of nozzle their
of the
of attaching specifications.
hydromechanical
used.
vector
centers
to the
support
are
establishes
alining
attached
engine
cells)
thrust
the and
bypass network.
installation
10 °. and
possibly
Inlet
277
DESIGN OF CONTROLS AND VALVES
,_-_
ACTUATOR_ --
-- ..... SHORT
/-"
LONG STROKE ACTUATOR
where
filling
during
buildup
of the
duced,
they
these loads AOTUA.OR --\ ".CON,,OORAT,O
\
STROKE
_-j_
actuators
R ,\,.\\
can
Since
OlMBAL
CENTER_
I I
--I
[i
I I
entirely
1
situation
I
ator Figure
7-13.-Engine
actuator
installations.
and
in one
plane.
components
"take"
this
limited, bers)
affected,
deflection.
proper
be able
to
capability
gimbal
restriction
be provided
(circular
gimbal
of the
actuators
must
instead
must If their
plane
(stops
or snub-
of square).
Selection on the
gimbal
the
actuator
gine
thrust
design
forces force
required.
the
Inlet
be 25 percent
The
force
duct
Heat
of the
is determined
ture,
if it has
by
does
shield
reactions
friction
reaction
Correction
(if any)
for misalinements
Aerodynamic Vehicle
loading
It is
stressed
size
these
that forces
and lightest
actuators, tion
of this
toward
this
of stable,
and
goal.
such
as
though
the
loads
different
from
This
engine
design
of hydraulic
careful
The
system
dual-load
Recognican
must
do much
be capable
when
prelaunch
encountered
those
cold
checkout, here
may
occurring
during
situation
may
gimeven
be quite
engine pose
fir-
serious
problems. During loads
startup
in excess
gimbaling itself.
can This
sion
area
(for
engines
of the of those
be generated is
especially
nozzles designed
being
engine
deflection,
sation
network
engine,
brief
occurring by the true developed
for altitude
peak
side
during
and
deflection
per
low
mass system is
and
compen-
low
analysis
conducted
designer
will
stiff-
the larger
hydraulic
system.
is
high).
in low
actuator
effective size
However,
so is
the
and the
stiffness. and
a detailed by engine
which
effec-
in degrees
stroke,
jointly
has
high
requiring
is bulky Only
actuator
However,
results
reduces and
and
expressed
determine flight
engine
rate
dimensions.
members.
for the
degree
configuration
actuator
arrangement
structural
oscil-
per
and
typical
powerful
design
hydraulic
best
gains,
spring
(gain,
inch
gimbaled rate
stroke
is high,
a more
long-stroke
the
as with
oscillation of this
short-stroke
mass is
over,
motion A delay
continued
of compactness.
Resolution
spring
actuator
frequency
two
of high
advantage and
i.e.,
engine
requires
Moreextra
design and
vehicle
configuration
is
system.
normal
thrust
for high
shows
the
gimbaled
"soft,"
the
system.
feedback
7-13
tive
If struc-
parameters. The
The
to an
its
engine is
of actuator
installations. ness,
cross-
deflection.
(lb/in),
and
a function
actuators
pump,
design
response
during
should
for smallest
equipment.
well-damped
baled,
ing.
the
to a minimum
associated
need
is
Figure
effects
weight
and
lation
engine
to translate
engine
natural
develop.
between
guidance
The
If it
may
structure
overshoot
result.
in its
to minimize
rate
promptly the
actuator
by actuator,
thrust
a actu-
"crosstalk."
be able into
not
of the
other
builder
spring
react
for by
may
(if any)
acceleration
Inertia of gimbaled mass Miscellaneous minor effects
reduce
vehicle
subsequent line
bearing
not
called
motion the
formed
a low
are
instabilities
delay
loop
and
of
(notifi-
installation,
to as
must
without
control
en-
reactions service
the
case,
following:
Flexible Gimbal
In a typical
may
level.
considering
is based
ends
designer
coordination
actuator
motion
and
affects
is referred close
The
design
Rate
wherein
designer and vehicle talk is essential.
pattern
at both
actuator
control
Therefore, is
re-
for the
vehicle
exist
is excessive, other
Spring
regarding
This
or at least
points
and
may
Unless
builder).
engine free
time
ones.
considered
attach
Crosstalk
a longer
shorter
eliminated
be
of vehicle
takes
with
be
must
and
cation
nozzle
than
chamber expan-
at sea operation),
level
System
Hydraulic Until system actuators.
other is
means
probably Its
basic
are
available,
required elements
to power are:
a hydraulic the
engine
278
DESIGN OF LIQUID PROPELLANT ROCKET ENGINES
Hydraulic pump Reservoir (low pressure, or "sump") Accumulator (high pressure) Servovalve Actuators Feedback (electric or mechanical) Lines, check valves, filters, connectors, instrumentation If continuous hydraulic power is required prior to engine start, such as for recirculation of the hydraulic fluid or for gimbal tests, an electrically driven auxiliary pump is also provided. In most instances, the auxiliary pump will be operated until vehicle liftoff only, and can, therefore, be ground powered. For upper stages, the accumulator will then provide, for a limited time, the hydraulic power required during staging and turbopump buildup following its unlocking. Since some of these components will be part of the engine system, while others are stage mounted, an important vehicle/engine interface exists. Through an auxiliary drive shaft, the main hydraulic pump may be driven from the engine turbopump. It is connected to the other hydraulic equipment and to the actuator through high-pressure lines, several of which must be flexible. These other elements may be mounted on the vehicle at the expense of longer lines which also must cross the gimbal plane and must therefore be flexible. Or, they may be engine mounted. This, however, increases the engine gimbaled mass and may pose space and envelope problems. To compensate for misalinements and thermal expansion and contraction, a certain amount of flexibility must be provided for the lines even in this case. It is possible to connect an electric generator to the main turbopump, and drive electrically a stage-mounted hydraulic pump. Only electrical wires will then cross the gimbal plane, with the exception of the hydraulic lines to the actuators which always must be flexible. Another possible simplification is to combine servo valve and actuator into one single unit. Figure 7-14 shows a typical hydraulic engine actuation system. Figures 7-15 and 7-16 may serve to identify the major components of this system. From the above it becomes apparent that numerous hydraulic connections will have to be made when installing the engine into the vehicle. All of them must fit, and permit adequate flexure,
Figure
7-I4.-Engine
actuation (hydraulic).
1
system
1
schematic
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11
TEIIIIp TI l N _'_DU_EEII
33
IESEIIVOII
Po£JrlON
7"15.-Accumulator-reservoir
TRANSDUCEI
schematic.
PRESS.
SUPPLY
RETURN PUMP
SUCTION
EXTEND
_1
RETRACT 9.
FILEEI
16
BLEED
17
SERVO-ACTUATOR
II.
PREFILTRAIION
19
SAMPLING
20
VALVE
DIFFERENTIAL
21 . CYLINDER
26
Figure
7-16.-Servoactuator
SERVO
23
SNUBBER
24.
PISTON
2S.
LOCKING
26
MECHANICAL PRESS.
PRESS. BYPASS
22.
30.
VALVE VALVE INDICATOR VALVE
VALVE
BYPASS
VALVE
MECHANI_d4 LOCK
TRANSDUCER
31.
[_:.W.
32.
FEEDBACK
TRANSDUCER TRANSDUCER
schematic.
must be long enough and of the proper pressure rating, and, above all, must have a mating part on the vehicle.
DESIGN OF CONTROLS
Furthermore, consider system
perform.
and
ature
and
the
will
The
and
disconnect
are
at liftoff, method.
hydraulic
fluid
tioned
ground
electrically
is
of this
systems,
vital
heating
of the hydraulic supplied
heaters,
a favored
by means
and
which temperature-
Continuous
of the
the
cleanli-
temperature
Groin.
electric
temper-
Thus,
components
required.
com-
very
reliability
thermostat-controlled
conditioning
and hydraulic
extreme
engine
sensitive
is often
are
adequate
On cryogenic more
the
sensitive.
for maximum
system. system
fluid
to specify
requirements
know
narrow-tolerance
hydraulic
have
conditioning
must
in which
contamination
designer
of the
designer
environment
will
ponents
ness
the
the
279
AND VALVES
recirculation of the
driven
aforemen-
auxiliary
pump
another.
Secondary
Injection (C)
Thrust vector control through secondary injection of matter into the thrust chamber nozzle (SITVC)
has
motors.
It has
been
experimental for upper The
only
in liquid
where
it appears
stage
engines,
required
are
principal
applied limited,
application
systems, forces
successfully
found
methods
factors:
propulsion
mentation
promising
in which
the
than
7-17.-Secondary
amplification (K,).
(2)
Gas
injection,
(a)
Inert
(b)
Thrust
(c)
Gas
boosters.
K=ISs
injection
Liquid
Other
injection
(a)
Inert
(b)
Propellants such been
In a gimbaled located
With an located
required
side
The
at the
of preheated but the
side
injector side throat
of any based
type upon
¢Is
=secondary
¢¢p
=primary
Fs
=side
(7-15) fVs/fV p
end. force and
force,
is
rate,
rate,
lb/sec
lb/see
pounds axial primary thrust, increase, pounds
= undisturbed primary
Is s
= side
Is a
= secondary axial specific onds) = AF a/fV s
of fluid
and
the
the
K_ factor system
force.
If both
total tem
effect on
specific (seconds)
impulse
of a given
a propulsion
the
side
the the
factors
(sec-
may
the quanforce,
penalty required
are
secondary system
Fs/_'s
determines
determines
of these
impulse of the = Fp/fyp
impulse
to obtain
Is to obtain
pounds
(seconds)=
K factor
required
overa_A
of secondary
axial chamber
specific
Essentially, tity
two
performance
flow flow
Isp force
Evaluations
is
(7-1a)
fVs/_V p
Fp/_'p
Fp =undisturbed AFa = axial thrust
proven
force.
system
as
where
at the point of injection, resulting moment arm which decreases the
performance
aug-
7-17A)
using-
injection
chamber,
approximately
Performance
injection
7-17C),
SITVC system, the applied downstream of the nozzle
approximately in an increased
(fig.
7-17B)
investigated
thrust
thrust defined
lsa_AFa/ws_AFa/Fp tapoff
as
Fp/_Vp
=lsp (fig.
(fig.
are
K,
fluid
methods,
hydrogen, have uneconomical.
is
chamber
axial
Fs/fvs_Fs/Fp
lsp
gas
generator
and
factors
follows:
using-
stored
(K)
These
are(l)
systems.
injection
lateral
with
of secondary
INJECI'O'R
to solid
predominantly
especially
smaller
Figure
LIQUID
known, injection
on the side the sys-
be determined.
28O
DESIGN OF LIQUID PROPELLANT ROCKET ENGINES
The K factor determines the quantity of secondary injectant fluid required (for a known duty cycle); the maximum flow rate; the additional tankage, pressurization fluid, and secondary injection hardware weight; and the effect of the added inert weight on vehicle trajectory. The K 1 factor evaluates the Is penalty on the propulsion system. If K_ is equal to 1, the specific impulse of the secondary fluid is equal to that of the primary fluid and, therefore, the propulsion system suffers no specific impulse penalty due to the SITVC system. Both the amplification factor K and the thrust augmentation factor K1 are influenced by the secondary injection orientation. For each application, a tradeoff must be made between the two factors to determine the optimum injection orientation for maximum propulsion efficiency. Let the force of an external jet of comparable geometry at right angles to the primary nozzle be unity. Then amplification factors greater than 2 are obtained if secondary injection is made with the nozzles pointing upstream, rather than in a normal or downstream direction. Side forces for a given _Ps are further increased if injection is made through a series of holes arranged on a horizontal arc, rather than through a single orifice. Note that the manifolds required in this case may adversely affect response, however. Test experience suggests that overall pressure ratio and injector size appear to have little effect, while gas temperature does, optimum values being a function of propellant combination. For an oxygen/hydrogen tapoff system, the range between 3000 ° and 4000 ° F appears most favorable; however, as with turbines drives, material strength and cooling problems will dictate values substantially lower, say 1800 ° F. In a typical tapoff SITVC system, the gas flow rate may be 1.5 to 2.5 percent of the primary flow rate, the upper value indicating the situation of maximum force required between two injection stations (two jets operating). The tapoff system offers simplicity and good performance. However, with low-duty cycles, a continuous bleed may be necessary to maintain temperatures at the valves. The performance of a gas generator SITVC system is comparable to that of a tapoff system, probably slightly better. This is offset by higher complexity (valves, injectors, ignition, cooling).
Liquid injection systems (inert fluid or propellants) offer the simplest arrangement. This is offset by their low performance, K-factors being in the order of unity, at flow rates from 5 to 6 percent of the primary flow. However, in systems with low-duty cycles, they may still be very attractive. As a rule, four elements are required for a given system, equally spaced on the main chamber circumference, of which no more than two adjacent ones would be operating at a given time. The control of the required valves is accomplished through a logic and a servosystem analogous to that of a hydraulic gimbal actuator system.
7.6 DESIGN CONSIDERATIONS FOR FLOW CONTROL COMPONENTS
FLUID-
By theirvery nature,liquidpropellantrocket engines use many control elements for regulating and measuring of fluid flows, such as valves, pressure regulators, and flowmeters. Some of the design considerations governing these cqmponents are discussed below.
Basic
Flow
Characteristics
of an Ideal Fluid
Fluids, by definition, include both liquids and gases. A liquid is an incompressible fluid which is characterized by a tendency to retain a fixed density or volume; but not shape. A gas is a compressible fluid which has no tendency to either a definite shape or volume. Its density or volume will vary according to the basic gas laws (eqs. 1-9, 1-12, and 1-13). In general, the same fundamental laws of force, mass, and velocity apply to matter in all forms, and thus are also applicable to the flow of fluids. The analysis of fluid-flow controls may be simplified by initially assuming ideal conditions. For the calculation of physical dimensions and functional characteristics of specific control components, the results can then be modified by additional assumptions and empirical factors, which often are the result of extensive testing. A frictionless (zero viscosity), incompressible fluid which is nonturbulent and loses no mechanical energy as heat is referred to as an ideal fluid. For steady, ideal-fluid flow in a closed conduit, Bernoulli's energy equation applies:
DESIGN OF CONTROLS AND VALVES
144pl z[ +-p
to at least 10 times its diameter for repeatable
V2
V2"I
+
= z2 + __ 144 P2 +_-=2 p
2g
Assuming z t =z 2, and sions, we obtain
constant
rearranging
(%2)
the
expres-
results. For liquid flows, this flow-measuring method is fairly accurate, if frictionlosses are compensated
for by the velocity coefficient Cv.
For gaseous
flows, however,
pressure and tem-
perature have a significant influence on the den144 (Pl - P2)_ p
fluid
In conformance flow
sity of the
v22 - v,_
(7-3)
2g
with
the
continuity
law
fluid
and
must
be taken
into
account
for calculations.
of OtFFE_ENTIAL
_IAPH_
C,kA
/ PrLOT
# = Cvpv,A 144
1 _ Cvpv2A2 144
_¢ALVE
(7-4)
and
vl
A2
v2
A_
(7-5) _ENTURI
where
_ATE
z z, z 2 =elevations P,,
P2 = static
at sections pressures
tions v,, p
of the
fluid
flow
=venturi
rate
This
Figure
3
flow
ft/sec
velocity
configuration
2
the
coeffi-
of the
which
de-
is determined
tests.
conduit The
above
be used
flow
control
striction, is inserted provided
areas at sections
basic
systems. as
in the for reading
of the I and
fluid-flow
to measure
such
the
An accurately an orifice,
the
2, in 2
characteristics
or sense
conduit.
fluid-flow
nozzle, Pressure
static
pressure
flow
rate
sized
and
to control
in
re-
is
differential
between
venturi
throat
2).
springs,
butterflies, between
sure
The
area
design
factors
degree
A 2 and the fluid density p are known,
tions,
including
velocities v, and v 2, and the flow rate _¢ can be
spring
forces,
calculated with the aid of equations
accuracy.
preceded
by a straight length of pipe equivalent
by
means
discussed
of orifices
usually
obtained
in subsequent
relapreslinear.
permit functions. will
permit
in a reasonable Flow-bench of,
flow
regulators sections.
calibra-
for instance,
increase
of fluid and
the
exactly
dynamic
to further
control
charac-
venturi
analyses
adjustments serve
1) and diaphragms,
parts, not
accuracy.
