Coupling Dynamic Meshing with 6-DOFRigid Body Motion for Store

Separation Modeling

Deryl Snyder, Ph.D. – Sverdrup Technology, Inc.Evangelos Koutsavdis, Ph.D. – Fluent, Inc.

Maj. John Anttonen, Ph.D. – U.S. Air Force

May 7, 2003

Background

• Store separation– Important for safety, accuracy– Early days – flight tests only– 1960’s – wind tunnel tests– Recent years – modeling and simulation

• CFD– Steady state– Combined with semi-empirical approaches– Chimera overset

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Introduction

• Structured overset mesh• Dynamic unstructured mesh

– Flexibility for complex geometry– Reduced generation time– Solution-adaptive refinement– Fewer cells (no overlapping

regions)

Unstructured dynamic mesh

Structured overset mesh

Dynamic Mesh

• Spring-based smoothing– Cell edges modeled as interconnected springs

• Iterative method to find nodal equilibrium positions after boundary movement

– Connectivity remains unchanged• Local remeshing

– Not performed every time step– Only cells selected based on volume and/or

skewness criteria

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6-DOF UDF• User-defined function

– cg_vel• Old velocity passed to UDF• New velocity passed back to Fluent

– cg_omega• Old angular rates passed to UDF• New angular rates passed back to Fluent

– dtime• Time step passed to UDF

DEFINE_CG_MOTION(six_dof, dt, cg_vel, cg_omega, time, dtime)

6DOF UDF Continued• Numerically integrate the Newton-Euler equations

of motion

• Aerodynamic forces computed by integrating pressure (and viscous forces) over the store

– f_glob: integrated aerodynamic forces (in global csys)– m_glob: integrated aerodynamic moments (in global csys)

Compute_Force_And_Moment(domain, tf1, x_cg, f_glob, m_glob, TRUE);

∑= GG fm

vr

&r 1 ( )BBBB M ωωω rrr&r LL ×−= ∑−1

6DOF UDF ContinuedGet previous

position/orientation/rateinformation

Return Vg and ωgto solver

Compute additionalforces and moments

(global c. sys.)

Integrate eq. of motion toget new Vg Transform angular rates

to body c. sys.Transform total appliedmoment to body c. sys.

Integrate eq. of motion toget new ωb

Transform ωb to wg

Get aerodynamicforces and moment

(global c. sys.)Compute_Force_And_Moment()DEFINE_CG_MOTION()

DEFINE_CG_MOTION()

Wing/Pylon/Store Case

• Geometry– Clipped delta wing with pylon– Standard 4-fin store– Sting attached to aft end of missile body

• Benchmark experimental data available– Trajectory information– Surface pressure– Mach 0.9 and 1.2

Computational Mesh• Tetrahedral Euler mesh• Gambit used to generate the

surface mesh– Starting from imported IGES

CAD files• TGrid used to generate the

volume mesh• Three levels of refinement

– 35,000/200,000/900,000 cells• Lateral extents located at

approximately 100 diameters

Results: Qualitative• Overall results very

satisfactory– Center of gravity

trajectory predicted well– Orientation less accurate,

but still good– Results for 200,000 cell

grid similar to Air Force Beggar code with 1.5 million cells

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Results: Location

Time (sec)

Dis

tanc

e(f

t)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

-5

0

5

10

15

20

ExperimentCFD CoarseCFD NominalCFD Fine

x

y

z

Time (sec)

Vel

ocity

(ft/s

ec)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

-10

0

10

20

30

40ExperimentCFD CoarseCFD NominalCFD Fine

vx

vy

vz

Results: Orientation

Time (sec)

Eule

rAng

le(d

eg)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

-10

0

10

20

ExperimentCFD CoarseCFD NominalCFD Fine

θ

ψ

φ

Time (sec)

Ang

ular

Rat

e(d

eg/s

ec)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

-60

-40

-20

0

20

40

60 ExperimentCFD CoarseCFD NominalCFD Fine

p

q

r

Results: Surface Pressure

x/L

Cp

0 0.2 0.4 0.6 0.8 1

-0.5

0.0

0.5

1.0

Experiment (t = 0.00)Experiment (t = 0.16)Experiment (t = 0.37)CFD (t = 0.00)CFD (t = 0.16)CFD (t = 0.37)Cp Sonic

(view from upstream)

Results: Time Step Refinement• Negligible effect on

CG location• For orientation

– No clear trend indicating finer time step producing better results

• Likely due to quasi-steady nature of experiment

• Also lack of viscous effects

Time (sec)

Eule

rAng

le(d

eg)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

-10

0

10

20

Experiment∆t = 0.01 sec∆t = 0.002 sec∆t = 0.0004 sec

θ

ψ

φ

Results: Integration Scheme• First-Order Euler

Integration• Fourth-Order Adams-

Moulton Integration– Multi-point– Negligible cost– Little effect on CG

location– Marked improvement to

orientationTime (sec)

Eule

rAng

le(d

eg)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

-10

0

10

20

Experiment1st Order4th Order

θ

ψ

φ

Dt = 0.002 sec

Conclusions

• Dynamic mesh approach effective and successful for transonic store separation– Trajectories captured well– Surface pressures in agreement– Quick turn-around time

• Meshing: 2 hours• Solution: overnight on 2-processor desktop

workstation

Future Work

• Viscous solution• Improved 6DOF

– Quaternions instead of Euler angles

– Multiple bodies– Moving control

surfaces