HYDRODYNAMIC EFFICIENCY OF VERTICAL THICK POROUS BREAKWATERS O. S. Rageh Associate Prof., Irrigation and Hydraulic Dept., Faculty of Engineering, Mansoura University, El-Mansoura, Egypt ABSTRACT The efficiency of the vertical thick submerged or emerged porous breakwaters was experimentally studied. This is under normal and regular waves with wide ranges of wave heights and periods under constant water depth. The efficiency of the breakwater is presented as a function of the transmission, the reflection and the wave energy loss coefficients. Different parameters affecting the breakwater efficiency were tested, such as, breakwater height (D), breakwater width (B), breakwater porosity (n) and wave number (k=2π/l). It was found that, both the transmission and the reflection coefficients decrease as the relative breakwater width (kb) increases, while the energy loss coefficient takes the opposite trend. Also, the breakwater is more effective in reducing the transmitted waves and reflecting the incident waves as the breakwater crest elevation higher than the still water level, in case of, the transmission coefficient is less than 0.3 and the reflection coefficient is more than 0.5, specially when the breakwater height reaches 1.25 the water depth. Also, this type of breakwater dissipates more than 50% of the incident wave energy when the breakwater height equals the water depth. 1. INTRODUCTION Porous structures, such as rubble mound breakwaters are used worldwide to protect harbors and beaches from wave and current action. Recently, vertical permeable or porous structures become increasingly popular to protect marinas, fishing harbors, and to control shoreline erosion at semi sheltered sites in rivers estuaries and lakes. Vertical porous structures offer an alternative to conventional fixed breakwaters, such as rubble mound breakwaters. This type of breakwaters is considered as a good and cost-effective substitute for the conventional type of breakwaters, especially for coastal works where the tranquility requirements are low. This type occupies small zone so that, not affecting the seabed creatures. The submerged types of this kind permit to exchange the water masses along the beaches which minimize the pollution aspects. In addition, the land side of the emerged types of this breakwater kind can be used for berthing purposes.
Thirteenth International Water Technology Conference, IWTC 13 2009, Hurghada, Egypt 2. LITERATURE REVIEW The functional performance of the porous breakwater is evaluated by examining the wave reflection, transmission and energy loss caused by this breakwater. Many experimental and theoretical studies were made for determining the efficiency of vertical submerged or emerged permeable or impermeable types. The first one who discussed the problem of wave transmission due to the rectangular submerged breakwater was Jeffreys (1944). The simple empirical equation for determining the transmission coefficient was formed as follows: 1 k t = (1) 1/2 1/2 2 h h D 2 2B 1 1+ 0.25 sin h D h T g h D in which h is the water depth, D is the breakwater height, B is the breakwater width, g is acceleration of gravity, and T is the wave period. Dick and Brebner (1968) presented theoretical and experimental studies for permeable and solid submerged structures. Mei and Black (1968) studied experimentally and theoretically surface piercing and bottom standing thick vertical barriers and used various formulations as the basis for numerical computations of the reflection and the transmission coefficients and obtained an accuracy within one percent for the numerical results. Sollitt and Cross (1972) presented a summary of previous analytical approaches to the problem of predicting the transmission and the reflection characteristics of a porous structure. Madsen (1974) produced a simple solution for the reflection and the transmission coefficients based on the assumption of relative long normally incident waves on a rectangular homogeneous porous structure. Seeling (1980) obtained the most information about wave transmission, reflection, and energy dissipation from hydraulic model tests. The measurements in the model tests were generally limited to the free surface oscillations on the landward and seaward sides of submerged breakwater. Abdul Khader and Rai (1981) investigated experimentally the damping action of impermeable submerged breakwaters of various shapes (thin, rectangular, trapezoidal and triangular). The effectiveness of the breakwater in damping the incident wave energy is measured in terms of coefficient of transmission. Kobayashi and Wurjanto (1989) modified the numerical model for predicting the up rush and down rush of normally incident monochromatic waves on rough or smooth impermeable slopes. Dalrymple et al. (1991) examined the reflection and transmission coefficient from porous structures under oblique wave attack. Abul-Azm (1993) analyzed the linear wave potential near submerged thin barriers using the Eigen Function Expansion to determine the breakwater efficiency. Isaacson et al. (1996) carried out an experimental investigation on the reflection of obliquely incident waves from a model rubble-mound breakwater of single slice. Losada et al.
