Numerical Investigation of Wave Interaction With Pile Breakwater

Transcription

1 Numerical Investigation of Wave Interaction With Pile Breakwater Pradeep Suryanarayana Barimar Rao Transportation Engineering Consultant 2500 Merchants Row Blvd, Apt 164, Tallahassee FL Sheryl Elizabeth Mathew, Praveen Suvarna, Arunakumar Hunasanahally Sathyanarayana, and Pruthviraj Umesh Department of Applied Mechanics and Hydraulics NITK Surathkal, Mangaluru, Karnataka, India sherylemathew@gmail.com, civilsuvarna@gmail.com, arunsaligram17@yahoo.com, pruthviu@gmail.com Abstract Pile breakwater consists of a number of piles spaced closely. It works similar to the offshore breakwater by attenuating the energy of the waves and it is due the turbulence caused because of wave-pile interaction. The efficiency of the pile breakwater of single row and two rows is investigated numerically. An open source Computational Fluid Dynamics (CFD) software REEF3D is used in the present study. Initially the grid convergence study is conducted in a rectangular wave flume with a two-dimensional setup and the results are evaluated by comparing the numerical wave profile with the theoretical profile in accordance with the adopted wave theory. The efficiency of the numerically modelled pile breakwater is investigated in terms of the transmission coefficient. The simulations carried out are in accordance with the physical model studies as reported by Subba Rao et al., (1999). The numerically obtained results are validated with the experimental data. The numerically obtained results for the pile breakwater has shown an average of 91.5% agreement with that of experimental results. Keywords Pile breakwater, Numerical model, CFD, Transmission coefficient 1. Introduction In coastal areas, to maintain the tranquility of the harbor, artificial protection structures are required. When perfect tranquility conditions are necessary, large structures like rubble mound breakwaters and vertical wall breakwaters are used. For small recreational harbors or fisheries harbors and at locations where large littoral drift and onshore, offshore sediment movement exist, unconventional types of breakwaters like floating breakwater or piled breakwaters can be constructed (Mani and Jayakumar, 1995; Subba Rao et al., 2002; Suh et al., 2006). Pile breakwaters are constructed and working successfully in many harbors for the protection works like, Auckland harbor in New Zealand, (Hutchinson and Raudkivi, 1984), concrete pile breakwater (1.4 m Diameter) at Pass Christian, Mississippi, USA and pile row breakwaters at Langkawi, Malaysia. A single or two rows of closely spaced circular piles of suitable diameter can act like a breakwater in such locations, in such cases pile breakwaters are more suitable. Depending upon the tranquility requirements and prevailing littoral movement conditions, the pile breakwater can be designed suitably. The sea water is kept relatively clean as pile breakwaters permits the circulation of water in and out of the harbor (Hagiwara, 1984). The interference of the pile breakwater with the littoral drift is also less when compared to conventional breakwaters. 1618

