Full text of DOI:10.2514/2.3827

JOURNAL OF SPACECRAFT AND ROCKETS
–
Vol. 39, No. 3, May June 2002
Numerical Analysis on Separation Dynamics
of Strap-On Boosters in the Atmosphere
Seongjin Choi,¤ Chongam Kim,† and Oh-Hyun Rho‡
Seoul National University, Seoul 151-742, Republic of Korea
and
Jeong-joo Park§
Korea Aerospace Research Institute, Yusung 305-606, Republic of Korea
A numerical technique for simulating the separation dynamics of strap-on boosters jettisoned in the dense
atmosphere is presented. Six-degree-of-freedom, rigid-body equations of motion are integrated into the three-
–
dimensional unsteady Navier Stokes solution procedure to determine the dynamic motions of strap-ons. An auto-
mated chimera overset grid technique is introduced to achieve maximumefŽ ciency for multibodydynamicmotion,
and a domaindivision technique is implemented in order to reduce the computationalcost required to Ž nd interpo-
lation pointsin the chimera grids. The  ow solver is validatedby comparingthe computed results around the Titan
IV launchvehiclewith experimentaldata.The completeanalysisprocess is then appliedto the H-II launchvehicle, a
major rocket in Japan’s space program, and the KSR-III soundingrocket, a three-stage vehicle being developed in
Korea. From the analysesseparation trajectories of strap-on boosters are predicted, and aerodynamiccharacteris-
tics around the vehicles at each time interval are examined. And separation-impulse devices, generally introduced
for safe separation of strap-ons, are properly modeled, and the guideline map of additional jettisoning force and
moment for safe separation is presented.
Nomenclature
the payload capabilities of rockets, and for the safe separation of
boosters without catastrophic collision the separation dynamics of
the spent strap-on bodiesfrom the parentrocketshouldbe analyzed
in detail. Many researchers have investigatedthis Ž eld numerically
or experimentally.Meakin and Suhs1 of NASA Ames analyzed the
c
ds
=
=
=
=
=
=
=
=
=
=
speed of sound, m/s
displacement vector, m
angular displacementvector, rad
 ux vectors
d
®
;
O
O O
E F G
;
(
)
N
solid rocket booster SRB separation of a space shuttle with a
F
resultant force vector, N
–
N
Navier Stokes solver. In his research, however, a prescribedtrajec-
Fx Fy Fz
F
;
;
scalar components of , N
N
tory was used for the dynamic analysis of body motion. Lochan and
Adimurthy2 attempted to analyze the separationdynamics of strap-
on boosters from the core rocket, but they used wind-tunnelsimula-
tion data for the measurement of aerodynamicforces. Lijewski and
Suhs3 developed an unsteady simulation technique for store sepa-
ration from a delta wing. In addition, with regard to vehicles with
strap-onboosters,PalmerandBuning4 analyzedthe owŽ eldaround
the Conestoga 1620 launch vehicle with six boosters. Similar anal-
yses were carriedout by Taylor et al.5 and Azevedoand Moraes6 for
the Titan IV with two boostersand for the AVLS launchvehiclewith
four boosters,respectively.Their studieswere, however,focusedon
steady-stateaerodynamic analyses without consideringthe relative
motion of boosters. In fact, only a few numerical investigations
seem to be reported, especially for the aerodynamic-dynamiccou-
pled analysis for the separation of strap-ons, although multistage
launch vehicles with boosters are widely used for many years.
Thus the present paper is focused on developing an efŽ cient
aerodynamic-dynamiccouplednumericalsolverto simulatebooster
separationdynamicsofmultistagevehicles.Six-degree-of-freedom,
rigid-body equations of motion are integrated into the three-
h
angular momentum vector
2
N
hx hy hz
h
¢
;
;
scalar components of , kg m /s
2
Ii j
¢
moment of inertia, kg m
N
M
resultant moment vector about
¢
mass center, N m
N
M
Mx My Mz
¢
;
;
=
=
=
=
=
=
=
=
scalar components of , N m
pressure, N/m2
p
O
Q
conservativevariable vector
velocity vector, m/s
N
v
°
½
speciŽ c heat ratio
density, kg/m3
N
¿
shear stress vector
angular velocity vector, rad/s
N
!
