modelling ricochet of a cylinder on water using the ale fe * and

Modelling ricochet of a cylinder on water using the ALE FE and SPH methods

Modelling ricochet of a cylinder on water using the ALE FE and SPH methods

Marina Seidl

22nd January 2015

1

Outline

Introduction

Fluid modelling

Lagrangian body

Comparison

Conclusion

Ricochet of cylinder Marina Seidl

Page 1/25

2

Ricochet

Definition: Rebound on surface

Not deformable, rigid body with no spin

Impact on water [4]

High forward velocity and small impact angle [3]

Figure: Stone skimming [16]


Page 2/25

3

Ricochet test case

High forward velocity of body requires a large fluid domain challenging example in computational costs

Ricochet has similarities to other fluid structure impact cases e.g. ditching of aeroplanes

Well defined initial conditions (size and material of rigid body, physical values of fluid)

Experimental data available [13]


Page 3/25

Ricochet Analytical models

Solid steel sphere on water with no spin

Experimental results [13]

Analytical ricochet model is dependent on velocity and impact angle of sphere [6, 8,12]

Solid steel cylinder on water with no spin

Derived from the 3D curve for infinite long cylinder [11]


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Aim and Methodology

Aim

Comparison of SPH and ALE

Verification of SPH

Investigate low angle impact problems

Methodology

SPH (Smooth Particle Hydrodynamics) model

Designed in Cranfield internal code

Program - MCM (Meshless Continuum Mechanics)

ALE (Arbitrary Lagrangian Eulerian) model

LS-DYNA (6.1.1)

Established software [9,10]


Page 5/25

Fluid domain

Page 6/25


Fluid domain - Ratio

SPH

1 part SPH particles with 0.5 mm particle spacing

1 particle row in z-direction

ALE

2 parts (water and vacuum) in Eulerian fixed grid with 0.5mm solid, cubic elements

1 element row in z-direction

x

x

y

y

y/2

Rectangular 2D basin, length x=800mm, height y=100mm, water

Page 7/25


Fluid domain - Boundary

SPH

Boundary constrained with symmetry planes

Material fluid defined for inviscid flow

Equation of state (EOS) Murnaghan quasi incompressible

ALE

Boundary condition with constrained with nodes

Material (*MAT_NULL) defined for inviscid flow

EOS Linear Polynomial

2D problem in 3D solver

Hydrostatic pressure applied with Dynamic Relaxation (DR) [3]


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Lagrangian body


Page 9/25

Lagrangian body - Material

FE-SPH

160 thick shell elements (hollow cylinder - density chosen to give correct cylinder mass )

Particle spacing : FE mesh is 1:1

Even element number for height for contact with nodes to nodes contact [14,15]

ALE

80 solid elements around circumference

Eulerian:Lagrangian mesh is 1:2

Avoidance of leakage cylinder wider in z-direction [9] -density chosen to give correct cylinder mass

Even element number for height [9] for contact with penalty stiffness coupling [1]

Rigid steel cylinder with diameter 1 (25.4) and mass =2


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Comparison


Page 11/25

Comparison Non ricochet

SPH

t = 15ms

x-displacement = 91mm

Pressure plot in

and initial

ALE

t = 15ms


Pressure plot in


Page 12/25

Pressure plot in


SPH

t = 75ms


Pressure plot in

and initial

ALE

t = 73ms


Pressure plot in


Page 13/25

Pressure plot in


SPH

t = 100ms


Pressure plot in

and initial

ALE

t = 100ms


Pressure plot in


Page 14/25

Pressure plot in

Comparison Ricochet


Page 15/25

Comparison Ricochet

SPH

t = 10ms


Pressure plot in

and initial

ALE

t = 10ms


Pressure plot in


Page 16/25

Pressure plot in

Comparison Ricochet

SPH

t = 50ms


Pressure plot in

and initial

ALE

t = 50ms


Pressure plot in


Page 17/25

Pressure plot in

Comparison Ricochet

SPH

t = 100ms


Pressure plot in

and initial

ALE

t = 100ms


Pressure plot in


Page 18/25

Pressure plot in

Case studies

ALE

Bulk modulus

Ambient pressure

Convergence study

Viscosity

SPH

Convergence study [11]


Page 19/25

Comparison


Page 20/25

Comparison

ALE

SPH


Page 21/25

Conclusion

Both numerical methods do not reach the expected boundary for the critical angle for higher impact velocities

Both numerical models agree in the prediction of ricochet for impact velocities and agree with the analytical model


Page 22/25

Future Work

Boundary curve of SPH 2D model for higher angles

Possibly a 2D ricochet LS-DYNA SPH model

Extent the comparison for 3D ricochet

Validation with experimental data


Page 23/25

Ricochet of cylinder

Any questions?

