Endo, Toru

Shigematsu, Takaaki

Tatebe, Yuya

Osaka City University Repository

Mem. Fac. Eng., Osaka City Univ., Vol. 46, pp. 77- 82 (2005)
An Experimental Study on Reaeration by a Breakwater Generating Vertical
Circulation Flow
'1~~~. ~~ f f~ ~a: ~tl'
Toru END{S*, Takaiki SHIGEMATSU** and Yuy~'rATEBE***
(Received September 30, 2005)
Synopsis
In summer seasons severe hypoxia or anoxia has been generated near the sea bottom in enclosed
seas. In order to restrain the hypoxia and anoxia, authors have developed a new breakwater which
generates vertical circulation flow. Hydraulic effectiveness of the developed breakwater has already
been verified. In this study, reaeration characteristic of the developed breakwater is examined by
laboratory experiment. At first, the reaeration coefficient k2 is estimated from the data of dissolved
oxygen in a reaeration volume with different water depths. Furthermore, substance transfer coefficient
KL is calculated from the estimated k2 • Finally, KL of the proposed breakwater is compared wit.h KL
of other structures such as the slit-type caisson or rubble mound breakwater.
KEYWORDS: breakwater generating vertical circulation flow, reaeration capacity, reaeration
coefficient, substance transfer coefficient
1. Introduction
In many seas surrounded by artificial structures such as vertical seawalls, the benthic ecosystems
or coastal bottom environment are suffering from a chronic hypoxia or anoxia which is generated near
sea bottom. It is necessary to restrain the hypoxia in such enclosed seas for restoration of coastal
environment. One of the reasons why the hypoxia is generated is that oxygen supply near the sea
bottom is obstructed by insufficient vertical mixing in front ,of the verticaJ wall especially under calm
wave condition in summer season. Authors have developed a new breakwater which generates the
~ 381:i~C0;< .Os loweruni
offshore
llpper-llnit
Figur~ 1: Illustration of the brea~water
promoting vertical circulation flow
Figure 2: Wave breakings in the upper horizon-
tal slit and bubbles, in the chamber
*
**
Student, Doctor Course of Dept. of Environmental Urban Engineering
Associate Professor, Dept. of Environmental Urban Engineering
*** Student, Bachelor Course of Dept. of Environmental Urban Engineering
77
vertical circulation flow from surface to bottom even under the clam wave condition. Schematic
illustration of the breakwater is shown in Figure 1. Local flow toward offshore is generated from
the lower horizontal slit by the pressure difference induced mass transfer when waves come into the
chamber through the upper horizontal slit. Because the vertical circulation flow is transported the
oxygen-rich surface water to the bottom, it is expected that the proposed breakwater is effective to
restoration of environment near the sea bottom.
Hydraulic characteristics of the proposed breakwater have already verified by laboratory experi-
ments 1),2),3). According to the experiments, wave breakings in the upper horizontal slit and many
bubbles in the chamber were observed (see in Figure 2). It makes us expected that the developed
breakwater has great reaeration capacity. However reaeration capacity of the proposed breakwater
has never been evaluated.
In this study, therefore, reaeration coefficient k 2 of the breakwater ~enerating vertical circulation
flow, which is widely well-known as the index evaluating reaeration capacity, will be estimated by
conducting laboratory experiment. Furthermore, substance transport coefficient KL, which is char-
acteristic coefficient of each structure, will be also estimated by using value of estimated k2, aeration
volume V and aeration area A.
2. Theory of the reaeration
Gas transfer from atmosphere into liquid was modeled by Streeter and Phelps' 4) as follows,
dCdi = -klL + k2(Cs - C) (1)
(2)
(4)
(3)
(5)
where C is concentration of dissolved oxygen (DO), Cs is saturation dissolved oxygen, t is a given
