Crowder, Winston

Foster, Winfred A., Jr.

Steadman, Todd E.

NASA Technical Reports Server

A Monte Carlo Analysis of the Thrust Imbalance for 
the Space Launch System Booster during Both the 
Ignition Transient and Steady State Operation
by
Winfred A. Foster, Jr.
Auburn University
Winston Crowder
Lockheed-Martin Corporation
Todd E. Steadman
NASA/Marshall Space Flight Center
https://ntrs.nasa.gov/search.jsp?R=20140012588 2019-08-31T18:05:11+00:00Z
Objective
To provide an estimate of the thrust 
imbalance versus time for the SLS solid 
rocket motor booster from ignition through 
tail-off
Approach
Couple a Monte Carlo analysis code with two 
legacy codes previously used for the internal 
ballistic analysis of the Space Shuttle solid 
rocket motor boosters
The ignition transient analysis used the code 
developed by Caveny and Kuo for the 
analysis of ignition transients in large 
segmented solid rocket motors
Approach
The steady state analysis was based on the 
simplified internal ballistics code developed 
by Sforzini, et.al., for large L/D solid rocket 
motors and which had been used in 
conjunction with the Monte Carlo analysis for 
the Space Shuttle boosters
 A MATLAB shell program was used to 
manage the execution, data input and 
graphical output for each of the codes
Approach
A statistical sample of 2000 solid rocket 
motors or 1000 pairs of boosters was 
generated using the Monte Carlo analysis for 
both ignition transient and steady state motor 
operation
Pairs of motors were constructed by putting 
an odd numbered motor with an even 
numbered motor
Approach
Statistical variations in performance 
properties were allowed between motors of 
the entire population and between motors of 
a single pair
The thrust imbalance in each analysis was 
determined by selecting a set of specific time 
points and determining the difference in 
thrust between the two motors of a pair at 
those times
Approach
Given the thrust imbalance versus time data, a 
thrust imbalance envelope about a zero mean 
value was determined by calculating the K-
sigma value at each time point 
 The predicted thrust imbalance envelope was 
then compared to the operational specification 
limit for thrust imbalance versus time provide by 
NASA/MSFC 
 The validity of this approach was verified 
previously using data obtained from Space 
Shuttle Flights for the steady state and tail-off 
portions of the thrust time trace
Space Shuttle Flight Data 
Comparison
Ignition Transient
Thrust Imbalance
Ignition Transient Variables
Variable Name Variable Definition
TPI initial propellant grain temperature
AT nozzle throat area
XP location where propellant begins
XG aft end of propellant
XE end of flow passage
GAMA ratio of specific heats
W molecular weight of combustion gases
TIGN igniter gas mean temperature
TFREF reference adiabatic flame temperature
RUFSUR port wall roughness
FKPR propellant thermal conductivity
ROPR propellant density
CPR propellant specific heat
TOREF reference propellant temperature
SIGP temperature sensitivity of burning rate a constant pressure
TPSCRI surface ignition temperature
RREF reference burning rate
PREF propellant property reference temperature
BREXP burning rate exponent
EBC Robillard-Lenoir constant
EBEX Robillard-Lenoir constant
DE diameter of the nozzle exit plane
CM nozzle thrust loss coefficient
EROAT nozzle erosion parameter
EROEXP nozzle erosion parameter
ALFAD nozzle divergence half-angle
TPSHFT reference PMBT difference between motors of a single pair
BRSHFT reference burning rate shift between motors of a single pair
ATSHFT reference throat area shift between motors of a single pair
DPSHFT` reference propellant density shift between motors of a single pair
DESHFT reference exit diameter shift between motors of a single pair
ETSHFT reference throat erosion rate shift between motors of a single pair
SHFTMI reference Δt time shift in mass addition versus time from the igniter
