Simulation of Buoyant Spherical Objects Segregation for Studying Beach Pollution

International Conference on
Fisheries, Aquatic, and
Environmental Sciences
26-27 September 2018,
Banda Aceh, Indonesia
1
Simulation of Buoyant
Spherical Objects
Segregation for Studying
Beach Pollution
Sparisoma Viridi1
*, Ghazi Mauer Idroes2
, Rinaldi Idroes2
,
Nurhayati3
, Johri Sabaryati4
, Dewi Muliyati5
,
Rachmad Mauludin1
, Fifi Fitriyah Masduki1
*dudung@fi.itb.ac.id
20180925_3

..
1
Institut Teknologi Bandung, Bandung 40132,
Indonesia
2
Universitas Syiah Kuala, Banda Aceh 23111,
Indonesia
3
Universitas Islam Negeri Ar-Raniry, Banda Aceh
23111, Indonesia
4
Universitas Muhammadiyah Mataram, Mataram
83127, Indonesia
5
Universitas Negeri Jakarta, Jakarta 13220, Indonesia
2

Outline
• Introduction
• Model
• Result s and discussion
• Summary
• Acknowledgments
3
..

4
Introduction

Segregation of spherical particles
• Observed for
sinking objects
in low viscosity
fluid
• Not yet for floating
objects
5
Samadani A, Kudrolli A 2000 Phys. Rev. Lett. 85 5102.

Floating object observation
6
Thiel M, Hinojosa IA, Joschko T, Gutow L 2011 J. Sea Res. 65 368.
German Bight
(North Sea)

> 5×1012
pieces, ~ 2.5×105
ton
7
Eriksen M, Lebreton LCM, Carson HS, Thiel M, Moore CJ, Borerro JC, Galgani F, Ryan PG, Reisser J 2014 PLoS one
9 e111913.

Dynamics of floating object
• It is interesting to study that
• Object interacts with its environment
(oscillating water surface)
• If it can be simulated, it will help us to
understand why there are some favorite
places for floating objects deposition
• How object properties, e.g. size and mass
density, influence its motion a long the water
8

Dynamics of floating object (cont.)
• Can they also segregate due to object physical
properties while floating?
9

One-dimensional system
• As water surface oscillates (–) floating body in
the form of sphere (--) will also oscillate
10
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.

One-dimensional system (cont.)
11
-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 (- - -)

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
12
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.

Two-dimensional system (cont.)
13

14
Model

Assumptions
• Floating object has the form of sphere
• There is no interaction between two objects
• Each object only interact with its
environment, i.e. earth gravitation, water
buoyancy, and water drag force
• Water surface wave has sinusoidal form
15

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
16
gDF bbG

ρπ 3
6
1
=
( )zfgDF BfbB

ρπ 3
6
1
−=
( ) ( )zfvvDF DfbfD

−−= πη3

Newton’s second law of motion
• Acceleration of floating body with mass mb at
time t can be found through
17
[ ]DAG
b
FFF
m
a

++=
1

Numerical integration
• Velocity v at time t + Δt is obtained from
• Position r at time t + Δt is obtained from
18
( ) ( ) ( ) tatvdtatvttv
tt
t
∆+≈+=∆+ ∫
∆+

( ) ( ) ( ) tvtrdtvtrttr
t
∆+≈+=∆+ ∫

0

Iteration
• After new position is obtained, it can be used
to calculate new acceleration and the process
begins again from the beginning
• Iteration stops until certain simulation time
19

20
Results and discussion

General parameters
• g = 9.81 m/s2
,
• ρf = 1.00×103
kg/m3
, ηf = 1 Pa·S (20 °C),
• A = 5 ×10-2
m,
f = 0.5 Hz,
λ = 1 m,
ϕ0 = 0 rad,
• Δt = 10-3
s, Tdata = 0.1 s, tend = 10 s
21

Floating object parameters
• Db =(2, 4, 6, 8, 10)×10-2
m,
• ρb = (2, 4, 6, 8, 10)×102
kg/m3
22

Position for ρb = 0.2 g/cm3
, D = 6 cm
23
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
-1 0 1 2 3 4 5
z (m)
x (m)

, Db = 6 cm
24
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
-1 0 1 2 3 4 5
z (m)
x (m)

, Db = 6 cm
25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
-1 0 1 2 3 4 5
z (m)
x (m)

, Db = 6 cm
26
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
-1 0 1 2 3 4 5
z (m)
x (m)

Position for ρb = 1 g/cm3
, Db = 6 cm
27
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
-1 0 1 2 3 4 5
z (m)
x (m)

Displacement for ρb/ρf variation
28
-1
0
1
2
3
4
5
6
0.2 0.4 0.6 0.8 1
Δx (m)
ρb/ρf

, Db = 2 cm
29
-0.1
-0.06
-0.02
0.02
0.06
0.1
-1 0 1 2 3 4 5 6 7 8 9 10
z (m)
x (m)

, Db = 4 cm
30
-0.1
-0.06
-0.02
0.02
0.06
0.1
-1 0 1 2 3 4 5 6 7 8 9 10
z (m)
x (m)

, Db = 6 cm
31
-0.1
-0.06
-0.02
0.02
0.06
0.1
-1 0 1 2 3 4 5 6 7 8 9 10
z (m)
x (m)

, Db = 8 cm
32
-0.1
-0.06
-0.02
0.02
0.06
0.1
-1 0 1 2 3 4 5 6 7 8 9 10
z (m)
x (m)

, Db = 10 cm
33
-0.1
-0.06
-0.02
0.02
0.06
0.1
-1 0 1 2 3 4 5 6 7 8 9 10
z (m)
x (m)

Displacement for Db variation
34
-1
1
3
5
7
9
11
0.02 0.04 0.06 0.08 0.1
Δx (m)
Db (m)

Segregation
35

36
Summary

Summary
• Simulation of floating object in the form of
sphere has been conducted
• Object with 6 cm diameter, the largest
horizontal displacement for density 0.8 g/cm3
• Object with 0.6 g/cm3
density, larger diameter
will also have larger horizontal displacement
• Segregation occurs due to size and density
differences
37

38
Acknowledgments

Acknowledgments
• P3MI ITB in presenting this work
• Unsyiah in arranging this event
39

40
https://osf.io/5axpf/

41
Thank you

Simulation of Buoyant Spherical Objects Segregation for Studying Beach Pollution

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