Its
pressure
(sec.
of these thus
to the
dynamic
w and is
actuator
ports,
resulting
of control
The
inlet
other
(p_ -P2)
The gate
valve.
by the
rate
theoretical
of the restriction (sec, 2). If the flow areas A I,
venturi or orifice meter should be
and flow
calculations
a pilot
sensing
approximations empirical
a venturi flow.
pressure
of the
venturi
differential
and
(7-3), (7-4),
Because
tionship
good
the flow
by
controlled
of the
fluid
fluid
controlled
teristics
in which
across
by a fluid-powered
is
(sec.
system,
of a butterfly
working
in turn
However,
are
by means
The
diaphragm
or venturi,
p,
differential
used
of a typical
control
is positioned
taps
P2 at the inlet (sec. I) and at the minimum
and (7-5). The
closed-loop,
system.
schematic
pressure
diaphragm. by
the
is regulated
position
A 2 =cross-sectional
can
static
flow
is
fluid-flow
is sensed
and of the fluid-flow and
7-18
closed-loop
fluid-flow,
is a function
characteristics,
A_,
of a typical
at sections
32.2
of the
or orifice
cient. sign
lb/ft
constant,
= weight flow ib/sec
Cv
7-18.-Schematic
Figure
fluid-flow control
fluid,
=gravitational
IP
at sec-
2, fps
= density
g
fluid
2, psia
of the
1 and
2, ft
of the
1 and
v 2 =velocities
1 and
this and
pressure
will
be further
282
DESIGN
Sample
Calculation
OF
LIQUID
PROPELLANT
ROCKET
A
=area
#
=viscosity (viscosity
(7-1)
The followingdata are given fora horizontal venturimeter,measuring liquidoxygen flow: Venturiinletdiameter,dj = 6 in Venturithroatdiameter,d2 = 3 in Venturiflow velocitycoefficient, Cv = 0.92 Pressure differential between inletand throat (Pl - P2) = 22.5 psi Density of LOX, p=71.38 Determine flow rate w.
A2
2
into equation
V2
=_
(7-3):
Substitute
2g
2× 32'2 ×i44
71._s1-
this
1 × 2i'5-55.9
into equation
fps
turbulent flow velocity distribution is more uniform across the conduit than with laminar flow.
(7-4): 77
Flow rate
Cvpv2A 2 ¢¢=-144 = 180.2
Real
Fluid
Flows
0.92 x 71.38 × 55.9 ×-_-x 9 144
lb/sec
Involving
Pressure
Even in turbulent flow there is always a thin layer at the conduit wall, the boundary layer, which moves as a laminar flow. Experiments and theoretical considerations have shown that the Reynolds number, R e of a given fluid flow can be used as a criteria to indicate whether a flow is laminar or turbulent.
Drops
All real fluids possess the physical property of viscosity; i.e., they offer resistance to shear stresses. The viscosity of the fluid directly affects friction. The basic correlation is given by Newton's law of viscosity (see fig. 7-19):
mA u
F
/ /
I
/
I
= shear stress = F/A, lb/ft: = shear or friction force of the fluid tangent to the surface in consideration, lb
I
/
I
l
I
/ t
where r F
I
/ (7-6)
-Figure
ira,
/
/ gU r =-gt
poise)
the fluid moves in layers, or laminae, one layer gliding smoothly over an adjacent layer, with only a molecular interchange of momentum. The velocity of the fluid is greatest at the center of the conduit and decreases sharply to zero at the conduit wall. As the flow velocity is increased above the "critical" point, the flow becomes turbulent. In turbulent flow an irregular random motion of the fluid exists, in directions transverse to the direction of the main flow. The
144 (p_- P2)_ v22_ (,_v2) 2 p
2 = 14.84
When a fluid is forced to flow through a closed conduit, its flow is laminar or nonturbulent below certain "critical" velocities. In a laminar flow,
1
V 1 = ¼V 2
this
=
[email protected]/ft2
=velocity of a fluid particle at the surface in consideration, ft/sec t =distance from the point where the velocity of a fluid particle is zero, to the surface in consideration, ft U/t =rate of angular deformation of the fluid
v2-A , \d,/ =-4
Substitute
ft 2
lb/ft-sec
U
lb/ft 3
(d2_
in consideration,
of the fluid, conversions:
- 4616.81b-see/in
(7-5):
VZ
of the surface
1 lb/ft-sec
Solution From equation
ENGINES
I _-veuoc_tv 7-I9.-Angular
OF FWtO PArTtcue_s zeao deformation
of a real
Iluid.
DESIGN OF CONTROLS AND VALVES
(R e : Dvp/tz, conduit,
where
ft;
D = equivalent
v=flow
velocity,
sity, lb/ft3; and/_=fluid For most calculations, flow
is
laminar
1200,
and
than
1200. Real
fluid
caused one
by rubbing
there
is
in pressure
in the
energy
is
heat
loss thus
may be extreme
be entirely
conduit
wall,
temperature
other
or isothermal
ambient
through
However,
flow
pipes
adiabatic
place
in nozzles,
valves
through
flow
is
orifices, which
by
to be
When
is
and
number
but
isothermal.
or tube
walls.
flows
may be
gram'
shown
at high
term,
pressure
drop
Ap (psi)
conduits
zontal
position
(7-7).
This
(4-32),
except
(ducts
can
of a fluid
or tubes)
be estimated
is essentially for the
the
flowing
in a hori-
by equation same
as
duct
control For
the
PV2 288 g
roughness"
to the
(e/D),
diameter.
components
friction
factor
modified
by
is a function
is
given
a measure
f obtained
of
values
in table
from
figure
7-3. shapes,
7-20
correction
Reynolds
of
engine
or for other
an empirical
dia-
projections e for rocket
are
of the
Moody
Average
passage
duct
dimensionless
roughness
projections
a curved-flow
of the
of turbulent
of the The
the
the Reynolds
factors
7-20.
roughness
upon
roughness
by means
surface
which L
found
relative
to be Ap:f
the friction
surface
flow
dimensions.
upon
of the
equation
(R e > 1200),
not only
in figure
"relative size
turbulent
Tile
and
moving
is
depends
also
to take
the
The
flow
factor
velocities.
in straight
the
friction
tubes,
fluid
(7-8)
f__6_4_4 Re
the
of liquids
assumed
number, and
The
Generally-at
short
the
can be arrived at by Poiseuille's equation for laminar flow
(constant-
is assumed
fluids, other
If the flow is laminar (R e < 1200), the friction
flow),
through
flow).
temperature-the
gases
sure at the outlet point. To calculate higher
drop
absorbed
extreme
is less than 10 percent of the fluid static pres-
factor is a function of the Reynolds
This
(adiabatic
dissipated
in the
with com-
the pressure drop Ap
Con-
energy.
entirely
in
itis recom-
that equation (7-7) be used
pressible fluids only where
against
flow.
Also, there will be a slight change
pressure drops of compressible methods should be used.
i.e.,
heat
case
mended
than
wall.
of the into
the friction factor. Consequently,
greater
particles
conduit
direction
ciably.
den-
friction
of energy;
converted
in one
or it may
the
a loss
produced
fluid,
fluid
against
less
numbers
involve
of the
and
sequently,
the
always
of the
lb/ft-sec.) that the
numbers
for Reynolds
flows
another
p=fluid
viscosity, it is assumed
for Reynolds
turbulent
diameter fps;
283
has
factor,
number
and
(7-7)
where L = length
of the
p = density
conduit,
of the
v = flow-velocity d = equivalent
TABLE
in
ness
fluid,
lb/ft
of the
fluid,
fps
of the
duct
diameter
3
Control or tube,
7-3.-Average Projections Component
Values for Rocket
of
Surface
Engine
Rough-
Fluid-Flow
Designs
in IRoughness
4 × duct
cross-sectional
area
Wetted I : friction
factor,
Equation flow tubes.
(7-7)
of any With
used
when
dled.
The
suitable density
great,
if the density
as
for laminar fluid
fluids
of compressible a function
pressure
drop
and
velocity
Surface
description
projection, _, ft
or turbulent
in ducts
or
it may
also
are
being fluids
of pressure; between will
Drawn tubing with very clean surface ........ Smooth machined and clean surface .......... Machined or commercial cold-rolled surface...
experimentally
restrictions
compressible
considerably fore,
is valid
shape)
perimeter
determined
incompressible
(any
two change
be
Rough machined surface .................... Smooth cast or forged surface ............... Commercial cast, forged and welded surface
..
0.000005 .00001 •00005 .0001 .0003 .0008
hanchanges there-
points appre-
is
1Moody, L. F., Friction Trans. ASME, Nov. 1944.
Factors
for Pipe
Flows,
284
DESIGN OF LIQUID
Figure
of the
design
creased can
configuration.
resistance
of a specific
be accounted or equivalent
which
is arrived
length
and
(L e + L), is then sents bends.
the
used
typical
Because
The
actual
flow.
resistance
in-
duct
sum
of this
passage
length,
(7-7) Figure
for the 7-21
characteristics
flow-control
diagram.
passage
of straight
in equation
of turbulent
ROCKET ENGINES
to it a ficti-
at empirically.
length
calculation
Le,
7-20.-Moody
the
flow
for by assigning
tious
equivalent
Sometimes
PROPELLANT
pre-
of 90 °
components
such
/ /
as
valves and fittings disturb the flow pattern, they produce an additional pressure drop in a duct or line
of tubing.
The
a flow-control sure
drop
component within
the pressure stream
loss
ducting
the
of pressure cQnsists
component
produced of the
itself,
as
preswell
as
drop in the upstream and downor tubing
in excess
of that
which
would normally occur if there were no component in the
line.
/
by
With
certain
exceptions,
the
fluid
Figure
7-21.-Typical
resistance o! 90 _ bends.
characteristics
DESIGN OF CONTROLS
flows are
through
rocket
usually
pressure only
drops
be
engine
treated
as
control
being
chargeable
evaluated
to the
accurately
The
Ap
true
components
through
7-22
shows
fluid-flow-control are
4 diameters
downstream
ated.
This
the
tapoff
nents.
The
U-tube
manometer,
pressure
and
caused
rupted
from
drop
which
straight
pipe
(a+b)=14
is
of the
diameters,
Ap that
by an unintersize
same
and
flow
length
The
condi-
any
control
components
great
virtually the
determination
able
instead
may
be already
employing
type
to obtain and
size
available.
it is
individual drop.
It is
This
can
be done
drop
the
vary
by K
flow
duct
(7-9)
its
lar
(constant
the
resistance the
rocket
to the
VALVE
fluid-How
constant range
flow
for
of Reyn-
is turbulent.
configuration,
K
the
higher
of the
component,
of size
is
were
in all
linear
only
space,
engines
are
minimum
etc.
component,
design
considerations
in table across
should
7-4. a flow-
flow-passage he
observed:
characteristic
flow
Avoid
abrupt
changes
of flow
area
(3)
Avoid
abrupt
changes
of wall
contour,
turns
in the
flow
length
of the
(5)
Provide flow
area
component
(2)
Minimize
fluid-
propellant
following
sufficient
design.
for various
drop
the
of these
geometric
of a given
of liquid
presented
be
by design
None
sizes
pressure
not the
structural
coefficients
components
depend
However,
require
various
simi-
would
influenced
necessarily
compo-
then
and
size. is
resistance
more
dimensions),
K would
of material,
available
the
to
resistance
geometrically
the
number
of the
the
of flow-control
sizes
economy
the for
cross-sectional
leading
In general,
control
(4) setup
in 2. to
K value.
of a component
sharp
test
of
open,
tends
If a series
for the
components.
same
the
coefficient
(1)-Allow
control
cross-
path
fully
a large
by component
strength,
For
7-22.-Typical
flow
size
ratio
flow-control
i-I
Figure
minimum
A smaller
Reynolds
Average
/CONTROL
com-
size.
g.
similarity /.--MANOMETER
I
the
is designed
of component
of different
upon
over
providing
considerations
/
the
of the
K is essentially
resistance
standards,
__
the
area the
independent
design
VALVE
this about
with
influenced pv 2
CONTROL
area
when
as
a higher
nents
corre-
Ap = K288---_
through
in the
area
type
coefficient
which
coefficient using
may
nearly
desir-
data
is
have
numbers, a given
the for
test
of the
passing
area
component
For
have
test
from
resistance
pressure
and
of a component
of pressure
a component
engines
conditions,
to extrapolate
calculating
of fluid-flow-
in rocket
of service
impossible
for every
number
used
variety
data
when lation
large
velocity
component
coefficient
given
olds of the
3
component.
tions. Because
flow
This
Usually
is ob-
measured
same
at the
net
psi
lb/ft
flow
sectional The
com-
method
lb/see
ponent.
the
7-22,
test
fluid,
of fluid
= characteristic
produces
component
caused
A*
gages,
data.
rate
to the
by the
fps
component,
compo-
tank
the
= flow
by the
test
by the
component,
10 diamat
weighting
of the
characteristic
pA*
disturbances
caused
repeatable
v= 144 _=
to be evalu-
of pressure
by subtracting
pressure
flow
points
and
drop
tained
the
for
chargeable
defined
in figure
=density
taps
and
component
combination
accurate
setup
Pressure
upstream
of the
minimizes
pressure
quite
test
components.
located
eters
a typical
as
shown
flow p
Figure
drop
ponent
tests.
the
= pressure
can
actual
285
where
components
turbulent.
AND VALVES
the
and
path flow
path
within
component a smooth passages
surface
finish
for the
286
DESIGN OF LIQUID PROPELLANT
TABLE Various Liquid
7-4.-Typical
Resistance
Propellant
Components
Rocket
for
main
oxidizer
of the
stage
engine.
Coefficients
Fluid-Flow-Control
ROCKET ENGINES
valve
Resistance coefficient K
Butterfly-type valves (fig, 7-33): 90 ° open ............................. 80 ° open............................. 70 ° open ............................. 60 ° open ............................. 50 ° open ............................. 40 ° open ............................. 30° open ............................. 20 ° open ............................. Ball-type valves (fig. 7-38): 90 ° open ............................. 70 ° open ............................. 50 ° open ............................. 30 ° open ............................. 20 ° open ............................ 10 ° open ............................
0.31 .41 ,77 198 5.68 15.45 44.7 124.2
Poppet-type valves (fig. 7-40): Full open Venturi-type valves (noncavitation) (fig. 7-41) ............................ Gate-type valve (fig. 7-42): Full open ............................ _Aopen .............................. ½ open ............................. _Aopen .............................. Poppet-type cheek valve (fig. 7-60) ....... Swing-gate-type check valve (fig. 7-61) .... Standard tee ........................... Standard elbow (90 °) .................... Medium sweep elbow .................... Long sweep elbow ..................... 45° elbow .............................
0.81 1.58 3.6 18.2 63 362 2.5-3.5
Liquid
oxygen
flow
Liquid
oxygen
density,
0.92 .56 .50 .50
d_/d I --tA ........................... d:/d 1:½ ........................... d2/d I :¾ ...........................
0.42 .33 .19
diameter,
Flexible
duct
actual
length,
Flexible
duct
equivalent
resistance
due
= 78 percent
will
be
further
A-I
discussed
through
in section
gpm
lb/ft in
L= 16 in
length
considering
passage
contour
characteristic
of duct
3
d=8
devi-
flow
area
area
Estimate: (a_.) The
pressure
drop
chargeable
to the
duct
The
pressure
drop
chargeable
to the
valve
Solution (a) Oxidizer The average
flexible duct flow velocity Q
is
_-
From
table
6-3,
0.277
× 10 -_
the
Dvp --_
Use
8x _
/z
duct.
chargeable
eq.
7-6).
in the
duet
0.00005 8 12
From
figure
equation to the
=2"94x
107
projection
size
• of
roughness
Substitute
(L e + L) into
flow
x 10 -s
roughness
or a relative
D
(see
of the
oxygen × 10-7
79"4 x 71"38 0.1282
a surface
0.00005
fps
= 0.277
lb/ft-sec
number
duct
of liquid
thus/1
10 -3
Reynolds
flexible
- 79.4
viscosity
lb-sec/in2;
x4636.8-0.1282x The
in the
12 420 d2 =3.12xTrx16
3.12x
f: 0.0112. flowing
to flow
ation, Le = 6 d Main oxidizer valve
Re
of fluids
Q = 12 420
inside
for the
orifices
of the
p = 71.38
duct
v= 0.18 120 5.6 24 2to 4 1 to 2.5 18 .90 .75 .60 .42
rate,
Flexible
0.8-I.5
Sudden enlargement: d_/d 2= ¼ ........................... d_/d2='_ ........................... dl/d2=_A ........................... Ordinary entrance ...................... Sudden contraction:
characteristics
type)
Engines
Component description
The
(butterfly
the
0 000075
7-20,
(7-7).
oxidizer
friction
equivalent The flexible
factor, total
pressure duct
length drop then
is
7.10. f(Le Sample The oxidizer
Calculation following pump
Ap =-
(7-2) design
discharge
data
are
flexible
given duct
for the and
the
+ b)pv
2
288 gd
_ 0.0112
(6 x 8 + 16) x 71.38
288 x 32.2 x 8
x (79.4)
2 = 4.34
psi
DESIGN OF CONTROLSAND VALVES
(b_._)gain oxidizer The characteristic
valve velocity
79.4 V:o.--._18= 101.6 From table
of the valve
fps
7-4, the resistance
butterfly valves K=0.31. Substitute equation (7-9) to obtain the pressure able to the main oxidizer valve:
Pv2 0"31×71'38×(101'6)2 Ap = g-_8_g 288 × 32.2
Control Fluid Pressure
coefficient
for
this into drop charge-
= 24.65
psi
Level
The working pressure level and the temperature of compressible fluid-flow-control system are important factors, since both govern the density of the fluid. Means of compensation for changes of pressure in a compressible fluid control system must always be provided. With an incompressible fluid, the pressure has relatively little influence on density. The working pressure level of the fluid determines the selection of the structural design of the components as well as of the sealing methods, especially for dynamic seals. Special provisions are often made to meet the stringent requirements in high-pressure applications. For example, the cutoff events in a high-pressure turbopump-feed engine system may be sequenced so that turbine power is cut first; thus the main propellant valves are not required to shut off against the high main-stage discharge pressures.