Introduction
HE accuratesimulationof separatedbodiesin the dense atmo-
sphere has been of great interest for several years. One major
applicationof thistechnologyis theseparationdynamicsof boosters
T
from the parent. The strap-on boosters have been used to increase
–
dimensionalunsteadyNavier Stokessolver.An automatedchimera
oversetgrid techniqueis introducedto achieve maximum efŽ ciency
for multibody dynamic motion, and a domain division technique is
implemented in order to reduce the computationalcost required to
Ž nd donor cells in the chimera grids. The developed  ow solver is
validated by comparing the computed results around the Titan IV
launch vehicle with experimental data. The complete analysis pro-
cess is then applied to two vehicle models of H-II and KSR-III.
H-II is a two-stage rocket with two solid strap-ons, which has been
a major rocket in Japan’s space program. KSR-III is a three-stage
soundingrocketwith two large strap-ons,which is now being devel-
oped in the Republic of Korea. The detailed geometry of vehicles
is described in the following section of this paper. From these anal-
yses trajectories of strap-on boosters during the separation stages
are predicted, and aerodynamic characteristicsaround the vehicles
Received 12 June 2001; revision received 26 September 2001; accepted
°c
for publication 28 September 2001. Copyright
2001 by the American
Institute of Aeronautics and Astronautics, Inc. All rights reserved. Copies
of this paper may be made for personal or internal use, on condition that the
copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc.,
222 Rosewood Drive, Danvers, MA 01923; include the code 0022-4650/02
$10.00 in correspondence with the CCC.
¤Doctoral Candidate, Department of Aerospace Engineering, San56-1
Shinlimdong.
†Assistant Professor, Department of Aerospace Engineering, San56-1
Shinlimdong.
‡Professor,Department ofAerospace Engineering,San56-1Shinlimdong.
Senior Member AIAA.
§Senior Researcher, Aerospace Research Group, 52 Eoundong.
439

440
CHOI ET AL.
at each time interval are examined. For safe separationof boosters,
some additional jettisoning forces and moments are generally in-
troduced by the separation-impulsedevices such as spring ejectors
or retrorockets. In this paper these separation-impulsedevices are
properly modeled, and the guideline map of additional jettisoning
force and moment for safe separation is presented.
on and aroundthe bodies. The obtainedaerodynamicforces includ-
ing gravity effect cause the relative motion of boosters. That is, the
trajectoryof boostersis predictedby the solutionsof six-degree-of-
freedom equations of motion with aerodynamic forces from a  ow
)
solver. The solution procedure is summarized as follows: 1 gen-
erate the overset grids around the bodies at the initial time level;
)
2 obtain the aerodynamicforces on the body surface from the  ow
Description of Vehicles
)
analysis routine; 3 convert the aerodynamic forces includinggrav-
ity and other additional control forces into the force and moment
components acting on the c.g. of the body; 4 solve the rigid-body
Both the H-II and the KSR-III investigated in the present paper
have symmetric conŽ gurations with two strap-on boosters, and the
details of the geometry are shown in Fig. 1. In the conŽ guration of
H-II, the strap-on boosters are much smaller than the core rocket in
diameter and length. However, the core and strap-ons of KSR-III
are aboutthe same size in order to employ the same rocketenginein
both components.Thus the interactionsbetweenthe core rocketand
boostersduringtheseparationstagesmightbeparticularlyimportant
in KSR-III. The nozzles of the rockets are not considered in actual
simulation assuming that their effects on the separation dynamics
are not critical. SpeciŽ cations of the weight of bodies, the positions
of centerof gravity,and separation-impulsedevicesfor two vehicles
are presentedin Table1. The corerockethas twoconnectorsforeach
booster, and the boosters are separated by the aerodynamic forces,
gravity, and additional jettisoning forces.
)
equations of motion, and get the new position and velocity com-
)
ponents of the body at a next time level; and 5 move the body
grids, and interpolate  ow information at fringe cells, and repeat
–
the unsteady analysis routine of 2 5.
