ISSN 2086-5953 observed. The second case study, however, aims to
show the clearance phenomena when the water enter the clearance of the obstacle.
2 METHOD VALIDATION
2.1 Methods of SPH
The kernel of SPH In the SPH model, the fluid is discretized
with a finite number of macroscopic fluid particles. Each particle a is characterized by mass m
a
, density ρ
a
, pressure p
a
, a velocity vector u
a,
and a position
vector r
a
. The kernel of SPH is the interpolation formula which evaluates the value of any flow
property A at the position r, in relation with all other fluid particles b and is denoted as
2
. ,
1
b b
k b
b
m A
A w h
O h
b
r r r
where w
h
is an interpolating function which plays a central part in SPH. It depends on the distance
between two particles and a parameter h is called the smoothing length and proportional to the initial
particle spacing. In order to reduce the number of particles involved in Equation 1 and thus to
reduce the calculation time, it is convenient to consider kernels characterized by a compact
support of radius h
t
which is proportional to the smoothing length h. Consequently, only particles
located in the disc or sphere, in 3D of radius h
t
and centred on a contribute to the evaluation of the function A relative to the particle a. General
expressions of kernels are given by Morris et al. [9] and Monaghan [7]. In most SPH codes, spline
kernels are used. Herein, we consider the fourth- order spline kernel in the present SPH model [5].
Equations of motion in SPH model
An SPH form of the Lagrangian continuity equation can be written as
d .
. .
2 d
a h
ab b
m w
t
ab ab
u r
2
where u
ab
= u
a
− u
b
and ε
ab
= r
a
− r
b
r
ab
. ˙w
h
corresponds to the spatial partial derivative of the kernel and ddt to a Lagrangian derivative
obtained by the motion of a particle. In a Lagrangian system, the equation of
motion is
d 1
3 d
e
P t
u u F
3 where
ν denotes the kinematic viscosity of the fluid, p
is pressure,
ρ is density and F
e
is external forces such as the gravity or the Lorentz force in
magnetohydrodynamics. In the SPH model, the viscous effect is commonly modelled by an
artificial pressure [9, 11] which is
2
16 .
. .
4
b h
ab b
a b
v v
m w
ab ab
a ab
2 ab
u r u
r r
with η
2
= 0.01h
2
introduced to avoid a zero
denominator and r
ab
= r
a
− r
b
.
The pressure of each particle is determined by the following stiff state equation [7]:
2
. 1
5
o o
o
c P
where ρ
o
represents a reference density, c
o
is a numerical speed of sound and
γ is a constant coefficient equal to 7. In order to simulate a nearly
incompressible flow, c
o
must be at least ten times superior than the maximal velocity of the flow. This
nearly-incompressible assumption thus induces a Mach number M less than 0.1. Consequently, the
relative variation of density, which scales as M
2
, is less than 1 see [9].
2.2 Validation of SPH model
Test problem: Collapse of a water column
A 2D water column is considered in a tank. The collapse of the water column occurs due to
gravity. A complete description of the experiment is given by [6] and a brief setup can be observed in
Fig. 1. The same setup was used by [11] to check the accuracy of their SPH code. The tank is 4m
long; the initial volume of water is 1m long and 2m high. The number of boundary particles is 4,000
and the number of fluid particles is 40,000. A smoothing length, h = 0.012m and a viscosity term,
α = 0.5 are considered.
Figure 1. Initial configuration of the water column
ISSN 2086-5953 At T = 0.4s, the maximum dam break
velocity is observed near the toe. The time history of toe velocity is compared with experimental data
in Fig. 2. At T = 0.8s the wave front has reached the right wall. At T = 1.1s, water climbs onto the right
wall. At T = 1.8s, water starts to fall over. The water height decreases near the left wall. The time
history of the water height is also compared with experimental data in Fig. 2.
