10
Scientific Technical Review, 2013,Vol.63,No.1,pp.10-16
UDK: 620.178:623.463.5
COSATI: 20-04, 16-02, 16-04
Numerical Simulations of Store SeparationTrajectories Using the
EGLIN Test
Yunus Emre Sunay1)
Emrah G��lay1)
Ali Akg��l1)
One of the most important topics for missile development projects is safe separation of the missile from air vehicles. Store
separation tests are expensive, time consuming and dangerous since tests can end up with fatal accidents; therefore, safe
separation simulations and missile trajectory predictions by using numerical methods became a critical issue. In this
study, the EGLIN test case is used to validate the predicted trajectory of a store separated from a wing. The EGLIN test
case is a generic store separation test case and most commonly used in the validation of trajectory prediction tools. the
experiments were performed in the transonic (M=0.95) and supersonic (M=1.2) flow regimes. The EGLIN store
separation test case is simulated by using the time-dependent Computational Fluid Dynamic (CFD) analysis. Coupled six
degree of freedom (6DOF) and flow solvers are used to predict the store trajectory. In addition, Navier-Stokes and Euler
computations are performed to investigate the viscous effects on the store trajectory analysis.
Key words:
computational fluid dynamics, numerical simulation, Navier-Stokes equations, air missile, store trajectory,
store separation, EGLIN test.
1) ROKETSAN Missile Industries Inc., P.K.30: 06780 Elmadağ-Ankara,TŰRIKYE
Notation and symbols
��
– Roll angle
��
– Pitch angle
��
– Yaw angle
Cp
– Pressure coefficient
Introduction
AFE separation of operational or newly designed
missiles from air vehicles is a critical issue in terms of
missile integration process. Detailed engineering analyses,
wind tunnel and flight tests are needed to be performed.
In the view of recent developments in computational
methods, the numerical analysis can replace flight and wind
tunnel tests in some cases for certification processes. Even
validated computational methods can be used to complete a
safe separation process. This will result in a cost and time
effective integration study. In this paper, the EGLIN test
case is used to validate an engineering approach to simulate
store separation at transonic and supersonic speeds [1,4].
The analysis results are compared with the experimental
values.
CFD Modeling & Simulation
In this part, CFD modeling and the simulation of an
EGLIN test case model will be explained. GAMBIT
(v2.4.6) and TGRID (v5.0.6) are used to generate
computational grids for a CFD analysis. Also, the FLUENT
commercial program (v12.0.16) is used as a solver. The
sign convention, the test case model, the computational
grids and the results of the analysis will be explained in
detail in the following sections [8,9].
Test Model Sign Convention
A generic EGLIN test model is used in the validation of
the CFD analysis. The test was conducted at the Arnold
Engineering Development Center in the Aerodynamic
Wind Tunnel (4T) in 1990. The EGLIN test model has
three parts; wing, pylon and finned body. The sketch of the
EGLIN test case model and the sting used in the wind
tunnel test are represented in Fig.1 [5].
The wing consisted of a clipped delta wing with 45��
sweep and a constant NACA 64A010 airfoil section. The
pylon has an ogive-flat plate-ogive cross section shape. The
store body was an ogive-cylinder-ogive with an aft
cylindrical sting. The fins on the store consisted of a
clipped delta wing with a 45�� sweep and a constant NACA
0008 airfoil section. The gap between the pylon and the
finned body is 0.1778 cm. The geometric specifications of
the body are represented in Fig.2.
S
SUNAY,Y.E. etc: NUMERICAL SIMULATIONS OF STORE SEPARATIONTRAJECTORIES USING THE EGLIN TEST
11
Figure 1. Sketch of the EGLIN test case
Figure 2. Geometric specifications of the EGLIN test case
Experimental Data
The experiments were conducted in transonic (M=0.95)
and supersonic (M=1.2) flow regimes. The position and the
orientation of the store are obtained during the test for both
flow regimes. The surface pressure distribution on the
model is only available for the transonic flow regime.
The sign convention used for the calculation of the
computational fluid dynamics simulations and experiments
is given in Fig.3.
Figure 3. Model and sign convention
In the test, aft and forward ejector forces are applied to the
store to provide safe separation. The store inertial/mass
parameters and ejector parameters are given in Table 1 [3].
