This document summarizes an investigation into the drag and added mass properties of mid-water arch structures for riser design. Hydrodynamic force analysis was conducted using Morison's equation and existing codes. Added mass coefficients were analyzed using panel methods and CFD simulations, finding panel methods provided better predictions than codes. Drag coefficients were found to vary with structure design and Reynolds number. CFD simulations matched published cylinder results and provided better coefficient predictions than codes.

1. INVESTIGATION OF DRAG &
ADDED MASS PROPERTIES OF
MID-WATER ARCH STRUCTURE
FOR RISER DESIGN
Presenter: Liangli(Michael) Li
Industry Supervisor: Dan Brooker ( Intecsea, Perth)
Academic Supervisor: Stuart Higgins (Curtin)

2. 1. Introduction
1

3. 2. Hydrodynamic Force Analysis
Morison Equation
◦ 𝐹 𝑡 = 𝐹𝑖 + 𝐹𝑑
◦ 𝐹𝑖 = 1 + 𝑪 𝒂 𝜌𝑉 𝑈
𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑑 𝑓𝑙𝑢𝑖𝑑 𝑚𝑎𝑠𝑠 (Froude–Kriloff force)
𝑎𝑑𝑑𝑒𝑑 𝑚𝑎𝑠𝑠 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡
◦ 𝐹𝑑 =
1
2
𝜌𝑪 𝒅 𝐴 𝑟 𝑈2 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡
𝑣𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡
𝐶 𝑎 =
𝑀 𝑎
𝜌𝑉
, 𝐶 𝑑 =
2𝐹 𝑑
𝜌𝑈2 𝐴 𝑟
𝐴 𝑟 Reference Area
𝑈 Flow Velocity
𝑉 Structure Volume
𝜌 Fluid Density
2

4. 3. Analyzing Using Existing code
MWA Design – buoyancy cylinder, gutters
Ca & Cd Analysis
◦ Code method - DNV-RP-C205
◦ Numerical approach–
◦ Panel Method, Ca
◦ Computational Fluid Dynamics, Cd
Compare to Code Method
Verify the results
3

5. 4. Panel Method
Directions DNV-RP-205
Circular Cylinder
DNV-RP-205
Square Cylinder
Panel Method
Surge, ZZ 0.919 0.72 1.6
Heave, YY 0.919 0.72 1.0
Sway, XX 0.137 0.125 0.08
3D Model
ANSYS APDL
HydroD
Added Mass Matrix
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6. 5. CFD Simulations
Velocity Reynolds
Number, Re
Circular
Cylinder
Square
Cylinder
CFD
0.5 m/s 1.8381x106 0.523 1.61 1.2076
1 m/s 3.6762x106 0.523 1.61 1.1978
1.5 m/s 5.5143x106 0.523 1.61 1.1464
2 m/s 7.3524x106 0.523 1.61 1.1396
3D Model
ANSYS ICEM
Fluent
Forces over time
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7. 6. Result Verification & Validation
Grid and Fluid Domain
◦ Grid Quality: 99.87% OK
◦ Wall interference
◦ Meshing size,5.4 million cells
Turbulence Models
Compare to Published Cylinder Result
Compare to Published MWA Results
Flow
Symmetry Plane
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8. Turbulence Model
Options Turbulence Model Options Applications Limitations
RANS
Spalart-Allmaras Model (1-eq)
Developed for aerospace applications,
suitable for external flow and flow with
adverse pressure gradient
Work well only on simple
geometry. Only work under
low Reynolds number flow
k-ε Model (2-eqn)
Suitable for internal flow and heat transfer
applications
Limited to high Re flow
condition, and not work
well if flow encounters bluff
bodies
k-ω Model (2-eqn)
Also developed for aerospace applications,
suitable for external flow and flow with
adverse pressure gradient, in both low and
high Re flow
Sensitive to free stream
turbulence
Laminar-Turbulent Transition
Models (3-4 eqn)
Provide prediction of laminar to turbulent
transition of boundary layer
Rely on mesh refinement
near wall and inlet initial
condition.
RSM (5 or 7-eqn)
Work with any complex flows, including
strong swirl and rotation
Most costly to run
SRS
SAS
(RANS-LES hybrid)
Provide more detailed vortex shedding
simulation (using von-Karman length scale)
High dependence on grid
size and time-steps
DES
(RANS-LES hybrid)
Provide more detailed turbulence simulation
(turbulence length scale)
High dependence on grid
size and time-steps
LES
(RANS-DNS hybrid)
Used for research purpose on sophisticated
geometry or small geometry scale
Only work with very fine
grid size and small time-
steps
DNS Used for 2D problems Most costly to run.
0.0
0.5
1.0
1.5
2.0
2.5
0 10 20 30 40 50
Cd
Time (s)
2m/s Case Drag Coefficient Time History
2m/s k-w-SST
2m/s DES-k-w-SST
Transient
response
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9. Turbulence Model
8

10. Compare to Published Cylinder Result
Cases Reynolds
Number
Cd after finite
length reduction (as
pre DNV Code)
Present simulation
hexahedron, 3D k-ω-SST
3.6762x106 0.314
Present simulation
tetrahedron, 3D k-ω-SST
3.6762x106 0.313
DNV-RP-C205 (Book: Fluid-
Dynamic Drag, 1965)
>1.0x106 0.523
Ong et al. 2009, 2D k-ε 3.6x106 0.368
Catalano et al. 2003, 2D k-ε 4.0x106 0.370
Shih et al, 1993, Exp ~3.5x106 ~0.33
Schewe, 1983, Exp 4.0x106 ~0.41
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11. Comparing with MWA Results
Cd = ~0.85
Re > 107
0
20
40
60
80
100
120
140
160
0 1 2 3 4
Drag(kN)
Velocity^2
Drag Force vs. Velocity^2
K-w-SST
DES-k-w-SST
0
50
100
150
200
250
0 1 2 3 4
Drag(kN)
Velocity^2
Drag Force vs V^2
Cd = ~1.17
Re > 106
Cd = ~1.18
Re > 105
Cd = ~0.86
Re > 105
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12. Closing Remarks
11
Added Mass Coefficient
• Ca varies with MWA design
• Code method has limitations
• Circular cylinder better than square cylinder
• Panel method gives better prediction of Ca
Drag Force Coefficient
• Cd varies with MWA design
• Code method gives a upper-lower bound
• Cd independent to Re, matches well to Morison eqn
• CFD gives better prediction of Cd
Possible Design Improvement
Future Work – other flow directions, roughness effect, model testing

13. Cd comparison DNV code vs. Others
12

14. 0.0
0.5
1.0
1.5
2.0
2.5
0 10 20 30 40 50 60 70 80 90 100
Cd
Time (s)
Drag Coefficient Over Time
0.5m/s k-w-SST
1.0m/s k-w-SST
1.5m/s k-w-SST
2.0m/s k-w-SST
MWA and Cylinder Plots
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0 20 40 60 80 100 120
Cd
Time (s)
Cd of Cylinder
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15. Quality Check by ICEM
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16. Allocating 12080x6232=75282560 pixel map.
57773920 pixels filled, area = 57.7731
Projected Area, Solidworks and Fluent
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