WAVE DISSIPATING PERFORMANCE OF AIR BUBBLE BREAKWATERS WITH DIFFERENT LAYOUTS*

ZHANG Cheng-xing

State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China

College of Urban Planning and Environmental Science, Xuchang University, Xuchang 461000, China, E-mail: zhangchengxing19@163.com

WANG Yong-xue, WANG Guo-yu

State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China

YU Long-mei

Dalian Port Construction Supervision and Consultation Co. Ltd., Dalian 116015, China

WAVE DISSIPATING PERFORMANCE OF AIR BUBBLE BREAKWATERS WITH DIFFERENT LAYOUTS*

ZHANG Cheng-xing

State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China

College of Urban Planning and Environmental Science, Xuchang University, Xuchang 461000, China, E-mail: zhangchengxing19@163.com

WANG Yong-xue, WANG Guo-yu

State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China

YU Long-mei

Dalian Port Construction Supervision and Consultation Co. Ltd., Dalian 116015, China

(Received December 28, 2009, Revised March 30, 2010)

The wave dissipating performance of air bubble breakwaters with different layouts is studied by experimental and numerical methods in this article. Based on the assumpation that the mixture of air and water is regarded as a variable density fluid, the mathematical model of the air bubble breakwater is built. The numerical simulation results are compared with the experimental data, which shows that the mathematical model is reasonable for the transmission coefficient Ctm. The influencing factors are studied experimentally and numerically, including the incident wave heightHi, the incidentt wave period T , the air amount Qm, the submerged pipe depth D and the single or double air discharging pipe structure. Some valuable conclusions are obtained for further research of the mechanism and practical applications of air bubble breakwaters.

Air bubble breakwater, wave dissiptating performance, experiments, variable density fluid

1. Introduction

The air bubble breakwater is composed of an air compressor and pipes with orifices. The pipes are often placed at the sea bottom, or at a certain depth in a deep water area. The air compressor is usually installed on the shore or on a boat[1]. The air bubble breakwater is used for protecting a harbor, the entrance of a port, a part of sea water against wave induced wrecks. The air bubble breakwater is one of mobile breakwaters, with several specific features such as mobility, temporality, and low cost. Besides, it may be pointed out that, with the use of the air bubble breakwater, from an environment point of view, one need not interrupt the exchange of water in harbors[2].

The first air bubble breakwater appeared in 1907, which was used by Brasher of New York to protect civil engineering works. The second was built in 1915 at El Segundo, California, under Brasher’s patent. With some more projects of that nature, the results, however, were not promising and the method fell into disuse. Fundamental tests were conducted by the Admiralty in 1924, by Russian scientists in 1935 and by Professor Thysse of Delft in 1936. During the Second World War, the research and analysis on air bubble and water jet breakwaters were carried out by White and Taylor[3].

In the early 1950’s, a wide publicity was given to an air bubble breakwater designed by Laurie to protect a train ferry dock entrance at Dover. Before that, Carr and Schiff studied the air bubbles breakwater in a model tank at the California Institute of Technology. With the use of the Dover installation, Evans conducted a series of model tests in 1954 in conjunction with the theoretical work by Taylor. Bulson reviewed the analytical and experimental studies carried out by himself and others, and in was concluded that the surface currents produced by the air bubble motion were the main mechanism of wave dissipation in the system of the air bubble breakwater. The empirical formulae were presented for the surface velocity and the thickness of the horizontal current produced by an air bubble curtain; and for the amount of free air required to suppress waves with certain length and height. Zhang et al.[4]studied the horizontal current generated by air bubble curtain in still water with a numerical simulation technique, which gave a further explanation of the wave dissipating mechanism of the air bubble breakwater. Furthermore, Zhang[5]carried out a preliminary study of the performance of the air bubble breakwater, and the results demonstrated the effects of air amount as well as incident wave period on the air bubble breakwater system.

Despite of those experimental and theoretical researches done in past years, due to the complexity of the interactions between air bubbles and water, the air bubble breakwater remains a topic of studies and the practical application data are very much in demand. This article presents our experimental and numerical studies of the wave dissipating performance of the air bubble breakwaters with different layouts.

Fig.1 The schematic diagram of the tests for the air bubble breakwater

2. Experiment

2.1 Equipment

The length scales 1:10 and 1:15 are adopted in our experiments in the large wave tank of the State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology. The large wave tank is 69.0 m long, 2.0 m wide and 1.8 m deep. The pipe to discharge air with orifices is made of plexiglass, with the length of 2.0 m, the orifice diameter of 0.0008 m and the distance between two orifices of 0.01 m. The compressed air is supplied by the air compressor up to the maximum amount of 3.0 m3/min. Figure 1 showes the schematic diagram of the tests for the air bubble breakwater.