2 Numerous experimental studies have been performed on the pile breakwater to observe the wave attenuation characteristics. Some of the previous studies include, single row and two rows of non-perforated and perforated piles by varying the pile spacing (Hutchinson and Raudkivi, 1984, Truit and Herbich, 1987, Subba Rao et al., 1999, Subba Rao et al., 2001, Bovin, R. 1964, Kakuno, S. and Liu, P.L.F., 1993, Koraim A.S et al., 2014 and Hongwei Liu et al., 2011), pile arrays of four rows (Van Weele et al, 1972), closely spaced piles breakwater (Hayashi et al., 1960). The aim of the current study is to generate a pile breakwater model using an open source software REEF3D, which can be used for the investigation of the hydrodynamic performance of pile breakwater. Single row and two rows of pile breakwater is simulated using REEF3D and to validate the developed model, the obtained results are validated with the experimental results achieved by Subba Rao et al., (1999). In this paper, section I discussed the inevitability and the prominence of pile breakwater. Section II designates the key features of the REEF3D software. Section III deliberates about the experimental and numerical setup of wave tank, pile breakwater arrangement and different wave parameters and water depths under which the pile breakwater has been tested. Section IV deals with the comparison of numerically obtained results with the experimental data and finally the Section V concludes the overall performance of the numerical pile breakwater model. 2. Numerical Model Numerical studies are gaining importance in coastal engineering due to the flexibility, scalability, repeatability and reduction in cost. Various numerical studies include, ocean wave energy conversion (Kamath et al., 2013, Hossain et al., 2016), wave interaction with structures (Kamath et al., 2015, Bihs et al., 2016). REEF3D is an open-source computational fluid dynamics (CFD) program with a deep focus on hydraulics, environmental engineering, offshore and coastal as well as Marine CFD. The usage of the level-set method enables it to analyze complex free surface flows (Bihs et al., 2016, Bihs and Kamath, 2017 and Alagan Chella et al. 2017). In the present numerical model, the incompressible Navier-Stokes equations are solved with RANS turbulence closure. Cartesian mesh is used to accomplish wave propagation with higher permanence and accurateness. Staggered grid with projection method is adopted to resolve the pressure, which guarantees tight pressure velocity coupling. Ghost cell immersed boundary method is utilized to contemplate the irregular boundaries. The numerical model is fully parallelized based on the domain decomposition strategy and MPI (message passing interface). The free surface is modeled with the level set method. (Kamath. A. et al., 2012). 2.1 Governing Equations Incompressible Reynolds-averaged Navier Stokes (RANS) equations are resolved in REEF3D along with the continuity equation to resolve the fluid flow problem. UU ii + UU UU ii jj = 1 XX jj ρ XX ii + UU ii xx ii = 0 (1) XX jj (vv + vv tt ) UU ii XX jj + UU jj XX ii + gg ii (2) Where u is the time averaged velocity, ρ is the density of the fluid, p is the pressure, ν is the kinematic viscosity, ν t is the eddy viscosity and g is the acceleration due to gravity. Projection method is used to determine the pressure and by using BiCGStab solver, the consequential Poisson equation is solved. K ω model is adopted for turbulence modeling. 2.2 Free Surface The free surface of the waves is modelled using level set method. The signed distance function (φ), is the shortest distance from the interface is determined by level set function. The sign of the function differentiates the two fluids at the interface and it is shown in the equation below. > 0 iiii xx iiii iiii pphaaaaaa 1 Φ (xx, t) = 0 iiii xx iiii iiii iiiiiiiiiiiihaaaaaa < 0 iiii xx iiii iiii pphaaaaaa 2 (3) 1619

3 Under the effect of external velocity field u j, the level set function is moved with the convection equation as described below. + UU jj = 0 (4) XX jj The convection term in Equation (4) is resolved with the Hamilton- Jacobi form of the WENO scheme (Jiang GS. et al., 2000) and for the time stepping, third-order TVD Runge Kutta scheme is adopted (Shu CW. et al., 1988). When the interface evolves, the level set function loses its signed distance property. In order to maintain this property and to safeguard mass conservation, the level set function is reinitialized after every time step. In the present paper, a PDE based reinitialization equation is resolved (Sussman M. et al., 1994). 3. Simulation and Validation of Pile Breakwater The piles are modelled as rigid solid cylindrical structures and the placement of the piles are done in accordance with the experimental setup as shown in Figure 1. Validation is accomplished by comparing the numerical results with the experimental results done by Subba Rao et al., (1999) for single and two rows of piles. Simulations are carried out on single row and two rows of piles by varying the spacing between each pile in a row (b) and also the spacing between the pile rows (B) as shown in Figure Experimental Model Setup Figure 1. Layout of piles with pile diameter D Subba Rao et al., (1999) has carried out physical experiments in a wave flume of length of 50 m, depth of 1.1 m and width 0.71 m. The flume has a flap type wave generator at one end and an absorption beach at the other end. The physical model pipes were galvanized iron pipes of diameter (D) m. Experiments were performed on a single row of piles and two rows of piles for different pile spacing within and between the pile rows. 3.2 Numerical Model of Pile Breakwater The pile breakwater is simulated in a three dimensional numerical wave tank of length 16 m, width m and height of 0.7 m. Owing to the symmetry of the wave flume, in order to reduce computational time and memory space, the width of the wave tank is reduced to half and the symmetry boundary condition is applied Single Row of Piles The piles are placed in a single row perpendicular to the incident wave is as illustrated in Figure 2. The investigation is conducted for different test conditions by varying the wave height and spacing between the piles as described in Table