Fluid-Flow
Velocity
The requirements for smooth component-flowpassage contours are more critical with controls for compressible, or low-density, fluids such as hydrogen than for incompressible fluids, because their design flow velocities usually are much higher than those of the denser liquids. Also, in general the design trend for high-thrust, highpressure engine systems is toward smaller propellant duct and valve sizes, and consequently toward higher flow velocities (over 100 fps). An important consideration in the design of high velocity flow-control components is the high-impact loading imposed upon the control
287
surfaces by the fluid stream. This is especially acute with the higher density liquids. To obtain reliable control performance characteristics with liquids at high velocities, the control components subject to impact loading must be designed to withstand the stresses involved. Also, they should be contoured so as to maintain small impingement angles with the fluid stream and to keep inpact forces to a minimum.
Fluid-Flow
Temperature
Temperature is an import_tnt consideration for the design of fluid-flow controls. This is especially true if the controls are for fluids at temperatures in excess of, or far below, norn_al ambient. In liquid propellant rocket engines, fluid-flow controls may have to handle hot gases at temperatures up to about 1700 ° F. Example: the control of a turbine working fluid. Hot liquids need not be considered, since none of the liquid propellants have sufficiently low vapor pressures to permit handling at high temperatures. Ability to operate at elevated temperatures without any form of lubrication is a prime objective in the mechanical design of fluid-flow control. This can be accomplished by using bearings of either extremely hard, wear-resistant alloys, such as stellite and sintered carbides (high loading condition), or relatively soft materials such as graphite (low loading condition). Bearings are usually subject to compression loads only and are therefore not subject to failure if the materials used are of low ductility. For structural members not subject to wear or bearing loads, conventional high-temperature alloys such as stainless steels and other nickel-base alloys may be used. For static and dynamic seals, metal gaskets and bellows, carbon or graphite face seals, and labyrinth-type seals are suitable at high temperatures. At the other end of the scale, liquid propellant rocket engine controls may see extremely low-temperature levels, such as in liquid hydrogen service (-425 ° F). Hero, two principal conditions must be considered: (1) The physical characteristics of the fluids which at these low temperatures may affect control performance; and (2) the physical characteristics of the materials from which the control components are made and
•
288
[
.
DESIGN OF LIQUID PROPELLANT ROCKET ENGINES
which may affect the operation and, thus, performance characteristics of the control devices.
the
Many of the cryogenic fluids, i.e., liquefied gases, experience somewhat unpredictable phase changes (two-phase conditions) for relatively small temperature changes. No serious difficulties need to be expected, however, if the heattransfer rate from components in critical control areas is low enough to prevent vaporization of the liquid. This is particularly important in liquid hydrogen service, where insulation may pose difficult design problems. At any rate, except for viscosity changes, nearly all liquids exhibit more stable physical characteristics with large temperature variations, within the range between their freezing and boiling points, than do gases if the temperature range reaches to their liquefaction temperatures. The construction materials for fluid-control components for low-temperature applications must be especially carefully selected. Practically every metal undergoes irregular phase changes at low temperatures which may seriously affect its physical properties. While the strength of metals generally increases with a decrease in temperature, further temperature decrease beyond certain limits may result in a decrease in strength. Many metals also become brittle at very low temperatures. Most of the aluminum alloys and the 300-series stainless steels exhibit much better stability at temperatures in the cryogenic range than do others. Elastomers such as Teflon, Kel-F, and Mylar, when used for sealing purposes, exhibit satisfactory mechanical characteristics at extremely low temperatures. Teflon-coated surfaces additionally have good anti-icing characteristics. For further detail on materials, see chapter II. Fluid-flow-control components for operation at cryogenic temperatures should be designed to be free of external icing effects. In addition to insulation, moisture-preventing purges should be provided internally in critical areas such as bearing interfaces. Also, actuators and/or bearings may require heating.
Rate
•
of Response
in Fluid-Flow
Controls
Response rate is an important design eration in any control system. Basically,
considthe
limiting factors governing response rate are (1) the speed with which signals can be transmitted, and (2) the mass/force ratio or its function, the inertia/force ratio of the main control organ. In many fluid-control systems the controlled fluid is used to transmit the sensed signal, In others, part of the sensing link employs electrical or mechanical means. However, in most cases, part or all of the sensing loop utilizes an impulse generated by a pressure change. This impulse is transmitted at the speed of sound in the fluid. As a typical example, the velocity of sound in water is five times that in air; accordingly, a control signal would be transmitted five times faster in water. The actuators for most fluid-flow-control mechanisms use pistons or diaphragms, powered by fluid pressure which, in turn, is regulated by some form of pilot valve. If suitable, the controlled fluid may be used as the actuating fluid. The response and flow capacity of the pilot valve, the effective area of actuator piston or diaphragm, and the actuating fluid pressure level influence directly the response rate of the control mechanism for given mass inertia and frictional or other resistances. To satisfy attain stable
certain operating conditions control it sometimes becomes
and to nec-
essary to introduce simple damping devices. In most control systems, stability is inversely proportional to sensitivity or response rate. Thus, the design of a fluid-flow-control system should reflect a realistic balance between sensitivity or response rate, control accuracy, and system stability. Figure 7-23 illustrates the schematic of a typical piston-type actuator for fluid-flow-control devices. The piston when actuated moves against the spring in the direction of the arrow. The basic correlation between the response rate or acceleration of the piston, and other operational parameters, can be expressed by Map -Alp g
1-A2p2-
Fr- Ft-
Fs-
Cx (7-10)
where M :effective piston, that of nected all the
mass accelerated by the actuator lb. It consists of piston mass, moving parts mechanically conto the piston, and of the mass of fluid columns in the system
DESIGN OF CONTROLS AND VALVES
ACTUATING SUPPLY
FLUID LINE
i SPRING
tons,
shafts,
Here,
too,
289
and
rods;
tant
design
fied
into
seals
is one
and
seats.
most
Seals
can
impor-
be
for medium-temperature
(-60 ° to 400 a F), ° F),
for valve
of the
considerations. those
to -425
and
temperature
classi-
service
low-temperature
service
(-60
high-temperature
service
(400 _ F
°
0 FI BODY
and
up).
the
materials
extent
The
on
service
involved. VSNT _-__!I!!
///,
seals
outstanding
p,sTo; N"I
Figure
7-23.-Schematic
they
of the
piston,
ft/sec
of the
piston
actuating
A s =area
of the
piston
vent
p_ =actuating
pressure,
side,
psia.
This
less
supply-line
pressure
on
rate
the
depends
the
acceleration P2 =vent
psia.
pressure,
plus also
function Fr = resistance
is
fluid
the
tile
drop
also
may
tion ap Ff = friction forces
is
the
vent-line
depends
sliding
drop
(again
function,
be a function
spring
=spring
rate,
force,
x
=distance
traveled
initial
position,
lb (at
a
practices seals
used
surfaces,
Design
x = 0) piston
from
its
DYNAMIC
SEALS
FOR
may
the as
Apart treated seals nents: ing)
from
in chapter are
required
seals cylindrical
the
static
seals,
which
IX, two
basic
types
will
elements
as
provide
backup
compo-
mended
(reciprocating such
will
of dynamic
for fluid-flow-control
for moving
be
actuator
and
rotatpis-
sures
will as
pressures
S00 above
is
as
psi
and
psi.
A
(table
7-25
In is
conusually
In addition,
seals
hard7-5).
diameter
designs
for static
and
O-ring
installation
in figure
O-ring
1500
safely. and
Past guide.
and
pressure maximum
section
space
permit.
seal
of compound
the
extrusion
nominal
shown
O-ring
of fluid
be tolerated
for dynamic over
pressure
of clearance
a useful
rings
leaving
the
can
O-ring
large
siderations
7-25),
determine
O-ring
O-ring
(fig.
will
prevent
is
O-rings
choice
combination
E that
failure
influences the
pres-
diametral
to the
after
it affects
combination
fluid
of seal
adjacent
seal
considsummarized
and
pressure)
pressure
The
chosen
COMPONENTS
gap
hardness
general,
cause
appli-
O-ring
are
between
deformation
because
ness
FLUID-FLOW-CONTROL
seals
hardness
under
Fluid
proper
OF
clearance (when
clearance
for
O-ring
correlations
static
design
frequent
plex and solution.
computer
and
of diametral-squeeze-type
chosen
success.
a typical
Important
compound
extrusion
design
in
as
design
recommended
dynamic shows
clearance.-A
reduced.
proper
represent
the
the
applied parts
for diametral-squeeze-type
seat.
hardness.
7.7 DESIGN
imper-
widely
cylindrical to assure
7-5
for a valve
O-ring
been
be observed
for typical
a permanent
a high-speed
minor part.
However,
table
7-26
1. sure,
have
seats.
Figure
groove
lb/in by the
The
is that
for Medium-Temperature
for moving
erations for dynamic as follows:
lb,
of accelera-
and
O-ring
Since the relations between p_, P2, Fr, and ap are not linear, equation (7-10) may become comrequire
must 7-24
design
into
C
seals
despite
O-rings
for valve
cations.
ambient
rate
ap) control
as
Figure
of
lb
Fs = initial
or elas-
possible.
mating
Seals
seals
techniques
which
pressure
on flow
(seals,
type
wherever
or the
of Dynamic
dynamic
well
source,
(a function
This
of acceleration force of the
which
etc.),
flow
as
ap)
pressure,
which
actuating
of fluid
of these
seal
Elastomeric
in s
in 2
at the
and
2
side,
pressure
to a large
nonmetallic
satisfactorily
in the
Design Services
A_ --area
used
and
is based
piston-type
actuator. ap = acceleration
soft
are
function
configurations
conditions
advantage
fections
of a typical
of the seals
Generally,
tomeric
A.
selection for these
Teflon are
recom-
at sealing O-ring
seals
presat
illtBl #: 29O
DESIGN OF LIQUID PROPELLANT
ROCKET ENGINES
STATIC
SEALING\ _ \BREAKCORNERS,
¢,-_ I'-: _b
"1 -,J
?o APPROX. o.oos' D
"="
. _L__L._4___ a_-_--L
D-GROOVE U:NGTH
l .-f
"-
CENTERLINE OF THE PISTON ACTUATOR
Figure 2. the
7-24.-Diametral-squeeze-type
Surface
sliding
O-ring
finish
requirements.-The
surfaces
seals
O-ring
in contact
should
be
as
finish
with
smooth
seals of
dynamic
as
that
longer
life
a finish than
ishes.
Codirectional
honing,
have
finish
better
surface and
again
slippery
proven
type
possible.
after
be hard
finished. surface
scratching.
The that
yields
as
best
sliding
an initial
plating
resists
the
plated
provides
of 60
7-5.-Recommended
rms
or bet-
Design
Practice
[See fig. 7-15 for explanation O-ring nominal section diameter
O-ring section diameter
1/16 3/32 1/8 3/16 1/4
0.070± 0.003 0.103 *_0.003 0.139 *_0.004 0.210 *_0.005 0.275 *_0.006
Diametral
squeeze, rain
Dynamic 0.010 .010 .012 .017 .029 Fluid
= +0.000, : +0.000,
-0.001. -0.005.
and
with N,
selection
the frictions
trade
increase
can
only
Accurate
design.
elastomer
compounds
names
such
as
Teflon,
of an O-ring
all dimensions
with
be obtained
compounds,-A
Viton,
is
diametral
of O-ring
great is avail-
Silicone and
compound
for Diametral-Squeeze-Type
of dimensions;
seal friction.
of temperature.
frictions for a given
Butyl,
seals.-The
running
hardness,
with
seals.
O-ring
O-ring
of O-ring
Buna
times
decrease
Selection
able,
O-ring
running
of O-ring
4.
Kel-F. and its
O-Ring
rubber, The physical
Seals
in inches] 2 x E-
C-glandwidth
aDynamic
0.015 .017 .022 .032 .049
0.057 .090 .123 .188 .240
pressure
and
experimentally
Static
(3-1000 psi 1000-2000 psi 2000 psi and higher aTolerance bTolerance
and
in contact
of a dynamic
three
pressure,
variety
a hard, wear,
applications.
O-ring
of dynamic
about
squeeze,
For
static
for surfaces
friction
usually
values
seal.
corrosion,
finish
by
finishing,
or nickel
Friction
breakaway
fluid
surface
and
diametral-squeeze-type
Breakaway
fin-
produced
to be the
dynamic
is recommended
3.
a
or smoother
chrome
A microinch
TABLE
range
of dynamic
results,
could
this
rougher patterns,
been
for any
still
within
either
ter static
They should be ground, honed, or polished to a microinch finish of 8 to 10 rms. It has been found
in typical
D-
bstatic 0.052 .083 .113 .173 .220
O-ring compound hardness 70 Shore "A" Durometer 80 Shore "A" Durometer 90 Shore "A" Durometer
groove length
R-
radius, rain
diametral clearance max
3/32 9/64 3/16 9,f32 3/8
1/64 1/64 1/32 3/64 1/16
0.005 .005 .006 .007 .008
291
DESIGN OF CONTROLS AND VALVES
_AOIAL
-,-x
_"
C k F.A,_I* N C _ __]_
_PRESSU_E
__
P_ESSURE
_"
7-27,
7-28,
dynamic valve
EXTRUSION UNDER
t"igure
OF
(_RING
RJNGS
PRESSURE
o[
O-ring
of the
under
backup
pressure
seats.
the
application
rings.
(dynamic 5.
of seal
has
and
been
applied
at temperatures
are
also
pressures
as low
reasonably
as
effective
molecular-weight
gases
such
over -425
when as
2000
° F.
psi,
They
sealing
helium
low-
and
'Z:,;_ ...........
°"' _°
I 1710 t
010
installation
of O-rings
....,oo,I
dur-
1, ...../
\ 1
important
k t, "-/->' 1 ;
L
chamfers
should be provided on all edges and in contact with O-rings to minimize the
possibility
of cutting
or scratching
during
the /
assembly
process.
L
6. O-ring seals for valve seazs.-O-rings be applied effectively as seals for valve
can seats
(fig.
absorbs
7-26). loads
The
resiliency
and
seals
of the
tightly
O-ring
at all pressures,
even when some dirt and grit are present system.
type
as parts
o[ diametral-squeeze-type
ing component assembly is extremely to assure an effective seal. Generous
shock
effectively
cylindrical
or static).
seals.-Proper
or radii corners
used
hydrogen.
Installation
O-ring
are
at sealing
and
properties (furnished by the producer) is based on operating conditions such as type of fluid or propellant, pressure, temperature, and type of seal
This
successfully
diamelraI-squeezeand
7-29)
for moving
PREVENT
EXTRUSION
7-25.-Extrusion
type
TO
and
seals
One
design
problem
is
k _IPSEALS 121 _(_QLIIRIEO
_TE
--A_A_ "_ _ _ °PIER
UNLESS aT_E_SE SPECJFP[I]I F_NISH SUtteES ANC} t_ SEALS
_
to
Figure
7-27.-Typical valve
rotating
lip-seal
actuator
shalt.
_
T_E
CONTACT
O_l i'LL ._AkS
WiTH
TO BE 12 RM$
OETTER.
in the
to prevent
_.
ALL
THE OR
NICENSIOhS
_H _NC_ES
design
[or
the
O-ring from being blown out of the groove. This can be prevented by providing a dovetail O-ring groove in a two-piece valve poppet (see fig. 7-26).
Design Services
of Dynamic
Seals
for Low-Temperature
For cryogenic or low-temperature services, lip-type seals made of elastomer sheets (figs.
VALVE
STEM
Figure VALVE
PRESSURE
'
POPPET
7-28.-Typical
[or butterfly-type
VALVE
_
seat
lip-seal
design
valves.
OUStNG
The basic employ ,_AL
valve
PRESSURE
I
pressure
RETAINING
the
design fluid
principle
pressure
at the sealing
of lip seals
to increase
surfaces.
is to
the
contact
Due to their
RING
lip Figure
7-26.-Typical design
valve
for poppet-type
seat valves.