Aerodynamic Analysis
Because the present vehicle does not contain massive  ow sepa-
rationregionsexceptthe base  ow regionwhoseeffectsare not con-
sidered in the present research, the three-dimensionalcompressible
–
thin-layerNavier Stokes equationsare adoptedfor an efŽ cient  ow
–
analysis. The thin-layer Navier Stokes equations can be written in
general curvilinear coordinates», ´, ³ as follows:
O
O
O
O
O
Q
E
F
G
G
@
@
@
@
1 @
v
( )
1
C
C
C
D
Re
@³
Numerical Methods
Solution Procedure
t
@
@»
@´
@³
where
To simulate the separation dynamics of bodies in compressible
 ow regime, it is necessary to understand the transient  owŽ elds
2
3
2
3
U
½
½
6
6
6
6
4
7
7
7
7
5
6
6
6
6
4
7
7
7
7
5
u
uU C x p
½
½
»
Table 1 Core rocket and booster characteristics
1
1
O
O
U C y p
Q D
½v
½w
e
E D
½v
»
;
Characteristic
H-II
KSR-III
J
J
U C z p
½w
»
c.g. of core rocket
c.g. of booster
Weight of core rocket
Weight of booster
20.60 m from base line
10.88 m from base line
120,000 kg
4.66 m from base line
3.42 m from base line
5,500 kg
e C p U ¡ t p
.
/
»
2
6
3
2
3
V
W
½
½
(
(
4,600 kg fuel free;
70,000 kg fuel free;
)
)
1,000 kg
11,000 kg
7
7
7
7
5
6
6
6
6
4
7
7
7
7
5
uV C x p
uW C x p
½
´
½
³
6
1
Location of ejector 1
Location of ejector 2
20.80 m from base line
4.00 m from base line
5.80 m from base line
1.00 m from base line
1
J
6
O
O
V C y p
W C y p
F D
½v
´
G D
½v
³
;
6
J
4
V C z p
W C z p
½w
´
½w
³
e C p V ¡ t p
e C p W ¡ t p
.
/
´
.
/
³
2
3
0
6
6
6
6
4
7
7
7
7
5
m1u C m2
³
³
³
x
1
O
m
C m2
Gv D
1v
³
y
J
m
C m2
1w
³
z
³
m m C m
u C
C
³yv ³w w/
.
2=3/.³
x
1
3
with
¡
¢
¡
¢
2
x
2
y
2
z
m D
C
C
m D
u C
C
¹ ³
³
³
.
;
¹ ³
³y v
³z w
³
1
2
x
³
³
c2
¹
¹ .
/
³
2
2
m3 D
u2 C
C
C
v
w /
³
Pr
¡
2
°
1
)
a H-II
U V W
are contravariant velocity components, which can be
and
;
;
written as
U D u C
C
V D u C
C
´y v ´z w
»
»y v »z w;
´
x
x
W D u C
C
³yv ³z w
³
x
( )
In Eq. 1 the viscousterms involvingvelocitygradientsin both»,
´ directionsare neglectedand in the normaldirection³ are collected
O
G
into the vector v. Turbulent viscous componentsare evaluatedus-
7
–
ing the Baldwin Lomax algebraic turbulence model with a modi-
8
–
Ž ed Degani Schiff technique.
For the temporal discretization of unsteady  owŽ eld, dual time
stepping is employed to obtain a second-orderaccuracy:
n C 1;s C 1
n
n ¡ 1
O
O
Q
O O
¡ Q C Q
)
b KSR-III
Q
@
3
4
n C 1;s C 1
O
( )
2
D ¡R
¡
t
21
Fig. 1 Geometry.
@¿

CHOI ET AL.
441
where
Because the moments and products of inertia of the body would
change continually as a result of its rotation, it is necessary to de-
termine their values as functions of time. It, therefore, is more con-
O
O
O
O
E
F
G ¡ G
@
@
@.
