(1)
Dr.
Vahid Chegini
Soil
Conservation & Watershed Management Research Center,
The
Ministry of Jihad for Construction,
P O Box
13445-1136, Tehran, I R of Iran, E-mail: aquasoil @ neda.net.ir
Abstract:
The prediction of reflection and transmission coefficients through single
perforated sheets and walls plays an important role in the assessment of the
hydraulic behaviour of upright perforated wave absorbers and perforated wall
breakwaters. In this paper, a new non-dimensional parameter is introduced to
describe the hydraulic characteristics of single perforated sheets. It is shown
that the reflection and transmission coefficients of waves through these sheets
and also the transmission coefficients of waves through upright perforated wave
filters are functions of this parameter.
Keywords:
wave screen interaction, upright perforated absorber, perforated wall breakwater
Wave absorbers are used for dissipation of wave
energy at the end of a wave flume or along the rigid boundaries of a wave basin.
According to the research of Ouellet and Datta (1986) the wave absorbers most
commonly used in laboratories throughout the world are sand, gravel stone or
concrete beaches. The slopes of these absorbers are usually 1:10.
An alternative solution for dissipation of the
incident wave energy at the boundaries of a wave tank is using of upright
perforated wave absorbers (Jamieson and Mansard, 1987; Chegini, 1995a). The
advantage of these absorbers is that they need less space for installation than
the conventional inclined wave absorbers known as beach absorbers. An upright
perforated wave absorber is composed of rows of vertical perforated sheets
installed in front of a solid back wall which would otherwise be highly
reflective. These absorbers may be made from sheets of the same porosity or
variable porosity. In the latter case, the porosity is decreased progressively
toward the rear of the absorber.
Wave filters are employed for reduction of wave
reflection from wave paddles. In addition the secondary modes of the generated
wave can be eliminated by using a wave filter ( Chegini, 1997b).
A perforated wall breakwater consists of a
perforated front wall and a wave chamber. The front wall allow flow into and out
of the chamber in which energy is dissipated by turbulence reducing wave
reflection, wave loads on the structure and overtopping. Perforated breakwaters
can also be designed to be permeable, where some wave transmission occurs. Such
a structure can consists of a slotted wave-screen supported by piling.
The prediction of reflection and transmission
coefficients through single perforated sheets plays an important role in the
assessment of the behaviour of these structures and their efficient design.
Figure (1) shows the definition sketch for reflection and transmission of an
incident wave through a perforated sheet.
The subject of wave reflection and transmission
through a small aperture / porous barrier has been the subject of a number of
theoretical and experimental studies within last three decades ( Tuck, 1971;
Porter, 1972; Guiney, Noye and Tuck, 1972; Packham and Williams, 1972; Hattori,
1972; Mei, Liu and Ippen, 1974; Macaskill, 1979; Owen and Bhatt (1985); Chwang
and Dong, 1984; Faure, Mc Bride, Smallman and Allsop, 1995; Chegini,
1995a,1997a, 1999 )
The reflection and transmission coefficients of
a wave through a thin perforated sheet can be expressed as a function of the
following variables:
(1)
where:
Kr
reflection coefficient
Kt
transmission coefficient
Hi
incident wave height
h
water depth
deepwater wave length
p
porosity of perforated sheet
G
geometry of perforations
The effect of geometry of perforations may be
described in terms of the discharge coefficient of the screen perforations,
.
Generally,
is
a function of the barrier thickness, the hole diameter, the screen porosity, the
geometry of perforations and the Reynolds number. For a thin barrier and high
Reynolds numbers, this coefficient becomes only a parameter of the screen
porosity and the geometry of perforations. The discharge coefficient increases
with increasing
,
therefore it is possible to incorporate these two parameters into a single
parameter as follows:
(2)
where a
is the screen factor. Using (2), equation (1) becomes:
(3)
Dimensional analysis leads to:
(4)
It may be shown that for
the relative water depth has a
minor effect on the coefficient of wave reflection (Chegini, 1995b).
Increasing a
causes more wave energy to be transmitted through the perforated sheet and
reduction of this parameter increases reflection from the screen.
Chegini (1995b) showed that the incident wave
steepness has a significant effect on the coefficient of wave transmission
through the perforated sheet. This coefficient decreases with increasing
(or
).
Therefore, generally, simulating the dissipation
of waves due to the perforated sheet to the wave attenuation by an inclined
permeable structure, it may be concluded that:
(5)
where:
(6)
is defined as
wave-screen parameter.