O-ring
seal
configuration,
is maintained Design
the
resilience
of these
seals
even at very low temperatures.
considerations
for lip
seals
are
similar
292
DESIGN OF LIQUID PROPELLANT ROCKET ENGINES
-Acrvz.
to those for O-ring seals. The design approaches can best be illustrated by examples. Figure 7-27 shows a typical valve shaft rotating lip seal arrangement, including dimensions and surface finishes, for liquid oxygen and hydrogen service. Figure 7-28 presents the valve seat lip seal of a butterfly valve for use with the same liquids. Valve seat O-ring seals (fig. 7-26) made of Kel-F have also been successfully applied in poppettype valves for liquid oxygen. The design of lip seals for piston-type actuators using lowtemperature helium gas as the actuating fluid is shown in figure 7-29. In liquid hydrogen service, metallic bellows (as shown in fig. 7-30) have been used to a great extent to achieve positive dynamic sealing. However, pressure levels and available space impose limitations on their application.
/' _o_
( CLOS_N& )
The metallic
Seals
bellows
FOR
SEALS
_.,:
.
',_
../'
;b"_
_L_tE_
_
.
}
001NV_ _.&LIN*
5t._f_3t5
LBO_H
_LVE
AN0
,_v_t
) L_PPED
N
8-10
B£LLOWS USEO AS Ty_P'_ D'yINiAIMI_;
(fig. 7-30) is most fre-
DOUBLE
LIP
i
ASEhqI._
Figure 7-30.-Metallic bellows used as reciprocating-type dynamic seals in a typical poppet valve for high- and low-temperature services.
for High-Temperature
quently used as reciprocating-type dynamic seals for high-temperature services. Two types of metallic bellows are distinguished: the hydraulicformed and the multidisk welded type. The former is made of one to three plys of sheet metal and is designed for all pressure ranges. The latter is for relatively low-pressure services and for high flexibility. A metallic bellows of any type behaves, in part, like a helical spring. The spring rate (lb/in of.movement) is a direct function of the
DOUBLE
.-T_P,Ca_ WEL._EO .N_N_ S,{'rUJXOm I,LA'II KLLDW$
W:
WELI)ED TYPE RIEC_PRI_C,ATING
Design of Dynamic Services
_
}_
_%ulO
,_
LIP
mum.
Generally, bellows design data, such as stock size, allowable working pressure, spring rate, materials and service temperature, are supplied by the manufacturers. Important design considerations are discussed in the following:
SEALS
ACTUATOR
elastic modulus, and of approximately the square of the thickness of the material. It is also a function of the outside-inside diameters and of the number of convolutions and their curvature. For maximum flexibility (inches of stroke/lb of load), a minimum inside diameter combined with a maximum outside diameter should be used. Also, material thickness (within stress limitations) and modulus of elasticity should be mini-
PISTON
/
1. Applicalion of pressure.-When a bellows is subjected to a differential pressure between interior and exterior, it is preferable to apply the
VALVE
[_ __-t__
_
_j;! _
ACTUATOR
i'_.>_AC
T UATOR
ROD
PISTON
Figure 7-29.-Lip seals for piston-type actuators. Double lip seals seal pressures both ways.
higher pressure to the exterior. This reduces stress, and permits higher pressures and longer life for a given design. 2. Provision of mechanical stops.-These should always be provided to prevent extension of the bellows beyond its permissible extended length and compression beyond its "bottomed" height.
293
DESIGN OF CONTROLS AND VALVES
3.
Selection
lows
or materials.-Selecting
material
patibility
should
or corrosion
temperature Some
and
high-temperature
steels,
Monel,
proven
suitable.
4. when yields
spring
such
and
Hastelloy
Inconel,
EHective
area.-This by a change
actual
is
can he approximated
that
as
stainless
volume.
nate
design
ring
to the
effective
× (inside
area
by
area
diameter
= 0.1963 +outside
diameter)
5. End attachment.-Typical the end attachment figure 7-30.
welded
2
(7-11)
joints for
of bellows are illustrated in
for low-temperature
was
up
shaft is
sealing
to 700
(fig.
as
psia.
has
7-31).
seats
basic
alterseal
which
is
the
shaft
Here, by the
flexibility
for high-temperature by metal-to-metal
in figures two
An graphite
bellows
achieved
shown
success-
1200 ° to
a flat-face
of valve
contact,
7-30
and
7-32.
requirements.
a finish
of 10 nns
or better
sealing
surfaces.
Secondly,
loading
must
be applied
deformation
from
compensated
is usually
design
operated
ranging
of a metallic
services
This
Firstly,
is required
for the
a high-enough
to create
unit
a compensating
of the sealing surfaces
and
to
achieve the intimate contact required to overcome
Silver brazing and soft soldering
can also be employed ices.
end
to the
The
length,
seal Bellow
which
is to attach
misalinement of the bellows.
which,
This
valve
at temperatures
welded
B have area
throttle
fully
1S00 ° F at pressures
operating
in bellows
displaced
com-
characteristics.
alloys
multiplied the
by fluid
considerations,
ranges,
gas
of bel-
be governed
manufacturing
tolerances, distortion of the
serv-
A typical design of a rotating-type dynamic seal for high-temperature services is illustrated in figure 7-31.
The
dynamic
PRESSURE HOT GAS
HOUSING VALVE
_
sealing is achieved
through the spherical mating surfaces between the graphite seal ring and the steel shaft collar. The
contact force of the sealing surfaces is
maintained
by the shaft thrust spring. Any
alinement between
shaft is compensated and side movement arrangement
mis-
the thrust bearing and the by the spherical seal face of the seal ring. This seal
has been applied to a turbine hot
SEAL
"X
O
SURFACES
ROTATE
FINISH tO OR BETTER
{a)
RMS
TO OPEN VALVE
CONVOLUTED HOT
_ •. _
/-
_..
_
\ BUTTERFLY
R_NG
GAS
VALVE
SHUTOFF
TYPE
VALVE
SEAT
BUTTERFLY
SEAL
SPRING
GAS
DISK
VALVE
_,
_
VALVE
sto,,
/
_b} S(AL _s, aN
typical
hot
rotating-type
gas
throttle
dynamic
POPPET
/
|
/ ......
7-3I.-Turbine
_N
_1_?,_,_ _ _,,_ HOT
Figure
USED
VALVE
PRESSURE
VALV¢_
GATE
VALVESHAFT
valve seals.
with
POSITIVE
SEAL
STOP
IO RMS
SPRING HOT
Figure
DISK GAS
TYPE
SHUTOFF
7-32.-Valve ture
VALVE
SEAT
POPPET
seat seals services.
HOUSING
SURFACES
SEAL
OR
FINISH
BETTER
USED
IN
A
VALVE
for
high-tempera-
A
_1
mi
_rx
DESIGN OF LIQUID PROPELLANT ROCKET ENGINES
294
valve parts due to temperature, internal stress, and mechanical loading of the mating parts. Figure 7-32(a) shows a convoluted-ring-type valve seat seal used in a hot gas shutoff butterfly valve. Depending upon the specific application, the convoluted ring may be made of hightemperature alloys such as Inconel-718. The rings effect a leakproof seal in the closed position, since the upstream fluid pressure tends to expand the convolute and produces a high contact unit force at the sealing surfaces. The curvature of the convolute ring tends to maintain a continuous contact with the valve seat. Figure 7-32(b) presents valve seat seal
a metallic-spring-disk-type used in a hot gas shutoff
poppet
valve. Again, the upstream gas pressure produces a high contact unit load on the sealing surfaces. The valve seat has a curved contour which effects a continuous contact with the flat face of the seal disk.
Sealing
Specifications
The degree of sealing (or the allowable leak rate) is a very important specification which will dictate the type of seal to be selected for a specific fluid-flow-control component design. The basic reference for leak rates is Specification MIL-S-8484. It states that a Grade A seal, the highest quality seal, shall have a leakage rate not to exceed 1 standard cubic centimeter
of
air/year/inch of seal at a pressure differential of 1 atmosphere. This corresponds to a leakage rate of 3.171 × 10 -s cc/sec/inch of seal. It is a design assumption that any seal leak rate below or equal to this value is considered zero leakage. For many applications, higher leak rates are permissible. For instance, a check valve may be specified with a leak rate of 5 scim's (standard cubic inches of gas per minute). This is still a relatively tight specification.
7.8 DESIGN
OF
PROPELLANT
VALVES
Propellant valves are used to initiate and terminate propellant flows to main thrust chambers and gas generators. They are usually openclosed, two-position, normally-closed valves. To meet specific sequencing requirements, other designs may provide for an intermediate opening position. For thrust-throttle or mixture-ratio-
control purposes, ability for continu,_usly variable opening position may be required. In addition to propellant compatibility and structural integrity, prime design considerations for propellant valves are: (1) No leakage of propellant through the valve when closed (2) Proper actuating time during opening and closing in accordance with the requirements of the control system (3) Minimum pressure drop A great variety of propellant valve types is available. Each design has certain characteristics which make it suitable for a specific application. Frequently used propellant valves, classified according to their design configurations, are: (1) Butterfly valves (2) Ball valves (3) Poppet valves (4) Venturi valves (5) Gate valves (6) Needle valves Butterfly-Type
Propellant
Valves
The butterfly valve is one of the most widely used propellant valve types in large liquid propellant rocket engines. It has established a reliable operational record in LO2/RP-1, LO2/ LH 2, storable, and other liquid propellant services. Existing butterfly valve designs range from 2 to 17 inches nominal diameter, for use at propellant pressures from 20 to over 1500 psia. With improvements in sealing and structural details, successful designs for higher capacities and propellant pressures are certain to be achieved. Fignre 7-33 presents a typical butterfly valve design. Sealing is provided by a lip seal, which engages a spherical surface on the valve gate, similar to figure 7-28. The valve gate pivots on the valve shaft, the axis of which passes through the geometric center of the spherical sealing surface. In most designs, the valve gate rotates 90 ° from the closed to the fully opened position. The valve is operated by a piston-type actuator, through a connecting link and shaft crank arm. Lip seals are used as dynamic seals for the rotating valve shaft (fig. 7-27). The actuating power is furnished either by noncryogenic propellant pressure, or by an inert gas supply, and
295
DESIGN OF CONTROLS AND VALVES
plsroN
_
O"Rr _'_pE
_-
/
/
-_
--
\
++
/
SEe:tON
:
A
i'
_-AT FL;LLYOP_NEO PO_ITIO"+, _ i
+ ...... ; .... • I,o+,,,o.......... + ......,.+o ....... -
\
A--A\
u_
L_.......o X__
+ I
.......
+,
+-
r---,_
valve
+ "-:"+-._
:
butterfly-type in the
piston. are
a pilot on the
Except
7-34
shows
gen
valve
booster
steels,
a 4-inch, used
of the
pins
most
of the
the
which
Butterfly
valves
have
relatively
flow.
They
are
to service. area
which
They can
have
be
valve
booster
engines.
liquid
A butterfly
smooth
fluid-flow
valve-gate
s
as
a throttle
(see
fig.
7-33
low
compact, a high
parts
oxy-
local
flow
A* = characteristic ds =inside in
area
diameter
characteris-
as
the
A-1
freezing.
The
butterfly
valve
(%12)
the
valve
position, Values area
nominal about
references) valve,
valve
seat
means
in _ lip
for A* (duct diameter,
87 percent
gate
area
at the
fully
open
in _ range
area
from
= v/4 in)
65 percent
dn 2, where
on a 2-inch
of the
duct
area
size
of the valve,
on a 12-inch
pressure.
linkage
between fuel
engine. attached ates
d_ = valve
the
During to the
shaft
position
of the
valve
the
engine
control
may
may
be
from of the
provides system open
indicators
for
system
RP-1
be normally
or nor-
may be
added;
be
accomplished
by
squib,
rather
by
main
7-35
valve
sequence
of the stroke, valve valve is also
indication gate.
than
illustrates
oxidizer
a potentiometer for continuous
fluid
a heater
7-33
the opening main oxidizer fuel
in table
arrangement
Figure the
sequence
_he igniter
Frequently, to
valve
opening
listed
in figure
of a pyrotechnic
pneumatic seal,
may
fluid-
actuating
to keep
position
of the
the
actuator-valve
valve
closed;
are
engine,
actuator shown
such
Typical
in a LO2/RP-1
for specific
needs: mally
as
stage
toward
effects
K at various
valve,
of used
tendency
valve
is used
at the
range when
cavitation.
oxygen
a relatively
Thus, little
coefficients
RP-1
required
igniter
Ag=projected
duct
of the
ICBM
a wide
adverse
of a butterfly
liquid
such and
it has
attendant
resistance
When
resistlight,
_-Ag
of the
liquid
Atlas
maintains over
positions.
propellant
positions 7-4.
ICBM
as
for dimension
main
Rocketdyne
valve
valve, with
closing where
on
stream
angular
flexibility A*-_-d -4
butterfly-type
used
valve.
as
Figure Atlas
expressed
7-34.-Four-inch
oxygen
the
to fluid
easy
Figure
turbulence
are
other
forgings.
Rocketdyne
is
actuator
which
butterfly-type,
on
shown
engine.
ance tic
and
of aluminum-alloy
,......
by a spring
side
for shaft
_
position).
valve
closed
closing
of stainless made
The
i"
propellant
closed
valve.
to be normally
installed
made
r --:-_ .... ---_
(shown
by
+,.<
_ +
design
designed is
,
7-33.-Typical
controlled
%A z,
I+.'-C
//.
Figure
•
valve A-1
the and
the
stage
the cam shaft actuto open. attached of the
to angular
DESIGNOF LIQUID PROPELLANT ROCKET ENGINES
296
_._tN
OXJDtZEk
OPE*WtNG P=E_J_E
VALV_
SIDE ADTIJATING. APPUED M,&pN OXIDIZ_I VALVE iN FULLY C_=ENED POSITION
FWID
AC IIJAIIN G
_CLOSlNG)
FtUIP
FUEL PIIS_U_! E_G_NE
INLET PORT AC_UMING (C_ENI*WG)
r_ow
CO_WIItOL
°
_, VALVI
POIATE TO J O_EN VALVt VALVl
SH_.= T --_
IGNiIEI FUEL SEOU_NC_ VALV_
IGNI_EI /,ND
C_mrDC_
IGNmON
MONIIO_
Figure 7-35.-Mechanically between the main oxidizer fuel
sequence
valve
VAtVt
linked arrangement valve and the igniter
of the A-I
stage
engine.
BUTTERFLYVALVE GATE
./
AXISOF VALVE / SHAFT
FLOW (a) DIRECTION
The amount of torque required to turn valve shaft and gate is determined by the summation of hydraulic and friction torques. Hydraulic torque is the unbalance of forces on the valve gate caused by the flow of fluid around it. If the axis of the valve shaft is located as shown in figure 7-36(a), the fluid striking the gate portion protruding farthest upstream is deflected more than that at a point near the other end of the gate. This produces an unbalanced force which tends to close the gate. Offsetting the valve gate as shown in figure 7-36(b) would further increase the closing torque, because the fluid velocity rises as it approaches the downstream side opening. Consequently, the resulting low-pressure, area tends to increase the unbalance in the closing direction. For this reason, butterfly valves are usually designed offset as shown in figure 7-36(c) (also see fig. 7-33). This produces a fluid velocity effect tending to ease opening of the gate, because of the lower net closing hydraulic torque acting on the valve gate. Nevertheless, the net hydraulic torque will still be acting in the closing direction for most angular gate positions (9°-80°), unless the valve gate is further offset. Friction torque always opposes rotation. For most operational valve designs
FARTHESTUPSTREAM PROTRUDING
To = Tt+ Th
(7-13)
T c = Tf-
(7-14)
Th
where To Tc Tf Th
FLOW (b) DIRECTION BUTTERFLY VALVEGATE
AXISOF VALVESHAFT ./
= required opening torque, in-lb = required closing torque, in-lb = friction torque, in-lb = hydraulic torque, in-lb (assumed the closing direction)
to act in
The friction torque Tt varies with the pressure differential across the valve gate, and with the valve gate projected area which is a function of gate angular position. Friction torque can be estimated by
(c) FLOW DIRECTION _
T! = Ktrsfmds2hp
____
(7-15)
\
BUTTERFLYVALVEGATE Figure ?-36.-Various axis with respect
locations to butterfly
of valve shaft valve gate.
where K[ = friction torque coefficient, which is a function of gate angular position (to be determined experimentally)
297
DESIGN OF CONTROLS AND VALVES
rs
=radius tion,
of valve in
fm = coefficient
shaft;
steel
shaft)
between
for aluminum 0.05
sec-
estimated
shaft journal
for needle
and
ator
has
and
all
seals.
bearing
and
of valve
differential
seat
across
lip the
seal,
torque
Th may
gate,
Kh ---hydraulic
torque
(7-16)
a function (to Figure and
7-37
closing
tions will
torques
type)
gate
of the
actuator
to three
the
forces
Opening
actu-
valves and
of
are
closing
milliseconds.
stage
diameter
needle Data
Test
experimental
oxidizer
valve
data
(butterfly
engine.
shaft
at bearing
of the
valve
section,
in seat
lip
seal,
in
Coefficient
valve
and
main
of valve
ds -- 7.7
posi-
(7-3)
of friction
between
bearing,
f m =0.05
angular deg
Ap,
shaft
and
maximum
REQUIRED OPENING (To=T f +T h )
Valve gate position,
TORQUE
5 ..............