/
v
O
R D
C
C
xyz
venient to use the coordinates
attached to the rotating booster
@»
@´
@³
as shown in Fig. 2, which ensures that its moments and products of
inertia maintain the same values during the motion. Then, the mo-
n
( )
s
Here ¿ representsa pseudotime, is the physicaltime level,and is
the pseudo time level. Equation 2 is discretized in pseudotime by
xyz
ment equations relative to the moving coordinate system
with
the Euler implicit method and is linearized using the  ux Jacobian.
This leads to a large systemof linear equationsin delta form at each
pseudo time step as
N
an angular velocity ! become
³
´
N
h
d
N
N
( )
7
Mcg
D
C N £ h
!
³
µ
¶
´
t
d
I
R
I
1:5
xyz
@
@
C
C
J t
1
Q
1
J
Q
1¿
xyz
Because the
axes coincide with the principal axes of inertia of
the rotating body, the angular momentum can be simpliŽ ed as
N
h
Qn C 1;s
¡
Qn C Qn ¡ 1
3
4
D ¡Rn C 1;s
¡
( )
3
( )
8
hx
D
x Ixx
h D y Iyy
h D z Izz
!
;
!
;
!
J
t
2 1
y
z
9
–
–
The lower upper symmetric Gauss Seidel scheme is used as
Then the moment equations of motion are expressed as
( )
the implicit time-integration method of Eq. 3 . The viscous  ux
Jacobian is neglected in the implicit part because it does not in u-
ence a solution accuracy, and local time stepping is used.
Mx D Ixx P ¡ I ¡ I
!
.
zz/!y !z
xx /!z !x
yy /!x !y
x
yy
(
C
As a spatial discretization,AUSMPW modiŽ ed advection up-
My D Iyy P ¡ I ¡ I
!
.
y
zz
10
)
stream splitting method press-based weight function has been
C
( )
9
applied.AUSMPW is designedto remove the nonmonotonepres-
Mz D Izz P ¡ I ¡ I
!
.
z
xx
sure solutions of the hybrid  ux-splitting schemes such as AUSM
which are usually referred to as the Euler’s equations of motion.
( )
C
and AUSM by introducingpressure weighting functionsas a lim-
iter at a cell interface.
With the force relation of Eq. 4 in scalar form,
F D m P F D m P F D m P
For a higher-order spatial accuracy the monotone upstream-
centered schemes for conservation laws11 approach is used. Primi-
tive variables are extrapolated at a cell interface, and the differen-
tiable limiter12 is employedto suppressunphysicaloscillationsnear
physical discontinuities.
(
)
10
vx ; vy; vz
z
x
y
( )
(
)
Equations 9 and 10 form a system of six differential equations
and have a unique solution if initial conditionsare given.
For the calculation of the equations of motion, the force equa-
(
)
directly,
XYZ
tionsare discretizedin the inertialcoordinatesystem
whereasmoment equationsare solvedin the movingcoordinatesys-
Dynamic Analysis
The basic equations of rigid-body motion with respect to the
(
)
. After computingthe forcesand momentsthe new velocity
xyz
tem
N
v
( )
attachedto the corerocket Fig. 2 are expressedas
XYZ
coordinates
n C 1
dsn C 1
and displacement
are obtained by
³
´
³
´
N
N
h
dv
d
n C 1
n
N
Fcg
N
N
¡ N
v
v
1
m
1
( )
4
D
m
Mcg
D
;
n
n
n C 1
v /1
dsn C 1
D
N C N
.v
2
t
N
F
( )
11
D
;
t
t
d
d
XYZ
XYZ
t
1
n C 1
and the new angular momentum !
N
( )
is calculated from Eq. 9 as
N
N h
In these equations v; are velocity and angular momentum vector
N
N
F
cg
Mcg
are external
with respect to center of mass of the body,
,
n C 1
n
x
¡
!
!
1
force and moment vectoracting on the c.g. of the body, and they are
representedas follows:
x
D
D
D
M C I ¡ I
[
[
.
zz /!y!z ]
xx /!z !x ]
yy /!x !y ]
x
yy
t
Ixx
1
n C 1
n
y
N
N
N
N
N
N
N
N
( )
5
Fcg D Fad C Fgv C Fct
Mcg D rN £ Fad C Fgv C Fct
;
.
/
¡
!
!