This parameter is comparable with the surf
similarity parameter, which is used for sloping porous structures. It should be
noted that the screen factor, a,
is indeed a representative of the screen perforations. Therefore for a thick
perforated barrier the effect of the barrier thickness should also be
incorporated in equation (2).
A set of experimental studies was carried out in
the Water Research Laboratory of the University of New South Wales (WRL) to
measure the reflection and transmission coefficients of waves through single
perforated sheets and upright perforated wave filters.
Two kinds of porous sheets, i.e. expanded
metals of 26, 42 and 58 percent porosity and perforated plates of 23, 40 and 62
percent porosity were employed for the experimental tests on single perforated
sheets. Only the normal position was used for the former screens. This position
is defined with the louvres of the sheets oriented downwards in the direction of
a wave propagation from the wave generator toward the sheet. The diameters of
screen perforations for sheets of 23, 40 and 62 percent porosity were 1.6, 6.35
and 7.94 mm, respectively. The support frame for the perforated sheet was made
of
mm steel angle.
Reflection and transmission coefficients of
waves were measured for double perforated plates and wave filters composed of
four perforated plates of the same porosity. The screens were aligned normally
to the direction of wave propagation. The porosity of the sheets was 40 and 62
percent.
The experiments were carried out in the deeper
section of the 0.9 m wide, 1.75 m deep, 50 m long wave flume of WRL. All the
tests were undertaken in water at a depth of 0.8 m. Only regular waves were used
in the laboratory experiments. The wave periods were 1.25, 1.35, 1.50, 1.75 and
2.50 seconds (
= 0.125 to 0.34). The reflection and transmission coefficients were measured for
waves of steepness ratios (Hi
/ L) ranging from 0.003 to 0.01. To attenuate the energy of transmitted
waves through perforated sheets, a permeable sloping wave absorber made of
artificial horse hair was installed at the end of the flume (Chegini, 1993).
Wave profiles were measured by four fixed
capacitive-wire wave probes located in either side of the screen / wave filter.
The distance between the probes at each side of the screen / wave filter was 40
cm. Lotus-Measure Software was employed to transfer the collected data to a
Portable Microcomputer. Four channels of data were recorded simultaneously at a
sampling rate of 50 samples per second on each channel. Fourier analysis was
used to evaluate the wave amplitude of the fundamental frequency. The reflection
coefficients were calculated from the “two probes technique” reported by
Thornton and Calhoun (1972).
Figure (2) indicates the coefficients of wave
reflection and transmission through single perforated sheets as a function of
the wave-screen parameter. As can be seen from this figure, the coefficient of
wave transmission (Kt)
increases with increasing the wave-screen parameter, whereas the coefficient of
wave reflection (Kr)
decreases as this parameter increases.
The comparison between the experimental results
of the present study and other investigations is shown in figure (3).
The discharge coefficients of screen
perforations were evaluated from the following empirical formula from Dailey et
al., 1966 (also used by Mei et al., 1974):
(7)
where
and
A are the perforated and the total
area of the screen, respectively.
Figures (4) and (5) depict the variation of
transmission coefficients of upright perforated wave filters composed of two and
four sheets, respectively, as a function of the wave-screen parameter.
The results of laboratory tests have been
presented for the reflection and transmission coefficients of waves through
single perforated sheets and the transmission coefficients of waves through
upright perforated wave filters aligned normally to the direction of wave
propagation.
A new non-dimensional parameter was introduced
to describe the hydraulic characteristics of single perforated sheets. This
variable is called the wave-screen parameter (G).
The coefficient of wave transmission through a
perforated sheet or an upright perforated wave filter increases with increasing
this parameter. The coefficient of wave reflection from the perforated sheet
decreases as the wave-screen parameter decreases.
The results obtained from the present study and
the other investigations have shown that the coefficients of wave reflection and
transmission through single perforated sheets can be described as a function of
this new non-dimensional parameter.
References
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“Reflection and Transmission of Water Waves through Single Perforated
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: “Design of Upright Energy Dissipators for Use
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degree of Doctor of Philosophy, Dept. of Water Eng., School of Civil Eng., Univ.
of New South Wales, Australia, March, 1995b.
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Fig. 1
Definition sketch for reflection and transmission of an incident wave through a
perforated sheet
Fig. 2
Characteristics of single perforated sheets as a function of the wave-screen
parameter
Fig. 3 The
comparison between the experimental results of the present study and other
investigations
Fig. 4
Transmission coefficients of double perforated plates as a function of the
wave-screen parameter
Fig. 5 Transmission
coefficients of upright perforated wave filters composed of four sheets as a
function of the wave-screen parameter