/FRICTION
friction
Data
Inside
In actual
of a butterfly
times
static
design
A-1
rs=0.8
opening
angular
valve.
the
20 to 200
for the
Radius
position
of required
butterfly the
two
is
experimentally)
plots versus
which
angular
be determined
practice, provide
of gate
shows
for a typical
design
coefficient,
In addi-
stroke,
propellant
acting.
from
following
given
Design where
fast
torques.
opening
the
Calculation
The
by
3Ap
closing
Butterfly-type
range
Sample
are Th = Khds
of the
in
valve
be estimated
and
start
to overcome
relatively
psi Hydraulic
opening
at the
times
diameter
Ap=pressure
bearing
tion,
(0.20
steel
= inside
at the
of friction
bearing
ds
shaft
TORQUE
(Tf)
W D 0 re" 0 I--
15
..............
40
..............
85
..............
Determine torques T,
ORQUE
0°
(Th)
90 °
tions
the at the
of the
psi
K[
1058
0.78
1.11 × 10 -a
769
0.78
2.55x
87.5
1.57
12.50×10
25
3.61
required
opening
10 -_ -_
-11.64×10
and
5° , 15 ° , 40 ° , and
valve
Kh
-3
closing
85 ° angular
posi-
gate.
Solution
OPENINg" From
equation TI=
REQUIRED '
=
--
CLOSING
(7-15),
the
friction
torques
Klrsfmds2.Ap
at 5°:
T[=O.78xO.8×O.O5×(7.7)2x1058 = 1960
in-lb
at
T[=0.78×0.8×0.05×(7.7)
2×769 = 1425
in-lb
2×87.5
TORQUE 15°:
)
o
at 40°:
T[=l.57x0.8×0.05×(7.7)
o
at85°:
T[=3.61×0.Sx0.05×(7.7)
-'- 326
in-lb
I--
= 214 GATE
0=
Figure ing
2×25
ANGULAR POSITION _ CLOSING
7-37.-Typical torques
butterfly
versus valve.
required gate
/
90 °
opening
angular
From
and
position
equation
(7-16),
the
hydraulic
in-lb
torques
Th = KhdsSAp at 5°:
Th = 1.11 x 10-3
at 15°:
Th;2.55x10
x (7.7)3
closfora
x 1058 =
-3x(7.7)
535
in-lb
895
in-lb
3×769 =
DESIGN OF LIQUID PROPELLANT
298
at 40°:
Th = 12.50x
10 -3 × (7.7) 3 x 87.5 = 500
at 85°:
Th=-11.64×10-3×(7.7)3x25
in-lb
equation
(7-13),
the
aCT_TOa
J_L =-133
From
ROCKET ENGINES
required
in-lb
opening
torques To = TI+
Th
at 5°:
To=1960+535
=2495in-lb
at15°:
To=1425+895
=2320in-lb
at 40¢:
To=326+500
=
at 85°:
To=214+(-133)=
From
equation
826in-lb 81in-lb
(7-14),
the
required
closing
torques Tc = (Ttat 5°:
Th)
Tc=1960-535
Figure
=1425in-lb
at l5°:
Tc=1425-895
=
at40°:
Tc=326-500
=-174in-lb
at 85°:
Tc=214-(-133)
= 347in-lb
7-38.-Typical
530in-lb
assembly
consists
metallic Ball-Type
Propellant
The
major
Valves
advantage drop,
since
stricted
flow.
Its
fluid
tural
soundness record
propellant
applications,
generators
as
bers
(up
inal
diameter
well
space
envelope
eters,
ball weight
ever,
for ground and
in all
sizes,
ball-type
7-38
not
a common
is accomplished riding
on
valve
ball.
and
the
where
the
design
ball
valves, Many
both oxidizer be sized either
according
to the
flows, The
by lip-
or be
in a
In our specific
case,
7-38
is
which
could
pressure.
actuator
the
balls valves
of a ballvalve
tive
angular
seals,
and
the
valve
seal
Typical open
position,
valves
can
devices,
such
characteristics
of a typical
ball
are
presented
ball
valves
can
by either
The
crank First,
mediate
position
fuel
motion motion
link
arm.
The
actuator
the
valves
are
the
of the the
valve
shown opened
opening),
of
and crank
sequence
by varying
between
(partial
pressure
to a rotary
opening
be adjusted
in
actuator,
reciprocating
of a connecting
positions
stages.
shown
by a piston-type The
by means
arrangement.
the
fully
is translated
two
of the
of the
be powered
gas
arm
surface
90 ° from
K for ball-type
positions
provided
to
or O-ring-type sealing
specific
surface.
rotates
geo-
7-39. activation
figure
of the
The
sealing
Flow
drops
angular
using the
flow-regulating
pressure
affected
through
Ball-type
throttling.
at various
or inert
and fuel individ-
as
position.
at the
as
bellows.
bellows.
ball
open
7-4.
to
an unbalanced
coefficients
determined
for constant
The
a
valve
fully
in table
in figure
mechani-
designed
sealing
to the
designed
bearings.
spherical
the
the
mounted
passes
of the
for propellant
valve
is trunnion
rotation
be used
the
attached
within
surface,
within
resistance as
readily as
of such
are
valve
an
of the
creates
on antifriction
designs,
listed
and
, is
area
sealing
ball
center
closed
(4ds2)
this
axles
of valve
are
arrangement,
elements
size. spherical
How-
designed
valve
metric
ring
enclosed
area
effective
on the
integral
axis
of a seal
closing, pressure
valves, to meet
the
fluid
fluid-flow
actuator.
valve
propellant
are
dual-valve
propellant
The diameter,
acting
by the
the
diam-
difficult
the
force
In most
to
frequently.
valves
cham-
infrequently,
critical,
quite
controlling valves can
shown,
volumetric
larger
applications
used
the
For
valve
Each
com-
requirements.
illustrates
Here,
cally linked, flows. The
have
are
are
respect
than
During
two
Up to a nom-
valves
only
envelope
by a single
as
used
main
seal
be less
storable gas
with
weight.
linked,
Figure
thrust).
increasingly
propellant
valve.
It has
some
thrust
ball
service
are
struc-
service. and
types
are
size
unre-
enhances
for lower
valve
and
mechanically operated
in-line,
also
50000-1b
and
flight
ually
as
valves
is its
for high-capacity
it becomes
weight
use
of 3 inches,
to other
because
it permits
in cryogenic
to about
parable
valve
for high-pressure
a reliable
bellows.
effective
of a ball
low-pressure
ball-type design.
relaaxles
has
two
to an interthen
to the
299
DESIGN OF CONTROLS AND VALVES
*,_l_
vAtvl
oo_Lt7
t
tooor_
I
i
700_
[
,2"-
'
_ svtL
P' I - X-_-__
.._--n-Jh_'_i_-_,,--_
' _-\1"'×
....
400---
=J 2_
30"
.t_"
._"
60"
ANGULAR
70"
gO"
=
_+
POSITION
OPEN
NOTE:
Zero _P2
Figure
f_
from
a5
-'%" PI
0"-
S'due
7-39.-Flow
pressure
lea1
Figure
angular
positions.
for
open
position
using
each
stage.
The
by venting the
tween
valve
are
ports
Dual
pistons
of the
opening
port.
them
sealing
closing
both
closing
separate
at
in the
balance
result varies
in the proper as a function
and
seals
provided
with
for all
for
is
This
type
pressurizing
flow
attd
a drain
cryogenic,
is effected be-
dynamic
Propellant
Figure
7-30
shows
valve.
valve
to the
is
to
sequence main
suitable
storable
propellant
as
which force at
A small
attached
high-pressure,
valve.
for high-
as
well
as
services•
Propellant
Figure
a typical seats.
closed. use
All
of elastomers. of all suitable
of poppet
plicity.
This
operation
of an
ment
requires
sage.
and
permits
actuator. turning
without
throat
of the
nonwiping
this
with
fluorine
their
and
relative
to the
the
direct, flow
Typical
design
A main
results
drops.
coefficients
achieved
due
of the
to use
de-
that
However,
consequently
high-pressure in table
is
is and
propellants. valves
lations,
seals,
for use
is largely
which
nection
dynamic
reactive
vantage
are
valve
nor-
Because
is particularly highly
valve
operated
sealings
characteristics other
poppet
This
to be pneumatically
mally
7-41
in-line
con-
inside
the
pas-
are
given
size
presents
the
(6 to 10 inches propellant hydrodynamic
size
actuator,
The
effective
nominal
valve.
unbalanced of the
design To
forces,
a balance area
and
of a typical,
and
the
thus
flow only.
the
pressure
(say rate
cavitating
to operate
as
Bernoulli's
minimum its
region the
pressure
of a
pressure.
forms
at the
throat.
throat
at the
veloc-
variations
beyond
the
pressure
differentials
across
of upstream
pressure),
venturi
as
on upstream a throttling
affords
smaller
and
throat.
_0 percent
used
a
energy
vapor
pressure
advance
is dependent
When
may
measurements. K for venturi
on
through
cannot
ducting venturi
7-4.
below
downstream
The
pressure
the
designed
the
to fall
moves
of sound,
that
Based
a gaseous
gas
venturi
pro-
is
fluid
a result,
disturbances
the
chamber
be
(7-2)),
made
Up to minimum
diameter), reduce
(eq. is
If this ity
7-40
poppet-type
As
may
venturi.
than in the
Adjacent
for flow
in table
venturi
equation liquid
resist-
valves
The
psi.
coefficients
given
cavitating
smaller
limit
conceivable
resistance are
instalreasons,
solution.
venturi
be used
for a
installed
is a possible
to a few it is
size
A valve
of the
penalties
permitting,
valves
arrange-
fluid-flow
contours
Typical
in relatively
K for poppet
of a venturi
sim-
this
duct.
design
In certain for various
of a nominal
main
simultaneously
reciprocating
a typical valve.
be desirable,
a valve
of the
drop
presents
it may
smooth
Valves
propellant
ad-
7-4.
Figure
vided.
so
seals
Valves
metal-to-metal
signed
large
of the
of poppet
venturi-type
ance
dimensioned
to ambient.
Poppet-Type
the
are
counteracting force of the unbalanced
mechanically
Venturi-Type
with
design.
chamber
positions
valve
valve
poppet-type
valve
constant
ball-type
various fully
large-size
propellant
ol a typical
......
7-40.-Typical
deslgn
characteristics
drops
various
to
\!;
the
pressure device, pressure
the drops,
3O0
DESIGN OF LIQUID PROPELLANT
ROCKET ENGINES
loaded -- VALVE
poppet
line
pressure
is used
,._j_
LET
in the
interconnecting
sure tNLET _---SOLENOID
PILOT
VALVE
same
SOLENO1D
PILOT
VALVE
to open,
valve
poppet
it can
be replaced
_
--------=_
FLOW
main
valve
I CLEARANCE
Figure
_---'-
\
"----VALVE POPP_
AREA
LVALV
VALVE
SCHEMATIC
?-41.-Typical
valve
designed
venturi-type and
Development
are
propellant
manufactured
by Fox
Gate-Type
Valve
Co.
parts
Figure pellant
7-42 gate
stricted since
the
effect
a near
rate
gaseous
and
linear
supply
to a square have
characteristics
been
pressure,
law.
The
venturi
systems
well
valve both,
as with
drop
flow
according
venturi
valves
in cryogenic
which
a shutoff
require
control
a cavitating
at a weight
pressure
than
It also
between tion
of the
7-42
uses
in the
the
flow
valve,
diffuser
of only
of only
the
valves
direction
line
systems. inches
of flow,
the
valve
size
and
However, nominal
built
vehicle
7-41
presents
propellant
valve
Fox
Development
Valve
shutoff divergent
valve
between This
The
is unre-
in low-pressure
a relatively and
outlet
design
short
distance
in the
direc-
shown
O-rings
limi-
will
pro-
and
at a
in figure
as the
valve-seat
ACTLIATrP,_G F'LUI_ INLET
f
PISTO_
TYPE
ACTUATOR
space
been
f
ACTUATOrl
_OD
DYP4,_,I_C O-PiNG
of
imposes
in engine up to
PORT
(O_ENING)
ST_TtC O.R VALVE SEAT
G_,TE t _
_SEAT
SPRING
10 IhlLE T
successfully
/_u=
_
OCTLET
systems. a typical and Co.
consists
section
long
length
valves have
designed
which
venturi
resulting inlet
of a pro-
the
4 to 6 times
application
venturi
diameter
for rocket Figure
a relatively
diameter.
on
design advantage
venturi.
occupy
nominal
limitations
a typical
provides
elastomer
of
reliability.
Its major
flow,
flow.
exist
number
Valves
shows
valve
small
and
INLET
Venturi
the
valvebody
rod and
services.
In fluid-flow as
rather fluid-flow
drop.
throat
between
successfully
propellant
tation
vide
relationship
applied
storable
at the
the
the
valve
no pathways
enhances
valve.
fluid
pres-
venturi
Since
The
Propellant
than poppet
causes
or actuator
seals,
further
the
and
The
seals.
to ambient.
the rate
in a reduced
to open.
no dynamic
is ener-
behind
spring
by a shaft
to as-
valve
through
results
and poppet
at a greater
valve
no dynamic pierced
moving
E SPRING
This the
poppet
for leakage
VENTUR)
out
and
upstream
spring
pilot
by leakage
area.
in a pas-
cavity
valve
the
As the
on the
pressure
is vented
overcoming
there _
the
When
valve
cavity
poppet force
propellant
sure
inserted poppet
the
as
7-41),
Normally,
seating
closure.
gized
is not
fills
direction
valve
is
the
pilot
or closed.
(fig.
throat.
pressure
contains
\
Propellant
open
valve
in venturi
clearance .,,_F---
pilot
additional
in the
valve
schematic
closed
provides
SPRING
valve
sageway propellant
I
throat.
by a solenoid
the
normally
an opening
C/_VITY
at the
controlled
to actuate
shown
POPPET
seated
POPPET
venturi-type
manufactured
by
_" SEAL _R_
\L
0 - RINI_ RET_INEA VALVE GATE GUIDE PLATE
It is a pilot-operated of a convergent-
with
V_LVE G_TIE GUIOE PLATE
a simple,
spring-
Figure
7-42.-Typical
gate-type design.
propellant
valve
301
DESIGN OF CONTROLS AND VALVES
seal.
These
are
temperature other
seal
types
designed psi.
suitable
services. are
valves
are
cations
Gate pressures
limited
to low
as
ground-support
relative
valves
as
generator
appli-
engine
and
into
Needle-Type
Propellant
A typical shown
for extremely
low
a dual-valve
linked
by
a mechanical
an integral
part
assembly.
Both
actuation
type
chambers.