4 Figure 2. Numerical model of single row of pile breakwater Table 1. Experiential conditions for single row of pile breakwater Parameters Water depth (d) = 0.40 m Water depth (d) = 0.50 m Diameter of piles (D) m m Spacing between each pile in a row (b) 0.75D, 1D 0.75D, 1D Incident wave height (H i) m to 0.17 m m to m Wave period (T) 1.5 Sec, 2 Sec 1.5 Sec, 2 Sec Two Rows of Piles The piles are placed in a two rows perpendicular to the incident wave is as illustrated in Figure 3. It is clearly seen from Figure 3 that the velocity of the transmitted wave is reduced due to the wave-structure interaction. The investigation is conducted for different cases by changing the wave height and spacing between the piles as described in Table 2. Figure 3. Numerical model of two rows of pile breakwater Table 2. Experiential conditions for two rows of pile breakwater Parameters Depth of water (d) = 0.40 m Depth of water (d) = 0.50 m Diameter of pile (D) m m Spacing between each pile in a row (b) 0.75D, 1D 0.75D, 1D Spacing between each row of piles (B) 1D, 2D 1D, 2D Incident wave height (Hi) m to m m to m Wave period (T) 1.5 Sec, 2 Sec 1.5 Sec, 2 Sec 1621

5 4. Results and Analysis The mean absolute percentage error (MAPE) is a degree of the prediction accurateness of a forecasting method in statistics. It is a measure of the size of the error in percentage. The MAPE is most widely used method of prediction accuracy due to its benefits of scale-independency and interpretability. MAPE = 100 nn nn Actual Forecast Actual tt=1 The mean absolute percentage error (MAPE) of the numerical results compared with the experimental results is determined for each test case. 4.1 Grid Convergence Study The performance of the numerical wave tank is carried out in a two-dimensional rectangular wave tank of length 12 m. Regular waves of wave height 0.08 m are generated based on linear wave theory in a water depth of 0.4 m. The elevation of the water depth is measured using the numerical wave probe in the working zone. Mesh size of 0.05m, m, m and m are used for studying grid convergence and the results attained for different mesh sizes are compared as illustrated in Figure 4. It is evident from Figure 4 that for the mesh size of 0.05 m, the crests and troughs of the waves are damped out and the results are improved for mesh size of m. The variation is negligible in the wave profile for m and m as both converge to a single solution and give the same results. Figure 4. Results of grid convergence study for mesh sizes of 0.05m, 0.025m, m and m From the grid convergence study it can be concluded that m is the optimum grid size and hence the same grid size is used to for the investigation of wave interaction with pile breakwater. 4.2 Influence of Wave Steepness and spacing on Wave Transmission The transmission coefficient (K t) represents the wave attenuation by the structure in terms of the incident wave. The corresponding wave transmission coefficient (K t) is plotted against the incident wave steepness (H i/gt 2 ) for the different test cases of spacing between the piles Single Row of Pile Breakwater The variation of transmission co-efficient (K t) with wave steepness (H i/gt 2 ) for a water depth of 0.4m is illustrated in the below figures. Figure 5 (i) shows the variation of K t for a pile spacing (b) of 0.5D and the MAPE is computed as 9.54%. Figure 5 (ii) illustrates the variation of K t for 1D pile spacing (b) and the MAPE is 6.49% for the present case. 1622

6 i) ii) Figure 5. Influence of wave steepness (H i/gt 2 ) on wave transmission co-efficient (K t) for a Water depth of 0.4m and i) b=1d spacing ii) b=0.5d spacing. Figure 6 (i) and Figure 6 (ii) illustrates the influence of wave steepness on wave transmission for a water depth of 0.5m. Figure 6 (i) represents the pile spacing of b=1d and the MAPE is 13.41% compared with the experimental data. Figure 6 (ii) represents the pile spacing of b=0.5d and the MAPE is 7.34% compared with the experimental data. i) ii) Figure 6. Influence of wave steepness (H i/gt 2 ) on wave transmission co-efficient (K t) for a Water depth of 0.5m and i) b=1d spacing ii) b=0.5d spacing. From the results of the single pile breakwater, it is observed that as the wave steepness increases, transmission coefficient decreases. When the pile spacing (b) is decreased from 1D to 0.5D, an average of 6% reduction in K t is observed at 0.4m water depth and 4% reduction in case of 0.5 m water depth Two Rows of Pile Breakwater The influence of wave steepness (H i/gt 2 ) on wave transmission co-efficient (K t) for two rows of pile breakwater is illustrated in Figure 7 (i) and Figure 7 (ii) at 0.4m water depth and constant spacing of piles b= 1D. Figure 7 (i) represents the variation of K t for B=1D row of piles spacing and the MAPE is found to be 7.08% compared with experimental results. Figure 7 (ii) represents the row spacing of B=2D and the MAPE is calculated as 7.12%. 1623

