Annual Journal of Hydraulic Engineering, JSCE, Vol.50, 2006, February

SIMULATIONS OF 3D SUSPENSION GRAVITYCURRENTS UNDER THE PRESENCE OF
A TURBIDITY FENCE
Jaswant SINGH1, Juichiro AKIYAMA2, Mirei SHIGE-EDA3
1Student member of JSCE, Graduate Student, Dept. of Civil Engineering, Kyushu Institute of Technology(1-1 Sensui cho, Tobata ku, Kitakyushu 804-8550, Japan)
2Fellow member of JSCE, Ph.D., Professor, Dept of Civil Engineering, Kyushu Institute of Technology
3Member of JSCE, Dr. Eng.,Asso.Professor, Dept. of Civil Engineering, Kyushu Institute of Technology.

A 3-D numerical model, which employs the large eddy simulation (LES) and the modified
Smagorinsky model, is used to simulate the motion and diffusion of 3D suspension gravity currents under
the presence of a turbidity fence. The model constants are determined using the existing data of 2D
suspension clouds, and then the validated model is applied for newly obtained experimental results on 3D
suspension gravity currents under the presence of a fence. It is confirmed that the model is capable ofpredicting the complex behavior of the currents to a reasonable accuracy, and the amount of sediments
contained within the fence to a good accuracy. In addition, numerical experiments are conducted todemonstrate that the model is a useful tool to examine the placement of a fence to effectively reduce
diffusion of turbidity in aquatic environments.
Key Words: Suspension gravity currents, Turbidity fence, Fluid particle flows, Numerical model.

1. INTRODUCTION
Large amount of dredge material, soil and rubble
is dumped into a body of water for waste disposal,
artificial land reclamation projects. Such dumping
results in formation of a suspension gravity current
over the bottom and causes diffusion of turbidity inwide area. Prediction and control of diffusion of
turbidity, therefore, are of particular importance forassessing the impact of such projects on aquatic
environments.
To reduce such diffusion of turbidity, a turbidity
fence is commonly used. It is usual, however, thatthe layout and arrangements of the fence have been
decided through experiences and/or simple analysis.
A logical based method or tool is required todetermine the layout and arrangements of the fence.
Numerical prediction of the motion anddiffusion of 2D and 3D gravity currents is a matterof serious investigation. For instance, Necker et al.1)
simulated 2D gravity currents in lock-exchange
configuration using a 3D numerical model based on
spectral-element discretization. Akiyama et al.2)
investigated 3D suspension thermals on horizontal
bed by using SMAC and MUSCL methods. Huang

et al.3) simulated the evolution of 3D turbidity
currents by the κ-ε model and reported that
turbulent Schmidt number larger than unity
provided good match with the experimental data.
Ying et al.4) investigated the motion of 2D particle
clouds produced by direct dumping of sediments
into water from the falling to spreading stage by
LES. Li and Zang 5) investigated the motion of 2D
and 3D particle clouds based on characteristic based
scheme with flux limiters. Singh at el.6) simulated
3D gravity currents induced by direct dumping of
sediments by LES and reasonable agreement withthe experimental data was obtained.
A numerical model may be a best tool for
examining the layout and arrangements of the fence,
considering the complex behavior of the currents
when the fence is presented. From such a point ofview, Akiyama et al.7) examined the motion anddiffusion of the 2D currents with a fence by LES.
This study presents numerical simulations andlaboratory experiments on the motion and diffusionof 3D suspension gravity currents under thepresence of a fence. The 3D numerical model
developed by the authors6) is employed and themodel parameters, namely, the turbulent Schmidt

number Sct, Smagorinsky constant Cs and acoefficient α for the net deposition rate of sediments
are quantified by utilizing the experimental data of
the 2D particle clouds reported by Akiyama et al.7).
Then the validated model is used to simulate 3D
suspension gravity currents under the presence of afence and the results are compared with the newly
obtained experimental data. In addition, numericalexperiments are conducted taking different heights
and placement of a fence to demonstrate that themodel is an effective tool to determine the layout
and arrangements of a fence.

