NUMERICAL SIMULATION OF WATER IMPACT
INVOLVING THREE DIMENSIONAL RIGID
BODIES OF ARBITRARY SHAPE
Z Z.Hu, D M Causon, CG Mingham and L. Qian
Department of Computing and Mathematics
Manchester Metropolitan University, United Kingdom
ICCE 2010
Objectives
Objectives
600
700
Experimental data
600
Force (N)
ƒ Development of a 3D flow solver based on the Euler equations
using a Riemann-based finite volume method and Cartesian cut
cell meshes for simulating water impact problems involving
arbitrarily complex moving rigid bodies.
Force (N)
500
Experimental data
Present result
500
Present result
400
300
200
400
300
200
100
100
0
0
0
0.5
1
0.0
1.5
0.5
1.0
z/d
Methods
Methods
Vertical force v time (45º)
ƒ Incompressible Navier-Stokes solver — Based on an artificial
compressibility method.
z/d
1.5
2.0
2.5
Vertical force v time (30º)
3.Water entry of various rigid 3D bodies
ƒ Surface-capturing method that treats the free surface as a
contact discontinuity in the density field so no special procedures
are required to track the free surface.
ƒ Input Body moves vertically toward an initially still water surface
at V=1m/s.
ƒ Fully two phase approach which solves in both the air and
water fluid regions.
ƒ Tank: 2.0m × 0.15m × 2.0m and water depth: h=1.0m.
ƒ R=0.15m, height=0.15m.
ƒ Cartesian cut cell Method
- flexibility for dealing with complex moving geometries
- no requirement to re-mesh globally: only requires
updates locally at cells on the background Cartesian mesh
that are actually cut by the moving boundary contour.
Results
Results
t =0.1s
1. Oscillating cone validation
t = 0.4s
t = 0.7s
t = 1.0s
ƒ Vertical position of a cone d(t) follows the form of a
Gaussian wave packet:
N
hπ ⎤
⎡
d ( t ) = A ∑ Z (ω n ) cos ⎢ ω n ( t − t 0 ) −
Δωn
2 ⎥⎦
⎣
n =1
Bobber
Cone
ƒ Experiments conducted by K. Drake et al.(2009).
ƒ Test case: A=50mm, m=9 and cone dead-rise angle of 45º.
ƒ Tank: 2.0m×1.6m, the water depth: h=1.02m and the initial
draught of the cone is z=0.148m.
Sphere
ƒ Dimensions: a =0.228m, d=0.2281m, b=0.05m
Wedge
ƒ CPU time on coarse mesh (dx=dy=0.02m) 15 hours
Velocity vectors
ƒ CPU time on fine mesh (dx=dy=0.01m) 41 hours
1.0
a
d
Non-dimensional vertical forces
b
z
AMAZON (Δ=0.01)
AMAZON (Δ=0.02)
Experimental data
0.8
0.6
0.2
ƒ Validations included forced oscillation of a cone and water entry
of a 3D rigid wedge.
0.0
-0.2
-0.4
-0.6
-0.8
-6
Geometry
Conclusion
Conclusion
0.4
-4
-2
0
t/T
2
4
6
Vertical force v time
2. Water entry of a 3D rigid wedge validation
ƒ Body moves vertically downwards towards an initially still
water surface at a velocity V=1.19m/s (45º dead-rise angle) and velocity
V=0.72m/s (30º dead-rise angle).
ƒ
Experimental data (Tveitnes et al. 2008).
ƒ Tank: 2.0m×0.4m×2.0m and the water depth: h=1.0m.
ƒ Uniform mesh: 80×16×80=102,400 (dx=dy=dz=0.025m).
ƒ Dimensions: breadth=0.6m, length=0.3m, height=0.3m.
ƒ AMAZON-SC3D has been successfully implemented for various
slamming cases involving the Manchester Bobber; cone; sphere
and wedge.
References
References
1. Drake,K., Eatock Taylor, R., Taylor, P. and Bai, W. (2009).
"On the hydrodynamics of bobbing cones." accepted.
2. Tveitnes T., fairlie-Clarke A.C., Varyani K. (2008). "An
experimental investigation into the constant velocity water
entry of wedge-shape sections," J. Ocean Eng. 35: 14631478.
3. Hu Z.Z., Causon D.M., Mingham C.G., Qian L. (2009).
"Numerical wave tank study of a wave energy converter in
heave." Proceedlings 19th ISOPE conference, Osaka, Japan.
Email address: [email protected] Sponsored by the Engineering and Physical Sciences Research Council (EPSRC) in U.K.
Grant Ref: EP-D077621