The
yoke.
of the
thrust
valves
are
The
trol
systems,
servo
for
valve
and
body
is
by a quick-response
Sealing
at the
at the
metallic
The
pintle
cating
as
vanes
motion
propellant
rods
is seal
well
as
as flow
of
valve
for the
(2)
No leakage
other
needed
CONTROL
special
for very
PILOT
low
ble
or con-
Impor-
for pilot
valves
are:
Sufficient
The
output
fluid
through
the
closed
actuating
power
systems
design
with
(4)
output
souree
at the
design
valve
can
of a pilot
compatipoint
be defined
W = Pd_'
as (7-17)
where W = pilot
space
VALVES
in turn is used to control or
A
F
iNLET
.......... .
valve
output
at the
design
point,
in-lb/sec
The
control
fluid
discharge
design point, psig volumetric flow rate
point,
in3/sec
most
frequently
may be classified
used
pressure at the
on-off
according
design
pilot
to their
at
valves
design
con-
into
(I)
Two-way
(2)
Three-way
types
(3)
Four-way
types
U(L
i]___'
?',
,;::"
.>
ENGINES
DESIGN INTEGRATION SYSTEM CALIBRATION
I
700
E
ROCKET
Design Engine
Requirements System
Because
FOR
ENGINE
for the Calibration
of unavoidable
mechanical
of an
toler-
ances, it may be expected that the operating characteristics and performance of the various engine system components will deviate somewhat from their nominal design value. A certain amount of calibration is always required for these components, as well as the engine system as a whole, to attain the desired engine performance characteristics within design specification. Therefore, provisions must be made in component and systems design to permit effective calibration during system integration. The specific impulse Is of an engine system is the ratio of thrust F to propellant weight flow rate &. Thus, any deviations affecting F or & will affect system performance. I s also is a function of propellant mixture ratio. It is desirable, therefore, and beneficial to calibrate an engine system by adjusting its propellant feed system. Prior to complete engine system calibration, the pressure or pressure drop versus flow characteristics of each individual component should be calibrated and evaluated. Hydraulic and pneumatic components, such as pressure and flow regulators, valves, flowraeters, ducts, and lines, can all be readily calibrated on flow benches. However, those components which operate at temperature extremes, such as thrust chamber assemblies, gas generators, and turbopumps, are best calibrated by combining the flow tests with actual hot firings. The characteristic propellant flow curve of an engine system is obtained by summing the pressure or pressure drop versus flow curves of the various components (figs. 10-5 and 10-6). The general design approaches toward calibrating an engine system to attain its design thrust at design mixture ratio are: (1) The design operating point of each component should be kept within the relatively flat region of its pressure or pressure drop versus flow curve. (2) The mechanical tolerances and built-in adjustments of each component should be designed so that the random deviation
391
ENGINE SYSTEMS DESIGN INTEGRATION
_MINIMUM _CURVE REGULATOR
OUTLET
PRESSURE
SYSTEM
_r
OE SIGN
POINT--\
LINE
PRESSURE
CALIBRATION
DROP_._
ORIFICE
--
VALVES
AND
/I
LINES_
//
VS r_.OW RESIST/kNCE
ORIFICE
/i
L_NE
_
_
//
{AT
/
_
ENTRANCE
DESIGN
/-_OESIGN
_
./
PLOW
PRESSURE
TO
VS
FLOW
CURVE
TANK)
CHAMBER
INLET
PRESSURE
CHAMBER OURVE
INJECTOR
pressure
feed
VS
END
FLOW
CURVE
PRESSURE
VS
J
PROPELLANT
Figure
PRESSURE SYSTEM
SYSTEM DESIGN PRESSURE VS FLOW CURVE OR SYSTEM RESISTANCE CURVE WITHOUT
_
/
/f
_
__--*_---'-_PRESSURANT
_
DESIGN PRESSURE DROP !N THE CHAMBER ( MANIFOLD COOLING_ PASSAGE AND INJECTOR -_
DESIGN CHAMBER _N,JECTOR END PRESSURE
/ _
_=/-_/
DESIGN PRESSURE DROP-_._ DESIGN PRESSURE DROPS iN
/ /
_'x= _
"_1
REQUIRED TANK CALIBRATED
/ \
PRESSURANT
OR CURVE
_
10-5.-Propellant
design
flow
FLOW,
characteristics
of
(oxidizer v--CALIBRATED \RESISTANCE
FUEL CURVE x--FUEL \CURVE
---....
LB/SEC
a
typical
engine
system
or fuel).
SYSTEM
SYSTEM RE, STANCE WITHOUT ORIFICE
_.
CURVE OXIDIZER
_-
WITHOUT SYSTEM
ORIFICE RESISTANCE
,,, ,---FUEL
PUMP
PRESSUI_:
CALIBRATION ORIFICE
"_,
DESIGN
PRESSURE
_
VS [
DROP
/--FUEL
FLOW
CURVE
PUMP
PRESSURE
AT
NZ
t Pfd
°°° J" OX,Q, i
i FUEL
Wfd
wfo
FLOW
LB/SEC
OXIDIZER
Wfb
%a
FUEL SYSTEM FLOW DESIGN CHARACTERISTICS Figure
IO-E-Propellant
of its
flow
flow
design
characteristics
sign
value
will
able
limit,
in order
calibration, components
from
be kept
and
its
to facilitate
systems
other
design
OXIDIZER SYSTE},IFLOW
de-
a reason-
ratio, ber
design
system
operating
Sufficient
pressure
aside
in each
system due
should
The be
or other
be
propellant
to compensate
to component
tions. then
head
engine
set feed
resistance
design
testing.
Certain
newly
designed
drops
allowed
The
propellant
feed
system
calibrated
by means
adjusting
means.
either
devia-
the
can
and
system
The the lated
for Calibration first
design from
design flow rated
rate
of a Pressure step
is
of each
systems
the
System
determination
propellant,
thrust,
Feed
design
as
of calcu-
mixture
.....
tank
the
versus
chamrates,
components be
may
the
at the
estimated
obtained
specific
from from
have
actual
to be
design
versus
flow
system
of design
is introduced
flow
pressure
system.
flow
for calibration. _ressure
can
pressure
shown
thrust
these
or as
for the by
component as
by actual on
components
summation
an orifice Design
point
design
teristics,
feed engine system.
various
data,
propellant
flow
of orifices
of the
operating
LB/SEC
DESIGN CHARACTERISTICS
verified Based
drops
previous
for contingencies
flow
Is (as
firings).
pressure
region. (3)
and test
FLOW
Wod
characteristics of the A-I stage turbopump
within
to keep
in their
ZER PUMP PRESSURE
can
chamber
design
10-5.
in each The flow
drop
by
versus charac-
In addition,
propellant
minimum
curve
of
pressure
pressure
in figure
curve
be obtained
flow
required
for each
propel-
is thus derived. In most pressure feed systems, the design orifice pressure drop for lant
systems
calibration
_ ----_:::.:=?:
determines
the
maximum
DESIGNOF LIQUID PROPELLANT ROCKET ENGINES
392
allowable cumulative pressure drop increase the components above their nominal values. suitable tank pressurization system can then designed, compatible with minimum required pressure versus flow characteristics.
of A be tank
Sam ple Calcu la tion (I0-I) The following data are available from analyses and component tests for the A-4 stage propulsion system, at rated thrust conditions: Thrust chamber injector end pressure range required to maintain rated thrust = 110 ¢ 3 psia Thrust chamber injector pressure drop range (both oxidizer and fuel) = 25 ¢ 2 psi Thrust chamber oxidizer dome pressure drop =3_ + 1 psi Oxidizer line pressure drop = 5-+ 1 psi Main oxidizer valve pressure drop (at the fully open position) = 4 ¢ 1 psi Thrust chamber fuel manifold pressure drop =4_+1 psi Fuel line pressure drop = 4 ¢ 1 psi Main fuel valve pressure drop (at the fully open position) = 4 ¢ 1 psi Pressure allowance required for mixture ratio control by oxidizer valve vernier positioning (fig. 7-4)=¢ 10 psi Determine the design pressure drops of the calibration orifices, and the minimum required tank pressures for design flow rates. Solution The design pressure drop of a calibration orifice must be equal to the sum of the maximum pressure drop increases of components above their design values. Thus: The design pressure drop of the oxidizer calibration orifice = 3 + 2 + 1 + 1 + 1 = 8 psi. The minimum required oxidizer tank pressure at the design flow rate = 110 + 25 + 3 + 5 + 4 + 8 + 10 = 165 psia. The design pressure drop of fuel calibration orifice=3+2+l + 1 +1 =8 psi. The minimum required fuel tank pressure at the design flow rate = 110+ 25 + 4 + 4 + 4 + 8 = 155 psia.
Design System
for Calibration
of a Turbopump
Feed
The propellant flow characteristics downstream of the pump discharges of a turbopump
feed system are similar to those of a pressure feed system. However, the difference in turbopump pressure or head versus flow characteristics from those of a pressurized system dictates a somewhat different approach to systems calibration. For mechanically coupled turbopump feed systems, such as the A-1 stage engine, systems calibration generally involves adjustment of the turbopump speed as well as the installation of an orifice in one of the propellant lines. For turbopump feed systems with dual turbine drive, such as the A-2 stage engine, the calibration can be accomplished by adjusting the speeds of both turbopumps. The design principles for the calibration of mechanically coupled turbopump feed engine systems are best illustrated by a typical example, as shown in figure 10-6. Here, the propellant system resistance curves without orifices (representing conditions downstream of the pump discharges) are constructed based on the designs and test results of the components for the A-1 stage engine system. Next, the discharge pressure versus flow curves of both pumps are constructed from test data obtained with the A-1 stage engine turbopump, operated at speed N1. These pump curves intersect the corresponding system resistance curves at point A. At this speed, fuel flow rate _/fa is above, and oxidizer flow rate _#oa is below the required design flow rates, Wfd and _i,od. To achieve the design oxidizer pump flow _Pod, at a desired discharge pressure Pod, the design operating speed of the turbopump assembly mr, st be raised to a required level N 2 by increasing the turbine gas flow. However, at this speed, the fuel pump, which is mounted on the same shaft as the oxidizer pump, would be delivering a flow rate d'fb considerably above the required design flow rate 1//fd (point B in fig. 10-6). To reduce the fuel flow to _fd, a calibration orifice is placed in the fuel line. This amounts to increasing the fuel pump discharge pressure at constant speed hr2 to Pfc, where _'fd is reached at point C. The pressure drop across the calibrating orifice is represented by Pfc-Pfd, where Pfd is the desired fuel pressure. If fuel flow rate _/fa is below and oxidizer flow rate _/o._ is above the required design flow rates, the calibrating process would be to speed up the turbopump to obtain the desired fuel flow,
393
ENGINE SYSTEMSDESIGN INTEGRATION
and to place an orifice in the oxidizer line. However, it is generally desirable to place the orifice in the system of the propellant with the higher boiling point. In this situation, therefore, and also when the pressure drop across a calibrating orifice tends to become excessive, it is customary to trim the pump impeller so as to reduce the effective speed, and thus attain the required flow and pressure levels. In view of pump efficiency effects, it is desirable to trim the pump drawing the smaller horsepower, usually the one with the lower mass flow rate, except in cases of extreme density differences. The adjustment of the turbine gas flow rate, and thus the turbopump operating speed, can also be made by means of orifices in the turbine inlet gas line, or in the gas generator propellant lines. In general, turbopump feed systems afford less stringent requirements for the various components regarding deviations from their design steady-state flow values, because the system is inherently more flexible. However, systems dynamic characteristics under transient conditions may restrict these deviations. Sample
Calculation
Determine
the location
The following design values and allowable deviations are given for the A-1 stage LOX/RP-1 engine system components, at rated thrust: Thrust chamber injector end pressure= 1095 _+30 psia Thrust chamber injector pressure drop (both oxidizer and fuel) = 200 ± 20 psi Thrust chamber oxidizer dome pressure drop =150+10 psi Oxidizer line pressure drop = 25 -+2 psi Main oxidizer valve pressure drop = 35 ± 3 psi Oxidizer pump specific speed, Ns = 1980 rpm Oxidizer pump suction pressure = 55 psia rain Oxidizer pump discharge pressure at 7000 rpm and a design flow rate of 1971 lb/sec = 1505 -+25 psia Thrust chamber fuel jacket and manifold pressure drop = 290 _+20 psi Fuel line pressure drop = 10 + 2 psi Main fuel valve pressure drop = 15 +-2 psi Fuel pump specific speed, Ns = 1090 rpm Fuel pump suction pressure = 45 psia rain Fuel pump discharge pressure at 7000 rpmand a design flow rate of 892 lb/sec = 1720-+ 25 psi
......LL
drop,
orifice,
and its
ex-
Solution(see sample calculation(6-2)) The required oxidizer pressure head at the design point = 1095 + 200+ 150 + 25 + 35 = 1505 psia. The required fuel pressure head at the design point = 1095 + 200 + 290 + 10 + 15 = 1610 psia. Since the LOX pump discharge pressure is 1505 psia, but the fuel pump discharge pressure is 1720 psia, the calibration orifice must be located in the fuel system. The nominal orifice design pressure drop = 1720- 1610= 110 psi. From a detail analysis, we have found that the change of the fuel pump discharge pressure, as a function of turbopump speed increase or decrease, is a fraction of that of the oxidizer pump discharge pressure. Due to the effects of chamber pressure deviations, therefore, the maximum value of fuel calibration orifice pressure drop is required exist:
(I0-2)
of the calibration
its nominal design pressure pected range of adjustment.
when the following
conditions
(a._) Thrust chamber injector end pressure its lower limit (1065 psia) (_b) All pressure drops in oxidizer are at their higher limits (c_) All pressure their lower
is at
passages
drops in fuel passages limits
are at
(d.._)Oxidizer pump discharge pressure is 25 psi below its nominal value at the turbopump speed commensurate with the stated specific speed (e)
Fuel pump discharge pressure is 25 psi above its nominal value, at the same speed
The equivalent required oxidizer pump discharge pressure under these conditions = 1065 +220+160+27+38+25= 1535 psia. Required oxidizer pump developed head H = 144 × (1535 - 55) _ 2990 ft 71.38 Oxidizer
pump volumetric
Q=
::---
flow rate
1971 ×449 12 420 gpm 71.38 =
394
DESIGN OF LIQUID PROPELLANT ROCKET ENGINES
Substitute the required
this into equation pump speed
(6-7) to obtain
N- Ns H°'Ts _ 1980 × (2990) °'Ts = 7190 rpm QOS (12 420) °-s Fuel
pump volumetric
From equation (6-7),the fuel pump nominal developed head at 7190 rpm
I333
or 4730 × 50.45 = 1666 psi 144
flow
892 × 449 = 7950 gpm Q50.45
H = (.NQaS_ \"_-s /
F6970 (7950) °'s11.aaa H = L: _ ] = 4730 ft
= f7170 × _ (7950)°s_ ] 1333 = 4900 ft
The equivalent fuel pump discharge pressure under these conditions would be 1666 + 45- 25 = 1686 psia. The required pressure drop of fuel line calibration orifice under these conditions would be 1686 - 1125- 220- 310- 12- 17=2 psi. Therefore the required range of adjustment for the pressure drop of the fuel line calibration orifice is from 2 to 216 psi.
or 10.4 ENGINE SYSTEM INTEGRATED PERFORMANCE CHARACTERISTICS
4900×50.45 144
-1715
psi
The equivalent fuel pump discharge pressure under these conditions would be 1715 +45 + 25 = 1785 psia. The required pressure drop for the fuel line calibration orifice thus would be 1785-1065-180 - 270 - 8 - 13 = 249 psi. Similarly, a minimum fuel calibration orifice pressure drop is required conditions exist:
when the following
(a_a_)Thrust chamber injector end pressure is at its higher limit (1125 psia), and conditions (b), (c), (d), and (2.) above are reversed The equivalent required oxidizer pump discharge pressure under these conditions = 1125 + 180 + 140 + 23 + 32 - 25 = 1475 psia. Required oxidizer pump developed head H=144(1475-55)=2870 71.38
ft
Substitute this into equation quired pump speed N =1980×(2870)°_ (12420) °.s From equation developed head
(6-7),
(6-7);
=6970
the re-
rpm
the fuel pump nominal
In the process of engine system design integration, an importanttask is the integration of engine system perfonnance characteristics. These data are preparedand compiled by the rocketengine designer to provide the vehicle systems engineer with intbrmationnecessary to integratethe propulsionsystem with the vehicle system. _ere possible,a briefexplanationof the data and itsapplicationshould be included to provide clearerunderstandingand greaterusefulness. The followingare importantaspects of integratedengine performance characteristics.
Nominal Engine Conditions
Performance
Values
at Rated
These are usually prescribed by the engine model specification. These data are for engine system nondnal steady-state operation, at rated conditions. Tables 3-2 to 3-5 are typical examples of nominal engine operating and performance parameters, which include nominal thrust, specific impulse, propellant combination, flow rates, mixture ratio, and various component operating data. Allowable deviations are specified for important parameters such as: thrust, -+3 percent, and mixture ratio, *-2 percent. Engine system specific impulse is usually specified at its minimum value. The performance of all deliverable engine systems must be above this minimum during acceptance tests.
395
ENGINE SYSTEMSDESIGN INTEGRATION
In addition to tables for nominal engine performance parameters, nominal engine performance graphs such as chamber pressure versus engine thrust, and engine specific impulse versus engine thrust, are often included as additional monitoring aid. Figure 10-7 presents a typical performance graph for the A-1 stage engine system, of chamber pressure versus engine thrust at sea level.