Stirring device
Siphoning of particleshTurbidity fence
Wd
xf
Side view

W0, A0L

X
M

2. EXPERIMENTS
The experiments were performed in a glass tank(200 cm length, 200 cm width and 75 cm height) byinstantaneously releasing a suspension composed ofwater and glass bead particles from a box. Fig.1
schematically shows the experimental setup andessential parameters used in this study, in which h =ambient water depth, W0 = total effective gravity
force (=A0 × ε0 × g), A0 = initial volume of asuspension (=L×M×N), L, M, N = length, breadthand height, g = acceleration due to gravity, ε0 =relative excess density of a suspension (= (ρ0-ρa)/ρa),ρ0 = initial density of a suspension, ρa = density ofambient water, xf = intrusion distance of the current,
and Wd =effective gravity force per unit area ofdeposited particles. In this study, A0 = 5120 cm3,
initial dimension of a suspension (L=40cm, M=8cm,
N=16cm), ε0= 0.0185. W0=92932 cm4/s2 and h =1.25 L were chosen. The diameter d and thesubmerged specific gravity of particle s were0.0044cm and 1.45, respectively. Placing the fenceof height 0.75M at a distance of 1.25L from the box,
and keeping W0 as 92932 cm4/s2 and the aspect ratio(=L/M) as 5, two cases of the fence placement, thatis, the fence with opening in the middle (Case 1)
and in the corner (Case 2) were considered as shownin Fig.1.
The motion of the currents was recorded
simultaneously by three VTR cameras placed one at
the top and two in the sides of experimental setup,
and was analyzed by PC. Laser slit light was used tovisualize the currents. Deposited particles were
siphoned from an area of 20cm×20cm shown in
Fig.1 after the current was completely seized. The
collected particles were dried up and then weighed
to calculate effective gravity force Wd. In order toincreases the reliability of the experimental results,
the experiment was repeated three times under thesame condition. The data presented herein are theaverage of these. The absolute relative error ofexperimental data for Wd is found to be about 5% of

N

20
cm
Fence opening Case 1

Y

20 cm
L

X
M

20
cm
Fence opening Case 2.

Y

20 cm
Fig.1 Schematic diagram showing the 3D
gravity current and experimental set up.

the average.

3. OUTLINE OF THE MODEL
The details of the model can be referred to Singhet al.6), and herein the outline of the model ispresented. The model employs one equation
Eulerian approach as a solid-fluid two phase flow
model, because the Lagrangian approach 8) is not
feasible for suspension gravity currents consistingof the extremely large number of particles. In themodeling, the particle phase is treated as fluid phaseand the drift velocity between fluid and particles isassumed to be the settling velocity of the particles,
which is estimated by the Rubey’s equation.

The model has been developed by solving 3D
Navier-Stokes
equations
with
Boussinesq
approximation and mass conservation equations
using large eddy simulation (LES), and themodified Smagorinsky model4) is used for
turbulence closure. As solution methodology,
using splitting approach, the governing equations
are split into three parts, i.e., advection, diffusionand pressure part. The advection equations are
solved by ULTIMATE QUICKEST9). The
diffusion part is solved by central difference
scheme and pressure part is solved by successive
over relaxation method.
The imposed boundary conditions for velocity,pressure and concentration are Ul = 0, for bottom
and side boundaries, ∂U1/∂x = 0, ∂U3/∂z = 0,and U2= 0, for top boundary, ∂P/∂xl = 0 and ∂C/∂xl = 0, forall boundaries. The free water surface is treated as ahorizontal rigid boundary. An additional boundary
condition is imposed to take the deposition ofparticles from the flow onto the bed into account.
The net deposition rate D is estimated by D = αVsCb,
where α = a coefficient to be calibrated withexperimental data, and Cb = near bed reference
concentration. The fence is created in thesimulations by taking no flow boundary condition
i.e. Ul = 0, C = 0, and P = 0 at the location of fence
in the domain.