time, L is biological oxygen demand, k1 and k2 are coefficient. k2 is called reaer~tion coefficient. For
the case of hydraulic experiment without biological reaction, the first term in right side of equation
(1) can be ignored. Hence equation (1) is rewritten
dCdi = k2 (Cs - C).
Equation (2) is rewritten by dimension~ess quantity for dissolved oxygen, D*,
D* = Cs - C
Cs - Co
where Co is initial concentration of DO in experiment. When equation (2) is solved after substituting
equation (3) into equation (2), we can obtain the following equation for k2. .
-lnD*
k2=---
t
It can be seen that we can obtain k2 if time history of DO are measured.
On the other hand, Whitman and Lewis 5) modeled substance transfer from gas to liquid by using
substance transfer coefficient KLas follows.
1 dm V de
N = A · dt = A · di = K L (Cs - C)
where m is mass of gas, A is aeration area, V is aeration volume. From equation (4) and (5), the
relationship between k2 and KL is obtained.
A
k2 = VKL (6)
From equation (4) and (6), KL means the gas transfer vel~city in the boundary layer of aeration area.
78
3. Experimental Setup
A schematic illustration of experiment is shown in Figure 3. Experiments were conducted in a
wave flume with 20 m long, 0.6 m high and 0.5 m wide at Osaka City University. The model of
the breakwater set 15.0 m away from a wave maker. Experimental conditions are shown in Table 1.
An incident wave period T is 0.75 s and the wave steepness H / L is 0.02. The wave conditions were
determined based on measured data in Osaka Bay during summer season because the hypoxia is easily
generated under the cal~ wave condition. Water depths were h = 30 cm, 35 cm and 40 cm, and wave
from offshore can not go into the chamber through the upper horizontal slit when water depth h is 30
em. In order to secure aeration volume V, a plastic film was installed at 2.0 m away from impermeable
wall for preventing substance from transporting through the plastic film without disturbing wave field.
Reflection coefficient K r of the proposed breakwater was evaluated from the data of water surface
elevations by using the estimation method of incident and reflection waves 6). The water surface
elevations were measured by using two capacitance wave gauges (KEYENCE). The wave gauges were
installed at 1.0 and 1.1 m away from the breakwater inside the aeration volume. Sampling frequency
of wage gauges is 50.0 Hz.
Time historical data of DO was measured by using two DO meters (YSI). On of them (No.1) was
set at the bottom in the chamber and the other (No.2) was set in the middle of water depth at one
wave length away from the breakwater. Before starting measurement, Cobalt chloride (CoCI2) and
sodium sulfite (Na2S0g) were added into the aeration volume in order to make the initial DO inside
the aeration volume 0.0 mg/I. Sampling frequency of DO meters is 1.0 Hz and they were measured
until the time enough to obtain k2 •
wave maker
wave gauge
hI2
~~---------2.0--------"P
impermeable wall
\
reakwater DO meter
. No.1 No.2
1UI....~---I'--1.0~----~
·.----------------20.0----------------..
Figure 3: Experimental Setup
Table 1: Wave conditions and experimental results of reflection coefficient K r
case h (cm) T (s) L (cm) H (cm) H/L K r wave breakings and bubbles
1 30.0 0.75 85.0 1.6 0.02 0.96 x
2 35.5 0.75 86.0 1.8 0.02 0.42 x
3 40.0 0.75 86.0 1.7 0.02 0.89 x
h: water depth, T: wave period, L: wave length, H: incident wave height, H/L: wave steepness, K r :
reflection coefficient, and the right column shows whether wave breakings in the upper horizontal slit
'and bubbles in the chamber were observed.
79
4. Results
Experimental results of reflection coefficient Kr is shown in Table 1. Kr for h =35 cm is 0.42
and Kr =30 cm and 40 cm are almost 0.9. It is found that wave absorbing function of the proposed
breakwater stronglydepep.ds on the water depth. This tendency is.shown in the experiments conducted