Sample
CalcuIation
(10-3)
The following data were obtained from design analyses and component tests of the A-1 stage LOX/RP-1 engine system at nominal rated conditions; i.e., 750000 pounds thrust at sea level: Thrust chamber sea level specific impulse at 1000-psia nozzle stagnation pressure, and a mixture ratio of 2.35 O/F=270 sec Turbine sec Oxidizer Oxidizer cent
exhaust
gas
specific
impulse
Required oxidizer flow for vehicle surization-3 lb/sec Determine the following nominal values at rated conditions: _.) Thrust gas (b) Thrust ber
generated
by the turbine
generated
by the main thrust
_)
system system system
Engine Engine (e_) Engine
-r' u
::)W (_ -r
l
'
A trial-and-error method is used to solve this
] IOO
Engine
oxidizer
mixture
ratio
the corresponding
can now be oxidizer
flow rate 2778x2.35 _i'° = (2.35+ 1) - 1948 lb/sec
Engine
flow rate = 1948 + 3 = 1951 lb/sec
fuel flow rate _i'f= 2778 - 1948 = 830 lb/sec
Oxidizer -
--/--
--
/
I.I000
"
chamber
used to approximate and fuel flow rates:
From equations (6-12) and (6-13), the required oxidizer and fuel pump drive horse power for this approximation are:
1150
1050
propellant flow rates mixture ratio specific impulse
problem. Our firststep is to approximate engine system and gas generatorpropellantflow rates. We substitutethrustchamber Is intoequation (1-28):
The thrust
1200
_'
cham-
Solution
Oxidizer
Z . -- t,t.I n., rr'
exhaust
= F _ 750 000 = 2778 lb/sec Is 270
Fuel pump developed head = 4790 ft Fuel pump overall efficiency =65.9 percent Gas generator O/F mixture ratio = 0.408 Turbine gas available energy content = 359 Btu/lb Turbine overall efficiency = 58.2 percent Required auxiliary drive shaft power = 500 bhp
n,., 0
performance
= 32.6
pump developed head--2930 ft pump overall efficiency = 70.7 per-
1250
tank pres-
--_
CONFIDENCE / _
LIMITS
pump horsepower
1951 × 2930 - 550 × 0.706 = 14720hp
- 830x 4790 = 10 96Q hp 550 x 0.659
[
The corresponding
7OO,OO0 7500(30 8OO,OO0 ENGINE THRUST, POUNDS Figure lO-7.-Chamber thrust at sea level
Fuel
pump horsepower
pressure versus engine [or the A-1 stage engine.
turbine
shaft
horsepower:
Thp = 14 720 + 10 960 + 500 = 26 180 hp From equation (6-19), bine gas flow rate:
the corresponding
tur-
DESIGN OF LIQUID PROPELLANT ROCKET ENGINES
396
0.707 x 26180 _i't= 359x0.582
Fuel pump flow rate -88.4
lb/sec =(91.7-
We use this
value
to start
a new calculation
Turbine
cycle to separate main chamber and gas generator data. The thrust generated by a turbine exhaust gas flow rate of 88.4 lb/sec = 88.4 x 32.6 = 2880 lb. Thus the main chamber thrust: Ft = 750 000Thrust
chamber
2880 = 747120
= 14850+
2769 ib/sec
_ 88.4 x 0.408 + 2769 x 2.35 + 3 1+0.408 1+2.35
Turbine
25.6) + (2769-
shaft
Turbine
lb/sec
horsepower
1970.6×2930 550x0.706
Thp-
1942) = 889.8
889.8x4790 + 550x0.659
+500=27090
turbine
(b__)Nominal
main thrust chamber thrust = 750 000 - 3000 = 747 000 lb
(c) Nominal
thrust chamber propellant flow rate = 747 000/270 = 2768 lb/sec
hp
We use this trial:
value
0.707x27090 359 x 0.582 for another
= 91.7 lb/sec
(e_) NominaI
engine
specific impulse = 750000/2860= 262.4
Main chamber
thrust
chamber
Ft = 750 000-2980
= 747 020 lb
flow rate _i'tc =
747 020 27-----0_ = 2768 lb/sec
pump flow rate
_ 91.7 × 0.408 _ 2768 x 2.35 + 3= 1970.6 1 + 0.408 1 + 2.35
Engine Performance Variations Off-Nominal Conditions Engine performance off-nominal conditions
calculation
The thrust generated by a turbine exhaust gas flow rate of 91.7 lb/sec=91.7 x 32.6=2980 lb.
Oxidizer
engine
gas thrust = 92 x 32.6 = 3000 lb
sec
gas flow rate wt-
Thrust
the assumptions
(a__)Nominal
Nominal
exhaust
_ 92 lb/sec
system propellant flow rate = 2768 + 92 = 2860 lb/sec Nominal engine system oxidizer flow rate 92 x 0.408 2768×2.35 + - 1967.7 lb/sec 1+0.408 1+2.35 Nominal engine system fuel flow rate -: (92 - 26.7) + (2768- 1941) = 892.3 lb/sec (d__)Nominal engine system O/F mixture ratio = 1967.7/892.3 = 2.20
lb/sec
Fuel pump flow rate = (88.4-
11 790+ 500= 27 140 hp
gas flow rate w_ = 0.707 ×27140 359 × 0.582
pump flow rate
= 25.6 + 1942+ 3= 1970.6
lb/sec
horsepower
This value closely confirms for the last trial. Thus:
flow rate l_,tc = 747270120
Oxidizer
1941)= 892.1
1970.6x 2930 892.1 x 4790 ThP = 550 x 0.706 + 550 × 0.659 + 500
Turbine
lb
shaft
26.6)+(2768-
lb/sec
Resulting
From
characteristics at various must be available to the
vehicle system engineer. They can be summarized in the graphic form such as figure 2-1 (engine thrust and specific impulse versus altitude curve), or by means of tabulated engine influence coefficients which will be discussed, The effects of off-nominal conditions of the system performance parameters vital for the design of a vehicle (1) Atmospheric pressure (2) Propellant densities (3) Pressures at _he engine (4) Propellant mixture ratio control (5) Vehicle acceleration
-,qmNlm
(6) Throttling
of the engine
following engine are considered system:
propellant inlets and vehicle PU
system
ENGINE
Engine
Influence
SYSTEMS
DESIGN
Coefficients
example,
the total
effects
of several
simultaneously termined
on by
an
summing
the
causes
the
percentage dependent
Dependent
change variables
variables
Engine
thrust,
Engine
specific
Engine Engine
mixture oxidizer
Engine
fuel
of
14.696
and nominal 750000
flow,
892.3
262.4
-0.1780 sec
2.20 ......... 1967.7 lb/sec. lb/sec
psia
for
C 2(po
- pen)+
C 3([
pon Poin)
the
A-1
can
[-
pfn)
Pfn
Cs(Pfi-
Pfin)
+
(10-26) Pfin
where F, F,
: engine system value, lb
Pa,
Pan
Po,
Pon
: atmospheric pressure and its nominal •value, psia : oxidizer density and its nominal value, lb/ft 3
P[,
= fuel density lb/ft s
Pfn
thrust
and its nominal
and its nominal
value,
Poi, Poin :oxidizer pump inlet suction pressure and its nominal value, psia Pfi, Pfin = fuel pump inlet suction pressure and its nominal value, psia C_, C 2, C a, C 4, C s :influence Sample
Calculation
coefficients
(10-4)
Estimate the thrust of the A-1 stage engine system operated at the following conditions, without considering the effects of C* correction: Atmospheric pressure, Pa = 10.2 psia Oxidizer density, Po = 71.00 lb/ft 3 Fuel density, p[= 50.90 lb/ft 3 Oxidizer pump inlet suction pressure, Poi = 65 psia Fuel pump inlet suction pressure, Pfi--49 psia
for
the
C* correction
A-I
versus
variables
Oxidizer density, 71.38 lb/ft
Stage mixture
Fuel a
density, 50.45 Ib,/ft a
Engine ratio and
System curve
shown
nominal
values
Oxidizer pump inlet suction pressure, 56
psia
in fig.
Fuel pump inlet suction pressure,
10-8]
C
_
correction 1.0000
45 psia
values:
lb ..........
impulse, ratio, flow,
Atmospheric pressure,
Pan)+
thrust
C* correction)
Poin
Independent
following
engine
Pan C4(Poi-
For
of
(without
+
de-
from the
of
system as:
Fn
Coefficient
to be obtained
increase variables
be
effects.
lO-1.-Influence
of C* correction
A 1-percent independent
can
change
( F - F n) _ C l(pa-
acting
system
individual
TABLE [Value
influences
engine
the
stage engine be expressed
These are used to convert or correct steadystate, main-stage engine system performance parameters (dependent variables) from one condition to another of parameters (independent variables) such as atmospheric pressure, fuel temperature, oxidizer density, etc. This may be a correction to standard sea-leveI conditions (firststage booster engine), or a conversion to other specified conditions. The coefficients are derived from the linearized solution of a set of steady-state differential equations which describe the performance of an engine system. These equations are solved by a digital computer and presented in tabular form, as shown in table 10-1 for the A-1 stage engine system. Each influence coefficient is expressed as a percentage and represents the change of a dependent engine variable, such as thrust, as produced by a 1-percent change in an independent variable, such as atmospheric pressure. A coefficient preceded by a positive sign (+) indicates that an increase of an independent variable produces an increase in the dependent variable. Conversely, a coefficient with a negative sign indicates a decrease in the dependent variable, as a result of independent variable increase. These influence coefficients are usually sufficiently accurate over the entire design operation range of an engine system. Because the influence coefficients are linear,
397
INTEGRATION
.....
.
-
1.8750
.1780
,2650
.0000 .0000
1.6420 2.0430
.0000
.6530
-0.7420 -
.0640
-1.3650 -1.1120 .3120
0,0440 .0072 .0270 .0465 .0207
-0.0066 - .0150 -
1.1030 1.1350
.0020 .0108
- .0260 - .0632
.0045
.0094
398
DESIGNOF LIQUID PROPELLANT ROCKET ENGINES
Solution From equation
(10-26)
(F - Fn)_ (-0.178) F_
and table
10-1, which are for the A-1 engine system. The change of engine mixture ratio is computed for changes in atmospheric pressure, propellant densities, etc., assuming the C* correction first to be zero. For the resultant change in engine mixture ratio, the C* correction is read from the graph. The value of C* correction found is then used with other independent variables to compute the changes in the remaining dependent variables.
10-1:
x (10.2 - 14.696) 14.696
+ 1.875 x (71.0 - 71.38) _ (-0.742) 71.38
x (50.90 - 50.45) 50.45
0.044 × (65- 55) + (-00066) × (49 - 45) 55 45 =0.04531
or 4.531
Engine system Pa = 10.2 psia: F = 0.04531
Sample
percent thrust
of an altitude,
x Fn + Fn = 0.04531
where
x 750 000 + 750 000
: 784 000 lb
Nonlinear
Calculation
(10-5)
Estimate the thrust of the A-1 stage engine system operated at the conditions listed for sample calculation (10-4), adding the effects of C* correction, Also, for the same conditions, estimate the thrust assuming an additional mixture ratio error of +10 percent, due to faulty calibration.
Corrections Solution
When the linear approximation is not sufficiently accurate, the usefulness of the engine influence coefficients can be extended by a technique which allows nonlinear corrections for certain parameters. An example of this method is the C* correction. For instance, a plot of C* correction versus engine mixture ratio change may be used in conjunction with a table of influence coefficients such as figure 10-8 and table
By analogy table 10-1, the change due to tion (10-4) are
with equation (10-26) and using engine system mixture ratio the conditions of sample calculadetermined as
(MR- MRn) _ 1.642 x (71.0MR n 71.38 -_ (-1.365)
(-0.002)
x (50.90 50.45
71.38)
- 50.45)
÷ 0.027 × (65- 55) 55
× (49-45)__0.0162 45
or -1.62
percent
-0,1 _-. Z L_
From figure 10-8, the C* correction for a mixture ratio change of-1.62 percent is approximately -0.02 percent. From table 10-1, the influence coefficient for engine system thrust is 1.1030, for a i percent C* correction. Thus
I
-02
i
Z
9 -o.3 i.-
e¢ _ u
-0.4
(Percent
change
in F) = 4.531 + (-0.02) = 4.509
-0.5
-O.6 -16
-12 CHANGE
-8
-4 IN
ENGINE
8 MIXTURE
12
Therefore, engine system effects of C* correction:
x 1.103
percent
thrust
considering
RATIO,
PERCENT
F= 750000 Figure 10-8.-C* engine mixture engine.
versus change in correction ratio curve for the A-1 stage
× (1 + 0.04509)
= 783 820 lb
If the mixture ratio error of 10 percent is added, the total mixture ratio change = 10-1.62
399
ENGINE SYSTEMSDESIGN iNTEGRATiON
= 8.38 percent. From figure 10-8, the C* correction then is approximately -0.11 percent. Thus (Percent
changein
F)=4.531 =0.441,
Engine
system
+(-0.ii)×
1.103
or 4.41 percent
thrust:
F = 750 000 × (i + 0.0441)
= 783 080 Ib
10.5 MECHANICAL INTEGRATION ENGINE SYSTEMS
OF
Basic Considerations Besides combining allcomponents and subsystems functionallyand physically,the design formechanical integrationof an engine system must considerti_eoverallenvelope of the system and itsweight. This includes the locationof the system's centerof gravity. Also, itshould permit simplifiedmaintenance and checkout practices. Judiciouspackaging design techniques should be applied to minimize the number of interconnectinghydraulic,pneumatic, and electrical lines, with their attendant fittings, connectors, joints, and other potential trouble spots. Welded and brazed joints should be used as much as possible. Problems introduced by vibration, high temperatures and pressures, leakage and space restrictions are thus more easily handled. Engine mechanical integration is a vital part of the system design concept; therefore, all factors related to integration and packaging of components and subsystems must receive careful consideration early in the preliminary design stage. In general, a modular engine packaging approach should be selected such as used for the A-1 (fig. 3-2) and A-2 (fig, 3-4) stage engine systems, as well as for many advanced operational engine systems. This assures engine integrity from time of manufacture through vehicle launch. It also provides a compact package for ease of handling, transportation, and installation in the vehicle. Ease of checkout and component accessibility is also afforded by the packaging concept. The engine should be completely assembled in the manufacturer's plant. Subsequent acceptance testing, air transportation, and installation
in the vehicle in the field should not require assembly of additional major components. Integrity of the propellant feed and hot-gas systems, once verified in a complete system during acceptance test, is not necessarily mdlified by the need to temporarily disassemble the engine for shipment. The integrated engine package concept provides added assurance that static teststand firing results have verified structural soundness of the package to a substantially greater degree, than is the case for a system where the vehicle provides portions of the engine structure. An example of a special case of mechanical integration of a liquid propellant rocket engine is the prepackaged storable liquid rocket propulsion system shown in figure 8-1. This system is a completely integrated assembly of all-welded construction, consisting of thrust chamber assemblies, propellant tanks, pressurization system, and necessary controls. This provides maximum assurance of system integrity from the time of manufacture, which includes loading of the propellants, through delivery, vehicle assembly, and launch. Complete propellant separation until systems start is achieved by hermetically sealed burst diaphragms for maximum safety. Acceptance tests are conducted by taking sample units at random from the production line, and hot firing them. In addition, destructive tests of various types are performed. Packaging
of Rocket
Engine
Components
Most major rocket engine components, such as thrust chamber (fig. 4-1) and turbopump (fig. 6-14) assemblies, readily form a logical, independent mechanical unit by virtue of their function and their physical shape. However, in the case of minor components such as control valves, gas generators and igniters, packaging design principles can best be served by making them an integral part of a major component assembly, or to integrate them by grouping. A typical example is a gas generator assembly externally attached to a turbine inlet flange (fig. 3-2). Similarly, gas generator propellant valves and combustor can be integrated into one unit (fig. 4-51). Certain types of hydraulic and pneumatic rocket engine control components lend themselves most conveniently to the packaging design. Here, one of the main objectives is to
4O0
DESIGNOF LIQUID PROPELLANT ROCKET ENGINES
reduce line runs, by combining all parts and passages into one housing. Such a housing (or mounting plate) is relatively leakproof, trouble areas now being limited to external line connections to other components. Furthermore, if components are packaged in this manner, reductions of weight and size are achieved through the use of common walls and through the elimination of extra mounting platforms, clamps, and fasteners. Since relatively few packages are required as compared to the usually large number of individual components, maintenance of such a system is greatly simplified. Integrated packages are about as easily removed and replaced as are the separate components making up each package. However, the packaged design is not necessarily desirable for every control system. Each case must be carefully studied. As a rule, one or a combination of the following methods is used for packaging engine control corn ponents: (1) Bank packaging: A group of similar flatsided component assemblies are bolted together in a bank or stack, with common porting through the mating surfaces from one unit to the next. (2) Subplate packaging: Attachment of two or more individually housed components to a subplate, so that all ports of the individual component housings lead into the subplate manifold, through their mating surfaces with the subplate, and on to the systems plumbing. (3) Cartridge packaging: Two or more components housed individually in cylindrical cartridges are in turn assembled in a common body with suitable manifolding to the systems plumbing. (4) Multiple-component packaging: Detail parts for two or more components are assembled in a normal fashion in a common housing or body. Figure 10-9 presents a typical pneumatic control package for a large liquid propellant rocket engine. This package combines two pressureregulator assemblies, two relief valves, a series of solenoid valves, filter units, and check valves. It controls the flow of helium gas to various engine components. When engine start is initiated, the helium control solenoid is energized allowing helium to flow through the main pres-
sure regulator to the control system. The helium is routed internally to the main control valves through a fail-safe check valve. This insures that the various engine propellant valves remain pressurized and thus open, should the helium gas supply system fail.
