The document discusses modeling the dynamics of a floating ball for harvesting energy from sinusoidal water waves. It presents a one-dimensional and two-dimensional model to simulate the motion of a spherical floating object under water wave oscillations. The models consider gravitational, buoyancy, and drag forces. Numerical integration is used to calculate the velocity and position of the floating object over time based on these forces. The energy harvested depends on the type of energy harvesting system used and how it interacts with the motion of the floating object under the water waves.

1. the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
1
Floating Ball Dynamics for
Harvesting Energy of
Sinusoidal Water Wave
Sparisoma Viridi*, Dwi Irwanto
Institut Teknologi Bandung, Jalan Ganesha 10, Bandung 40132, Indonesia
*dudung@fi.itb.ac.id, dirwanto@fi.itb.ac.id
20180926_0

2. Outline
• Introduction
• Model
• Result s and discussion
• Summary
• Acknowledgments
the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
2
..

3. the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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Introduction

4. Vibration energy harvester
• Ambient vibrations are in general random and
broadband
• Some sources, e.g. ocean waves and human
motion, are always provided
• There is difficulty in matching resonant
frequency of the device with frequency of
ambient vibrations
the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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Wei C, Jing X 2017 Renew. Sust. Energ. Rev. 74 1.

5. Piezoelectric-based system
the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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Untoro T, Viridi S, Suprijanto, Ekawati E 2017 J. Phys.: Conf. Ser. 877 012042.

6. Piezoelectric-based system (cont.)
the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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7. Flexible EHD based on BCTZ-NW
the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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Jin CC, Liu XC, Liu CH, Wang Y, Hwang HL, Wang Q 2018 Mater. Design 144 55.

8. Flexible EHD .. BCTZ-NW (cont.)
the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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9. Broadband micro electrostatic EH
the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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Zhang Y, Wang T, Luo A, Hu Y, Li X, Wang F 2018 Appl. Energy 212 362.

10. .. micro electrostatic EH (cont.)
the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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11. Triboelectric nanogenerator
the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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Wu H, Shi Q, Wang F, Thean AV-Y, Lee C 2018 Small Method 2 1800078.

12. Triboelectric nanogenerator (cont.)
the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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13. Hybrid generator: TENG + EMG
the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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Chen X, Guo H, Wu H, Chen H, Song Y, Su Z, Zhang H 2018 Nano Energy 49 51.

14. Hybrid ..: TENG + EMG (cont.)
the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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15. One-dimensional system
• As water surface oscillates (–) floating body in
the form of sphere (--) will also oscillate
the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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S Viridi, Nurhayati, J Sabaryati, "Dinamika Satu-Dimensi Butiran Berbentuk Bola yang Terapung
pada Permukaan Fluida“, Simposium Nasional Inovasi dan Pembelajaran Sains (SNIPS), 9-10 Juli
2018, Bandung, Indonesia.

16. One-dimensional system (cont.)
the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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-2.5E-2
-2.0E-2
-1.5E-2
-1.0E-2
-5.0E-3
0.0E+0
5.0E-3
1.0E-2
1.5E-2
2.0E-2
2.5E-2
0 2 4 6 8 10 12 14 16 18 20
z
t
Relaxation stage Oscillation stage
Floating body (–––)
Water surface (- - -)

17. Two-dimensional system
• If diameter of floating object Db is not too
small compared to water surface wavelength
λf then it can also move in horizontal direction
the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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S Viridi, Nurhayati, J Sabaryati, D Muliyati, "Dinamika Dua-Dimensi Butiran Berbentuk Bola yang
Terapung pada Permukaan Fluida yang Merambatkan Gelombang“, Seminar Nasional Fisika (SNF),
14 Juli 2018, Jakarta, Indonesia.

18. Two-dimensional system (cont.)
the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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19. Influence of ρb/ρf and D
the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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-1
0
1
2
3
4
5
6
0.2 0.4 0.6 0.8 1
Δx (m)
ρb/ρf
Viridi S, Idroes GM, Idroes R, Nurhayati, Sabaryati J, Muliyati D, Mauludin R, Fitriyah F 2018
International Conference on Fisheries, Aquatic, and Environmental Sciences (ICFAES), 26-27
September 2018, Banda Aceh, Indonesia.

20. Influence of ρb/ρf and D (cont.)
the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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-1
1
3
5
7
9
11
0.02 0.04 0.06 0.08 0.1
Δx (m)
Db (m)

21. Influence of ρb/ρf and D (cont.)
the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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22. the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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Model

23. Considered forces
• Gravitational force
• Buoyant force
• Drag force
with fB(z) and fD(z) is the dependence on the
vertical position of water surface z
the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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gDF bbG

ρπ 3
6
1
=
( )zfgDF BfbB

ρπ 3
6
1
−=
( ) ( )zfvvDF DfbfD

−−= πη3

24. Considered forces (cont.)
• The functions with fB(z) and fD(z) are due to
partially immersing in water of the floating
object
the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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25. Newton’s second law of motion
• Acceleration at time t can be found through
with mb is mass of the floating body
the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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( ) ( )[ ] ( )[ ] ( )[ ]{ }tvFtrFtrF
m
ta DAG
b

++=
1

26. Numerical integration: Euler
• Velocity v at time t + Δt is calculated using
• Position r at time t + Δt is calculated using
the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
26
( ) ( ) ( ) ( ) ( ) ttatvdttatvttv
tt
t
∆+≈+=∆+ ∫
∆+

( ) ( ) ( ) ( ) ( ) ttvtrdttvtrttr
t
∆+≈+=∆+ ∫

0

27. Obtained energy
• It depends on the type of energy harvesting
system (EHS), which is included fEHS
the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
27
( ) ( ) ( )[ ]tvtrftE

,EHS=

28. the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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Results and discussion

29. f = 0.5 Hz, λ = 1 m
the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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30. A= 5 cm, λ = 1 m
the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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31. f = 0.5 Hz, A = 5 cm
the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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32. Form of fEHS
• It must be digitized from data in reported
experimental results, where the wave is
assumed to be sinusoidal
• One of the example is the experiment using
spherical-shaped water based triboelectric
nanogenerator or SWTENG (Shi et al., 2017)
the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
32
Shi Q, Wang H, Wu H, Lee C 2017 Nano Energy 40 203.

33. the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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Summary

34. Summary
• Vibration properties of sinusoidal water wave,
e.g. frequency, wavelength, amplitude, and
also physical properties of spherical buoyant
object, e.g. size and mass density, determine
vibration motion of the object
• Type of energy harvester must consider object
vibration motion for efficient energy
harvesting
the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
34

35. the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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Acknowledgments

36. Acknowledgments
• KK FNB in presenting this work
• FMIPA + LPPM ITB in arranging this event
the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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37. the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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https://osf.io/7emhp/

38. the 2nd International Conference
on Energy Sciences (ICES)
24-26 September 2018,
Bandung, Indonesia
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Thank you