(1996a, b) investigated non-breaking regular waves and non-breaking directional random waves interacting with permeable submerged breakwaters. Heikal (1997) examined the efficiency of an impermeable, vertical thin submerged breakwater sited on sloping impermeable bed experimentally and numerically by using the Eigen Function Expansion method. Twu et al. (2001) studied theoretically, using the Eigen Function Expansion method, the problem of wave transmission over a rectangular and vertically stratified with multi-slice porous material. Koraim (2002) investigated experimentally and theoretically the wave interaction with impermeable, submerged thin and thick breakwaters, rectangular and trapezoidal, on horizontal and sloping beaches. Stamos et al. (2003) conducted a parametric experimental study to compare the reflection and transmission characteristics of submerged hemi-cylindrical and rectangular rigid and water-filled flexible breakwater models. Ting et al. (2004) investigated how the porosity of submerged breakwaters affects non-breaking wave transformations. Eight model geometries each with six different porosities, from 0.421 to 0.912, were also considered. Twu and Liu (2004) developed a computational model to investigate the wave damping characteristics of a periodic array of porous bars. The transmission and reflection coefficients as well as the wave energy dissipation are evaluated relating to the physical properties and geometric factors of bars. Jeng et al. (2005) investigated experimentally the mechanism of dynamic interaction among water waves, a submerged breakwater, a vertical wall, and a sandy seabed. Shirlal et al. (2007) experimentally investigated the armor stone stability of the submerged reef and the influence of its varying distances from shore and crest width on ocean wave transmission. 3. EXPERIMENTAL WORK The experiments were conducted in the Irrigation and Hydraulics Laboratory, Faculty of Engineering, El-Mansoura University. The runs were carried out to measure the transmission and the reflection coefficients due to the existence of the suggested porous breakwater models using different parameters. The flume dimensions are 15.10 m long, 1.00 m width, and 1.00 m deep. The wave generator type is a flap type, which is hinged at the bed and connected with a flying wheel and variable speed motor. Two wave absorbers were used at the beginning and the end of the flume to prevent the wave reflection. The wave period, length and height were recorded by using Sony MVC-CD 500 Digital Still Camera. The suggested breakwater model consists of a steel box made from a steel screen with steel angles on its corners and filled by gravels. Figure (1) shows the details of the flume and the tested breakwater models. The following parameters were used for the experimental set up: - Water depth (h) = 40 cm; - Range of incident wave height (H i ) = 7 10.5 cm; - Range of incident wave period (T) = 0.70 1.20 sec.; - Range of incident wave length (L) = 75 180 cm;
Thirteenth International Water Technology Conference, IWTC 13 2009, Hurghada, Egypt - Breakwater widths (B) = 0.3h, 0.45h, 0.6h; - Breakwater heights (D) = 0.75h, h, 1.25h; - Gravel porosity (n) = 0.41, 0.46; and - Gravel equivalent size diameter (d 50 ) = 29, 18 mm. Fig. (1) Details of the wave flume and breakwater model The maximum and the minimum wave heights (H max. and H min. ) at the wave generator side, upstream the breakwater, and the transmitted wave heights (H t ) at the wave absorber side, downstream the breakwater, were measured to estimate the reflection and the transmission coefficients (k r and k t ) as follows: H i = (H max. + H min. ) / 2 (2) H r = (H max. H min. ) / 2 (3) Then; k r = H r / H i (4) k t = H t / H i (5) in which, H i and H r are the incident and the reflected wave heights, respectively. The energy equilibrium of an incident wave attack the structure can be expressed as follows: E i = E r + E t + E L (6) in which, E i is the energy of incident wave (E i =ρg H i 2 /8), E r is the energy of reflected wave (E r =ρg H r 2 /8), E t is the energy of transmitted wave (E t =ρg H t 2 /8), and E L is the wave energy losses. Substituting the values of E i, E r, and E t into equation (6) and dividing through by E i, yields:
2 r i 2 t H H E L 1 = + + (7) H H E i i Combining equations (4), (5) and (7), the wave energy loss coefficient (k L =E L /E i ) can be expressed as follows: k L 2 r 2 t = 1 k k (8) 4. EXPERIMENTAL RESULTS AND ANALYSIS When a structure is installed in a marine environment, the presence of that structure will alter the flow pattern in its immediate neighborhoods, resulting in one or more of the following phenomena: 1. Formation of lee-wake vortices behind the structure. 2. Generation of turbulence. 3. Occurrence of reflection and diffraction of waves. 4. Occurrence of wave breaking. These phenomena results in dissipating the wave energy in addition to the dissipation caused by the breakwater itself. Many parameters affecting the breakwater efficiency are studied, such as the wave number, (k=2π/l), the water depth (h), the breakwater width (B), the breakwater height (D), and the breakwater porosity (n). The analysis is presenting the efficiency of the breakwater in the form of relationships between transmission, reflection and energy loss coefficients (k t, k r, k L ) and the dimensionless parameters representing the wave and structure characteristics as in the following equation: k t, k r, and k L = f (kb, kh, D/h, n) (9) Figure (2) presents the relationship between the transmission coefficient (k t ) and the relative breakwater width (kb=2bπ/l). This is when the breakwater height ratios (D/h) are 0.75, 1.0, and 1.25 for two different values of the breakwater porosity (n= 0.41 and 0.46). The figure shows that, the transmission coefficient (k t ) decreases as kb increases. This means that, the breakwater reduces the transmitted waves as the breakwater width (B) increases or the wave length (L) decreases. The abovementioned behavior could be attributed to two reasons. First, the increase of the breakwater width causes the increase of the friction between the breakwater surface and the transmitted waves, causing more wave energy loss. Second, as the wave becomes short, the water particle velocity and acceleration suddenly change and the turbulence caused due to this sudden change causes dissipation in the wave energy. Also, the transmission coefficient (k t ) decreases as D/h increases. This may be attributed to the decrease in the transmitted wave energy due to decreasing the area which water path through. The transmission coefficient (k t ) decreased from 0.95 to 0.8 when D/h=0.75, decreased from 0.75 to 0.5 when D/h=1.0, and decreased from 0.4 to 0.15 when D/h=1.25 for increasing kb from 0.42 to 2.0.
Thirteenth International Water Technology Conference, IWTC 13 2009, Hurghada, Egypt Fig. 2. Effect of relative breakwater height and width (D/h and B/h) on the transmission coefficient: (a) n = 0.41 (b) n = 0.46 Figure (3) presents the relationship between the reflection coefficient (k r ) and kb when D/h = 0.75, 1.0, and 1.25 for n= 0.41 and 0.46. The figure shows that, k r decreases as
