Applied Mechanics and Materials Vol. 302 (2013) pp 326-331 Online available since 2013/Feb/13 at www.scientific.net Β© (2013) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMM.302.326
Study of a Wave Absorber in Various Distance Placed In a Sinusoidal Propagate Wave Zhen-Zhong Yuan1, a, Bhupendra Singh Chauhan2,band Hee-Chang Lim3,c School of Mechanical Engineering, Pusan National University, Pusan. Republic of Korea a
[email protected],
[email protected],
[email protected]
Keywords:Wave maker, wave absorber, reflectance, incident wave, reflected wave
Abstract.Since there has been a rapid progress to understand the dynamics of an offshore floating body under an ocean environment, we undertake to generate the ocean waves in a lab-scale windwave flume. The study is aiming to observe and optimize the similar ocean environmental condition as input wave and to reduce the wall reflective wave. Several absorption methods are suggested to optimize the propagate wave by measuring the maximum and minimum of the standing wave envelope. There has been no optimized absorption method, as they highly depend on the wave period and the wave length. One of the methods - two fixed wave gauges measuring two wave heights and one wave phase - is applied in this study. In the present paper various approaches were used to analyze the results using the flume, by position of probes, with absorber and without absorber, different position, condition and angle of the wave absorber, This paper also focuses on the analysis of fundamental equations which describe the separating method of the incident and reflective wave, and finally we confirm that the wave absorber is highly efficient considering all the permutation and combination.From the study it is clear that there is a change in the wave amplitude at the receiving end then the generated end; wave absorber is a strong source to control the energy of the coming wave. With the changing the period of the wave, the reflectance is increasing when the period becomes larger. Introduction Theoretical analysis, numerical analysis and model experiments are used to resolve the marine engineering-related issues, these methods are not only mutual complementation but also confirm each other to be verified. Numerical simulation in the base of a computer platform is in rapid development now, but also it canβt take every factor into consideration so thatthe laboratory experiment is still very important and necessary for the optimized design of certain target model. Since all the external environmental conditionsare the most important factor, it is not easy to reproduce completely in the laboratory such as a wave flume. In order to make a proper measurement in this regard, a variety of the equipmentsare also necessary. One of the difficult things in the laboratory measurement, the reproduction of the external environment in the offshore such as general periodic waves.When a wave is usually generatedin one end of the wave flume, the propagating wave moves toward the other end so that the reflective wave is also produced. This phenomena becomes the analysis more complicating, i.e., these waves make the superposition, the separation and the merging each other. Usually, these multi-reflection waves should not occur in the laboratory, which is not possible in the real field, such as offshore area and even ocean environment. Therefore, in order to reproduce these ocean environments effectively, an optimized design of wave absorber is practically necessary. This paper observed the behavior of the propagating waves which is separated into the incident and the reflected wave. This method is a common method developed by Healy to estimate the reflection of regular waves by measuring the maximum and minimum of the standing wave envelope. In addition, it requires a slowly moving wave gauge in the wave flume along a line parallel to the direction of the wave propagation. Even though this methodwas simple and convenient to analysis, due to the continuous reflected wave the error wassubstantially large. [1]In the other hand, there werealternative methods of separating the incident and reflected wave, one is All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP, www.ttp.net. (ID: 164.125.59.39, Pusan National University, Pusan, Korea, South-18/03/13,09:58:51)
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to use two fixed wave gauges for measuring two wave heights and one wave phase, and the other three fixed wave gauges for measuring three wave heights and two wave phases. [2][3]Due to the limitation of the wave flume, the method suggested by Goda and Suzuki seems to be appropriate in our test condition. In the paper, a study of the wave generation with an absorber was carried out by using a wave flumewithwave absorber. The reflectance andwave height variation on the free surface under severalwaveperiods were evaluated. A variety of wave absorber models with more accurate approaches are covered in this paper. The study was done at the laboratory scale and the wave was induced using a piston arrangement propelled by a stepping motor. The mesh porosity is made by a nylon mesh as it is free from corrosion, wear and tear, long life and its porosity can be easily changed. Three different arrangements were taken by varying angle of absorber and position of absorber. The entire study was done by using electronic level gauges and a control unit which was connected with the personal computer for data acquisition. Design of laboratory experiments
Fig. 1 Snapshot of a wind and wave tunnel used in the experiment Experimental set up of wave flume The experiment was carried out in a wind wave flume which has a length of 5m, a width 0.4m and the height 0.85m, and the wind tunnel cross section is 400mmΓ400mm.(see Fig.1) The wavemaking system sitting in one end of the tunnel is a piston type and a 5 phase stepping motor (PK596AWM) is applied. The wave absorber is installedin the other end of the tunnel. The wind tunnel with a maximum speed of 35m/s is a blow-down type and no used in this measurement, but the combination of wind and wave will be one of interesting study for the further work. Two wave gauges(KENEK Wave Height Meter CH-606) were used in the experiment and the distance is defined as , where should not be half an wave length and larger than 0.1L(L is wavelength), in order to distinguise clearly between incident wave and reflected wave the position was so chosen. Two wave guage were installed depending on the experimental condition, but thesepositions were suitably chosen in the direction of wave propagation, which is carefully considered as the different wave zone to measure the maximum and minimum wave heightwhile evaluating incident and reflected wave. The wave was generated by a combination of the piston cylinder assemblyanda stepping motor controlled by a AVR 128electric circuit and visual basic program. The ouput of wave gauge probes was also taken by the data logging unit (NIUSB-9151) which stores the analog signal and send it to the computer hard disk. The shematic diagram is as shown in Fig. 2.
