CFD Transonic Store Separation Trajectory Predictions with Comparison to Wind Tunnel Investigations

Abstract

The prediction of the separation movements of the external store weaponscarried out on military aircraft wings under transonic Mach number and variousangles of attack is an important task in the aerodynamic design area in order todefine the safe operational-release envelopes. The development ofcomputational fluid dynamics techniques has successfully contributed to theprediction of the flowfield through the aircraft/weapon separation problems. Thenumerical solution of the discretized three-dimensional, inviscid andcompressible Navier-Stokes equations over a dynamic unstructured tetrahedralmesh approach is accomplished with a commercial CFD finite-volume code. Acombination of spring-based smoothing and local remeshing are employed withan implicit, second-order upwind accurate Euler solver. A six degree-of-freedomroutine using a fourth-order multi-point time integration scheme is coupled withthe flow solver to update the store trajectory information. This analysis is appliedfor surface pressure distributions and various trajectory parameters during theentire store-separation event at various angles of attack. The efficiency of theapplied computational analysis gives satisfactory results compared, whenpossible, against the published data of verified experiments.

Full text

Page 1

Elias E. Panagiotopoulos & Spyridon D. Kyparissis
International Journal of Engineering (IJE), Volume (3): Issue (6) 538
CFD Transonic Store Separation Trajectory Predictions with
Comparison to Wind Tunnel Investigations


Elias E. Panagiotopoulos
Hellenic Military Academy
Vari, Attiki, 16673, Greece

Spyridon D. Kyparissis
Mechanical Engineering and
Aeronautics Department
University of Patras
Patras, Rio, 26500, Greece
hpanagio@mech.upatras.gr

kypariss@mech.upatras.gr

Abstract

The prediction of the separation movements of the external store weapons
carried out on military aircraft wings under transonic Mach number and various
angles of attack is an important task in the aerodynamic design area in order to
define the safe operational-release
computational fluid dynamics techniques has successfully contributed to the
prediction of the flowfield through the aircraft/weapon separation problems. The
numerical solution of the discretized three-dimensional, inviscid and
compressible Navier-Stokes equations over a dynamic unstructured tetrahedral
mesh approach is accomplished with a commercial CFD finite-volume code. A
combination of spring-based smoothing and local remeshing are employed with
an implicit, second-order upwind accurate Euler solver. A six degree-of-freedom
routine using a fourth-order multi-point time integration scheme is coupled with
the flow solver to update the store trajectory information. This analysis is applied
for surface pressure distributions and various trajectory parameters during the
entire store-separation event at various angles of attack. The efficiency of the
applied computational analysis gives satisfactory results compared, when
possible, against the published data of verified experiments.

Keywords: CFD Modelling, Ejector Forces and Moments, Moving-body Trajectories, Rigid-body
Dynamics, Transonic Store Separation Events.
envelopes. The development of


1. INTRODUCTION
With the advent and rapid development of high performance computing and numerical algorithms,
computational fluid dynamics (CFD) has emerged as an essential tool for engineering and
scientific analyses and design. Along with the growth of computational resources, the complexity
of problems that need to be modeled has also increased. The simulation of aerodynamically
driven, moving-body problems, such as store separation, maneuvering aircraft, and flapping-wing
flight are important goals for CFD practitioners [1].

The aerodynamic behavior of munitions or other objects as they are released from aircraft is
critical both to the accurate arrival of the munitions and the safety of the releasing aircraft [2]. In

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Elias E. Panagiotopoulos & Spyridon D. Kyparissis
International Journal of Engineering (IJE), Volume (3): Issue (6) 539
the distant past separation testing was accomplished solely using flying tests. This approach was
very time-consuming, often requiring years to certify a projectile. It was also expensive and
occasionally led to the loss of an aircraft due to unexpected behavior of the store being tested.

In the past, separation testing was accomplished solely via flight tests. In addition to being very
time consuming, often taking years to certify a weapon, this approach was very expensive and
often led to loss of aircraft. In the 1960s, experimental methods of predicting store separation in
wind tunnel tests were developed. These tests have proven so valuable that they are now the
primary design tool used. However, wind tunnel tests are still expensive, have long lead times,
and suffer from limited accuracy in certain situations, such as when investigating stores released
within weapons bays or the ripple release of multiple moving objects. In addition, because very
small-scale models must often be used, scaling problems can reduce accuracy.

In recent years, modelling and simulation have been used to reduce certification cost and
increase the margin of safety of flight tests for developmental weapons programs. Computational
fluid dynamics (CFD) approaches to simulating separation events began with steady-state
solutions combined with semi-empirical approaches [3] - [7]. CFD truly became an invaluable
asset with the introduction of Chimera overset grid approaches [8]. Using these methods,
unsteady full field simulations can be performed with or without viscous effects.

