Solid-propellant rocket motor ballistic performance variation analyses

196 Pages·2009·14.03 MB·English

NASA CONTRACTOR
REPORT
NASA CR-144264
(NASA-CF-144264) PCLID-PROPELLANT ROCKET N76-23354
MOTOF BALLISTIC PEBFOFMANCE VARIGTIOS
ANALYSES Firlal Repcrt (Ruburn Univ.) 197 p
HC $7.50 CSCL 21H Ur,clas
(~3120 2691 3
SOLID-PROPELLANT ROCKET MOT% BALL1 STIC PERFORMANCE
VARIATION ANALYSES
By Richard H. Sforzini and Winfred A. Foster, Jr.
Auburn University
Auburn, Alabama 36830
October 1975
Final Report
Prepared for
NASA-GEORGE C. MARSHALL SPACE FLIGHT CENTER
Marshall Space Flight Center, Alabama 35812
TECHNICAL- REPORT STANDARD TITLE Pk.iE
1 REPORT NO. 12. GOVERNMENT ACC.ESSION NO. 13. RECIPIENT'S CATALOG NO.
I.. I I I
NASA CR-144264
f 4 TITLE AN0 SUBTITLE 15. REPORT DATE
Solid- Propellant Rocket 1,Iotor Ballistic Performance October 1975
Variation Analyses 6. PERFORMING ORGANIZATION CODE
1
7R. iAcUhTHaOrRd( SH) . Sforzini and Winfred A. Foster. Jr. 8. PERFORMING ORGANIZATION REPOR r ff
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NAME AND ADDRESS 10. WORK UNIT NO.
i - 1
Auburn University 1 1. CONTRACT OR GRANT NO.
NCA8-00 106
Auburn, Alabama
113.1 rYP4E O.F R1EPOR ;' B PERIOD COVERED
112 SPONSORING AGENCY NAME AND ADDRESS Contractor, Final
I
National Aeronautics and Space Administration
Washington, D. C. 20546 SPONSORING AGENCY CODE
1
l-lj, SUPPLEMENTARY NOTES
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i
V
$ lS, ABSTRACT
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i The report presents the results of research aimed at improving the assessment of off-
1 nominal internal ballistic performance including tailoff and thrusl imbalance of two large
/
solid-rocket motors (SRMs) firing in parallel. Previous analyses by the authors using tho
f
Monte Carlo technique (NASA Contractor Report NASA CR-120700) have been refined to
k
2 permit evaluation of the effects of radial and circumferential propellant tempt?rature gradients.
I
t Sample evaluations of the effect of the temperature gradients are presented. A separate
theoretical investigation of the effc dt of strain ratc on the burning rate of propellant indicates
f that the thermoelastic coupling may cause substantial variations in burning rate during
highly transient operating conditions. An approach for additional invcstigation of the
phenomenon is outlined. The Monte Carlo approach has also been modified to permit the
I effects on performance of variation in the characteristics between lots of propellants and other
materials to be evaluated. This permits the variabilities for the total SRM population to be
determined. A sample case shows, however, that the effect of these betwcen-lot variations
on thrust imbalances within pairs of SRMs is minor in comparison to the effect of the within-
lot variations. The design analysis program presented in NASA CR-12!)024 and 12'3025 is
modified to improve the results when all tabular values are used during tailoff and additional
refinements are included. Errata to NASA CR-120700 are presented and discussed. The
revised Monte Carlo and design analysis computer programs along with instructions including
format requirements for preparation of input datl and illustrative examples are presentcd in
the Appendices.
!. I I. KEV WORDS ! 18. OlSTRleUTlON STATEMENT
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UNC LASSIFIED-ITNLIMITED
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19. SECURITY CLASSIF. (dt hl. r*pdl 20, SECURITY CLASSIF. (of thlm pane) 21. NO. OF PAGES 22. PRICE
Unclassified Unclassified 197 NTIS
r - b
vlSFC Form 3 2 9 2 (Rev December 19 7 2 ) For sale hy Notiocal 'I'ecl~nicrlI cfornlatinn Service, Sprinpli~'Ic1,V irgi~ri:2~2 15 1
ACKNOWLEDGEMENTS
Tne authors express appreciation to personnel a t
the George C. Mawhall Space Flight Center for their
maray useful suggestions which materially aided this
investigation and in particular to B. V. Shackelford,
Jr., (NASA Project Coordinator) who additionally pro-
vided data for analysis and helpful encouragement to
this effort.