in the past with larger scales 3). Altho~ghwave breakings in the upper horizontal slit and many bubbles
in the' chamber were observed in the larger scale experiments, both of them 'Yere not observed in this
experiment. Therefore following discussion on the oxygen transfer from atmosphere into water does
not include the effect of the bubbles and turbulence induced by wave breaI{ings. '
Figure 4 shows the time histories of dimensionless concentration of the dissolved oxygen after
starting experiments. 0 represents the date of the concentration of DO in the chamber (No.1), and
6, represents that at one wave l~ngth away from the breakwater (No.2). Figure 4 (a), (b), and
(c) represent the results for the case of water depth h = 30, 35, 40 cm respectively. In the figure
dimensionless concentration of DO is presented by using th~ initial concentration Co and saturate
concentration CS.
For the case of h == 30 cm, the concentration of DO at the offshore measurement point No.2 begin
to recover faster than that in the chamber since water depth is too small to go into the chamber.
For the case of h == 35 cm and 40 Crn, which waves go into the chamber, the concentration of DO in
, the chamber recover slightly faster than the concentration of DO at the offshore measurment point.
Considering ~o the results on the reflection rate, the recovery velocity of the dissolved oxygen has a
close relationship with mechanism of wave absorbing.
On the basis of the experimental results on the concentration. of DO measured in the chamber,
the reaeration coefficient k2 was calculated. Figure 5 showed time history of - In D*. It is found that
- In D* increases linearly as time progresses. k2 is obtained by calculating the gradient of the data
of -lnD*. Obtained k2 for h = 30,35 and 40 cm are 1.48 x 10-5 ,1.17 X 10-4 ,1.96 X 10-5 ~-1
respectively. That is to say that k2 for the case of h = 35 cm is one order higher than the other cases.
Kakuno 'et al. 7) have already conducted th~ ex~eriment in order to obtain k2 under the partial
standing wav~s·. According to their experiments,,:,k2 under the partial standing waves was 1.56 x
1O~5s-1. Comparing with their result and k2 for h = 30 and 40 em presented in this study, it is found
that both of the~ have almost same value an~.· that experimental results presented in' this study were
reasonable.
" r.irially, KL was calculated from k2 , A and V. A was assumed to be equivalent to. the area of water
surface at re~t·between i:rp.permeable wall and a plastic film because' w~ve breakings in the upper slit
and bubbles in the chamber were not observed. Table 2 shows value of KL of the proposed breakwater
1.0 1.0 1.0
-0- in the chamber -0- in the chamber
-0-- in the chamber
0.8 ~offshore 0.8
~offshore
--A- offshore0.8
al aO•6 al aO•6 IJ'1""a
Oo6
.
uu uu
I I ' I I I I
U u'" u u... u t.,)'"
0.4 0.4 0.4
0.2 q.2 0.2 .
i
'0·0 0.00 . 0·02. 4 6 8 10, 12 14 16
·2 3 4 5 6 7 :8 2 4 ·6 8 10 12 14 16
'time (hr) time' (hr) time (hr)
(a) h == 30 cm (b) h = 35 cm (c) h = 40 cm
Figure 4: Dimensionless concentration of DO in the aeration volume
80
4.0 4.0 4.0
-4 -Ik2 = 1.17 x 10 (s )
3.0 3.0 ~ 3.0-5 -1 -5 -1k2 = 1.96 x 10 (s ) k2 = 1.96 x 10 (s )* * *~ ~ ~
=2.0 =2.0 I:: 2.0
I I I
1.0 1.0 1.0
0.00 0.00 0.0014400 28800 43200 57600 7200 14400 21600 28800 14400 28800 43200 57600
time (s) time (s) time (s)
(a) h = 30 cm (b) h = 35 cm (c) h = 40 cm
Figure 5: Time history of - In D* and k2 at the bottom in the chamber
estimated in this study, slit-type caisson, rubble mound breakwater and slope with 1/20 estimated
by Kakuno 7). K r of the proposed breakwater were larger than those of slit-type caiss9n and rubble
mound breakwater. Although K L for h == 30 and 40 cm have one order smaller than that for slit-type
caisson and rubble mound breakwater, KL for h = 35 cm has same order as them. That is to say
that the proposed breakwater generating vertical circulation flow has oxygen transfer function from