0
1
Iyy
y
M C I ¡ I
.
y
zz
t
1
N
N
F
F
ct representgravityand additionalcontrolforces and the
Here
,
gv
aerodynamic forces
n C 1
n
z
¡
!
!
1
Izz
z
(
(
)
)
M C I ¡ I
[
.
12
13
Z
z
xx
t
1
N
Fad
( )
6
D
¡pnO C N
¿/ d
S
.
Finally the angular displacementis updated as
s
n C 1
1
n
n C 1
/1
d
D
N
C N
!
t
®
2 .!
From the preceding dynamic analysis the new position and ve-
locity components at a next time level are determined.
Grid Scheme
With moving body problems it is essential to have the initial
grid distribution strictly adjusted to the motion of bodies. In this
regard, unstructuredgrid techniquesand oversetgrid techniquesare
known to be the most pertinent ones. Although the unstructured
grid technique has a good  exibility in generating grids around
complex geometry, all grids close to bodies should be carefully
regenerated for any motion of bodies to maintain the quality of
initial grids. The chimera overset grid technique can maintain high
grid quality only by rotating or translating initial grids in those
movingproblems.Thus thechimeraoversetgridtechniqueproposed
by Steger et al.13 is adopted in the present paper. For the efŽ cient
communicationof conservativevariableson the oversetregions,the
trilinear interpolation technique is introduced, and this is based on
Fig. 2 Reference frames.

442
CHOI ET AL.
Table 2 Nondimensionalaerodynamicforces
and moment in the initial stage of separation
Vehicle
Cx
Cz
Cm
H-II
KSR-III
0.1161
0.5709
0.0006
0.0070
0.0065
¡0.0577
)
a Initial stage
(
Fig. 4 Pressure contours around Titan IV launch vehicle Mach = 1.6,
angle of attack = 0 deg .
)
)
b Moving stage
Fig. 3 Grid system.
–
the Newton Raphson method in isoparametric coordinates. If any
of the eight donor cells exists inside the hole region, the nearest
cell around the donor in nonhole region is used as substitutes.With
the trilinear interpolationit is very important to ensure that the grid
distributionsof the common, overlappingvolume are not drastically
different.Radicaldifferencescanleadtopoorinterpolationresults.14
Poor interpolationcan in turn lead to increasedcomputationaltime
as a result of poor solution convergence. Therefore, in the present
paper grid distributions of the overlapping volume are carefully
treated to have good similarity.
Fig. 5 Comparison of computed surface pressure with wind-tunnel
data along the centerline of the core rocket .
(
)
In three-dimensionalproblemit generallytakes much time to Ž nd
the donor cells in the whole grid region. Especially for unsteady
problems, this search should be repeated at every time interval, and
it takes a considerableportionof the whole computationtime. In the
presentpaper, in order to reducethe searchingtime of donor cells in
target domain, a simple domain division techniqueis introduced.In
this technique, prior to Ž nding the donor cells the target domain is
dividedinto a number of subdomains.The subdomainincludingthe
fringe cell is then predeterminedby simple comparison of position
coordinates. This allows even faster searching in the determined
subdomain. The core rocket grid and the booster grid generated by
GridgenV.13 are shownin Fig. 3a.One of the movinggridsis shown
in Fig. 3b.
Fig. 6 Directions of nondimensional aerodynamic
forces and moment.
Results and Discussion
Flow Solver Validation
Separation Dynamics of H-II
In this section the aerodynamic characteristics around the H-II
vehicle at the initial stage of separationare Ž rst examined, and then
simulationsofseparationdynamicsare presentedbasedon theinitial
As a validation of the developed  ow solver, which directly in-
 uences the trajectoryof vehicles, wind-tunneldata of the Titan IV
launch vehicle are used.5 The freestream Mach number is 1.6, and
stage results. The freestreamMach number is 2.0, and the Reynolds
7
6
£
£
£
£
the Reynolds number is 1.1 10 with zero angle of attack. For
number is 9.0047 10 , and 101 66 121 grid points are used
£
£
£
£
the grid system overset grids of 101 66 121 points for the core
for the core rocket and 51 66 101 for the booster.