The participation of Joseph S. Johnson, Jr., of
the Auburn University Computer Center who assisted in
modification of the statistical analysis program is also
acknowledged. Finally, the authors express grateful
appreciation to Harry Aultrnnn, Jr., who prepared the
figures and assisted in obtaining computer results, and
to Mrs. Marjorie N. PlcCee who typed the manuscript.
TABLE OF CONTENTS
. . . . . . . . . . . . . . . . . . . . . . . . .
Acknowledgements ii
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Abstract iii
. . . . . . . . . . . . . . . . . . . . . . . . . . .
Nomenclature ix
. . . . . . . . . . . . . . . . . .
I. Introduction and Summary 1
11. Prediction of Thrust Imbalance and Comparison with
. . . . . . . . . . . . . . . . . . . . . . . .
Test.Results 5
. . .
Titan IIIC Predicted versus Measured Thrust Imbalance 5
Prediction of Thrust Imbalance of Space Shuttle
. . . . . . . . . . . . . . . . . . . . . . .
Type SRM Pairs 9
. . . . . . . . . . . . . . . . . . .
Discussion of Results 11
.
.
111. Temperature Distribution Throughout the Propellant Grain 13
. . . . . . . . . . . . . . . . . . . .
The General Approach 13
. . . . . . . . . . .
The Radial Temperature Gradient Inputs 15
. . . . . . .
Circumferential Propellant Temperature Profile 20
. . . . . . . . . . . .
Modification of the Ovality Analysis 24
. . . . . . . . . . . . . . . . . . . . . . . .
Sample Case. 26
. . . . . . . . . . . . . . . . . . .
IV. Total Motor Population 34
. . . . . . . . . . . . . . . . . . .
V. Thermoelastic Analysis 4 0
. . . . . . . . . . . . . . . . . . . . .
Method of Analysis 40
. . . . . . . . . . . . . . . . . . . . . . . . . .
Results 4 1
. . . . . . . . . . . . . . . . . . . . . . . .
Conclusions 42
iii
. . . . . . . . . . . . . . . . .
VI Design Analysis Modifications 46
. . . . . . . . . .
Use of A l l Tabular Values during Tailoff 46
. . . . . . . . . .
Axisymmetric Grain Temperature Gradients 46
. . . . . . . . . . . .
Transition Pressure and Burning Rate 46
. . . . . . . . . . . . . . . . . . .
VXI Errata to Previous Report 48
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
References 50
Appendic.es . . . . . . . . . . . .
A The Monte Carlo Computer Program 53
. . . . . . . . . . . .
B The SRM Design Analysis Program 133
LIST OF FIGURES
Fig. 11-1. Histograms of absolute values of max.im.um. t.hr.us.t . . .
imbalance for Titan IIIC SRM pairs 7
Fig. 111-1. Radiation .he.at. f.lu.x .de.si.gn. c.on.d.iti.on.s .(N.AS.A .TM. . . .
X-64757) 16
Fig. 111-2. Ambient temperature .de.si.gn. p.oi.n.t c.on.d.iti.on.s . . . . .
(NASA 'I'M X-64757) 17
Fig. 111-3. Temperature profiles (4 days) ba.se.d .on. a.xi.sy.m.me.tr.ic .
transient conduction analysis. 19
Fig. LII-4. Types of tangential grain temperature profil.e s at
the 5urning perimeter for' odd numbered SRMs
A) Alternative types of distribution.
B) Hyperbolic secant distributions with different
degrees of peakedness corresponding to various
concentrations of heat flux. Even numbered
motors have similar profiles but TA an.d .T B are
replaced by T C and TD ' respectively- 21
Fig. 111-5. Orientation ct' the thermal gradient with re-
spect to the ovali.ty. o.f .th.e .pr.op.eL.la.nt. b.or.e . . . . .
an2 the exterior 25
Fig. 111-6. Input temperature distributions Cur comp.ar.- . . . . .
isons of temperature gradienf ctfects. 28
Fig. 111-7. Thrust versus time of SRM pai :: one motor with
a uniform propellant temperaLure and one with both
. .
radial and circumferential temperature gradients 30
Fig. 111-8. Thrust imbalance versus time of BID1 pair: one
motor with a uniform propellant temperature and
one with radial and circumferential temperature
. . . . . . . . . . . . . . . . . . . . .
gradients 31
Fig. 111-9. Thrust versus time of SRM pair: one motor with
radi radial circumferential propellant temperature
gradient and one with an axisymmetric radial
. . . . . . . . . . . . . . . .
temperature gradient 32
Fig. 111-10. Thrust imbalance versus time of SRM pair: one
motor with radial and circumferential propel-
lant temperature gradient and one with an
axisymetric radial temperature gradient. Note
difference in scale between Figs. 111-10 and
1 1 1 - 8 . . . . * * n . . . . . . . . . . . . . . . . . 3 3
.