Four wave gauges of capacitance type are installed as shown in Fig.1. The transmission coefficient Ctmof the air bubble breakwater is calculated by the Goda method[6]. In the tests, the same case is tested for three times, to obtain the average value.

Table 1 The parameters of tests with different length scales

Fig.2 The apparatus of the air bubble breakwater system

The prototype parameters include the incident wave height H=3.55 m, the incident wave period T=4s , 5 s and 6 s, and the water depth d=12 m. With respect to two length scales, the incident waves are governed by the law of gravity similarity, the corresponding parameters in model tests are shown in Table 1. The subscript of m and p means the model and prototype, respectively, in the article.

During the tests, the air is pushed by the air compressor to the pipe, and then the air bubbles are produced continuously from the orifices and an air bubble curtain will appear across the tank width. The incident wave passes the air bubble curtain, and the wave dissipation occurs due to the wave deformation and the wave break. In the tests, the flow meter is installed at different locations along the pipe for the measurement of air amount Qm. Figure 2 shows the apparatus of the air bubble breakwater.

2.2 Results and discussions

The incident wave height Hiand the transmitive wave height Htcan be obtained from the test data by the Goda’s method. The transmission coefficient Ctmis expressed as Ctm=Ht/Hi. The impacts of the incident wave period T and the air amount Qmon the wave dissipating performance of the air bubble breakwater are compared and analyzed.

Figure 3 shows the relations of the transmission coefficient Ctmversus the air amount Qmwith different length scales and different incident wave periods T. It is found that the wave dissipating performance of the air bubble breakwater is closely related with the air amout Qm, and it can be improved by the increase of air amount Qm.

From Fig.3, it is seen that the incident wave period T is the key factor influencing the wave dissipating performance of the air bubble breakwater. Take Fig.3(a) for example, the incident waves with three different wave periods are dissipated with various air amounts Qm. In the case of the incident wave period T =1.26s, the transmission coefficient Ctmchanges from 0.87 to 0.48 when the air amount increases from 5 m3/h·m to 20 m3/h·m. However, the

transmission coefficient Ctmchanges but little for the cases of the incident wave period T =1.58s and T =1.91s. It is demonstrated that the wave dissipating performance of the air bubble breakwater is affected evidently for short period waves with a given air amount Qm, and the wave dissipating performance of the air bubble breakwater is good for short period waves.

Fig.3 Test data of Ctmagainst different air amountsQm

3. Numerical simulation

3.1 Mathematical formulation

The mixture of air and water is considered as a fluid of variable density. The density and the dynamic viscosity coefficient of the fluid are defined as

where a0,ρ0, μ0are the volume fraction, density and the dynamic viscosity coefficient of water, and a1,ρ1, μ1are the corresponding parameters for air. The volume fractions of both phases aq(q =0,1) can be solved from Eqs.(3) and (4)

The continutiy equation is expressed as Eq.(5), and the momentum equation is the Reynolds averaging equation in the form[7-10], as shown in Eqs.(6) and (7), in which the density and the dynamic viscosity coefficient of the fluid is defined by Eqs.(1) and (2). The pressure pattern and the velocity pattern take the average values.

where μtis the turbulent viscosity coefficient, μ =ρC k2/ε, C is a constant, C=0.09, the

tμμμ turbulent kinetic energy k and the turbulent diffusionε are governed by Eqs.(8) - (9)[11,12]. As mentioned previously, it is assumed that the mixture of air and water is regarded as a variable density single phase liquid, so the standard k?ε equation can be used in this condition.

where Gkis the turbulent kinetic energy produced

Fig.4 A schematic diagram of the numerical simulation model of the air bubble breakwater

3.3 Model validation

In order to verify the rationality of the numerical model of the air bubble breakwater presented in the article, numerical computations are conducted and the schematic diagram of the numerical simulation model is shown in Fig.4. The length scales 1:10 and 1:15 are selected, the wave parameters and the air amounts Qmare the same as the experimental cases, as shown in Table 1. transmission coefficient Ctmof the test results would be smaller than those in other cases.

It is seen from Figs.5 and 6 that the air amount Qmplays an important role in the wave dissipating performance of the air bubble breakwater, at the same time, the transmission coefficient Ctmis reduced with the increase of air amout Qm. It is also found that the incident wave period T affects the performance of wave dissipating, and the air bubble breakwater would have good wave dissipating performance when the incident wave has a short period T. All these are verified by experimental results.

3.4 Results and discussions

The factors that influence the wave dissipating performance of the air bubble breakwater are studied by numerical simulations, including the incident wave height H, the pipe submerged depth D and the spacing between two air discharging pipes dsfor the air bubble breakwater with double air discharging pipes. Based on the results obtained from numerical simulations, various influencing factors are analyzed to determine their impacts on the wave dissipating performance of the air bubble breakwater. A schematic diagram of the numerical wave tank is shown in Fig.4. The wave tank is 330 m long and 15 m deep, and the grids are refined in the region from X =110 m to X =130 m, with the air bubble curtain located at X =120 m. The transmission coefficientCtpis obtained at the monitor #3 as the numerical results.