kb increases. This may be attributed to the increase of the wave energy loss as the width of the porous media increases. Also, the reflection coefficient (k r ) increases as D/h increases. The reflection coefficient (k r ) decreased from 0.35 to 0.15 when D/h=0.75, decreased from 0.4 to 0.2 when D/h=1.0, and decreased from 0.75 to 0.45 when D/h=1.25 for increasing kb from 0.42 to 2.0. Figure (4) presents the relationship between the energy loss coefficient (k L ) and kb when D/h = 0.75, 1.0, and 1.25 for n= 0.41 and 0.46. The figure shows that, k L increases as kb increases. Also, the energy loss coefficient (k L ) increases as D/h increases up to D/h=1.0, then it decreases. This may be due to the decrease of the transmitted waves, in which, the losses caused by friction between transmitted waves and breakwater porous media decreases. The energy loss coefficient (k L ) increased from 0.1 to 0.2 when D/h=0.75, increased from 0.4 to 0.75 when D/h=1.0, and increased from 0.25 to 0.7 when D/h=1.25 for increasing kb from 0.42 to 2.0. Figure (5) presents the effect of the breakwater porosity (n) on the different hydrodynamic coefficients (k t, k r, k L ) for the different values of D/h. Figure (5a) shows that, k t decreases as the porosity (n) increases from n=0.41 to n=0.46 by about 2 to 5%. Figure (5b) shows that, k r increases as the porosity (n) increases from n=0.41 to n=0.46 by small values (less than 4%) when D/h=1.25. When D/h=1.0 and 0.75, the reflection coefficient (k r ) not affected by the increase of n. Figure (5c) shows that, k L increases by about 2 to 10% as the porosity (n) increases from n=0.41 to n=0.46. Figure (6) presents the relationship between the transmission coefficient (k t ) and the dimensionless wave number (kh=2πh/l) when D/h= 0.75 and B/h=0.3, 0.45, and 0.6 for n=0.41 and 0.46. Also, the figure presented the comparison between the present experimental results of the transmission coefficient and the results obtained from Jefferys (1944) [Equation (1)]. The figure shows that, the Jefferys and the present transmission coefficients slightly decrease as kh increases. Also, a reasonable agreement obtained between the present results and the Jefferys' results. 5. CONCLUSIONS The efficiency of the vertical thick submerged or emerged porous breakwaters was experimentally studied. This is under normal regular waves with wide ranges of wave height, wave period, and constant water depth. The main drawn conclusions from this study can be summarized as follows: 1. The transmission and the reflection coefficients decrease as the relative breakwater width (kb) increases, while the energy loss coefficient takes the opposite trend. 2. The breakwater is effective in reducing the transmitted waves and reflecting the incident waves as the breakwater crest elevation higher than the still water level. In case of, the transmission coefficient (k t ) is less than 0.3 and the reflection coefficient (k r ) more than 0.5, specially when D/h=1.25 3. The breakwater dissipates more than 50% of the incident wave energy when the breakwater crest elevation equals the still water level. 4. The efficiency of the breakwater is slightly affected when the breakwater porosity increases from n=0.41 to n=0.46.
Thirteenth International Water Technology Conference, IWTC 13 2009, Hurghada, Egypt Fig. 3. Effect of relative breakwater height and width (D/h and B/h) on the reflection coefficient: (a) n = 0.41 (b) n = 0.46
Fig. 4. Effect of relative breakwater height and width (D/h and B/h) on the wave energy loss coefficient: (a) n = 0.41 (b) n = 0.46
Thirteenth International Water Technology Conference, IWTC 13 2009, Hurghada, Egypt Fig. 5. Effect of breakwater porosity (n) on the different hydrodynamic coefficients for different values of D/h
Fig. 6. Comparison between the present experimental results and the corresponding ones obtained from Jeffreys (1944) when D/h = 0.75
