Effect of geometric dimensions on the transmission coefficient of floating breakwaters Mohammad Hosein Tadayon, Khosro Bargi 2, Hesam Sharifian, S. Reza Hoseini - Ph.D student, Department of Civil Engineering, College of Engineering, University of Tehran, 2- Professor, Department of Civil Engineering, College of Engineering, University of Tehran tadayon@ut.ac.ir doi:88/ijcser.2264 ABSTRACT Nowadays, marine structures such as floating breakwaters, floating berths, floating platforms, etc. are used widely. Floating structures have some advantages such as more compatibility with marine environment, easier and faster transportation for temporary works and capability to install at any depth. The most commonly used type of floating breakwaters are rectangular ones as they have simple and rapid installation and also their deck can be used. For behavior study of floating breakwater, mostly structural response and transmission coefficient are considered. This article investigates effect of adding two thin boards vertically to the sides of rectangular floating breakwater to convert it to Π shaped floating breakwater and other geometric dimensions on the transmission coefficient of floating breakwaters. The results show that adding side boards and, mooring and fixing floating breakwater may reduce transmission coefficient considerably. In addition, dimensional aspects of can effect significantly on behavior of floating breakwater. Keywords: Floating Breakwater, Transmission Coefficient, Geometric Dimension, side board. Introduction Floating breakwaters are alternatives to conventional breakwaters for several reasons. firstly, the construction cost of a floating breakwater is slightly dependent on the water depth and bottom foundation conditions, whereas the costs of a gravity-type breakwater is proportional to the square of the water depth and it is often impractical to build in water deeper than about 5 m, secondly, floating breakwaters have the ecological advantage of sea water circulation, biological exchange and sediment transport beneath the structure and thirdly, floating breakwaters are transportable and may be essential for temporary facilities. They are useful in preserving small marinas and recreational harbors. Floating breakwaters with rectangular cross-section are the most common because of their usable deck area. Various methods have been proposed to improve the performance of floating breakwaters. As such, this paper considers the changes in the performance of a floating rectangular breakwater due to the attachment of wave boards (vertical plates) to its up-wave and down-wave sides (Lee et.al.,22). 775
In this paper performance enhancement due to attaching two vertical boards to the sides of a rectangular floating breakwater is studied. For this, an eigenfunction expansion matching method is applied for the oblique wave case.. Theoretical Formulation An incident train of monochromatic, small amplitude waves of height H and circular frequency σ propagate in water of constant water depth h past a breakwater as shown in Fig.. A Cartesian coordinate system (x, y, z) is defined with the x y plane at the undisturbed free surface, y is directed along the breakwater axis and z is measured vertically upwards. The direction of wave propagation is measured counterclockwise from the x-axis. The breakwater is assumed impermeable and infinitely long, so that end effects can be neglected and the system is idealized as two-dimensional through the assumption of pure periodic responses of a flexible breakwater in space and time. The breakwater has a rectangular cross-section with vertical plates attached to the up-wave and down-wave faces as shown in Fig.. The characteristic dimensions of the breakwater are its beam B, draft d, and plate height b below the underside of the breakwater, and the vertical plate thickness is considered here as very thin compared to other dimensions and thus assumed to be zero in the analysis described below. The clearance between the seabed and the plate tip is denoted as h'. The water is assumed to be inviscid and incompressible, and the flow is irrotational, so that the flow field can be described in terms of a velocity potential. The fluid domain is divided into three regions: region for upstream, region 2 for below breakwater, and region 3 for downstream shown in Fig.. The velocity potential Φ p (x, y, z, t) in the p-th region may be expressed differently. For regions and 3 is used simple methods according to (Drimer,992) and for region 2, concepts of (Geshraha, 26) is employed. Figure : Schematic Diagram of floating breakwater 776