3.4.1 Incident wave height

The cases considered in the numerical simulations include various incident wave heights H, incident wave period T and air amount Qpas shown in Table 2, and the results are illustrated in Fig.7.

Figure 7(a) shows the variation of the transmission coefficient Ctpwith incident wave heights Hiand the air amount Qpfor T=4s. It is found that the transmission coefficientCtpdecreases with the increase of air amount Qp. But the reduction of transmission coefficient Ctpvaries with different incident wave heights Hi, the smaller the incident wave height Hi, the smaller the transmission coefficientCtpbecomes. The same results can be seen from the Figs.7(b) and 7(c) for T=5s and T=6s.

Fig.5 The comparison of Ctmbetween experimental experimental and numerical simulations(Length scale, 1:10)

Fig.6 The comparison of Ctmbetween and numerical simulations (Length scale, 1:15)

Figures 5 and 6 show the comparisons of transmission coefficient Ctmbetween experimental and numerical results. It can be seen from Figs.5 and 6 that the maximum deviation of transmission coefficient Ctmbetween numerical results and experimental results is 9% except the case of the length scale 1:10, the incident wave periodT =1.26s and the air amount Q=20 m3/h· m . In the

m experiments, the incident wave will be broken with the horizontal flow produced by a large air amount Qm, but the wave broken phenomenon is not considered in the numerical simulation. So the

Table 2 Cases for numerical simulations with different incident wave heights Hi

Fig.7 Transmission coefficient Ctpversus air amounts Qpfor different incident wave heights Hi

It is demonstrated from Fig.7 that the transmission coefficient Ctpis reduced by a large amount with a small incident wave height Hifor the same air amountQp. which means that the wave dissipating performance of the air bubble breakwater is good for the small incident wave height Hiwith a given air amount Qp, the reason of which may be illustrated from the view of wave energy.

When the water depth d and the incident wave period T are constants, the greater the incident wave height Hi, the greater the wave energy will be. The wave dissipating performance of the air bubble breakwater is not good when the incident wave height is large at a certain air amountQp.

3.4.2 Submerged pipe depth

The different submerged pipe depths D are considered with different air amounts Qpand different incident wave periods. The submerged pipe depth is defined as the vertical distance from the location of air discharging pipe in the water to the water surface. Three submerged pipe depths are considered in the article. The cases with different parameters in numerical simulations are shown in Table 3.

Figure 8 shows the variation of the transmission coefficient Ctpwith the increase of air amount Qpfor different submerged pipe depths D and the incident wave periods T=4 s, 5 s and 6 s, respectively.

Figure 8(a) shows the variation of the transmission coefficient Ctpversus the air amount Qpfor various submerged pipe depths D. It is found that the transmission coefficient Ctpdecreases with the increase of air amount Qpfor different submerged pipe depths D. The greater the submerged pipe depth D , the smaller the transmission coefficient Ctpwill be. The sameresults can be seen from Figs.8(b) and 8(c). transmission coefficient Ctpdecreases with the increase of the submerged pipe depth D for the same air amount Qp, which means that the submerged pipe depth D is one of influencing factors related to wave dissipation in the air bubble breakwater system. It is also seen that when the incident wave period T is short, the effect of the submerged pipe depth D is significant. Furthermore, the air amount Qpplays an important role in the wave dissipating performance of the air bubble breakwater, which is consistent with the experiment results.

Table 3 The numerical simulation cases with different submerged depths of air discharging pipe D

Fig.8 Transmission coefficient Ctpversus air amounts Qpfor different submerged pipe depths D

Fig.9 The profile of Vmversus water depth ( X =134 m, t=67 s , Q=500 m3/h· m )

Figure 9 shows the variation of the horizontal flow velocity Vmgenerated by the air bubble curtain versus the water depth d at the locationX =134 m in the calm water, when the water depth d =12 m,air amount Q=500 m3/h· m , the time

p

t=67 s and the submerged pipe depthD=6 m and 12 m, respectively. It can be found that the flow velocity Vmproduced by the pipe with the submergence D=12 m is greater than that with the submergence D=6 m under the same air amountQpin the calm water. According to the wave dissipating mechanism of the air bubble breakwater, as the effects of the horizontal flow velocity Vmon the incident waves, the greater the horizontal flow velocity Vm, the better the wave dissipating performance will be. It is seen that the wave dissipation of the air bubble breakwater is affected by the submerged pipe depthD.