Packaging of Turbopump Feed Engine Systems In earlierhigh-thrustrocket propulsionsystems, some of which may still be in operational use, allmajor engine components were mounted into a cage-shaped thrust mount, which was bolted to the vehicle thrust frame by way of lugs. Figure 2-4 allows several typical examples. With these systems, vehicle steering was accomplished by means of carbon jet vanes protruding into the jet (V-2 and Redstone), or by swiveling the thrust chamber (Thor, Jupiter). In the latter case, the high-pressure feed lines between pumps and injector had to be much more flexible than for misalinements and thermal expansion/ contraction alone. Most advanced liquid rocket engines are tightly packaged. All major components are attached to the main thrust chamber, directly or by means of mounting structures, as shown in figures 3-2, 3-4, and 9-1. Here, the thrust chamber serves as the principal structural member of the entire engine system. For steering, the complete engine package is gimbaled from a gimbal bearing which attaches directly to the thrust chamber dome. The other half of the bearing is attached to the vehicle thrust structure. The low-pressure propellant supply duets must be sufficiently flexible to accommodate the gimbal motions. It is noted that vehicle steering through gimbaling of a single engine or chamber is effective only for the pitch and yaw planes. For roll control, at least two engines are required. For vehicles with a duster of engines, therefore, this poses no difficulties. For single-engine vehicles, special roll-control devices are needed. These may be small auxiliary nozzles, possibly simultaneously used as vernier engines after main-engine cutoff. The use of the turbine exhaust for roll control has also been proposed. Whether the engine attaches to the vehicle thrust structure by means of a thrust frame or a gimbal bearing, either device must be designed to be capable of transmitting the full thrust
401
ENGINE SYSTEMS DESIGN INTEGRATION
5 MICRON FILTERBLEED PRESSURE REGULATOR-_ \ MA,NSTA_F ..........
HIGH
CC1NT _\
fG.G._ BLEED VALVE CONTROL SOLENOID HELIUM CONTROL SOLENOID VALVE / /---'--'--MAIN PRESSURE REGULATOR tlJ_.._/_ ,/._t_
j.---,GN,T,ON
PHASE CONTROL L
_
PRESSURE
VALVE
/
-..-1::;-_:_i'_>_!_
__FAIL-SAFE
__
_
RELIEF VALVE
t
CHECK 10MICRON
_x__LOW
VALVE
FILTER
PRESSURE RELIEF VALVE
HELIUM INLET
PNEUMATIC
VENT
PORT CHECK
CONTROL
PACKAGE
SCHEMATIC
VALVE
PRESSURE RELIEF VALVE
HELIUM IN LET
IGNITION
PHASE
SOLENOID VALVE
CONT.
VENT CHECK
VALVE VENT PORT CHECK VALVE
INSTAGE SOLENOID CONTROL VALVE HELIUM CONTROL SOLENOID VA LVE BLEED PRESSURE REGULATOR
Figure
lO-9.-Typical
G.G
pneumatic
control
package systems.
design
BLEED VALVE
used
in
CONTROL
liquid
SOLENOID
propellant
rocket
VALVE
engine
J
402
DESIGN OF LIQUID
forces
at full
adequate The
gimbal
reserve
bolt-hole
tolerance
pattern
and
must
deviations.
vehicle one
deflection,
for normal
including
an
for side
loads.
permit
adjustment
In general,
attachment
halves
PROPELLANT
engine
must
be
ROCKET ENGINES
for and
designed
for
another. LU|E
Figures
10-10
and
aging
design
tem.
It is a LO2/RP-1,
constant engine
details
chamber
10-11
illustrate
of a typical
pump
fixed-thrust
pressure
package
the
consists
of the
feed
TANK
sys-
engine
control.
OIL
pack-
The
with
basic
following
sub-
packages: (I)
Gimbaled
main
(thrust dizer (2)
elbow,
Turbopump
trol
and
gearbox,
heater, Gas
chamber
injector,
auxiliary
generator
oxi-
mount)
(propellant lube
pumps,
pump,
electric
drive)
assembly
valves,
assembly
dome,
gimbal
assembly
turbine, (3)
thrust
chamber,
regulator
(combustor, and
turbine
coninlet L_N
duct) (4) Main oxidizer duct assembly main oxidizer valve) (5) Main fuel duet assembly
OX_OIZE_ V_LVE
(including Figure
10-I I.-System
(including main
the
packaging
engine
shown
design
in figure
detail
of
10-10.
fuel valve) (6) Turbine exhaust duct assembly
(includ-
ing heat exchanger) (7) Engine
start subsystem
(oxidizer and
fuel tanks, control valves) (8) Turbopump
lube subsystem
Electrical
(11)
Engine
The
(lube oil tank
and fittings) (9) Pneumatic
(10)
control package
system
control thrust
majority
of the
packages
are
major
of the
engine
The
thrust
chamber
frame
through
the
thrust
Mechanical
assembly
component
installed
periphery main
package
frame
thrust
frame
sub-
or at the assembly.
assembly
is attached
a gimbal
Protection
and
within
to
mount.
System
of Engine
Packages It is normal between gine
the
vehicle means
age
in transit
and
shock.
and
contain Figure
lO-lO.-Major
packages rocket
of engine.
component turbopump-[ed
vent
desiccant
holes,
subsystem
warn,
change
liquid
propellant
trusion
of moisture.
require
communication
system
pack-
moisture,
dirt,
applied
propellant and
Certain with
such to valve
inlets,
these
which
of undesired lines,
and
closures
indicators
the
and con-
closures,
plates
of color,
en-
user, must
simple
Frequently, bags
and
engine
cover
elapse
rocket
by the
against
include
and
may
therefore,
the
or storage
openings. through
accepted
to protect
plugs,
years propellant
Design,
These
regulator
to other
and
flight.
sider
caps,
several
a liquid
is completed
its
as
that date
in-
however,
ambient
air
may
ENGINE SYSTEMS DESIGN INTEGRATION
are many
4O3
tasks, such as sequencing
which can
be accomplished
nmch
more effectively electri-
cally than would
be possible by mechanical
means. It is not possible nor necessary,
in the frame-
work of this book, to describe the physical laws
FUEL
and the general fundamentals cuitry. They _CLOSURE
literature. Moreover,
COVER
of electrical cir-
are covered abundantly
in the
in contrast with most other
basic liquid engine subsystems,
the rocket en-
gine designer will try to use commercially able "off the shelf" components system.
However,
avail-
for his electrical
other cognizant
members
of
the design team will have to provide the basic circuit diagram (schematic)
and other data in
support of the installation of the required electrical components. trical system "_'__THRUST
CHA,_SE/_ CLOSURE
last subsystems
EXIT
Characteristically, the elec-
of a rocket engine is one of the to be "frozen" before produc-
tion. This is because
COVE_
sequencing
for start and
stop represents one of the major engine developFigure
10-12.-Various
protective
closure
covers ment activities, often resulting in repeated modi-
for the
engine
shown
in [igure
10-10. fication of the electrical system progresses.
("breathing").
In this
equipped
with
of dry air
only.
desiccant
for installation
Others
will
sible
be left
and
clearly
their
protective
LR79-NA-
the as
left
shows
closures
access
must
be
such
10-12
be
be re-
flexibilityof electrical design. this process analyses
engine
readily with
bright
in place
the
for the
is acces-
recently,
(see sec. 10.2).
location
Electrical
Schematic
The complete
inadof
Rocketdyne
11 engine.
electrical schematic
ground- and vehicle-based sizable drawing.
elements,
fills a
With the aid of figure i0-13,
presents a portion of an earlier engine
discussed
SYSTEM
of a typi-
cal liquid rocket engine system, including its
which
ELECTRICAL
More
has been greatly aided by dynamic
static-firingschematic, 10.6
as development
is therefore placed on the
to vehicle.
until
being
may
to permit
covers
must
marked,
Figure
various
closures
of engine These
to prevent
vertently.
of the
in place
operated.
colors,
the
filters
Some
moved actually
case,
Emphasis
as follows.
the basic features are In ordinary wiring dia-
grams, such as that of a radio receiver, all the All rocket engines electrical system
depend
on some
for their operation.
true for solid systems,
where
type of
This is
at least ignition is
contacts of, for instance, a multiple switch or a tube are drawn
initiated electrically, as well as for liquid sys-
crossovers
tems, in which
overs would
the electrical system assumes
to appear in the same
location, as
they do in reality. This requires numerous in the diagram. become
The
number
wire
of cross-
prohibitive in a typical
numerous additional tasks. As with any common household device, electrical circuits in rocket
engine electrical schematic
engines have caused
troubles, due to poor de-
poses it has long been found preferable to draw
sign, misapplication,
abuse, poor maintenance,
the basic diagram
human
errors, and wear.
Properly applied, how-
and may lead to
confusion and errors. For rocket engine pur-
separately.
so as to show
each
circuit
In this "functional flow diagram,"
ever, electrical circuits can" substantially sim-
the various contacts of a relay, for instance,
plify the operation of a rocket engine, and will
appear in different places, and often away
increase its usefulness
the circuit for the corresponding
and reliability. There
from
relay coil. The
4O4
DESIGN OF LIQUID PROPELLANT ROCKET ENGINES
Figure
I 0-13.-Typical
liquid
rocket
drawing system also will materially simplify later troubleshooting. The diagram, of which figure 10-13 shows a portion, was drawn sequentially from left to right; i.e., circuits which are energized during test preparation and start are shown in the left portion, while those associated with the cutoff sequence appear on the right. In the schematic, connectors are shown as continuous double lines, or portions thereof, running horizontally through the diagram (J16, P16-- receptacle 16 and plug 16, etc.). Each of the contacts is called out by a letter (T, G, K, etc.). All wires are numbered, as indicated. Power buses, like connectors, are shown as horizontal lines, or portions thereof (heavy, single line = positive buses, usually shown near the top of the drawing; and double lines = negative or ground bus). The meaning of the remaining symbols becomes clear by following the circuit at the left of figure 10-13. Plug P5 is shown connected to the main power bus K101 at terminal TB1-8. If certain facility signal contacts are properly closed, such as those verifying "'Cooling water OK," "Firex armed," "Observer on Station," and many more, power returns through plug P5, contact "Z," and is applied to relay coil K31C. The "B" contact of this relay closes a circuit to lamp DS31C, which lights up. The "A" contacts of the same relay are in the chain to the coil of K34C, together with the normally open contacts of several other relays, such as K29C, "Heater Power On," and.
engine
electrical
diagram
(partial).
K28C, "Hypergol Cartridge Installed," as well as the normally closed contacts of cutoff relay KglC. If all contacts are properly closed, the "C" contacts of K34C will cause signal light DS34C to light up. Following selection of the ig-nition power source by means of switch S16C, ignition can now be initiated by means of pushbutton $51C, since the "D" contacts of K34C are now closed, and provided ignition disconnect timer K54C has not picked up (TDPU e time delayed pickup : 0.1 seo). In the diagram, several circuit elements appear which are part of other circuits not discussed. Note that in places two relays are used in parallel (e.g., K16C), if the number of contacts required is too large for one relay. The numbers shown in hexagonal frames refer to the channels of an inking sequence strip chart recorder or equivalent instrument. A special test bus K615 is provided which when energized makes all signal lights go on and thus permits spotting burnt-out bulbs. In earlier engine designs, many of the elements shown in figure 10-13 were installed in an engine-mounted relay box. The trend has been to place as many parts of the electrical system on ground as possible. This is easier with first stages, which start while still connected to ground, or even held down mechanically until released, for brief periods following start, than it is with upper stages which must start and stop, and sometimes restart, some time after takeoff.
Beca_se
of individual
approach
and of
ENGINE SYSTEMS DESIGN INTEGRATION
preferences guards two
for the
required,
designers
different
Specifically
with
and
advised, more
are
The lays,
than
applied
Solid-state
shown
Transistor
as
fulfill
the the
a bias
long
as
in R,,
the
Transistor
is
employed engines.
effecLs.
base
are
in a "turned at a higher
emitter.
This V 2.
is no
appreciable will
off"
be
Thus,
is held
in a "turned
off"
QI
except
that
here
the
by
will
this
turns
until
on,
current
the
At
base
This
(1b,) occurs
max
(10-27)
R 4 is
combined
out
"turns load.
to
potential
voltage,
Ib2 flows
to the
switched
to flow. As Ic base of Q2 is
on,"
This
Vbe2.
of the
base
thereby
occurs
At of
supply-
when
Vo, Rs(Icbol+lcbo2)>(V2+Vbe2)
mode
The
base
the
switch
input
vo
is turned
signal,
the
lock-in
switch
10-15
is immersed module
L
LOAD
The
tiN
shows
shown,
for engine
wiring
metically
potting a small
are
comparable
portion
and
together
connectors,
sealed
box
of an diagram.
with
operation,
the
others
including are
connect-
housed
in a her-
or can.
Although
the
two diagrams
signal
emitted
at pin
the
a module Overall
sequence-controller
modules
required ing
a
solid-state
compound.
after
10-16
engine-mounted
--------_v.
through
of a matchbox.
Figure
"_
INPUT
input
input
feeding
the base of Q, switch.
assembly,
in a potting
static
after by
a typical
Following
dimensions
to those
Ichor//
output
to the
shorting off the
shows
module.
removing
another
accomplished
back
(10-28)
of Q_.
maintain
is
voltage
Figure OUTPUT
off by either
base
(to
is removed)
output
max
Vin , or by using
to ground
signal
METHOD
R2
the
+VI)
resistor
transistor
current
Q2
DIODE
+(
voltage,
on.
Q2 base-emitter
diode. In this case, must be used to turn
IM '4-"
Ix
potential,
is overcome.
into
to turn
it reaches
the
point,
the
i t
flow
the
ing
V2
R4
current
base
(V_),
lowered
Switch
LOCK-IN
applied,
Q,
begins at the
Q2 and
flow
_
L'I
be at ground
base-emitter
transistor
Q,
switch ,
is
the
Again, through
off.
ground, and current Ic, increases, the potential of V 2 and
essentially 2.
fashion,
mode
be seen,
is
essentially
voltage
current
the
When
as
current
Vo-V
point,
flows
Vin
Q,
the
ground.
voltage
bias
volt-
raises
above
remain
raises
emitter.
a bias
current
R3(Icbol)>(Vbel
of this
emitter
will
combined plus
causing
which
Q1 will
This
the
less
voltage
can
the
(Vbel),
leg,
base
input
until
than inserting
V 1 volts
and
flow.
this
emitter
R 2, the
will
by
when
is achieved
As
R I and
potential
no appreciable
of re-
It functions
base
potential
are
much
A circuit
10-14.
held
In
function.
advantage
thus
as
long
When
to
switches
the
and
potential
as
potential,
re-
rocket
in the
emitter
do
continue
voltage,
there
while that at the will remain off.
in a similar
may
of which
a similar
have parts
Q2 is
than
inserting
caution by them-
and
above
in figure
by maintaining potential
arrive
of inter-
applied,
(transistorized)
which
to vibration
type is follows:
number
elements
of today's
moving
sensitive
may diagrams.
to the
types
switches no
V_,
discussed
in several
quiring
age,
engine
to malfunction
solid-state
being
is accomplished
good.
diagram
others,
be at a lower
This
circuit
well-developed
be used
must
used,
circuits
these
subject
harm
safe-
of component
electrical
respect
monitoring since
selves
of interlocks,
type
of a comparable
at substantially
locks
types
and
40,5
are
not
related,
X of receptacle
J-5
in
GROUND
figure Figure
I 0-14.-Typical switch
circuit
rocket or "module"
engine
solid-state
diagram.
start
10-13
would
at contact
Similarly,
the
be suitable
A of plug signal
emitted
P51
to initiate in figure from
pin
engine 10-16.
K of plug
406
DESIGN OF LIQUID
PROPELLANT
ROCKET ENGINES
Electrical
Components
To implement
rocket,
cuitry
such
as
10-13, These
a number are:
Relays
and
Relays
and,
the
engine
one
of components
more
in figure
are
used
recently,
are
command
signals
from
and
to translate
center
cir-
shown
required.
Switches
switches trol
electrical
partially
the
to receive the
solid
usually vehicle them
sequenced actuation signals valves and other elements.
state
low
current
or ground into
con-
properly
to igniters, control In combination with
interlocking relay contacts, bias voltages, valve Figure
lO-15,-Assembled module
soJid-state
be[ore
and
after
position switches, continuity monitors, tempera-
switch
ture sensors, spark plug monitors, voltage sen-
potting.
sors, timers, and other devices, they form an engine-contained P51
in figure
10-16,
with
the
relay,
could
be used
to assure
in the
chain
leading
to the
figure
10-13.
aid
engine
coil
sometimes
of an auxiliary
sponse
readiness
of relay
K34C
in
stop.
*
(
GIN[
Jal
FO_
will execute a
to only two external signals: In practice many
changed
R
logic which
elaborate starting sequence
between
in restart and
more signals are ex-
engine and vehicle and/or
ST*AT
20m$
_l_
P_r
•5,
.
I