The challenge with using CFD is to provide accurate data in a timely manner. Computational cost
is often high because fine grids and small time steps may be required for accuracy and stability of
some codes. Often, the most costly aspect of CFD, both in terms of time and money, is grid
generation and assembly. This is especially true for complex store geometries and in the case of
stores released from weapons bays. These bays often contain intricate geometric features that
affect the flow field.

Aerodynamic and physical parameters affect store separation problems. Aerodynamic
parameters are the store shape and stability, the velocity, attitude, load factor, configuration of the
aircraft and flow field surrounding the store. Physical parameters include store geometric
characteristics, center of gravity position, ejector locations and impulses and bomb rack. The
above parameters are highly coupled and react with each other in a most complicated manner
[9] - 11]. An accurate prediction of the trajectory of store objects involves an accurate prediction
of the flow field around them, the resulting forces and moments, and an accurate integration of
the equations of motion. This necessitates a coupling of the CFD solver with a six degree of
freedom (6-DOF) rigid body dynamics simulator [12]. The simulation errors in the CFD solver and
in the 6-DOF simulator have an accumulative effect since any error in the calculated aerodynamic
forces can predict a wrong orientation and trajectory of the body and vice-versa. The forces and
moments on a store at carriage and various points in the flow field of the aircraft can be computed
using CFD applied to the aircraft and store geometry [13].

The purpose of this paper is to demonstrate the accuracy and technique of using an unstructured
dynamic mesh approach to store separation. The most significant advantage of utilizing
unstructured meshes [14] is the flexibility to handle complex geometries. Grid generation time is
greatly reduced because the user’s input is limited to mainly generation of a surface mesh.
Though not utilized in this study, unstructured meshes additionally lend themselves very well to
solution-adaptive mesh refinement/coarsening techniques, especially useful in capturing shocks.
Finally, because there are no overlapping grid regions, fewer grid points are required.

The computational validation of the coupled 6-DOF and overset grid system is carried out using a
simulation of a safe store separation event from underneath a delta wing under transonic
conditions (Mach number 1.2) at an altitude of 11,600 m [15] and various angles of attack (0° , 3°
and 5° ) for a particular weapon configuration with appropriate ejection forces. An inviscid flow is
assumed to simplify the above simulations. The predicted computed trajectories are compared
with a 1/20 scale wind-tunnel experimental data conducted at he Arnold Engineering
Development Center (AEDC) [16] - [17].

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Elias E. Panagiotopoulos & Spyridon D. Kyparissis
International Journal of Engineering (IJE), Volume (3): Issue (6) 540
2. WEAPON / EJECTOR MODELLING
In the present work store-separation numerically simulation events were demonstrated on a
generic pylon/store geometric configuration attached to a clipped delta wing, as shown in
FIGURE 1. Benchmark wind-tunnel experiments for these cases were conducted at the Arnold
Engineering Development Center (AEDC) [16], and the details of the data can be found in
Lijewski and Suhs [18]. Results available from these studies include trajectory informations and
surface pressure distributions at multiple instants in time. The computational geometry matches
the experimental model with the exception of the physical model being 1/20 scale.



FIGURE 1: Global coordinate system OXYZ for store separation trajectory analysis.

It can be seen from FIGURE 1 the global coordinate system orientation OXYZ for the store
separation simulation analysis. The origin O is located at the store center of gravity while in
storage. X-axis runs from the tail to nose of the store, Y-axis points away from the aircraft and Z-
axis points downward along the direction of the gravity.

The aircraft’s wing is a 45-degree clipped delta with 7.62 m (full scale) root chord length, 6.6 m
semi-span, and NACA 64A010 airfoil section. The ogive-flat plate-ogive pylon is located spanwise
3.3 m from the root, and extends 61 cm below the wing leading edge. The store consists of a
tangent-ogive forebody, clipped tangent-ogive afterbody, and cylindrical centerbody almost 50 cm
in diameter. Overall, the store length is approximately 3.0 m. Four fins are attached, each
consisting of a 45-degree sweep clipped delta wing with NACA 008 airfoil section. To accurately
model the experimental setup, a small gap of 3.66 cm exists between the missile body and the
pylon while in carriage.

In the present analysis the projectile is forced away from its wing pylon by means of identical
piston ejectors located in the lateral plane of the store, -18 cm forward of the center of gravity
(C.G.), and 33 cm aft. While the focus of the current work is not to develop an ejector model for
the examined projectile configuration, simulating the store separation problem with an ejector
model which has known inaccuracies serves little purpose [9].