2. Numerical results and Discussion Calculations was performed for freely floating and fixed floating breakwaters with various geometric properties on different domains. To generalize obtained results, they are presented in dimensionless forms. In this paper, it has tried to study effect of geometric dimensions on transmission coefficient of floating breakwaters. Figure 2 shows effect of adding side boards to freely floating breakwaters on the transmission coefficient ( ) of various waves. As expected, floating breakwater is transparent for the great period (or long) wave incidence. For a given dimensionless wave frequency (), the transmission coefficient decreases with an increase in relative side plate height (b/b). The transmission coefficient decreases from. in the long wave limit to zero at the point of complete reflection, where the breakwater acts as a complete vertical barrier. Dimensionless wave frequency of complete reflection point decreases with an increase in relative side plate height. As dimensionless frequency of wave increases further, transmission coefficient increases again. Here, transmission coefficient decreases with increase in relative side plate height. b/b= b/b=. b/b= b/b= b/b= b/b=..5 2 2.5 3 3.5 4 4.5 5 5.5 6 Figure 2: Effect of different height of side boards on wave transmission coefficient of freely floating breakwater (B/h=., d/b=5, =) In figure 3, the transmission coefficient is calculated for different relative breakwater width (B/h). For a given relative drift (d/b) of floating breakwater, it is shown that effect of relative width of breakwater is not great. However, lower relative width leads to higher transmission coefficient. 777
B/h=2; d/b=5 B/h=; d/b=5 B/h=; d/b=5. 2 3 4 5 6 Figure 3: Effect of different breakwater width on wave transmission coefficient of freely floating breakwater (b/b=, =) Figure 4 and figure 5 show effect of various relative drift and relative width of breakwater on its transmission coefficient. For a given relative width of breakwater, an increase in relative drift may decrease full barrier point and transmission coefficient. By comparing figures 3, 4 and 5, it can be find that, for study of effect of relative width of a floating breakwater, it is not relative drift to width of breakwater (d/b) that is effective, but relative drift of breakwater to water depth (d/h) is important. For a given "d/h", the lower is relative width of breakwater the more is transmission coefficient. B/h=2; d/b= B/h=2; d/b=5 B/h=2; d/b=..5 2 2.5 3 3.5 4 4.5 5 5.5 6 778
Figure 4: Effect of different breakwater drifts on wave transmission coefficient of freely floating breakwater (b/b=, =) B/h=; d/b=2. B/h=; d/b=.5 B/h=; d/b=.. 5 5.25.5.75 2 2.25 2.5 2.75 3 Figure 5: Effect of different breakwater drifts on wave transmission coefficient of freely floating breakwater (b/b=, =) In figure 6, the transmission coefficient is studied for different wave directions. For great period wave incidence, there is no significant difference in transmission coefficient related to different wave directions, but for medium or low period waves, transmission coefficient increases with an increase in wave incident angle. b/b=; α= b/b=5; α= b/b=5; α=3 b/b=5; α=45 b/b=5; α=6..5 2 2.5 3 3.5 4 4.5 5 5.5 6 Figure 6: Effect of different wave incident angle on wave transmission coefficient of 779
freely floating breakwater (B/h=., d/b=5) All of above results are for freely floating breakwaters. Figure 7 shows a comparison between freely and fixed floating breakwaters. For the same floating breakwaters, fixed one have significantly lower transmission coefficient than free one. As expected, for a given relative width of breakwater, more relative drift of breakwater ends in lower transmission coefficient. In addition, for a constant relative drift, transmission coefficient decreases with an increase in relative width of breakwater or adding longer side boards. F.F.; B/h=2; b/b=; d/b=5 Fixed; B/h=2; b/b=; d/b=5 Fixed; B/h=2; b/b=; d/b=5 Fixed; B/h=.4; b/b=; d/b=5 Fixed; B/h=.4; b/b=.; d/b=5..5 2 2.5 3 3.5 4 4.5 5 5.5 6 Figure 7: Comparison of wave transmission coefficient of freely floating (F.F.) and fixed breakwaters 3. Conclusions This paper studied the effect of various geometric dimensions on wave transmission coefficient of freely and fixed floating breakwaters. In addition, the possibility of performance enhancing of rectangular breakwaters by attaching two side boards is examined. The results are presented in dimensionless forms. Following items were found after obtaining numerical results: Floating breakwater is transparent for the great period wave incidence. Adding the side boards resulted in lower wave transmission coefficient. Effect of relative width of breakwater is apparent for constant drift to water depth ratio. More relative width of breakwater lessens the wave transmission coefficient. Wave incident angle may decrease transmission coefficient of waves with intermediate and small period, but it has no significant effect on large period waves transmission. 78
By fixing floating breakwaters, transmission coefficient is decreases considerably. 4. References. Lee, J. and W. Cho, 22, Effects of Mean Wave Drift Force on Mooring Tension and Performance of a Moored Floating Breakwater, KSCE journal of civil engineering, 6(2): pp 93-2 2. Yamamoto, T., 98, Moored floating breakwater response to regular and irregular waves, Applied Ocean Research, 3(): pp 27-36 3. Gesraha, M.R., 26, Analysis of [pi] shaped floating breakwater in oblique waves: I. Impervious rigid wave boards, Applied Ocean Research, 28: pp 327-338 4. Drimer, N., Y. Agnon and M. Stiassnie, 992, A simplified analytical model for a floating breakwater in water of finite depth, Applied Ocean Research, 4: pp 33-4 5. Stiassnie, M., 98, A simple mathematical model of a floating breakwater,applied Ocean Research, 2 (3): pp 7-78