6

Sct =1.00
Sct =0.75
Sct =0.50
Sct =0.25
Experiment

5

H*

4
3
2
1
0

0

2

4

6

8

10

z*
Fig.2 Sensitivity of Sct on H*

0.8

Sct =1.00
Sct =0.75
Sct =0.50
Sct =0.25
Experiment

0.7
0.6

V* 0.5
0.4
0.3
0.2
0.1
0.0

4.MODEL CONSTANTS

1.2

The computations are performed on a structured
grid of size ∆x = ∆y = ∆z = 0.25M (2cm). The time
step ∆t =0.0025 second. In order to determine thevalues of model constants, namely, Smagorinsky
constant Cs, turbulent Schmidt number Sct, and acoefficient α for the net deposition rate of sediments,
simulations are carried out taking the data from 2D
particle clouds experiments, which deals with the
motion and diffusion of the clouds induced by directdumping of sediments from the falling to spreading
stage, reported by Akiyama et al.7).
Cs and Sct are quantified via the falling stage, andα is via spreading stage of the particle clouds. The
distance measured from the water surface to themass center of the cloud z, half width H, masscenter velocity V and average effective gravity force
B (=W0/A) of the falling clouds and the effective
gravity force of deposited particles Wd of the
spreading clouds are non-dimensionalised as z* =z/A01/3, H* = H/A01/3, V* = V/((W01/2)/A01/3)), B* =B/(W0/A0) and Wd* =Wd/W0 respectively. A is thearea of the cloud at z. The value of Cs typicallyranges from 0.07 to 0.2710). From simulation runs, it
was observed that on this grid resolution, H*, V* and

1.0

0

2

4

6

10

Sct =1.00
Sct =0.75
Sct =0.50
Sct =0.25
Experiment

0.8

B*

8

z*
Fig.3 Sensitivity of Sct on V*

0.6
0.4
0.2
0.0

0

2

4

6

8

z*
Fig.4 Sensitivity of Sct on B*

0.030

10

α = 1.5
α = 2.0
α = 2.25
α = 2.5
Experiment

0.025

Wd*

0.020
0.015
0.010
0.005
0.000

0

10

20

40
x* 30
Fig.5 Sensitivity of α on Wd*

50

x

x

y

0.10 0.12

Fig.6 Spreading of the current for case 1. Experiment(above) and simulation (below)
x
4
3
2
1
0.10

1
A

0.08

B2

0.02 0.04 0.06 0.08

0.04

y

3C

0.02

4
E

3

2

0.04 0.06 0.08 0.10 0.12

4

1
0.10

1

0.08
0.06

2

0.04
0.02

3

0.02

4

* *
Fig.
7 Contours
case
1. Experimentd dforFig.7
ContoursofofWW
forCase
1. Experiment(above)(above)andandsimulated
simulated(below)(below).
0.15
Simulation
Experiment

0.10

Wd*
0.05
0.00
0
0.15

3

Simulation

0.10
Wd*
0.05
0.00
0

2
(X axis)

x*

4

5

6

y

B
2

0.04

3C

0.02

4E

4

3

2
0.08

1
0.10

0.06

1
2

0.04
0.02

3
4

Fig.10Contours
ContoursofofW
Wd**forforCasecase 2.
2. Experiment
ExperimentFig.10d(above)simulated(below)(above)andandsimulated(below).
0.15

Simulation

Experiment

0.00
0Turbidity fence

1

0.15

Experiment

2
3 * 4
5
y
(Y axis)Fig. 8 Wd* along the X axis (above) andthe Y axis (below) for Case 1.