Table 1. Store inertial/mass and ejector parameters
Mass
907 kg
Center of Mass
1417mm (aft of store nose)
Roll moment of inertial
27 kg.m2
Pitch moment of inertial
488 kg.m2
Yaw moment of inertial
488 kg.m2
Forward ejector location
1237.5mm (aft of store nose)
Aft ejector location
1746.5mm (aft of store nose)
Forward ejector force
10.7kN
Aft ejector force
42.7kN
Solid Model & Computational Mesh
The EGLIN geometry was generated for CFD studies
based on a test model used in the Arnold Engineering
Development Center in the Aerodynamic Wind Tunnel.
The geometry consists of three different parts; wing, pylon
and store. The generated solid models are shown in Fig.4.
Figure 4. Solid model of the EGLIN test case.
12
SUNAY,Y.E. etc: NUMERICAL SIMULATIONS OF STORE SEPARATIONTRAJECTORIES USING THE EGLIN TEST
The initially generated grid for Euler computations has
2,112,822 cells. Deformed computational grids at different
time steps are given in Fig.5.
Figure 5. Computational grids for the CFD analysis using Euler equations
at different time steps
The initial generated grid for the Navier-Stokes analysis
has 3,412,792 cells and is shown in Fig.6.
Figure 6. Computational grid for the CFD analysis using the NS equation
(t=0sec)
The deformed computational grid for the Navier-Stokes
analysis at the 0.2 seconds of the analysis is given in Fig.7.
The boundary layer part of the computational grid for the
Navier-Stokes analysis is not deformed during the solution.
Figure 7. Computational grid for the CFD analysis using the NS equation
(
t=0.2sec)
The computational domain inlet was located at 17 wing
length, outlet was located at 25 wing length, upper
boundary was located at 17 wing length, lower boundary
was located at 25 wing length and side boundary was
located at 17 model length away from the center of the
store. The solution domain is shown in Fig.8.
Figure 8. Solution domain and a part of the EGLIN test model
Flow Solver and Boundary Condition
The FLUENT commercial flow solver was used to
predict the trajectory of the EGLIN test model by using
Euler and Navier-Strokes Equations.
Euler
The implicit, compressible, unstructured-mesh solver
was used. The three-dimensional, Euler equations were
solved using the finite volume method [6,7]:
V
V
WdV
F dA
HdV
t
∂
+
⋅
=
∂ ��
��
��
v
(1)
where
SUNAY,Y.E. etc: NUMERICAL SIMULATIONS OF STORE SEPARATIONTRAJECTORIES USING THE EGLIN TEST
13
,
u
u pi
W
v F
v pj
w
w pk
E
E p
��
�Ѧ�
��
�Ѧ�
��
�Ѧ�
��
�Ѧ�
��
�Ѧ�
��
⎧
⎫
⎧
⎫
⎪
⎪
⎪
⎪
+
⎪
⎪
⎪
⎪
=
=
+
⎨
⎬
⎨
⎬
⎪
⎪
⎪
⎪
+
⎪
⎪
⎪
⎪
+
⎩
⎭
⎩
⎭
(2)
The calculations took about 3 seconds of the CPU time
per iteration and convergence was achieved in about 1,800
iterations for the steady part of the solution [10].
Navier-Stokes Equation
The three-dimensional, Reynolds-Average Navier-
Stokes (RANS) equations were solved using the finite
volume method [6,7]:
[
]
V
V
WdV
F G dA
HdV
t
∂
+
−
⋅
=
∂ ��
��
��
v
(3)
where
0
,
,
xi
yi
zi
ij j
u
u pi
W
v F
v pj G
w
w pk
E
E p
q
��
�Ѧ�
��
�Ѧ�
��
��
�Ѧ�
��
��
�Ѧ�
��
��
�Ѧ�
��
�� ��
⎧
⎫
⎧
⎫
⎧
⎫
⎪
⎪
⎪
⎪
⎪
⎪
+
⎪
⎪
⎪
⎪
⎪
⎪
=
=
+
=
⎨
⎬
⎨
⎬
⎨
⎬
⎪
⎪
⎪
⎪
⎪
⎪
+
⎪
⎪
⎪
⎪
⎪
⎪
+
+
⎩
⎭
⎩
⎭
⎩
⎭
(4)
The boundary conditions are represented in Fig.8.
Downstream, upstream, and all-side boundaries, except the
right-side one, were set as far field (characteristics-based
inflow/outflow), with a standard atmosphere model for 26,000
ft altitude temperature and pressure free stream conditions. The
right-side boundary was defined as symmetric. Solid surfaces
were modeled as no-slip, adiabatic wall boundary conditions
for the Navier-Stokes analysis [3, 10].