An accurate water height H near the left wall and dam toe advance X proves the proper
behaviour of fluids on boundary. Fig. 2 shows how H
and X fit data provided by the experiment [6] in an accurate way. Comparing both SPH results,
water height H calculated by [11] fits slightly better the experimental data, while our SPH results about
the dam toe advance X are closer to experimental data than results of [11].
Figure 2. Collapse of a water column in a tank simulated with SPH model dash line comparing with experimental data solid
circle [6] and [11] results solid line
3 RESULT DISCUSSION
Fig. 3 presents some snapshots of the flow at different times. A dimensionalised time t, is used
for explaining different stages of the problem. At t = 0.0 sec the water column is allowed to flow. A
relatively high velocity and shallow water depth flow in x-direction quickly form e.g. t = 0.4 sec.
As time increases, the flow impacts on the vertical wall at the two sides of the obstacle and this
happened at t = 0.8 sec. An upward water jet is suddenly formed that rises until gravity overcomes
the upward momentum around t = 1.2 sec. At this moment, the jet becomes thicker and the flow starts
to reverse. Due to the oncoming flow, an adverse momentum gradient is created that results in an
over-turning wave around t = 1.3 sec. This wave formation continues until the wave tip reconnects
with the incident shallow water flow that now has less forward momentum [1]. Therefore, the impact
pressure flow on a wall of the obstacle is 2.39Nm2 and velocity in y-direction is 4.32 msec.
The other side of water column has the same phenomena with
this side.
Figure 3. Dam break flow and impact against the obstacle
Time sequences of evolution of the dam break flow from time t = 0.0 sec to t = 1.1 sec are
shown in Fig. 4. At time t = 0.0 sec, the water column was allowed to flow. A relatively high
velocity and shallow water depth flow in x- direction quickly formed and this happened at t =
0.35 sec. As time increased, the two flow are facing each other and this happened at t = 0.85 sec. Due
to momentum, this two flow impacted the vertical wall.
The particles
maintain an
orderly configuration until they meet the obstacle and
clearance then simulate a splash [8] and happened at t =1.1 sec. Maximum pressure when the first time
the flow touch the obstacle is 3.12 Nm2 from the bottom.
H X
ISSN 2086-5953
Figure 4. Dam break flow and impact against the obstacle and clearance.
4 CONCLUSIONS
The SPH model has been established in this study. This model can catch the large deformations
of the free surface and the complicated interaction between fluids and solids. Also, this model can be
used to predict phenomenon of over-turning wave of dam break flow impact against the obstacle or
splash phenomena with obstacle-clearance.
ACKNOWLEDGMENT
Funding from
the university
is gratefully
acknowledged by the authors. The authors are grateful to the reviewers for their valuable
comments and helpful recommendations.
REFERENCES
[1] Abdolmaleki, K., Thiagarajan, K.P., and
Morris_Thomas, M.T.2004. Simulation of the dam break problem and impact flows
using a
navier-stokes solver.
15th Australasian Fluid Mechanics Conference
The University of Sydney , 13-17 December,
Sydney, Australia. [2]
Brufau, P. and Garcia_Navarro, P.2000. Two dimensional dam break flow simulation.
International Journal Numerical Method Fluids
, 33: 35-57 [3]
Buchner, B.2002. Green water on ship-type offshore structures. PhD. Thesis, Delft
University of Technology, Netherland. [4]
Dalrymple, R.A., and Rogers,B.D.2006. Numerical modeling of water waves with the
sph method. Coastal Engineering, 53:141- 147.
[5] Issa, R., Lee, E.S., Violeau, D., and Laurence,
D.R.2005. Incompressible separated flows simulations with the smoothed particle
hydrodynamics gridless method. International Journal for Numerical Methods in Fluids
, 47: 1101-1106.