3.4.3 Double air discharging pipes

The air bubble breakwater with double air discharging pipes is designed and its schematic diagram is shown in Fig.10 for studying the wave dissipating performance of the air bubble breakwater. Two different spacings between air discharging pipes ds=6 m and 10 m are considered in the article. The locations of air discharging pipes are atX =117 m and X=123m for ds=6 m and atX =115 m and X =125 m for ds=10 m , respectively.

Fig.10 Schematic diagram of the air bubbles breakwater with double air discharging pipes

The wave dissipating performance of the air bubble breakwater with double air discharging pipes are studied, considering different spacings between double air discharging pipes dsand different air amounts Qp, which are taken as the total air amounts of both pipes for the case of double air discharging pipes. The incident wave period T=5s, the incident wave height H=3.55 m and the water depth d=12 mare adopted in the numerical simulations. The total air amountQpis selected from 100 m3/h·m to 580 m3/h·m with increment of 80 m3/h·m.

Figure 11 shows the comparison of transmission coefficient Ctpbetween single and double air discharging pipe structures with various total air amounts Qp, where (a) for ds=6 m and (b) for ds=10 m . It is found from Fig.11(a) that the transmission coefficientCtpof the single and double air discharging pipe structures sees no significant difference for various total air amounts Qpfor ds=6 m , which means that the wave dissipating effects of the air bubbles breakwaters of both structures are similar. It is also found from Fig.11(b) that the transmission coefficient Ctpof the single air discharging pipe structure is smaller compared with that of the double air discharging pipe structure for ds=10 m for various total air amountsQp, which means that the spacing between double air discharging pipes affects the wave dissipating performance to a certain extent.

Fig.11 The comparison of transmission coefficient Ctpbetween single and double air discharging pipe structures with various total air amounts Qp

Figure 12 shows the pattern of velocity vector generated by the double air discharging pipes in the calm water at the time t=67 s with the air amount Q=500 m3/h· m , the spacing d=6 m and 10 m,

p s and the water depth d=12 m. Figure 13 shows the distribution of the horizontal flow velocity Vmalong the water depth at the position X =134 m with the the same condition referred above. It is found from Fig.12(a) that the pattern of the circulation flow produced by the air bubble’s motion is similar to that by the single air discharging pipe for the spacing ds=6 m , so the wave dissipating capability isnearly the same between two kinds of structures. But for the spacing ds= 10 m, on the other hand, as shown in Fig.12(b), there are two minor vortexes between twoair discharging pipes. The existence of the two minor vortexes affects the distribution of the part of the total energy generated by the air bubble’s motion, which would reduce the horizontal flow velocity Vm. Figure 13 also shows obviously that the horizontal flow velocityVmdecreases with the increase of the spacing ds. It is seen that the wave dissipating performance of the air bubble breakwater with double air discharging pipes may not be improved as compared with the air bubble breakwater with a single air discharging pipe, especially, when the spacing between double air discharging pipes dsis large.

Fig.12 The pattern of velocity vector with different spacings between double air discharging pipes dsin the calm water (t =67 s , Q=500 m3/h· m )p

Fig.13 The profile of Vmversus water depth ( X =134 m, t=67 s ,Q=500 m3/h· m )p

4. Conclusions

In the article the wave dissipating performance of the air bubble breakwater and the influencing factors are studied by experiments and numerical computations. In the numerical model, the mixture of water and air is regarded as a variable density liquid, the Reynolds averaging equation and the standard k?ε equations are adopted as the governing equations, the method of VOF is used to track the two-phase interface; an additional mass source is added in the continuity equation and an additional momentum source is added in the momentum equations. The following conclusions are drawn.

(1) By the comparison of experimental results and numerical simulation results, it is demonstrated that the mathematical model in this article is reasonable.

(2) The wave dissipating performance of the air bubble breakwater depends closely on the air amount Q. With the increase of the air amount Q, the wave dissipating performance of the air bubble breakwater is improved.

(3) The wave dissipating performance of the air bubble breakwater is affected significantly by the incident wave period T, especially, for the incident wave with short period T.

(4) With the increase of the incident wave height Hi, the wave dissipating performance of the air bubble breakwater becomes worse.

(5) The increase of the submerged pipe depth D would improve the wave dissipating performance of the air bubble breakwater.

(6) With the same total air amount Q, the wave dissipating performance of the air bubble breakwater with double air discharging pipes may not be improved in comparison with the air bubble breakwater with a single air discharging pipe, especially, when the spacing between the double air discharging pipesdsis large. It may be a good choice to use the single air discharging pipe structure instead of the double air discharging pipe structure.

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10.1016/S1001-6058(09)60102-5

* Project supported by the National Natural Science Foundation of China (Grant No. 50809015).

Biography: ZHANG Cheng-xing (1977-), Male, Ph. D., Lecturer