mooring implementation in sph models
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Mooring implementation in SPH models
anxo.barreiro@uvigo.es, Iberian SPH workshop, Dec 2015
A. Barreiro, J.M. Dominguez, A.J.C. Crespo, O. Garcia-Feal and M. Gomez-Gesteira
Table of contents1. Introduction
2. Floatings & moorings
3. Conclusions
Iberian SPH workshop, Dec 2015
1.1 What is a mooring?1.2 Why is important to solve moorings?
Iberian SPH workshop, Dec 2015
Table of contents1. Introduction
2. Floatings & moorings
3. Conclusions
Iberian SPH workshop, Dec 2015
All the objects are floating in the water and moored, thus a proper formulation is needed and must be validated.
Floatings & Moorings
Iberian SPH workshop, Dec 2015
2.1 Fluid driven objects2.2 Moored lines
2.2.1 Static approach2.2.2 Mooring classification2.2.3 Model validation
2.3 Application cases
Table of contents1. Introduction
2. Floatings & moorings
3. Run-off on real terrains
4. Conclusions & future work
Iberian SPH workshop, Dec 2015
2.1 Fluid driven objects
ππ =
πβπππ
πππEach particle k (FB) experiences a force per unit mass given by
πππππ = βπππππ
Where πππ is the force per unit mass by the fluid a on particle k,
πππ½
ππ‘=
πβπ΅ππ
ππ ππ
πΌππ
ππ‘=
πβπ΅ππ
ππ ππ β πΉ0 Γ ππ
Newtonβs equations for rigid body dynamics:
Floatings & Moorings
ππ = π½ + π΄ Γ ππ β πΉ0
The movement of FB is derived by considering its interaction with fluid particles and using these forces to drive its motion
Iberian SPH workshop, Dec 2015
2.1 Fluid Driven objects
Validation for floating objects
Fekken (2004) & Canelas et al. (2015)
Floatings & Moorings
πππππππ‘ = 1,200 kg Β· πβ3
Comparison of numerical data and DualSPHysics results for displacement and velocity of the sinking cylinder.
Iberian SPH workshop, Dec 2015
2.2 Moored lines
π¦ = π coshπ₯
π
-1
1
3
5
7
9
11
13
15
-4 -3 -2 -1 0 1 2 3 4
Floatings & Moorings
Iberian SPH workshop, Dec 2015
2.2 Moored lines
π¦ = π coshπ₯
π
-1
1
3
5
7
9
11
13
15
-4 -3 -2 -1 0 1 2 3 4
Catenary function
Floatings & Moorings
π = 1
π = 2
π = 3
Iberian SPH workshop, Dec 2015
2.2 Moored lines
T is the line tension.
A is the cross-section area of the line.
E represents the elasticity modulus.
F and D correspond to the mean hydrodynamic
forces both normal and tangential direction
respectively.
π is the submerged weight per unit length.
Floatings & MooringsDiagram of the different forces acting on an element of a mooring line
Iberian SPH workshop, Dec 2015
ππ β πππ΄ ππ§ = π π ππ π β πΉ 1 + π π΄πΈ ππ
π ππ β πππ΄ ππ = π πππ π + π· 1 + π π΄πΈ ππ
π = ππ» + πβ + π + πππ΄ π§
2.2.1 Static approach
Faltinsen (1993)
Floatings & Moorings
The tension exerted by a mooring on a floating body can be expressed as:
Iberian SPH workshop, Dec 2015
2.2.1 Static approach Floatings & MooringsParameters that define a mooring line.
Iberian SPH workshop, Dec 2015
π = π β β 1 + 2π
β
12+ π coshβ1 1 +
β
ππ = ππ» π
2.2.1 Static approach Floatings & MooringsParameters that define a mooring line.
Iberian SPH workshop, Dec 2015
π = π β β 1 + 2π
β
12+ π coshβ1 1 +
β
ππ = ππ» π
0
50
100
150
80 85 90 95 100
TH
(kN
)
X (m)
Line 1
Line 2
- Line 1, π=850 NΒ·m-1, h=20 m and l=100 m.
- Line 2, π=1000 NΒ·m-1, h=20 m and l=100 m.
2.2.1 Static approach Floatings & Moorings
Iberian SPH workshop, Dec 2015
x
y
Οi
THi
The equations shown before can begeneralized for a multiple lineproblem with the properimplementation.