Directionsofthenondimensionalaxialforce , thenormalforce
£
£
Cx
rocket and 81 66 101 for the booster are used. Figure 4 shows
the cross-sectional pressure contour of the Titan IV vehicle and
Fig. 5 for the calculatedsurface pressure along the centerlineof the
vehicle compared with experimental wind-tunnel data. The close
agreement between experimental and computed values can be ob-
servedin most regionsexceptthe connectingpointof the corerocket
and booster, where the computed values are a little underestimated
because of the effect of a connectingcable in the wind-tunneltest.5
Cz
Cm
, andthe pitchingmoment
actingon thesurfaceof thebooster
are deŽ ned as shown in Fig. 6. Pressure contours on and around the
vehicle are shown in Fig. 7, and the nondimensional forces and
Cx
moment are presentedin Table 2. At the initial stage
and producesthe downward motion of boostermainly becauseof its
Cz Cm
are also positive values and makes the outward
is positive
weight.
and
positive pitching motion of booster.

CHOI ET AL.
443
6
(
)
.
Fig. 7a Pressure contours around the H-II initial stage, Mach = 2.0, Re = 9.0047 £ 10
Fig. 7b Pressure contours on the
(
surface of the H-II initial stage,
Mach = 2.0, Re = 9.0047 £ 106
.
)
(
Fig. 9 Booster trajectory of H-II with pressure contours nondimen-
)
sional jettisoning force = 0.060, jettisoning moment= 0.030 .
Separationdynamicsof strap-onboosters is then simulated at the
physical time step of 0.005 s. In this simulation the chimera overset
moving grid scheme is used with the domain division technique.
First, free body separation is simulated where the booster is simply
released from the core rocket. From the design of H-II, the initial
distance between the core rocket and booster is set to 0.4 m. As
predicted from the initial stage analysis, the booster falls vertically
with a small positive pitching motion as time evolves. In Fig. 8 the
trajectory of booster and corresponding pressure contours around
the bodies are shown at every 0.1 s after separation.In this simula-
tion the booster seems to be quite close to the core rocket during all
of the stages. Thus it would be better to introduce some additional
jettisoning forces and moments using separation-impulsedevices.
The H-II uses the spring ejection systems as separation-impulse
devices, and in the present paper their effects are replaced by the
impact normal forces of different magnitude acting at the two con-
necting points for initial 0.005 s. Then a forced separation case is
simulated with the nondimensional jettisoning force of 0.060 and
moment of0.030.Figure9 showsthe boostertrajectoryand pressure
(
Fig. 8 Booster trajectory of H-II with pressure contours free separa-
tion, no jettisoning force and moment .
)

444
CHOI ET AL.
6
(
)
.
Fig. 10a Pressure contours around the KSR-III initial stage, Mach = 2.0, Re = 9.0047 £ 10
Fig. 10b Pressure contours
on the surface of the KSR-III
(
initial stage, Mach = 2.0, Re =
9.0047 £ 106
.
)
Fig. 11 Attitude deŽ nitions of booster.
(
Fig. 12 Pressure contours at various distances of booster Mach = 2.0,
)
Re = 9.0047 £ 106
.
contouraround the vehicle in this simulation,and a safer separation
is expected.
This adverseaerodynamicfeatureseems to be fromthe expansion
waves of the core rocket. Concerning this matter, some additional
aerodynamic characteristics are examined at various attitudes of
booster. As shown in Fig. 11, attitudes of booster are represented
by two factors: the distance from the core rocket and the nose angle
with respectto the core rocket. In Figs. 12 and 13 pressure contours
around the vehicles at different distances and different nose angles
are shown, respectively. In Fig. 14a the nondimensional aerody-
namic forces and moment acting on the surface of booster are com-
Separation Dynamics of KSR-III
In the same manner the aerodynamic characteristicsof KSR-III
at the initial stage of separation are examined, and the results are
compared with those of H-II. Because the boosters are located near
the nose/cylinderexpansionregionof the coreatthe initialstage,the
 owŽ eld characteristicsof KSR-III are more complex. Thus some
additional investigationsare added to analyze the effects of expan-
sion waves of the core on the booster. And at last, based on the re-
Cm
pared at various distances. In this Ž gure variation of
is most
remarkable, and it changes from a negative to positive value as the
distance increases. Similarly in Fig. 14b, the aerodynamic forces
Cz Cm
sults, simulationsof separationdynamicsare presented.Freestream
6
£
Mach number is 2.0, and the Reynolds number is 9.0047 10 .
are compared at variousnose angles.