7 i) ii) Figure 7. Influence of wave steepness (H i/gt 2 ) on wave transmission co-efficient (K t) at a water depth of 0.4m for b=1d spacing and i) B=1D ii) B=2D The influence of wave steepness on transmission co-efficient is illustrated in Figure 8 (i) and Figure 8 (ii) at a water depth of 0.5m. Figure 8 (i) shows the variation of K t for B=1D spacing and the MAPE is 6.53% with the experimental results. Figure 8 (ii) shows the variation of K t for B=2D spacing and the MAPE is 4.07%. i) ii) Figure 8. Influence of wave steepness (H i/gt 2 ) on wave transmission co-efficient (K t) at a water depth of 0.5m for b=1d spacing and i) B=1D ii) B=2D Figure 9 (i) and Figure 9 (ii) illustrates the effect of wave steepness on transmission of waves for 0.4 m water depth. In the present case a constant spacing of b=0.75d is maintained between the pile rows. The MAPE calculated for B=1D spacing is 8% as illustrated in Figure 9 (i). The MAPE is found to be 6.73% for b=2d spacing as illustrated in Figure 9 (ii). 1624

8 i) ii) Figure 9. Influence of wave steepness (H i/gt 2 ) on wave transmission co-efficient (K t) at a water depth of 0.4m for b=0.75d spacing and i) B=1D ii) B=2D The variation of transmission co-efficient with wave steepness is illustrated in Figure 10 (i) and Figure 10 (ii) for a water depth of 0.5m. The MAPE for pile spacing of B=1D is 5.18% with the experimental results as shown in Figure 10 (i). Whereas for B=2D spacing, the MAPE is 7.81% as illustrated in Figure 10 (ii). i) ii) Figure 10. Influence of wave steepness (H i/gt 2 ) on wave transmission co-efficient (K t) at a water depth of 0.5m for b=0.75d spacing and i) B=1D ii) B=2D The results obtained for two rows of piles from the REEF3D and experimental are in good agreement for waves with high steepness. For B=1D spacing and for 0.4 m water depth, an average of 12% reduction in K t is observed when the b is decreased from 1D to 0.75D and the similar trend is observed for 0.5 m water depth. Increase of spacing B from 1D to 2D results in decrease of K t to an average of 4% for 0.4 m water depth and 28% for 0.5m water depth. It is observed from the current study that, as the wave steepness increases, K t decreases. From the Figure 5 to Figure 10, it is observed that introducing of two rows of piles at same spacing b=1d resulted in decrease of wave transmission of about 3% to 4%. When the pile spacing b is decreased from 1D to 0.5D, resulted wave transmission is equivalent to that of two rows of piles. The streamline flow pattern for a single row of piles with the spacing b=0.5d is shown in Figure 11. The velocity of the incident waves is intercepted by the row of piles resulting in the increase of turbulence which in turn gives rise to reduction of wave height by loss of wave energy. 1625