1A

0.10

0.06

Wd*
0.05

0.10
Wd*
0.05

Turbidity fence

1

0.08

0.10

Turbidity fence

1Time =15 sec

Fig.9 Spreading of the current for case 2. Experiment(above) and simulation (below)
x
4
3
2
1

0.06
0.04

Time =10 sec

Time =5 sec

0.12Time =15 sec

0.025 0.050 0.075 0.100 0.125 0.02 0.04 0.06
0.08 0.10

Time =10 sec

Time =5 sec

y

6

0.00
0

2
3 * 4
5
6
x
(X axis)Simulation
Experiment

Turbidity fence

1

2
3
4
5
y*
(Y axis)Fig.11 Wd* along the X axis (above) andthe Y axis (below) for Case 2.

6

Table 1. Conditions for numerical experiments
Case
1
2
3
4

Turbidity
Fence
No fence
Fence
Fence
Fence

Fence
height-------3/4 M
1/4 M
3/4 M

Distance fromsuspension box---------3/4 L
3/4 L
1/2 L

80

80
0.001
0.002

60
0.004

40
20

40
60
Case 1

80

20

60

0.003
0.004

40
60
Case 280

0.002 0.001
0.003
0.004

40

40

20

20
20

40
60
Case 3

80

20

40
60
Case 480

Fig. 13 Simulated contours of Wd* under thedifferent positions and height of fence.

Case 2Time 44 sec

Time 16 sec

20
80

0.001
0.002

60

Time 44 sec

0.003
0.004

40

80

Time 16 sec

60

0.003

20

Case 1

0.001
0.002

computations, Cs = 0.15, Sct =1.0 and α = 2.25 will
be used.

5. RESULTS AND DISCUSSION

Case 3Time 44 sec

Time 16 sec

Case 4
Time 16 sec

Time 44 sec

Fig. 12 Simulated currents under the different
positions and height of the fence.

B* are found insensitive to Cs, so that Cs = 0.15,
which is reported by Ying et al.4) and Akiyama etal.7), is adapted. The value of Sct is varied from 0.25
to 1.0. The sensitivity of Sct to H*, V* and B* is
examined as shown in Figs.2~ 4, and Sct =1.0 isfound to yield the closest match with theexperimental results.
α is optimized taking α =1.5, 2.0, 2.25 and 2.5.
Fig.5 shows the comparison of simulated Wd* withthe experimental result of the spreading stage of 2D
particle clouds. It is observed that Wd* is almost
insensitive to α, but α=2.25 is found to be closest to
the experimental result. In the following

The computations are performed on cartesian
grid of 200×200×25 nodes. The initial suspension
is defined on the bottom of the domain and occupies
4×20×8 nodes. The analysis is carried out for the¼ portion of the domain shown in Fig.1, because theidentical results were observed in the rest.
Fig.6 shows the comparison of experimental
photographs and simulated currents for Case 1. The
square in the figure measures an area of 10×10 cm2.
The shape and position of simulated currents at eachtime are in reasonable agreement with theexperimental photographs. It is observed that theflow is more dominant along the X axis, owing to
the effect of the aspect ratio, and that when thecurrent reaches the fence, some of sediments
overflow the fence and diffuses out of the fence.
Fig.7 shows the comparison of contours ofsimulated non-dimensional effective gravity force of
deposited particles Wd* (=Wd/W0) with theexperiments. x and y are the distances along the X
axis and Y axis and are non-dimensionalised as x* =x/A01/3 and y* = y/A01/3, respectively. It is observed insimulations as well as experiments that the most of
the sediments are deposited close to the source. Wd*
decreases with increase in distance from the source.
The contours of simulated Wd* are in reasonableagreement with the experiments.
Fig. 8 shows the comparison of the calculated
profiles of Wd* along both axis, i.e., X axis and Y
axis, with the experimentally observed ones. It isobserved that the model underestimates Wd* along
the X axis, and reproduces Wd* to a reasonableaccuracy along the Y axis. The total amount ofdeposited sediments contained within the turbidity
fence is about 90% of the initial total amount of
sediments released in the experiments, whereas in
the simulations about 93%.
Figs. 9~11 show the comparisons for Case 2.
The matching between experimental and calculated
results are identically reasonable as Case 1. In Case2, as the opening is farther from the box, more timeis required for the front to reach the opening andhence results in more deposition of particles. The
total amount of deposited sediments within thefence is about 95% of the initial total amount of
sediments, whereas in the simulations about 97%.