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Fig. 2Schematic diagram of the wave flume experimental design Wave theory and reflectance ( ) It is supposed that a wave paddle makesthe waves propagating forward in a wave flume and reflected by the other end. Then, the reflected waves move back to the wave-paddle side and are reflected again. The re-reflected waves propagated forward again and this condition is repeated until the multi-reflected waves are fully attenuated. The wave train in the positive direction is called the incident waves and that in the negative direction the reflected waves. It is also supposed that the amplitude of the incident waves be ππΌ and the amplitude of the reflected waves beπ [2]. The wave modeling in this conditionis summarized from equation 1 to equation 13 to obtain the incident and reflected wave followed by making an appropriate curve fitting.Twodifferent waves can be formulatedin the form of πΌ
ππΌ
(
πΌ)
π
(
(1)
)
(2) (3)
where πΌ and are incident and reflected waves, respectively, and L is the wavelength and is the number of 2Ο/L, where L is wavelength. ππΌ
πΌ
ππΌ ππΌ
(
ππΌ
(
πΌ πΌ) πΌ)
π
(4)
π
(5)
π (
)
π (
πΌ
(6)
)
(7) (8)
πΌ
(9) The observed profiles of composite waves will be: (
πΌ
)
(10)
(
πΌ
)
(11)
In the equation above, all of the constant can be calculated and by the Fourier analysis. ππΌ
|
|
β(
)
(
can be calculated
)
(12)
Applied Mechanics and Materials Vol. 302
π
|
|
)
β(
Therefore, the reflectance (
329
(
)
(13)
) can be calculated by using eq. (3)
Results and Discussion
Wave height(mm)
Figure 3 shows a typical example of the sinusoidal wave generated by the wave maker in the transverse direction of the wave flow. As shown in the figure it is clear that the probe close to the absorber hasrelatively higher amplitude than that of the probe at position a.It is due to high turbulence created,the length and strength of dampingwave is highest at the absorber end. The absorber is placed just before the end wall of wave flume, this region act as the damping zone where incident wave and reflected wave superimposed each other due to different directions. The intensity of damping effect decreases with increase in the distance of the tank and hence it is lower at position a.In the figure,it is clear that the overall trends seem to be similar with the results from Kwon[4]. a
10
b
5 0 -5 -10 0
2
4
6 Time(s)
8
10
12
Fig. 3Wave generation at the two probes position
Wave height(mm)
The typical behavior of the generated wave without absorber and with absorber is shown in Fig.4. In the figure,the maximum height of the propagating waveswithout absorber reaches about 21mm in irregular pattern, butwith absorber in the wave flume it substantially reduces to 11mm in regular pattern. It is easily conjectured that these absorbed heights give us the idea how we change the potential energy and kinetic energy of the coming and going wave. with absorber
25.00
without absorber
15.00 5.00 -5.00 -15.00 -25.00 0
5
10
15
T(s)
20
25
30
35
40
Fig. 4 Wave condition which with wave absorber and without wave absorber The Figure 5 shows the variation of the calculated reflectance against different position of wave absorber. The wave absorber placed away from the reflecting wall having lower value of reflectance due to high absorption efficiency for maximum wave propagation in the flume.With the changing the period of the wave, the reflectance is increasing when the period becomes larger. The thickness of the wave absorber has a substantial effect in absorbing the reflected wave. In this study, when the thickness of the wave absorber is 1.35m, the wave absorber has the lowest reflectance and remains stable. The lowest reflectance is 0.035 when the non-dimensional frequency is 0.9.