The ejector forces were present and operate for the duration of 0.054 s after releasing the store.
The ejectors extend during operation for 10 cm, and the force of each ejector is a constant
function of this stroke extension with values 10.7 kN and 42.7 kN, respectively. The basic
geometric properties of the store and ejector forces for this benchmark simulation problem are
tabulated in TABLE 1 and are depicted in a more detail drawing in FIGURE 2.

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Elias E. Panagiotopoulos & Spyridon D. Kyparissis
International Journal of Engineering (IJE), Volume (3): Issue (6) 541
As the store moves away from the pylon, it begins to pitch and yaw as a result of aerodynamic
forces and the stroke length of the individual ejectors responds asymmetrically.



FIGURE 2: Ejector force model for the store separation problem.

Characteristic Magnitudes Values
Mass m, kg
907
Reference Length L, mm
3017.5
Reference Diameter D, mm
500
No. of fins
4
Center of gravity xC.G., mm
1417 (aft of store nose)
Axial moment of inertia IXX, kg·m2 27
Transverse moments of inertia
Iyy and Izz, kg·m2
488

Forward ejector location LFE., mm 1237.5 (aft of store nose)
Forward ejector force FFE, kN 10.7
Aft ejector location LAE, mm 1746.5 (aft of store nose)
Aft ejector force FAE, kN 42.7
Ejector stroke length LES, mm 100

TABLE 1: Main geometrical data for the examined store separation projectile.

3. FLOWFIELD NUMERICAL SIMULATION
The computational approach applied in this study consists of three distinct components: a flow
solver, a six degree of freedom (6DOF) trajectory calculator and a dynamic mesh algorithm [12].
The flow solver is used to solve the governing fluid-dynamic equations at each time step. From
this solution, the aerodynamic forces and moments acting on the store are computed by
integrating the pressure over the surface. Knowing the aerodynamic and body forces, the

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Elias E. Panagiotopoulos & Spyridon D. Kyparissis
International Journal of Engineering (IJE), Volume (3): Issue (6) 542
movement of the store is computed by the 6DOF trajectory code. Finally, the unstructured mesh
is modified to account for the store movement via the dynamic mesh algorithm.

3.1
Flow Solver
The flow is compressible and is described by the standard continuity and momentum equations.
The energy equation incorporates the coupling between the flow velocity and the static pressure.
The flow solver is used to solve the governing fluid dynamic equations that include an implicit
algorithm for the solution of the Euler Equations [11] - [14]. The Euler equations are well known
and hence, for purposes of brevity, are not shown. The present analysis employs a cell-centered
finite volume method based on the linear reconstruction scheme, which allows the use of
computational elements with arbitrary polyhedral topology. A point implicit (block Gauss-Seidel)
linear equation solver is used in conjunction with an algebraic multigrid (AMG) method to solve
the resultant block system of equations for all dependent variables in each cell. Temporally, a first
order implicit Euler scheme is employed [14] - [23].

The conservation equation for a general scalar f on an arbitrary control volume whose boundary
is moving can be written in integral form as:

∫

()
gf
VVVV
fdVf uu dA fdAS dV
t
ρρΓ
∂∂
∂
∂∫
+−=∇+
∫∫
rr
rr
(1)

The time derivative in Eq.(1) is evaluated using a first-order backward difference formula:


()()
k 1
+−
k
V
fVfV
d
fdV
dtt
ρρ
ρ
∆
=
∫
(2)

where the superscript denotes the time level and also


k 1
+=
k
dV
VVt
dt
∆+
(3)

The space conservation law [24] is used in formulating the volume time derivative in the above
expression Eq.(3) in order to ensure no volume surplus or deficit exists.

3.2 Trajectory Calculation
The 6DOF rigid-body motion of the store is calculated by numerically integrating the Newton-
Euler equations of motion within Fluent as a user-defined function (UDF). The aerodynamic
forces and moments on the body store are calculated based on the integration of pressure over
the surface. This information is provided to the 6DOF from the flow solver in inertial coordinates.
The governing equation for the translational motion of the center of gravity is solved for in the
inertial coordinate system, as shown below:


v
GG
mf
= ∑
r
r&
(4)

where G
the force vector due to gravity.

The angular motion of the moving object ωΒ
coordinates to avoid time-variant inertia properties:


vr& is the translational motion of the center of gravity, m is the mass of the store and G f
r
is
r
, on the other hand, is more readily computed in body
()
1
B
LML
ω
&
ωω
−
ΒΒΒ
=−×
∑
r
rrr
(5)