Fig. V-1, Temperature. (and te.m.~e.ra.tu.re.d i.ff.er.en.ce.s .vs. . . . . .
radial position. 43
Fig. V-2. Calculated temperature differences between
thermoelastic and heat conduction analyses.
(Cross-hatched areas denote regions of zero
. . . . . . . . . . . . . . . . . . . .
difference). 44
. . . . . . . . . . . . . . .
Fig. A-1 schematic of data deck 65
LIST OF TABLES
Table 11-1. Mean (u) and standard deviations .( a.) .o f. i.n p.u .t . . . .
variables for the sample cases 8
Table 11-2. Mean (g) and standard deviations (s) of
selected performanc.e .c h. a.r a.c t.e r.i s.ti c.s .f o.r . f i.f t.y . . . .
146-in. dia. SRMs 10
Table 111-1. Input variables for Space Shuttle type SRM with
hyperbolic secant circumfe.r e.n t.ia .l p.r o.p .e l.la n. t . . . . .
temperature distribution 29
Table IV-1. Input for sam. p.le .e v.a .lu .at i.o n. o.f .t o.t a. l. S R.M . . . . . . .
population 35
Table IV-2.. Statistical output .f o.r . m .o to. r .p a. ir.s .a n.d .t o. ta. l. . . . .
population of 100 37
Table IV-3. Comparison of Monte Carlo evaluations for 50
SRM pairs with (w) and without (w/o) between
pair variations in mean values of input
v a r i a b l e s . . . . . . . . . . . . . . . . . . . . . . 3 8
. . .
Table A-1. Example data sheets for the Monte Carlo Program 66
Table A-2. Portion of Monte Car.lo .c o.m .p u.t e.r p.r o.g r.a m. p.r i.n t.o u.t . . .
for sample problem 70
. . . .
Table A-3. Monte Carlo performance analysis of SRM pairs 71
. .
Table B-I.. Example data sheets for design analysis prograic 148
Table B-2. Sample co.m .p u.t e.r p.r i.n t.o u. t .f o. r. d e.s i.g n. a.n .a ly. s.is . . . .
program 150
. . . . . . . .
Table B-3. SRM design and performance analysis 152
vii
NOMENCLATURE
English
Symbol Definition Units Used
Propellant burning rate coefficient below inlsec-psin
and above t.h e transition pressure, re-
spect ively
Major and minor semiaxis, respectively, in.
ac
pbc of grain exterior in the ovality analysis.
a b Major and minor semiaxis, respectively, of in.
gs g
grain interior in the ovality analysis.
.
c Spec ifi c heat in-lbf / lom°F
Coefficient of variation; i.e., the ratio -
of the standard deviation to the mean.
-
C Integer designating shape of grain ends.
P
0
e Difference in distance burned between line of in.
ha
maximum radial temperature gradient and radial
line 90' away Ior a cosine circumferential
distributign of grain temperature.
e The eccentricities of the center of the grain in.
xh eyh
interior with respect to the center of the
grain exterior in the x s and y s directions,
respectively.
E Modulus of elasticity. lbf /in2
Radial reference erosion rate of the nozzle in/sec
'ref
F Thrust lbf
-
K Statistical confidence coefficient
Burning rate exponent or number of observa- -
tions of a statistically distributed variable.
Burning rate exponent below and above the -
"1 '"2
transition pressure, respectively.
viii
NOMENCLATURE (Continued)
English
Symbol Definition Units Used
Pressure. lbf /in2
Transition pressure at which the burning psia
rate coefficient and exponent change.
Burning rate. in/sec
Radial coordinate ~f exterior and burning in.
surface of the grain, respectively.
The propellant oxidizer to aluminum weight in.
ratio.
Ratio of the burning rate exponent above to
the burning rate exponent below the
' transition pressure.
Standard deviation of a sample of a statis- units vary
tically distributed variable.
Burning perimeter. in.
Time. sec.
Grain burning surface temperature on line of OF
maximum radial temperature gradient and on a
diametrically opposed line for a hyperbolic
secant circumferential distribution of grain
iemperature.
Bulk temperature of the propellant grain. OF
Coordinates of the grain exterior used in in.
the ova! ity analysis.
Coordinates of the grain interior used in in.
the ovality analysis.
Value of general statistically distributed units vary
variable.
Distance propellant has burned from initial in.
surf ace.