πΉπ₯ = ππ»π πππ πΉπ
2.2.1 Static approach
πΉπ¦ = ππ»π π πππΉπ
Floatings & Moorings
Spread mooring approach:
Iberian SPH workshop, Dec 2015
2.2.2 Mooring classification
Normal conditions are already covered but there are two different states that are not solved yet
Anchor point
(a)
(c)
(b)
(d)
Floatings & Moorings
Anchor point
(a)
Iberian SPH workshop, Dec 2015
2.2.2 Mooring classification
Normal conditions are already covered but there are two different states that are not solved yet
ππ§ β πβπ
Floatings & Moorings
Iberian SPH workshop, Dec 2015
2.2.2 Mooring classification
Normal conditions are already covered but there are two different states that are not solved yet
Floatings & Moorings
Anchor pointAnchor point
(a)
(c)
(b)
(d)
ππ = π1 + π2 + π3 + π4 Β·Β·Β·
πΉππ₯ = πΉπ Β· cos ππ Β· cosπππΉππ¦ = πΉπ Β· cos ππ Β· sin πππΉππ§ = πΉπ Β· sin ππ
πΉππππ πππ π πππππππ
πΉππ₯ =πΉππ₯ Β· cosππ ππ cosππ
πΉππ¦ =πΉππ¦ Β· sin ππ ππ sinππ
πΉππ§ =πΉππ§ Β· sin ππ ππ sin ππ (d)
Iberian SPH workshop, Dec 2015
2.2.2 Mooring classification
Normal conditions are already covered but there are two different states that are not solved yet
Floatings & Moorings
Iberian SPH workshop, Dec 2015
2.2.3 Model validation
Johanning (2007), Laboratory dimensions.
Floatings & Moorings
One line validation I
(b) (c)
Iberian SPH workshop, Dec 2015
2.2.3 Model validation
Parameter Value
h 2.651 m
Ο 1.036 NΒ·m-1
l 6.98 m
Minimum extension 5.735 m
Maximum extension 6.367 m
0
5
10
15
5.5 6
Ten
sion
(kN
)
Position (m)
Experiments
Axial Loading
DualSPHysics
One line validation I
Floatings & Moorings
Johanning (2007), Laboratory dimensions.
Iberian SPH workshop, Dec 2015
2.2.3 Model validation Floatings & Moorings
One line validation II Johanning (2006), Real dimensions.
(b) (c)
Iberian SPH workshop, Dec 2015
2.2.3 Model validation
Parameter Value
h 50 m
Ο 918.75 NΒ·m-1
l 150 m
Minimum extension 102 m
Maximum extension 140 m
0
25000
50000
75000
100000
125000
150000
175000
100 105 110 115 120 125 130 135 140 145 150
Ten
sio
n (
N)
Distance (m)
Johaning
DualSPHysics
Floatings & Moorings
One line validation II Johanning (2006), Real dimensions.
Iberian SPH workshop, Dec 2015
2.2.3 Model validation Floatings & Moorings
Multiple line validation
Johanning (2006),Real dimensions.
Iberian SPH workshop, Dec 2015
2.2.3 Model validation
Parameter Value
h 50 m
TH0 50 kN
l 75 m
Minimum extension
from resting point
-15 m
Maximum extension
from resting point
15 m
Multiple line validation
0
50000
100000
150000
200000
250000
300000
350000
-20 -10 0 10 20
Ten
sion
(N
)
Position (m)
LineA Johanning
LineA DualSPHysics
LineB Johanning
LineB DualSPHysics
Merge Johanning
Merge DualSPHysics
Floatings & Moorings
Iberian SPH workshop, Dec 2015
Floatings & Moorings2.3 Application cases
VIDEO LINK
Iberian SPH workshop, Dec 2015
Floatings & Moorings2.3 Application cases
VIDEO LINK
Iberian SPH workshop, Dec 2015
Table of contents1. Introduction
2. Floatings & moorings
3. Conclusions
Iberian SPH workshop, Dec 2015
Conclusions
-Moorings & Floating bodies
The functionalities necessary to simulate mooringswere implemented in DualSPHysics. The newimplementation is able to solve properly both chainforces and the effect moorings in the floating bodies.
The buoyancy of the floating bodies was validatedagainst numerical data from VOF showing a reallygood agreement.
The implementation of moorings was validatedagainst experimental data and compared with othernumerical models. This validation provided reallygood agreement with both numerical andexperimental data at various scales.
Two application examples were presented, the firstone is a boat under the action of side waves and onlyone moored line. The second application consisted ofa wind-turbine base with three moorings under theeffect of extreme waves.
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