,
are both increasingas
£
£
£
£
Cx
A 101 66 121 grid is used for the core rocketand 81 66 101
the nose angle increases, but
is nearly constant in all cases. The
Cz Cm
for the booster.
behaviors of
,
are believed to be caused by the expansion
In Fig. 10 pressurecontourson and aroundthe vehicleattheinitial
stage are shown. The aerodynamicforcesand moment are presented
in Table 2. Comparing these aerodynamiccharacteristicswith those
waves of the core rocket striking the nose of booster. From these
resultsitmight be saidthatan offsetdistanceand positivenose angle
of booster at the initial stage of separation are advantageousfor an
easy separation.
Cm
of H-II, an interesting feature is found. The pitching moment
is a negative value, which is opposite to the result of H-II. Thus the
booster trajectory of KSR-III in the separationstages might be also
quite different from that of H-II.
Based on theprecedingaerodynamicresults,separationdynamics
of KSR-III is simulated at the physical time step of 0.005 s. In
Fig. 15 thetrajectoryofboosterandcorrespondingpressurecontours

CHOI ET AL.
445
(
Fig. 15 Booster trajectory of KSR-III with pressure contours free
separation, no jettisoning force and moment .
)
(
Fig. 13 Pressure contours at various nose angles of booster Mach =
2.0, Re = 9.0047 £ 106
.
)
Fig. 14a Aerodynamic forces and moment at various distances of
booster.
(
Fig. 16 Booster trajectory of KSR-III with pressure contours nondi-
mensional jettisoning moment= 0.356 .
)
Fig. 14b Aerodynamic forces and moment at various nose angles of
booster.
Figure 16 shows the booster trajectory and pressure contour
around the vehiclewhen the nondimensionaljettisoningmoment of
0.356 acts on the booster. In this case the booster hits the downside
of the core rocket after 0.4 s of its separation as a result of exces-
sive jettisoningmoment. This result suggests that some restrictions
of jettisoning moments are desired to avoid collision. Numerous
forced separation cases were simulated with various combination
of jettisoning forces and moments. Figure 17 shows the map of jet-
tisoning forces and moments necessary for the safe separation of
aroundthe bodiesareshownatevery0.1s afterfreebodyseparation.
From the design of KSR-III, the initial distance between the core
rocketand boosteris set to 0.15 m. The boosterfalls with a negative
pitchingmotion.Because this slightnegativepitchingmotionmight
increase the negative pitching moment of the booster as mentioned
in the preceding attitude analyses, the upside collision is inevitable
during the separation stages. Thus additional jettisoningforces and
moments are necessary for a safe separation of booster.

446
CHOI ET AL.
an example of safe separationwhen the nondimensionaljettisoning
force of 0.475 and moment of 0.238 act on the booster.
Conclusions
An efŽ cient three-dimensional aerodynamic-dynamic coupled
code is developed to simulate the separation dynamics of strap-on
boosters in the dense atmosphere. The chimera overset grid tech-
nique is used for the multibody dynamic motion, and a domain
division technique is implemented in order to reduce the computa-
tional cost requiredto Ž nd interpolationpointsin the chimera grids.
The trajectories of the separated boosters are then predicted for the
H-II launchvehicleand the KSR-III soundingrocket.From the anal-
yses it is observed that vehicles with large strap-ons can produce
more complex  owŽ eld characteristics.Collisionsof bodies during
the separation stages might result if the attitudes of boosters are
not properly controlled. A guideline map of jettisoning force and
moment guaranteeing the safe separation has been generated for
the KSR-III using the computational approach, demonstrating the
utility of the technique.
Acknowledgments
Fig. 17 Guideline map of jettisoning force and moment for KSR-III.