atmosphere into water as same as slit-type caisson and rubble mound breakwater under a certain
water depth but that the function depends on the water depth. With considering to the function of
generating vertical circulation flow, the proposed breakwater would be expected to be effective for
restoration of sea bottom environment. K r and KL obtained by Kakuno with wave breakings over
the inclined slope with 1/20 has one order higher value than that of the other structures. It implies
that strong turbulence and bubbles induced by wave breakings affect k2 and KL.
Table 2: Comparison of k 2 and KL with different structures
structure h (cm) T (s) H/L K r k2 (S-l) KL (cm/s)
VCF 30.0 0.75 0.02 0.96 1.48 x 10-5 4.44 X 10-4
VCF 35.0 0.75 0.02 0.42 1.17 x 10-4 4.10 X 10-3
VCF 40.0 0.75 0.02 0.89 1.96 x 10-5 7.84 X 10-4
Slit 30.0 0.88 0.02 0.33 3.58 xl0-5 1.07 x 10-3
Rubble 30.0 0.88 0.02 0.29 5.82 x10-5 1.56 x 10-3
Slope 30 I 0.88 I 0.06 I I 1.87 X 10-3 I 1.27 x 10-~ I
VFC: breakwater generating vertical circulation flow, Slit: slit-type caisson, Rubble: rubble mound
breakwater, Slope: slope with 1/20.
5. Conclusions
The conclusions of this study are summarized as follows, :
(1) It is confirmed that reaeration capacity of the proposed breakwater depends on the water depth
strongly by estimating k2 and KL of the proposed breakwater.
(2) KL of the breakwater generating vertical circulation flow for h = 35 cm was 4.10 x 10-3s-l
and KL for h = 40 and 30 cm were one order smaller than KL for h = 35 Cffi. '
(3) KL of the proposed breakwater was compared with that of slit-type caisson and rubble mound
breakwater. It is found that the proposed breakwater has oxygen transfer function from atmosphere
into water as same as those structures under a certain water depth.
81
It should be noted that wave breakings in the upper horizontal slit and bubbles in the chamber
were not generated in this experiment. Therefore, this experimental results have the possibility that
KL was underestimated more than that of the actual scale. In the future, we thought that it is
necessary to carry out the larger scale experiment in order to examine effect of wave breakings and
bubbles on reaeration.
Refere~ces
1) T. Shigematsu, K. Ikeda, K. Oda, and T. Fujita (2002): Development of a seawall generating
vertical circulating flows for improving the bottom environment, Annual Journal of Coastal
Engineering, JSCE, Vo1.49, pp.796-800, (in Japanese).
2) T. Shigematsu, K. Ikeda, K. Oda, T. Koike, R. Nobuhiro, T. Endo, T. Fujita, and S. Togawa
(2003): Effectiveness of a seawall generating vertical circulating flows in stratified wave field,
Annual Journal of Coastal Engineering, JSCE, Vo1.50, pp.1206-1210, (in Japanese).
3) T. Endo, T. Shigematsu and K. Oda (2005): Large-scale Experiments on Effectiveness of a
Breakwater Promoting Vertical Circulation Flow, Asian and Pacific Coasts 2005, pp.239-242.
4) Streeter, H. W. and Phelps, E. B. (1925): A study of the pollution and natural purification
of the Ohio River 3. Factors concerned in the phenomena of oxidation and reaeration, Public
Health Bulletin, 146,75~
5) Lewis, W. K. and Whitman, W. C. (1924): Principles of gas absorption, Industrial and Engrg.
Chemistry, Vol.16.
6) Y. Goda, Y. Suzuki, Y. Kishira, and O. Kikuchi (1976): Estimation of incident and reflected
waves in random wave experiments,' Technical Note of, P.H.R.I., No.248, 24p.'
7) S. Kakuno, Y. Nakata, M. Saito, N. Nakatani, T. Yoshida and K. Oda (1994): Experime;ntal
Study on Aeration Characteristics of Coastal Structures, Annual Journal of Coastal Engineering,
JSCE, Vo1.41, pp.1036-1040, (in Japanese).
82


An Experomental Study on Reaeration by a Breakwater Generating Vertical

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An Experomental Study on Reaeration by a Breakwater Generating Vertical

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