Bomb Maneuvering Prediction for Mine...

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Bomb Maneuvering Prediction for Mine Breaching

Dr. Peter C. Chu and LT Greg RayNaval Postgraduate School

Peter FleischerNaval Oceanographic Office

Paul Gefken, SRI

Sponsored by CNMOC MIW Directory ONR Coastal Engineering

Seventh International Symposium on Technology and the Mine Problem, NPS, Monterey, CA 93943, May 2-4, 2006

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Bomb Strike for Mine Clearance

ONR JDAM Assault Breaching System (JABS)

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References

• Chu, P.C. and C. Fan, 2004: Three dimensional rigid body impact burial prediction model. Advances in Fluid Mechanics, 6, 43-52.

• Chu, P.C., and C.W. Fan, 3D rigid body impact burial prediction model. Advances in Mechanics, 5, 43-52, 2004.

• Chu, P.C., C.W. Fan, A. D. Evans, and A. Gilles, 2004: Triple coordinate transforms for prediction of falling cylinder through the water column. Journal of Applied Mechanics, 71, 292-298.

• Chu, P.C., A. Gilles, and C.W. Fan, 2005: Experiment of falling cylinder through the water column. Experimental and Thermal Fluid Sciences, 29, 555-568.

• Chu, P.C., and C.W. Fan, 2005: Pseudo-cylinder parameterization for mine impact burial prediction. Journal of Fluids Engineering, 127, 1515-1520.

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References• Chu, P.C., and C.W. Fan, 2006: Prediction of falling cylinder through

air-water-sediment columns. Journal of Applied Mechanics, 73, 300-314.

• Chu, P.C., G. Ray, and C.W. Fan, 2006: Prediction of High Speed Rigid Body Maneuvering in Air-Water-Sediment Columns, Advances in Fluid Mechanics, 7, 123-132.

• Chu, P.C., and C.W. Fan, 2007: Mine impact burial model (IMPACT35) verification and improvement using sediment bearing factor method. IEEE Journal of Oceanic Engineering, in press.

• Chu, P.C., 2007: Mine impact burial prediction from one to threedimensions. IEEE Journal of Oceanic Engineering, in press.

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References

• Chu, P.C., A. Evans, T. Gilles, T. Smith, V. Taber, Development of Navy’s 3D mine impact burial prediction model (IMPACT35), Sixth Monterey International Symposium on Technology and Mine Problems, NPS, Monterey, California, May 10-14, 2004.

• Chu, P.C., G. Ray, P. Fleischer, and P. Gefken, Development of three dimensional bomb maneuvering model, DVD-ROM (10 pages). Seventh Monterey International Symposium on Technology and Mine Problems, NPS, Monterey, California, May 1-4, 2006.

• Chu, P.C., C. Allen, and P. Fleischer, Non-cylindrical mine impact experiment, DVD-ROM (10 pages). Seventh Monterey International Symposium on Technology and Mine Problems, NPS, Monterey, California, May 1-4, 2006.

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SRI Bomb Trajectory Experiment

• SRI International performed an experimental research program in which 1/12-scale high fidelity Mk84 bombs were launched into a deep-water pool at velocities of up to about 1000 ft/s.

• Using two underwater high-speed video cameras, they determined the underwater trajectory of the Mk84 bombs for a nominal vertical entry and for different possible tail configurations included a complete warhead section with (1) a tail section and four fins, (2) a tail section and two fins, (3) a tail section and no fins, and (4) no tail section.

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SRI Experimental Data (Two-Dimensional, 12 Sets)

• With a Tail Section: COM location only, no orientation data• No Fin: Test-16, -17, -18 • 2 Fins: Test-10, -11, -19• 4 Fins: Test-2, -3, -4.

• With a Tail Section COM location and Orientation• Test-13, -14, -15 • Only the three sets of data are used for STRIKE35

development and Verification

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Model-Data Inter-Comparison STRIKE35 vs SRI Experiment (Test 13)

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Prediction of Bomb Maneuvering Trajectory

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3D Bomb Maneuvering Model (STRIKE35)

• Triple Coordinate Systems• Momentum Equations• Moment of Momentum Equations• Parameterization of Hydrodynamic Forces and

Torques on Bomb• Supercavitaion• Bubble Dynamics

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Triple Coordinate Transform

• Earth-fixed coordinate (E-coordinate)

• Bomb’s main-axis following coordinate (M-coordinate)

• Hydrodynamic force following coordinate (F-coordinate).

