This document describes the hydrodynamic analysis of the IPS Buoy wave energy converter including the effect of non-uniform acceleration tube cross-section. The IPS Buoy system uses the relative motion between a submerged vertical acceleration tube and a piston inside the tube to generate power as they oscillate in heave motion due to incoming waves. The analysis involves developing mathematical models of the system and its components under assumptions like one-dimensional flow inside the tube. Numerical results are presented for the power absorbed and other parameters in regular and irregular wave conditions.
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IPS Buoy
1. HY D R O D Y N A M I C S OF TH E IPS BU O Y WA V E EN E R G Y CO N V E R T E R
IN C L U D I N G TH E EF F E C T OF NO N -UN I F O R M AC C E L E R A T I O N TU B E
CR O S S SE C T I O N
A N T Ó N I O F . O . F A L C Ã O
J O S É J . C Â N D I D O
P A U L O A . P . J U S T I N O
J O Ã O C . C . H E N R I Q U E S
IPS Buoy
Abhishek Mondal
IIT Kharagpur
IDMEC, Instituto Superior Técnico, Technical University of Lisbon, 1049-001 Lisbon, Portugal
Laboratório Nacional de Energia e Geologia, Estrada Paço do Lumiar, 1649-038 Lisbon, Portugal
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2. What is IPS Buoy ?
A wave energy converter
Initiated by Swedish Company Inter
Project Service (IPS)
Connected to fully submerged vertical
acceleration tube oscillating in heave
motion
Relative motion of piston and floater-tube
system generates Power Take Off (PTO)
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3. Assumptions
The buoy-tube-piston system is mathematically modelled using the
following assumptions :
Buoy-tube system has heave motion only
The tube is sufficiently below the water surface; thus the
excitation & radiation force become negligible.
Negligible interaction between the wave fields at tube ends
Flow inside the tube is one dimensional
Piston has negligible length and mass
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4. Mathematical Modelling
V(t) : Piston Velocity
A1 : Cross-section of inner tube
A2 : Cross-section of outer tube = α2 A1
A(ξ) : Cross-section at conical transition
Flow Velocity
Pressure
where
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5. Hydrodynamic Analysis in Regular Waves
Force on piston:
fp(t)= -Mxx - Myy+Ky+Cy
Power absorbed by PTO
P = fp(t)y
Wave excitation force
fe(t) = AwΓ(ω)eiωt
Force on the tube
ft(t) = -mxx - myy
• x(t): floater-tube position
• y(t): position of piston
• K : spring stiffness
• C : PTO damping coeff.
• Aw: linear wave amplitude
• ω: wave frequency
• Mb: buoy mass (mb) +
added mass (μb)
• Mt: tube mass (mt) +
added mass (μt)
• Γ(ω): excitation force coeff.
• β : half-angle
• l : added length
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6. Hydrodynamic Analysis in Regular Waves
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Where
Mx = ρA1(L+2l)
My = ρA1(b1+α-2(b3+b4+2l)+2b2α-1)
mx = ρA1[0.667b2(α2+α-2) + (α2 -1)(b3+b4+2l)]
my = ρA1[2b2(1 - α-1) + (1 – α-2)
Equation of motion :
{x(t), y(t), fe(t)} = {X, Y, Fe}eiωt
(Mb+Mt)x + Bx + ρgSx = fe(t) + ft(t) + fp(t)
7. Hydrodynamic Analysis in Regular Waves
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Solving governing equation of motion of the system under the
influence of linear sinusoidal wave field :
-ω2(Mb+Mt+mx+Mx)X + iωBX + ρgSX - ω2(my+My)Y = Fe --> (1)
-ω2MxX - ω2MyY + (K+iωC)Y = 0 --> (2)
Linear algebraic equations (1) & (2) is further solved to find
X & Y and thus x(t) and y(t) are obtained
8. Numerical Results in Regular Waves
For a cylindrical buoy of radius a submerged upto the depth a,
following non-dimentional parameters are obtained :
μb
* = μb/(ρπa3)
B* = B/(ρπa3ω)
T* = T(g/a)1/2
M1
* = 1+ (Mt/mb)
M2
* = ρA1(L+2l)/mb
C*(ω) = C/B(ω)
X* = |X|/Aw
Y* = |Y/X|
P* = P/Pmax
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For the case α = 1
_ _ _
9. Numerical Results in Regular Waves
Time averaged wave power P = 0.5ω2C|Y|2
Pmax = (g3ρAw
2)/4ω3
Maximum absorbed power attained for Xopt = |Fe|(2ωB)-1
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For the case α = 1, T* = 10, P* = 1
_
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15. Key Benefits of IPS Buoy
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Renewable energy source
Produces electricity for desalination
plants and remote areas
Cluster of buoys act as wave breaker
Easily expandable by adding more units
Easy installation and maintenance
Low production cost/kWh
50-100 MW annual power generation
Measures weather parameters and
forecast
17. References
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Falcão AF de O. Wave energy utilization: a review of the technologies. Renew
Sust Energy Rev 2010; 14:899-918.
Masuda Y. Wave-activated generator. Int. colloq. exposition oceans, Bordeaux,
France; 1971.
Noren SA. Apparatus for recovering the kinetic energy of sea waves. US Patent
No. 4,773,221; 1988 [original Swedish Patent No. 8104407; 1981].
Salter SH, Lin CP. Wide tank efficiency measurements on a model of the sloped
IPS buoy. In: Proc. 3rd European wave energy conf., Patras, Greece; 1998. p.
200-6.
Evans DV. The oscillating water column wave-energy device. J Inst Math Appl
1978;22:423-33.
Munson BR, Young DF, Okiishi TH. Fundamentals of fluid mechanics. 2nd ed.
New York: Wiley; 1994
Falnes J. Optimum control of oscillation of wave-energy converters. Int J
Offshore Polar Eng 2002;12:147-55.