The calculations took about 9 s of the CPU time per
iteration and convergence was achieved in about 1,800
iterations for the steady part of the solution. The time step is
0.001 sec and 20 iterations were done for each time step.
In this simulation, Fluent uses an implicit, node-based
finite volume scheme. Roe��s flux difference splitting scheme
is used to compute inviscid fluxes at the boundary of each
control volume for the Navier-Stokes analysis and viscid
fluxes at the boundary of each control volume for the Euler
analysis. A second-order accurate, upwind extrapolation is
used to determine the values of the flow variables at the
boundary. The
k-�� model was designed especially for
aerospace applications involving wall-bounded flows and has
been shown to give good results for boundary layers
subjected to adverse pressure gradients. Turbulence modeling
is achieved by using the wall treatment
k-�� two-equation
turbulence model which is suitable for
y+=1. The first height
of the boundary layer of the computational grid was
determined according to
y+=1. The
y+ values on the wing-
pylon and the store are given in Fig.9.
Figure 9.
y+ on the wing-pylon and the store
Convergence was determined by tracking the change in
the flow residuals and the aerodynamic coefficients during
the solution. The solution was deemed converged when the
aerodynamic coefficients with respect to the time step had
the same frequency and wave length in the solution time.
Fig.10 shows residual changes with respect to iteration for
the unsteady solution for the Navier-Stokes analysis.
Figure 10. Residual versus iteration for the unsteady solution
Mesh Deformation Method
As the store starts to move due to gravity and
aerodynamic forces acting on the body, the position of the
store has to be changed on the mesh. If the displacements of
nodes are large compared to the local cell sizes, cells can
become degenerated. This will invalidate the mesh (e.g.,
result in negative cell volumes) and, consequently, lead to
convergence problems. By checking the mesh quality,
degenerated cells have to be smoothed or new cells have to
be generated. Up to some quality criteria, skew cells are
smoothed by the spring analogy method. If the quality of
cells exceeds the predefined limit, the mesh has to be
updated. Bad quality cells are replaced by created new cells
using the re-meshing method. These two methods are
explained briefly in the following sections [6,7].
Spring Analogy
In the spring-based smoothing method, the edges
between any two mesh nodes are idealized as a network of
interconnected springs. The initial spacing of the edges
before any boundary motion constitutes the equilibrium
state of the mesh. A displacement at a given boundary node
will generate a force proportional to the displacement along
all the springs connected to the node. Using Hook��s Law,
the force on a mesh node can be written as
(
)
in
i
ij
i
j
j
F
k
x
x
= ��
�� − ��
G
G
G
(5)
where
i
x
��
G and
j
x
��
G are the displacements of the node i and its
neighbor node
j,
ni is the number of neighboring nodes
connected to the node
i, and
kij is the spring constant
between the node
i and its neighbor
j. The spring constant
for the edge connecting the nodes i and j is defined as
1
ij
i
j
k
x
x
=
−
G
G
(6)
14
SUNAY,Y.E. etc: NUMERICAL SIMULATIONS OF STORE SEPARATIONTRAJECTORIES USING THE EGLIN TEST
At equilibrium, the net force on a node due to all the
springs connected to the node must be zero. This condition
results in an iterative equation such that
1
i
i
n
m
ij
i
j
m
i
n
ij
j
k x
x
k
+
��
��
��
=
��
G
G
(7)
Since displacements are known at the boundaries (after
the boundary node positions have been updated), Eq.7 is
solved using a Jacobi sweep on all interior nodes. At
convergence, the positions are updated such that
,
1
m converged
n
n
i
i
i
x
x
x
+ =
+ ��
G
G
G
(8)
where
n+1 and n are used to denote the positions at the next
time step and the current time step, respectively [6-7].
Re-meshing
In the re-meshing method, cells are marked based on cell
skewness, minimum and maximum length scales as well as
an optional sizing function. Each cell is evaluated and is
marked for re-meshing if it meets one or more of the prede-
fined criteria. If the cell skewness is greater than a specified
maximum skewness, or the cell length scale is smaller than
a specified minimum length scale, or the cell size is larger
than a specified maximum length scale, marked cells are
deleted and new cells are created [6,7].
Results
The experimental and numerical results are compared
and presented in this part of the report.
Transonic Flow
Time-dependent CFD analyses were performed for Mach
number 0.95 during 0.45 seconds. The experimental store
position and orientation data are compared with the CFD
analyses results in Fig.11 and 12, respectively.