Ignition Transient Thrust Imbalance 
Envelopes
PMBT 40o-90o F  (K=3.472) 
Ignition Transient Thrust Imbalance 
Envelopes 
PMBT 40o-90o F  (K=3.472)
Thrust Time Traces
PMBT 40o-90o F
Thrust Time Traces
PMBT 40o-90o F 
Thrust Time Traces
PMBT 40o-90o F
Typical Ignition Transient 
Thrust Imbalance 
PMBT 40o-90o F  (K=3.472)
Typical Thrust Time Traces
PMBT 40o-90o F
Steady State and Tail-Off
Thrust Imbalance
Definition of Nominal Motor
Required since the simplified internal ballistics 
code does not rigorously account for all of the 3D 
motor geometry, particularly in the aft end, head 
end dome and star to CP transition
Used a design optimization approach to determine 
the adjustments to the code geometric variables to 
match the thrust time trace obtained from static 
test data
This approach is valid since the thrust imbalance 
only involves Δ’s between motors of a pair
Typical Grain Design Variables
Thrust Time Trace to Establish 
Nominal Motor Performance
Steady State & Tail-Off Variables
Variable Name Variable Definition
RHO propellant Density
A1 burning rate coefficient
A1SHFT reference burn rate coefficient shift between motors of a single pair
N1 burning rate exponent
ALPHA erosive burning rate coefficient
BETA erosive burning rate coefficient
ROAL oxidizer to aluminum ratio
DE exit plane diameter
DTI initial throat diameter
THETA cant angle of the nozzle
ALFAN nozzle cone half-angle
XT aft end taper dimension
ZO aft end taper dimension
ZC aft end taper dimension
RONDCN nozzle end  case out of roundness parameter
RONDCH head end case out of roundness parameter
RONDGN nozzle end grain out of roundness parameter
RONDGH head end grain out of roundness parameter
EXN eccentricity in x at nozzle end
EYN eccentricity in y at nozzle end
EXH eccentricity in x at head end
EYH eccentricity in y at head end
ALPHAH angular orientation of ovality at nozzle end
ALPHAN angular orientation of ovality at head end
ERREF reference throat erosion rate
TGR grain bulk temperature
TGSHFT reference PMBT difference between  motors of a single pair
DO outside CP grain diameter
DI initial inside CP grain diameter
THETAG aft end taper angle
LGCI initial length of CP propellant grain
LGNI aft end tapered grain length
THETCN nozzle end closure angle
THETCH head end closure angle
RC propellant star grain outside radius 
FILL star valley fillet radius
RP initial radius of truncated star
RIS initial radius at the bottom of the truncated star slot
Steady State Thrust Imbalance Envelopes 
PMBT 60o F (K=3.472)
Steady State Thrust Imbalance Envelopes 
PMBT 60o F (K=3.472)
Thrust Time Traces
PMBT 60o F (K=3.472)
Typical Steady State Thrust Imbalance  
PMBT 60o F (K=3.472)
Typical Steady State Thrust Time Traces  
PMBT 60o F 
Steady State Thrust Imbalance Envelopes 
PMBT 40o-90o F (K=3.472)
Steady State Thrust Imbalance Envelopes 
PMBT 40o-90o F (K=3.472)
Thrust Time Traces
PMBT 40o-90o F (K=3.472)
Typical Steady State Thrust Imbalance  
PMBT 40o-90o F (K=3.472)
Typical Steady State Thrust Time Traces  
PMBT 40o-90o F
Steady State Thrust Imbalance Envelopes 
PMBT 90o F (K=3.472)
Steady State Thrust Imbalance Envelopes 
PMBT 90o F (K=3.472)
Summary
 Two legacy internal ballistics codes were coupled 
with a Monte Carlo analysis code to determine the 
thrust imbalance as a function of time during the 
ignition transient, steady state and tail-off for the 
SLS vehicle solid rocket boosters
 A MATLAB shell program was created to manage 
the input data, execution and graphical results of the 
analyses
 The predicted values for thrust imbalance versus 
time obtained from the Monte Carlo predictions 
agree well with the current NASA design 
specifications for the SLS boosters


A Monte Carlo Analysis of the Thrust Imbalance for the Space Launch System Booster During Both the Ignition Transient and Steady State Operation

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