Page 24/25

Ricochet of cylinder

Thank you for your attendance!

Page 25/25

Refernces

N. Aquelet, M. Souli, and L. Olovsson. Euler-lagrange coupling with damping effects. Computational Methods in Applied Mechanical Engi-neering, 195(1-3):110, 2005.

T. W. Bruke and W. Rowe. Bullet ricochet: A comprehensive review. Journal of Forensic Sciences, JFSCA, 1992.

I. Do. Simulating Hydrostatic Pressure. Livermore Software Technology Corporation (LSTC), 2008.

R. E. Gold, M. D. Schecter, and B. Schecter. Ricochet dynamics for the nine-millimetre parabellum bullet. Journal of Forensic Sciences, JFSCA, 1992.

J. Hallquist. LS-DYNA Theory Manual. Livermore Software Technology Corporation (LSTC), March 2006.

I. M. Hutchings. The ricochet of spheres and cylinders from the surface of water. Int. J. mech. ScL, 1976.

W. Johnshon. The ricochet of spinning and non-spinning spherical projectiles, mainly from water (part II). Int. J. Impact Engng, 1998.

W. Johnshon and S. R. Reid. The ricochet of spheres o water. Journal of Mechanical Engineering Science, 1975.

Livermore Software Technology Corporation (LSTC). LS-DYNA Examples Manual, March 1998.

Livermore Software Technology Corporation (LSTC). LS-DYNA Key-word User's Manual, August 2012.

L. Papagiannis. Predicting Aircraft Structural Response to Water Impact. PhD thesis, Cranfield University, 2014.

L. Rayleigh. On the resistance of fluids. Philosophical Magazine, 1876.

A. S. Soliman, S. R. Reid, and W. Johnshon. The effect of spherical pro-jectile speed in ricochet off water and sand. Int. J. Mechanical Science, 1976.

T. D. Vuyst. Hydrocode Modelling of Water Impact. PhD thesis, Cran-field University, 2003.

T. D. Vuyst, R. Vignjevic, and J. Campbell. Coupling between meshless and finite element methods. Int. J. of Impact Engng, 31:1054, 2005. .

www.bethtop5percent.com, 27th May 2013

APPENDIX

Ricochet

Rebound on surface

High forward velocity and low impact angle [3]

Surface is liquid (for this scenario) [4]

No deformation of rigid body

Solid body sinks (c, d)

Solid body ricochets (a, b)

Scenario of cylinder trajection [7]

29


Model of Birkhoff et. al (REF)

Critical angle of ricochet on liquid surface

Density of surface (water )

Solid body (steel )

The solid body ricochets for an impact angle (REF johnson)


Model of Birkhoff et. al got extended (REF)

Non-spinning solid sphere

Dependent of impact velocity , gravity g and radius r


Derived from 3D case (REF)

Non-spinning solid cylinder

Dependent of impact velocity , gravity g and radius r

Fluid domain Initial conditions

SPH

Equation of state (EOS)

Murnaghan quasi incompressible

Pressure p defined as:

Adiabatic coefficient [11]

ALE

EOS Linear Polynomial

Pressure p defined as:

Bulk modulus B to (decrease speed of sound)

Hydrostatic pressure applied with Dynamic Relaxation (DR) [3]

Lagrangian body - Material

SPH

Thick shell elements (hollow cylinder - density chosen to give correct cylinder mass )

160 elements around circumference

Particle spacing : FE mesh is 1:1

ALE

Solid elements

80 elements around circumference

Eulerian mesh: Lagrangian mesh is 1:2

Rigid steel cylinder with diameter 1 (25.4) and mass =2

Initial velocity is split in a vertical and horizontal component

Gravity is applied in negative y-direction


Lagrangian body - Modifications

SPH

4 element rows for height

in z-direction

Density chosen to give correct cylinder mass

Contact with nodes to nodes contact [14,15]

ALE

2 element rows for height [9]

Avoidance of leakage - wider in z-direction [9]

Density chosen to give correct cylinder mass

Contact with penalty stiffness coupling [1]



Pressure plot in

ALE and initial

Comparison Ricochet

Pressure plot in

ALE and initial

2

N

m

modelling ricochet of a cylinder on water using the ale fe * and

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