Figure 11. Trajectory of the center of gravity locations
Figure 12. Trajectory of the angular orientation
The pressure distribution along the store body at the
cross section by ��=5º with vertical axes for different time
steps is shown in Figs. 13-15.
Figure 13. Pressure distribution of the store (
t=0sec)
Figure 14. Pressure distribution of the store (
t=0.17sec)
Figure 15. Pressure distribution of the store (
t=0.32sec)
The experimental and numerical store position and
orientation values are compared in Fig.16.
Figure 16. Position of the store w.r.t. time (M=0.95)
Supersonic Flow
The time-dependent CFD analyses for the supersonic
store separation test case at Mach number 1.2 were
performed for 0.8 seconds. The experimental store position
SUNAY,Y.E. etc: NUMERICAL SIMULATIONS OF STORE SEPARATIONTRAJECTORIES USING THE EGLIN TEST
15
and orientation data are compared with the CFD analyses
results in Fig.17 and 18, respectively.
Figure 17. Trajectory of the center of gravity locations
Figure 18. Trajectory of the angular orientation
The experimental and numerical store position and
orientation values are compared in Fig.19.
Figure 19. Position of the store w.r.t. time (M=1.2)
Conclusions
In this study, an engineering approach for store
separation is studied by using a well-known generic store
separation EGLIN test case. The store trajectory and
orientation are predicted by using coupled 6DOF and
Euler/Navier-Stokes equations. Grid deformation
techniques and re-meshing algorithms are used to obtain a
grid for the next time step. The Euler and Navier-Stokes
results are compared with the experimental data and a good
agreement is obtained. It can be concluded that the viscous
effects have negligible influence on the results of this type
of problems. Hence, the presented engineering approach
can be used in the trajectory prediction of real store
separation problems.
Acknowledgments
The authors thank ROKETSAN from Ankara for their
support in the study of the problem of missile separation
from the aircraft wing.
References
[1]
PARIKH,P., PIRZADEH,S.:
Unstructured Grid Solution to a
Wing/Pylon/Store Configuration, Journal of Aircraft, 31(6) (1994)
[2]
LEE,J.M.:
Studies of Combined Use of CFD and Wind Tunnel Test
Approaches to Simulate a Store Separation form F-15E Using
Efficient CFD Database Generation, 22nd Applied Aerodynamics
Conference and Exhibit, AIAA 2004-4724
[3]
PANAGIOTOPOULOS,E.E., KYPARISSIS,S.D.:
CFD Transonic
Store Separation Trajectory Prediction with Comparison to Wind
Tunnel Investigations, International Journal of Engineering, 3(6)
[4]
LIJEWSKI,L.E., SUHS,N.E.:
Time-Accurate Computational Fluid
Dynamics Approach to Transonic Store Separation Trajectory
Prediction, Journal of Aircraft, 31(4) (1994)
[5]
HEIM,E.R.:
CFD Wing/Pylon/Finned Store Mutual Interference
Wind Tunnel Experiment, Arnold Engineering Development Center,
AD-B152 669, September 10-17 1990
[6]
Fluent Theory Manual, Version 2009, ANSYS, Inc., April 2009
[7]
Fluent User��s Guide, Version 2009, ANSYS, Inc., April 2009
[8]
SUNAY,Y.E., GÜLAY,��., AKGÜL,A.:
Validation of CFD
Simulation of Store Separation for EGLIN Test Case, 5nd
International Scientific Conference OTEH 2012, 18-19 september
2012., Belgrade, SERBIA
[9]
GÜLAY,��.,
AKGÜL,��.,
ISAKOVIĆ,J.,
MANDIĆ,S.:
Computational Fluid Dynamics and Experimental Investigation of
Wrap-Around-Fins Missile Rolling Moment, Scientific Tehnical
Review, ISSN 1820-0206, 2011, Vol. 61, No.3-4, pp.8-15.
[10] AGSARLIOGLU,E., AKGÜL,��.:
Numerical Prediction of Lateral
Jets for Missile Like Geometries, Scientific Tehnical Review, ISSN
1820-0206, 2012, Vol. 62, No.2, pp.3-9.
Received: 20.02.2013.