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Reflectance [Kr]
0.4
x=0.95m x=1.15m x=1.35m
0.3 0.2 0.1 0 0.7
0.9 1.1 1.3 1.5 Non-dimensional frequency [Ο2h/g]
1.7
(a)
(b)
Fig. 5Reflectance efficiency at different position of absorber Figure 6 shows the effect of the number of wave absorber, i.e., single, double and triple absorber.In the figure, there was a minor scatterin the reflectance profileof the wave flow. The porosity of wave generator gives us the idea about the wave energy suppression efficiency. The results are all good agreement even in different combination of absorber.This result gives the behavior of wave reflection coefficient for different porosities of slotted wall with change in frequency. As significant wave period increased frequency decreases with increase in reflectance. The reflection coefficient generally decreased as the porosity increases.However, due to the weak mesh of the wave absorber, more careful experiment will be made in the future work. Reflectance [Kr]
0.3
one plate two plates three plates
0.2 0.1 0 0.7
0.9 1.1 1.3 1.5 Non-dimensional frequency [Ο2h/g]
(a)
1.7
(b)
Fig. 6The reflectance distribution using different absorber conditions Figure 7 shows the effect of the angle of wave absorber -37 , 45 and 6 . The best absorption is observed in the angle of 37 and the other two cases have a relatively high value of reflectance.Therefore, as shown in Fig.5, the distance between the mesh and the end wall was shown as one of the parameters and the angle of the wave absorber can be another to choose the best absorber.Note that the volume enclosing the water inside the mesh is quite a bit different each other (e.g., 0.14916m3 in this case 37 and 0.16566m3 in this case 60 ). In addition, when the angle becomes 45 and 60 (i.e., larger volumes than 35 ),it indicates that the datadoesnot show a clear trend (i.e., a decrease of reflectance), but we judge thatit might be a substantial effect on the second level gauge rather than having the volume effect of the wave absorber
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Reflectance [Kr]
0.3
331
60Β° 45Β° 37Β°
0.2 0.1 0 0.7
0.9
1.1
1.3
1.5
1.7
Non-dimensional frequency [Ο2h/g]
(a)
(b)
Fig.7Variation of reflectance with change of angle of absorber Conclusion The wave generation study was madeby using a combination of a wave flume and an absorber in laboratory scale. The generated wave was measured by two different wave gauges.The measured data was evaluatedin the base of the wave theory and reflectance parameter at two points separated by a distance. From the study it is clear that there is a change in the wave amplitude at the receiving end then the generated end; wave absorber is a strong source to control the energy of the coming wave. With the changing the period of the wave, the reflectance is increasing when the period becomes larger.The thickness of the wave absorber has a substantialeffect in absorbing the reflected wave. In this study,when the thickness of the wave absorber is 1.35m, the wave absorber has the lowest reflectance andremains stable. By changing the angle of wave absorber the reflectance cofficient varies due to volume handled by it. In this preliminary experiment, the wave generation was sucessful but the further experiment should be made for the appropriate absorber. For the further study, therefore, it is more helpful to perform a various porous material, different location and wave generation methods, etc., which is necessary to minimize the uncertainties or errors. Acknowledgements This work was supported by Human Resources Development of the Korea Institute of Energy Technology Evaluation and Planning(KETEP) grant funded by the Korea government Ministry of Knowledge Economy. (No. 20114010203080) In addition, this work was also supported by the Ministry of Education, Science and Technology (MEST) in 2011. References [1] Healy, J.J., (1952), Wave damping effect of beaches, Proceedings of Minnesota International Hydraulics Convention, pp. 213-220. [2] Goda, Y., Suzuki, Y., (1976), Estimation of incident and reflectedwaves in random waves, Proceedings of the fifteenth Conference on Coastal Engineering, ASCE, New York, pp.828865. [3] Masard, E.P.D., Funke. E.R., (1980), The measurement of coexisting random wave energy, Poceedings of the fifteenth Conference on Coastal Engineering, ASCE, New York. [4] Kwon S.H., Moon W.M., Lee H.S., (2003), Experimental and numerical studies on the development of a new wave absorber, Ocean Engineering, pp. 185-203.
Advanced Engineering and Materials 10.4028/www.scientific.net/AMM.302
Study of a Wave Absorber in Various Distance Placed in a Sinusoidal Propagate Wave 10.4028/www.scientific.net/AMM.302.326