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E and M Coordinate Systems

, M M M M M= × = ×j k i k i j

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E-Coordinate, FE(O, i, j, k)

• COM Position: X = xi +yj + zk,

• Translation velocity:

dX/dt = V, V = (u,v, w)

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Transform Between E- and M-Coordinate Systems

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F-Coordinate System

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E- and F-Coordinate Transform

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Momentum Equation in E-Coordinate System

Fh is hydrodynamic force (drag, lift)

Fv is the bubble force (drag, lift)

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Moment of Momentum Equation in M-Coordinate System

Inertial terms are small

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M-Coordinate

The moment of gyration tensor for the axiallySymmetric cylinder is a diagonal matrix

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Bomb Trajectory Modeling

Core PhysicsBomb Trajectory Model (STRIKE 35)

Drag & LiftForces/TorquesDynamic

FluidModel

DynamicBubbleModel

Cd, Cl

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There is no existing formulae for calculating Cd and Cl for MK-84 Bomb.

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Two-Step Modeling

• (1) Determine drag and lift coefficients for a particular bomb (usually from experiments)

• (2) Predict bomb trajectory using stand-alone bomb strike model (STRIKE-35) with the known drag and lift coefficients.

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STRIKE 35 Modeling

Core PhysicsBomb Trajectory Model (STRIKE 35)

Drag & LiftForces/TorquesDynamic

FluidModel

DynamicBubbleModel

Cd, Cl

Experiment

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Dynamical Determination of Drag/Lift Coefficients

vc

fb

mc

fg

V

fc

fdrag

flift

α

β

γσ v σ f

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β bomb elevation angle γ : bomb velocity angle

α β γ= − : attack angle

V : water velocity relative to Bomb

cm : center of mass cv : center of volume

cf : center of drag and lift forces

dragf : drag force liftf : lift force bf : buoyancy force

gf : Gravity

fσ : the distance between cm cfand

vσ

vσ

: the distance between cm and cv

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Theoretical Base

Here, v is the translation velocity of COM,

( ) drag d lift ldm m g f fdt

ρ= Π − + +v k e e

( )v b f drag lift rddt

= × + × + +ΩI r f r f f Mi

Ω is the angular velocity.

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Determination of Cd and CLfrom Experimental Data

( )

( )

2

2

/12

/12

d dd

l ll

m g md dtC

DLV

m g md dtC

DLV

ρ

ρ

ρ

ρ

Π − −=

Π − − ⋅=

k e v e

k e v e

i i

i

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Analytical Formulae for (Cd, Cl) Using Three Sets of SRI MK-84 Data without Tail

( ) ( )

( )

2Re8sin 2 0.02 if sin 2 0 and Re Re

Re

Re0.34 sin 2 0.02

Re

refref

dref

C

otherwise

α α

α

⎧ ⎛ ⎞+ ≥ ≥⎪ ⎜ ⎟

⎪ ⎝ ⎠= ⎨⎛ ⎞⎪ +⎜ ⎟⎪⎝ ⎠⎩

( )

( )

1.2 1.2ReRe2.5sin 2 min , if sin(2 ) 0Re Re

0.16sin 2 if sin(2 ) 0

ref

reflCα α

α α

⎧ ⎡ ⎤⎛ ⎞ ⎛ ⎞⎪ ⎢ ⎥ ≥⎜ ⎟⎪ ⎜ ⎟⎜ ⎟= ⎢ ⎥⎨ ⎝ ⎠⎝ ⎠⎣ ⎦⎪<⎪⎩

7Re 1.51 10ref = ×

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Determination of Center of Hydrodynamic Force from Experimental Data

* f vf L

σ σσ

−=

( )322

2

*

2 2

1 22 6 8 2

1 12 2

vvr rr r v b b r f r v

rf v

b d d l l r

Ld L Vd C DL Vdt dt

LC DLV C DLV

σσσ ρ σ

σ σρ ρ

⎡ ⎤⎛ ⎞ΩΩΩ⎛ ⎞⎢ ⎥⎜ ⎟+Ω − × + + + + Ω⎜ ⎟ ⎜ ⎟⎝ ⎠⎢ ⎥⎝ ⎠⎣ ⎦= −⎛ ⎞× +⎜ ⎟⎝ ⎠

eI e e e f e

e e e e

i i i

i

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Analytical Formulae for Using Three Sets of SRI MK-84 Data without Tail