Numerička simulacija putanje odvajanja rakete od letelice primenom
EGLIN testa
Jedan od najvažnijih problema u razvoju projektovanja raketa je bezbedno odvajanje rakete od letelice. Sami testovi
odvajanja su skupi, vremenski zahtevni i opasni pošto sami testovi mogu biti sa fatalnim posledicama, stoga numeričke
simulacije bezbednog odvajanja i predviđanja trajektorija rakete primenom numeričkih simulacija predstavlja kritični
deo istraživanja. U ovoj studiji, korišćen je EGLIN test za verifikaciju predviđene trajektorije odvajanja od krila.
EGLIN test je opšti model procesa odvajanja i gotovo redovno se koristi kao alat za verifikaciju trajektorija.
Eksperimenti su bili razmatrani u transoničnom (M=0.95) i supersoničnim (M=1.2) domenima strujanja. EGLIN test
model odvajanja je simuliran koristeći vremenski-zavisnu numeričku analizu dinamike fluida (CFD). Kombinacija
16
SUNAY,Y.E. etc: NUMERICAL SIMULATIONS OF STORE SEPARATIONTRAJECTORIES USING THE EGLIN TEST
modela od šest stepeni slobode (6DOF) i solvera za strujanje je korišćena za predviđanje trajektorije odvajanja rakete
od krila letelice. Za tu svrhu su korišćene, Navije-Stoksove i Ojlerove proračunske metode za uključivanje efekata
viskoznosti fluida na trajektoriju kretanja rakete tokom odvajanja od krila.
Ključne reči: numerička dinamika fluida, numerička simulacija, Navije-Stoksove jednačine, avionska raketa, putanja
rakete, odvajanje rakete, EGLIN test.
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�ڧ� ��֧��� ���֧�֧ߧ֧� ��ӧ�ҧ�է� (6DOF) �� ���ݧӧ֧�� (��֧�ѧ�֧ݧ�) �����ܧ� �ҧ�ݧ� �ڧ���ݧ�٧�ӧѧߧ� �էݧ� ����ԧߧ�٧ڧ��ӧѧߧڧ�
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���ݧ��֧ӧ�� ��ݧ�ӧ�: ��ڧ�ݧ֧ߧߧѧ� �ԧڧէ��էڧߧѧާڧܧ�, ��ڧ�ݧ֧ߧߧ�� �ާ�է֧ݧڧ��ӧѧߧڧ�, ���ѧӧߧ֧ߧڧ� ���ѧӧ��-�����ܧ��, ��ѧܧ֧���ݧѧ�,
���ѧ֧ܧ���ڧ� ��ѧܧ֧��, ��֧ѧܧ�ڧӧߧ�� ��ѧ٧է֧ݧ֧ߧڧ�, EGLIN-��֧��.
Simulation num��rique de la trajectoire de s��paration du missile de
l��a��ronef par le test EGLIN
La s��paration en s��curit�� d��un missile de l��a��ronef repr��sente l��un des probl��mes les plus importants dans le
d��veloppement de la conception des missiles. Les tests m��me de la s��paration sont coûteux, demandent beaucoup de
temps et ils sont dangereux puisqu��ils peuvent avoir des cons��quences fatales. C��est pourquoi les simulations num��riques
des s��parations en s��curit�� ainsi que les pr��visions des trajectoires des missiles par les simulations num��riques
repr��sentent la phase critique des recherches. Dans cette ��tude on a utilis�� le test EGLIN pour la v��rification de la
trajectoire pr��vue pour la s��paration de l��aile. Le test EGLIN est un mod��le g��n��ral du processus de la s��paration et il
s��utilise r��guli��rement comme un outil pour la v��rification des trajectoires. Les essais ont ��t�� consid��r��s dans le domaine
courants transsoniques (m = 0,95) et les supersoniques (m = 1,2). Le test mod��le EGLIN a ��t�� simul�� au moyen de
l��analyse num��rique de la dynamique des fluides (CFD) qui est d��pendante temporellement. La combinaison du mod��le
de six degr��s de libert�� ( 6 DOF ) avec le solveur pour les courants a ��t�� utilis��e pour pr��voir la trajectoire de s��paration
du missile de l��aile de l��a��ronef . Dans ce but on a appliqu�� les m��thodes de computation de Navier-Stokes et de Euler
pour examiner les effets de la viscosit�� des fluides sur la trajectoire du missile lors de la s��paration de l��aile d��a��ronef.
Mots cl��s: dynamique num��rique des fluides, simulation num��rique, ��quations Navier-Stokes, missile d��a��ronef,
trajectoire de missile, s��paration de missile, test EGLIN.