The authors would like to thank the Korea Aerospace Research
Institute and the Brain Korea 21 Project for Ž nancial support.
References
1Meakin, R. L., and Suhs, N. E., “Unsteady Aerodynamic Simulation of
Multiple Bodies in Relative Motion,” AIAA Paper 89-1996, June 1989.
2Lochan, R., and Adimurthy, V., “Separation Dynamics of Strap-On
Boosters in the Atmosphere,” Journal of Guidance, Control, and Dynamics,
–
Vol. 20, No. 4, 1997, pp. 633 639.
3Lijewski, L. E., and Suhs, N. E., “Time-Accurate Computational Fluid
Dynamics Approach to Transonic Store Separation Trajectory Prediction,”
–
Journal of Aircraft, Vol. 31, No. 4, 1994, pp. 521 526.
4Palmer, G., andBuning,P.,“Three-DimensionalComputationalAnalysis
of Complex Launch Vehicle ConŽ gurations,” Journal of Spacecraft and
–
Rockets, Vol. 33, No. 1, 1996, pp. 49 53.
5Taylor,S.,and Wang,J. C. T.,“Launch-Vehicle SimulationsUsinga Con-
–
current, Implicit Navier Stokes Solver,” Journal of Spacecraft and Rockets,
–
Vol. 33, No. 5, 1996, pp. 601 606.
6Azevedo, J. L. F., and Moraes, P., Jr., “Code Validation for High-Speed
Flow Simulation Over Satellite Launch Vehicle,” Journal of Spacecraft and
–
Rockets, Vol. 33, No. 1, 1996, pp. 15 21.
7Baldwin, B. S., and Lomax, H., “Thin Layer Approximation and Al-
gebraic Model for Separated Turbulent Flows,” AIAA Paper 78-257, Jan.
1978.
8Degani, D., and Schiff, L. B., “Computation of Turbulence Supersonic
Flows Around Pointed Bodies Having Cross ow Separation,” Journal of
–
Computational Physics, Vol. 66, No. 1, 1986, pp. 173 196.
9
–
Yoon, S., and Jameson, A., “Lower-Upper Symmetric Gauss-Seidel
Method for the Euler and Navier Stokes Equations,” AIAA Journal, Vol. 26,
–
1988, pp. 1025, 1026.
No. 9,
10Kim, K. H., Kim, C., and Rho, O. H., “Accurate Computations of Hy-
personic Flows Using AUSMPWC Scheme and Shock-Aligned-GridTech-
nique,” AIAA Paper 98-2442, Jan. 1998.
11Van Leer, B., “Towards the Ultimate Conservative Difference Scheme.
V. A Second Order Sequel to Godunov’s Methods,” Journal of Computa-
–
tional Physics, Vol. 32, No. 2, 1979, pp. 101 136.
(
Fig. 18 Booster trajectory of KSR-III with pressure contours nondi-
12Anderson, W. K., Thomas, J. L., and Van Leer, B., “Comparison of
FiniteVolumeFluxVector SplittingsfortheEulerEquations,”AIAA Journal,
)
mensional jettisoning force = 0.475, jettisoning moment= 0.238 .
–
Vol. 24, No. 9, 1986, pp. 1453 1460.
13Steger, J. L., Dougherty, F. C., and Benek, J. A., “A Chimera Grid
Scheme,” Advances in Grid Generation, FED Vol. 5, edited by K. N. Ghia,
the booster obtained from the computations. Region A represents
the upside collision zone where the upside of booster hits the core
during the separation stages by the negative aerodynamic pitching
moment. In this regioncollisionoccurseven with a large jettisoning
force becausethe jettisoningmoment is not enoughto overcomethe
negative pitching motion of booster.Region B representsthe down-
side collision zone where the excessive jettisoning moment causes
too large positive pitching motion of the booster. Figure 18 shows
–
American Society of Mechanical Engineers, New York, 1983, pp. 59 69.
14Meakin, R. L., “On the Spatial and Temporal Accuracy of Overset Grid
Methods for Moving Body Problem,” AIAA Paper 94-1925, June 1994.
P. Weinacht
Associate Editor