Marina Seidl 22 nd January 2015 Outline Introduction Fluid modelling Lagrangian body Comparison Conclusion Ricochet of cylinder Marina Seidl Page 125 Ricochet Definition Rebound on surface ID: 162576
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Slide1
Modelling ricochet of a cylinder on water using the ALE FE – and SPH methods
Marina Seidl
22nd January 2015Slide2
Outline
IntroductionFluid modellingLagrangian body
ComparisonConclusion
Ricochet of cylinder – Marina Seidl
Page 1/25Slide3
Ricochet
Definition: Rebound on surfaceNot deformable, rigid body with no spin
Impact on water [4]High forward velocity and small impact angle [3]
Figure: Stone skimming [16]
Ricochet of cylinder – Marina Seidl
Page 2/25Slide4
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
aeroplanesWell defined initial conditions (size and material of rigid body, physical values of fluid)Experimental data available [13]
Ricochet of cylinder – Marina
Seidl
Page 3/25Slide5
Ricochet – Analytical models
Solid steel sphere on water with no spinExperimental 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]
Ricochet of cylinder – Marina
Seidl
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Aim and Methodology
AimComparison of SPH and ALE
Verification of SPH Investigate low angle impact problemsMethodologySPH (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]
Ricochet of cylinder – Marina
SeidlPage 5/25Slide7
Fluid domain
Page 6/25
Ricochet of cylinder – Marina
SeidlSlide8
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
Ricochet of cylinder – Marina
SeidlSlide9
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 nodesMaterial (*MAT_NULL) defined for inviscid flowEOS Linear Polynomial
2D problem in 3D solver
Hydrostatic
pressure applied with Dynamic
Relaxation (DR) [3]
Ricochet of cylinder – Marina
Seidl
Page 8/25Slide10
Lagrangian body
Ricochet of cylinder – Marina
Seidl
Page 9/25Slide11
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 1:2Avoidance 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
𝑖𝑛𝑐ℎ (25.4𝑚𝑚) and mass 𝑚=2𝑔Ricochet of cylinder – Marina
Seidl
Page 10/25Slide12
Comparison
Ricochet of cylinder – Marina
Seidl
Page 11/25Slide13
Comparison – Non ricochet
SPH
t
=
15ms
x-displacement =
91mm
Pressure
plot in
and initial
ALE
t
=
15ms
x-displacement =
91mm
Pressure plot in
Ricochet of cylinder – Marina
Seidl
Page 12/25
Pressure
plot
in
Slide14
Comparison – Non ricochet
SPH
t
=
75ms
x-displacement =
372mm
Pressure plot in
and initial
ALE
t
=
73ms
x-displacement =
372mm
Pressure plot in
Ricochet of cylinder – Marina
Seidl
Page 13/25
Pressure
plot
in
Slide15
Comparison – Non ricochet
SPH
t = 100ms
x-displacement
= 492mm
Pressure plot in
and initial
ALE
t = 100ms
x-displacement = 475mm
Pressure
plot in
Ricochet of cylinder – Marina
Seidl
Page 14/25
Pressure
plot
in
Slide16
Comparison – Ricochet
Ricochet of cylinder – Marina
Seidl
Page 15/25Slide17
Comparison – Ricochet
SPH
t =
10ms
x-displacement =
91mm
Pressure plot in
and initial
ALE
t
=
10ms
x-displacement =
91mm
Pressure plot in
Ricochet of cylinder – Marina
Seidl
Page 16/25
Pressure
plot
in
Slide18
Comparison – Ricochet
SPH
t
=
50ms
x-displacement =
379mm
Pressure plot in
and initial
ALE
t =
50ms
x-displacement =
384mm
Pressure plot in
Ricochet of cylinder – Marina
Seidl
Page 17/25
Pressure
plot
in
Slide19
Comparison – Ricochet
SPH
t
=
100ms
x-displacement =
695mm
Pressure plot in
and initial
ALE
t
=
100ms
x-displacement =
642mm
Pressure plot in
Ricochet of cylinder – Marina
Seidl
Page 18/25
Pressure
plot
in
Slide20
Case studies
ALE
Bulk modulus
Ambient pressure
Convergence study
Viscosity
SPH
Convergence study [11]
Ricochet of cylinder – Marina
Seidl
Page 19/25Slide21
Comparison
Ricochet of cylinder – Marina
Seidl
Page 20/25Slide22
Comparison
ALE
SPH
Ricochet of cylinder – Marina
Seidl
Page 21/25Slide23
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
Ricochet of cylinder – Marina
Seidl
Page 22/25Slide24
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
Ricochet of cylinder – Marina
Seidl
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Ricochet of cylinder
Any questions?
Page 24/25Slide26
Ricochet of cylinder
Thank you for your attendance!
Page 25/25Slide27
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 2013Slide28
APPENDIXSlide29
Ricochet
Rebound on surfaceHigh 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]Slide30
Ricochet – Analytical models
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
)
Slide31
Ricochet – Analytical models
Model of Birkhoff
et. al got extended (REF)Non-spinning solid sphereDependent of impact velocity ,
gravity g and radius r
Slide32
Ricochet – Analytical models
Derived from 3D case (REF)
Non-spinning solid cylinderDependent of impact velocity , gravity g and radius r
Slide33
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]
Slide34
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
𝑖𝑛𝑐ℎ (25.4𝑚𝑚) and mass 𝑚=2𝑔
Initial velocity is split in a vertical
and horizontal
component
Gravity
is applied in negative
y-direction
Ricochet of cylinder – Marina
SeidlSlide35
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]
ALE2 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]
Ricochet of cylinder – Marina
SeidlSlide36
Comparison – Non ricochet
Pressure plot in
ALE
and initial
Slide37
Comparison – Ricochet
Pressure plot in
ALE
and initial