Thirteenth International Water Technology Conference, IWTC 13 2009, Hurghada, Egypt REFERENCES 1. Abdul Khader, M.H. and Rai, S.P. (1981) A Study of submerged breakwaters J. of Hydraulic Research Vol. 18, No. 2. 2. Abul-Azm A.G. (1993) Wave diffraction through submerged breakwaters Waterway, Port, Coastal and Ocean Eng., Vol. 119, No. 6. 3. Mei C. C, and Black J. L. (1969) Scattering of surface waves by rectangular obstacle in water of finite depth J. Fluid Mech., Vol. 38, 499-511. 4. Dalrymple, R. A., Losada, M. A., Martin, P. A. (1991) Reflection and transmission from porous structures under oblique wave attack J. Fluid Mech. Vol. 224, 625-644. 5. Dick, T.M. and Brebner, A. (1968) Solid and permeable submerged breakwaters Proc. 11 th. Conf. On Coastal Engineering, ASCE, New York, N.Y., II, 1141-1158. 6. Heikal, E. M. and Attar, A. A. (1997) Effect of beach slope on the efficiency of submerged breakwaters 2 nd Int. Conf., Mansoura Univ., Mansoura, Egypt. 7. Isaacson, M., Papps, D., Mansard, E. (1996) Oblique reflection characteristics of rubble-mound structures J. Waterways, Port, Coastal, Ocean Eng., ASCE, Vol. 122, No. 1. 8. Jeffreys, H. (1944) Note on the offshore bar problem and reflection from a bar Grt. Birt. Ministry of Supply, Wave Report 3. 9. Jeng, D. S., Schacht, C., and Lemkert, C. (2005) Experimental study on ocean waves propagating over a submerged breakwater in front of a vertical seawall J. Ocean Engineering Vol. 32, Iss. 17-18. 10. Kobayashi, N., and Wurjanto, A. (1989) Wave transmission over submerged breakwaters. J. Waterway, Port, Coastal and Ocean Eng., Vol. 115, No. 5. 11. Koraim, A. S. (2002) Effect of beach characteristics on submerged breakwaters efficiency A Thesis Submitted for Partial Fulfillment of Master Degree in Civil Eng., Zagazig University, Zagazig, Egypt. 12. Losada, I. J., Silva, R., Losada, M. A. (1996a) 3-D non-breaking regular wave interaction with submerged breakwaters J. Coastal Engineering Vol. 28, No. 4. 13. Losada, I. J., Silva, R., Losada, M. A. (1996b) Interaction of non-breaking directional random waves with submerged breakwaters J. Coastal Engineering Vol. 28, No. 4. 14. Madsen, O. S. (1974) Wave transmission through porous structures J. Waterways, Ports, Coastal, Ocean Eng., Vol. 100, No. 3. 15. Mei, C. C. and Black, J. L. (1969) Scattering of surface waves by rectangular obstacles in water of finite depth J. of Hydraulic Research, IAHR, Vol. 38. 16. Seelig, W. N. (1980). Two-dimensional tests of wave transmission and reflection characteristics of laboratory breakwaters Tech. Report No. 80-1, U. S. Army Coastal Engineering Research Center, Fort Belvoir, Va. 17. Shirlal, K. G., Rao, S., and Manu (2007) Ocean wave transmission by submerged reef - a physical model study J. Ocean Engineering Vol. 34, Iss. 14-15. 18. Sollitt, C. K. and Cross, R. H. (1972) Wave transmission through permeable breakwaters Proc., 13 th Coastal Eng. Conf., ASCE.
19. Stamos, D. G., Hajj, M. R., and Demetri, P. (2003) Performance of hemicylindrical and rectangular submerged breakwaters J. Ocean Engineering Vol. 30, Iss. 6. 20. Ting, C. L., Lin, M. C., and Cheng, C. Y. (2004) Porosity effects on non-breaking surface waves over permeable submerged breakwaters J. Coastal Engineering Vol. 50, Iss. 4. 21. Twu, S. W., Liu, C. C., and Hsu, W. H. (2001) Wave damping characteristics of deeply submerged breakwaters J. Waterway, Port, Coastal and Ocean Eng., Vol. 127, No. 2. 22. Twu, S. W., and Liu, C. C. (2004) Interaction of non-breaking regular waves with a periodic array of artificial porous bars J. Coastal Engineering Vol. 51, Iss. 3. NOTATION The following symbols are used in this paper: B D d 50 E i E L E r E t g H i H r H t h k k L k r k t L n T ρ = breakwater width; = breakwater height; = equivalent size diameter of the gravel; = energy of incident waves; = energy wave losses; = energy of reflected waves; = energy of transmitted waves; = acceleration of gravity; = incident wave height; = reflected wave height; = transmitted wave height; = water depth at the breakwater site; = incident wave number at breakwater site; = energy loss coefficient; = reflection coefficient; = transmission coefficient; = Wave length at breakwater site; = porosity of the gravel; = wave period; and = water density.