(2)The model is found to be capable ofreproducing the complex behaviors of 3D
suspension gravity currents under the presence of afence to a reasonable accuracy, and the amount of
sediments contained within the fence to a good
accuracy.
(3)Numerical experiments are conducted todemonstrate that the present model is a useful toolin optimizing the position of a fence to achieve adesired level of diffusion of turbidity induced bydirect dumping of sediments into a body of water.
REFERENCES

Necker, F., Hartel, C. and Moiburg, E.: Highresolution simulations of particle-driven gravity
currents, International Journal of Multiphase Flow,
Vol.28 (2), pp. 279-300, 2002.
6. NUMERICAL EXPERIMENTS
2) Akiyama, J., Shigeeda, M. and Maeda, Y.: Threedimensional numerical simulations of suspension
Numerical experiments are conducted bythermal on horizontal bed, Annual Journal ofchanging positions and heights of the fence asHydraulic Engineering, JSCE, Vol.48, pp.1165-1170,
shown in Table 1. The computational domain is
2004.
12.5M×12.5M×2.5M. The suspension is introduced 3) Huang, H., Imran, J. and Carlos, P.: Numerical modelas 1×5×4 nodes just below the surface of the domain.
of turbidity currents with a deforming bottom
boundary, Journal of Hydraulic Engineering, ASCE,
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Vol.131(4), 2005.pp283-293.
Fig.12 and 13 respectively show the simulated
*
4)
Ying,
X.,
Akiyma, J. and Ura, M.: Numericalresults of the flow pattern and the contours of Wd .
investigationon 2-D particle clouds, Annual Journal
The followings is observed. The placement of fenceof
HydraulicEngineering, JSCE, Vol.44, pp.1239is effective in reducing diffusion of turbidity. More
1244,
2000.
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height lowers. Substantial amount of turbidity 5) Li, C.W. and Zang, F.: Three-dimensional simulationof clouds using a split operator scheme, International
escapes from the opening in the corner when a
Journal of Numerical Methods in Heat and Fluid
higher fence is placed close to the dumping point,
Flow, Vol.6 (2), pp.23-25, 1996.
Most of the sediment is deposited near the dumping6) Singh, J., Akiyama, J. and Shigeeda, M..: Numericalpoint. The distribution of sediments in the fence
simulation of axisymmetric gravity current induced bywith lower height is almost similar to the case of no
direct dumping of sediments, Annual Journal offence. The sediment deposited in areas under two
Hydraulic Engineering, JSCE, Vol.49, pp.1399-1404,
different positions of fence placement in Case 1 are
2005.
98% and 88%, respectively. The sediment diffused 7) Akiyama, J., Jha, A.K., Ying. X. and Ura, M.:
out of the fence area for Case 2, 3 and 4 are
Numerical study of 2-D particle clouds and effect ofidentical 1%, 1.2% and 1.5% of the total sediments,
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Hydraulic Engineering, Vol.19 (1), pp.141-152, 2001.
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3D numerical simulations as well as newly
9)
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difference
scheme applied to unsteady onegravity currents under the presence of a turbidity
dimensional
advection,
Computer Methods in Applied
fence are presented. The following are findings andMechanics
andEngineering,Vol. 88, pp.17-74, 1991.
suggestions obtained from this study.
10) Murakami, S. and Iizuka, S.: CFD analysis of(1)The values of model constants are identified as
turbulent flows past square cylinder using dynamic
Cs = 0.15, Sct =1.0 and α = 2.25 by using theLES, Journal of Fluids and Structures, Vol.13,
existing data of 2D suspension clouds although α
pp.1097-1112, 1999.

may be need to express in terms of local flow
conditions in order to reproduce the depositing
mechanism of the currents.

1)(Received September 30, 2005)