*fσ

** 1 3 1 1sinh and

8 2 2 2 2f v f

f L Lσ σ σπσ α

− ⎛ ⎞⎛ ⎞= = − − ≤ ≤⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

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2 4 6 8 10

x 107

0

0.5

1

Re

Dra

g F

orce

Coe

ffici

ent (

Cd)

test13

2 4 6 8 10

x 107

0

45

90

135

180

Atta

ck A

ngle

α (

o )

ExpProf

2 4 6 8 10

x 107

−1

0

1

Re

Lift

For

ce C

oeffi

cien

t (C

l)

2 4 6 8 10

x 107

0

45

90

135

180

Atta

ck A

ngle

α (

o )

ExpProf

2 4 6 8 10

x 107

−0.5

0

0.5

Re

RH

F C

ente

r σ f*

2 4 6 8 10

x 107

0

45

90

135

180

Atta

ck A

ngle

α (

o )

ExpProf

• Test-13

• Cd, Cl, *fσ

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• Test-14

• Cd, Cl, *fσ

2 4 6 8 10

x 107

0

1

Re

Dra

g F

orce

Coe

ffici

ent (

Cd)

test14

2 4 6 8 10

x 107

0

45

90

135

180

Atta

ck A

ngle

α (

o )

ExpProf

2 4 6 8 10

x 107

−1.5

−1

−0.5

0

0.5

1

Re

Lift

For

ce C

oeffi

cien

t (C

l)

2 4 6 8 10

x 107

0

45

90

135

180

Atta

ck A

ngle

α (

o )

ExpProf

2 4 6 8 10

x 107

−0.5

0

0.5

Re

RH

F C

ente

r σ f*

2 4 6 8 10

x 107

0

45

90

135

180

Atta

ck A

ngle

α (

o )

ExpProf

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• Test-15

• Cd, Cl, *fσ

2 4 6 8 10

x 107

0

0.5

1

1.5

Re

Dra

g F

orce

Coe

ffici

ent (

Cd)

test15

2 4 6 8 10

x 107

0

45

90

135

180

Atta

ck A

ngle

α (

o )

ExpProf

2 4 6 8 10

x 107

−2

−1

0

1

Re

Lift

For

ce C

oeffi

cien

t (C

l)

2 4 6 8 10

x 107

0

45

90

135

180

Atta

ck A

ngle

α (

o )

ExpProf

2 4 6 8 10

x 107

−0.5

0

0.5

Re

RH

F C

ente

r σ f*

2 4 6 8 10

x 107

0

45

90

135

180

Atta

ck A

ngle

α (

o )

ExpProf

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STRIKE35 and SRI Data Inter-ComparisonTest-13

−5 0 5 10

−20

−15

−10

−5

0

Y(m

)

X(m)

Experiment test 13 time:0.485s

−5 0 5 10X(m)

Model time:0.485s

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−2

0

2

4

6

8

Xc

(m)

ExpModel

−25

−20

−15

−10

−5

0

5

Yc

(m)

ExpModel

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45−100

−50

0

50

100

Time (s)

Ele

vatio

n (o )

ExpModel

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−5 0 5 10

−20

−15

−10

−5

0

Y(m

)

X(m)


−5 0 5 10X(m)

Model time:0.406s

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−2

0

2

4

6

8

10

Xc

(m)

ExpModel

−25

−20

−15

−10

−5

0

5

Yc

(m)

ExpModel

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4−100

−50

0

50

100

150

Time (s)

Ele

vatio

n (o )

ExpModel

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−5 0 5 10−20

−15

−10

−5

0

Y(m

)

X(m)


−5 0 5 10X(m)

Model time:0.233s

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−2

0

2

4

6

8

Xc

(m)

ExpModel

−20

−15

−10

−5

0

5

Yc

(m)

ExpModel

0 0.05 0.1 0.15 0.2−100

−50

0

50

100

Time (s)

Ele

vatio

n (o )

ExpModel

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Conclusions

• (1) STIRKE-35 has capability to predict bomb trajectory.

• (2) A key issue for the prediction is the determination of drag and lift coefficients (Cd, Cl) for a particular bomb.

• (3) Bomb trajectory experiment is needed for determining (Cd, Cl).

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