[6] Khosizuka, S. and Oka, Y.1996. Moving
particle semi
implicit method
for fragmentation of compressible fluid. Nuclear
Science Engineering
, 123: 421- 434. [7]
Monaghan, J.J.1992. Smoothed particle hydrodynamics. Annual Review of Astronomy
and Astrophysics
, 30: 543-574. [8]
Monaghan, J.J.1994. Simulation free surface flows with SPH. Journal of Computational
Physics
, 110: 399-406. [9]
Morris, J.P., Fox, P.J., and Zhu, Y.1997. Modelling
low reynolds
number incompressible flows using sph. Journal of
Computational Physics
, 136 : 214-226. [10]
Stoker, J.J.1957.
Water waves:
the mathematical theory with applications, pure
and applied
mathematics. Interscience
Publishers , Inc., New York.
[11] Violeau, D. and Issa, R.2006. Numerical
modelling of complex turbulent free surface flows with the sph method: an Overview,
International Journal for Numerical Methods in Fluids
, 53: 277-304. [12]
Zhou, Z.Q., Kat, J.O.D., and Buchnes, B.A.1999. A nonlinear 3-D approach to
simulate green water dynamics on desk. 7th InternationalConference
Numerical Ship
Hydrodynamics , Nantes.
91 ISSN 2086-5953
STRUCTURAL TRANSITION AND MAGNETIC PROPERTIES OF ZN-DOPED FE
3
O
4
BY CO-PRECIPICATION METHOD
Sigit Tri Wicaksono
1
, Haizan
2 1,2
Materials and Metallurgical Engineering, FTI, ITS Jl. T.Industri Kampus ITS Sukolilo Surabaya 60111
Email: sigitmat-eng.its.ac.id
ABSTRACT
Magnetic properties of Zn-doped Fe
3
O
4
have been synthesis by using co-precipitation method at
low temperature. X-Ray diffraction result shows that the sample was crystalline structure and form
Zn
x
Fe
3-x
O
4
stoichiometry. Further refinement of diffractions data show that the crystal structure has
change from cubic to hexagonal structure and lattice volume decrease 10 times by increasing of
doping and occur . The magnetic properties of sample have also studied. The results show that
Zn
x
Fe
3-x
O
4
was exhibit ferrimagnetic characteristic at room temperature.
Keywords: Co-precipitation method, doping, magnetic properties.
1 INTRODUCTION
Lie and Kuo
[1]
were conduct toward the doping of ZnO into Fe3O4 to see the effect of
Fe3O4 magnetic resistance using mechanical alloying method. They succeed to exhibit the
paramagnetism phenomenon in room temperature. In pervious study we have synthesis the
manganese- based magnetic materials to exhibit the magnetic properties of Mn
3
O
4
with nano-Fe3O4 by using co-precipitation method. The results show
that sample exhibit the same condition as paramagnetism phenomenon. In this study we have
doped Fe3O4 with ZnO by the same method.
The sample
exhibit the
Zn
x
Fe
3-x
O
4
stoichiometry as shown form X-ray diffraction pattern. Further refinement of diffractions data by
using Rietica program show that there was transition phenomenon of crystal structure from
cubic to hexagonal lattice. Another phenomenon was decreasing of lattice volume 10 times by
increasing of doping. The magnetic properties of sample such as Magnetic saturation, magnetic
remanent, and coercivity have also studied. The results show that Magnetic saturation Zn
x
Fe
3-x
O
4
was decrease by increasing of doping and exhibit ferrimagnetic characteristic at room temperature.
2 EXPERIMENTAL PROCEDURE
Magnetite Fe3O4 as the parrent phase has synthezed by chemical procedure as done in
previous research
[2]
by following
chemical procedures:
3Fe3O4+8HCl
2FeCl+FeCl2+3Fe2O3+3H
₂ O+H 2.1
ZnO + 2HCl
ZnCl2
+ H2O 2.2
2FeCl2+FeCl3 + ZnCl2 + NH
4
OH
Zn
x
Fe
3-x
O
4
+ H
2
O + NH
4
Cl + H
2
+ Cl
2
2.3
3 RESULT
3.1 Structural Transition