9 Figure 11. The streamline flow pattern for a single row of piles with b=1d spacing Figure 12 shows the streamline flow pattern for two rows of piles with the pile spacing of b=1d and B=1D. The interception of piles is not causing much turbulence with the incident waves due to the higher spacing between the piles in the rows. Figure 12. The streamline flow pattern for two rows of piles with b=1d and B=1D spacing. B It is clearly seen from Figure 11 and Figure 12 that the captivation of orbital velocity and development of turbulence is more in case of a single row of piles as compared with the two rows of piles. Thus convincing that decrease in pile spacing in a row from 1D to 0.5D is more effective than proving two rows of piles at 1D spacing. 5. Conclusions In the present study the validation of the numerical model has been done by comparing the transmission coefficient obtained from REEF3D with the experimental results reported by Subba Rao et al., (1999). The numerical results are in good agreement with the experimental results. It has been observed that for both single and two rows of piles, as the spacing between the piles increases, the transmission co-efficient increases. The average MAPE for single row pile breakwater is 9.19% compared with the experimental results, whereas for two rows of piles the average MAPE is 8.15%. The reduction of spacing between the piles (b) in a single row proved to be more effective in attenuating the waves than introducing two rows of piles. The numerical model developed using REEF3D can be further extended to study the hydrodynamic performance of the pile breakwater by varying the number of pile rows and diameter of the piles. In the future studies, the staggered arrangement of piles can be considered for multiple number of rows by varying the spacing between the piles. The effectiveness of the perforations can be examined by incorporating perforations to the piles of different proportions. 1626

10 Acknowledgements The authors would like to extend their gratitude to the authorities of Dept. of Applied Mechanics and Hydraulics, NITK Surathkal and Centre for System Design (CSD), NITK Surathkal for providing with the necessary resources for the study. References Alagan Chella, M., Bihs, H., Myrhaug, D., and Muskulus, M., Breaking solitary waves and breaking wave forces on a vertically mounted slender cylinder over an impermeable sloping seabed, Journal of Ocean Engineering and Marine Energy, vol. 3, no. 1, pp. 1-19, Bihs, H., and Kamath, A., A combined level set/ghost cell immersed boundary representation for floating body simulations, International Journal for Numerical Methods in Fluids, vol. 83, no. 12, pp , Bihs, H., Kamath, A., Chella, M. A., Aggarwal, A., and Arntsen, Ø. A., A new level set numerical wave tank with improved density interpolation for complex wave hydrodynamics, Computers & Fluids, vol. 140, pp , Bovin, R., Comments on vertical breakwaters with low coefficients of reflection, Dock and Harbour Authority, vol. 45, pp , Hagiwara, K., Analysis of upright structure for wave dissipation using integral equation, Proceedings of the 19 lh Coastal Engineering Conference, Houstan, Texas, New York, pp , Hayashi, T., Hattori, M., and Shirai, M., Closely spaced pile breakwater as a protection structure against beach erosion, Coastal Engineering in Japan, vol. 11, pp , Hongwei Liu, Mohamed S. Ghidaoui a, Zhenhua Huangb, Zhida Yuanb and Jun Wangb, Numerical investigation of the interactions between solitary waves and pile breakwaters using BGK-based methods, Computers and Mathematics with Applications, vol. 61, pp , Hossain, Jakir, Sarder Shazali Sikander, and Eklas Hossain, A wave-to-wire model of ocean wave energy conversion system using MATLAB/Simulink platform, 4 th International Conference on the Development in the in Renewable Energy Technology (ICDRET), Hutchinson, P.S. and Raudkivi, A.J., Case history of a spaced pile breakwater at Halfmoon Bay Marina, Auckland, New-Zealand, Proc. 19th Coastal Engineering Conference, Houstan, pp , Kakuno, S. and Liu, P.L.F., Scattering of water waves by vertical cylinders, Coastal and Ocean Engineering, vol. 119, no. 3, pp , Kamath A., Alagan Chella M., Bihs H. and Arntsen Ø.A., CFD Investigations of Wave Interaction with a Pair of Large Tandem Cylinders. Ocean Engineering, vol. 108, pp , Kamath A., Bihs H., Arntsen Ø.A., Investigating OWC Wave Energy Converters Using Two-Dimensional CFD Simulations, International Workshop on Ocean Wave Energy, Chennai, India, Kamath A., Hans Bihs., Mayilvahanan Alagan Chella and Øivind A. Arnsten., CFD Simulations to Determine Wave Forces on a Row of Cylinders, 8th International Conference on Asian and Pacific Coast (APAC 2015), Procedia Engineering, pp , Koraim, A.S., Hydraulic characteristics of pile supported L-shaped bars used as a screen breakwater, Ocean Engineering, vol. 83, pp , Mani, J.S., and Jayakumar, S., Wave transmission by suspended pipe breakwater, J. Waterway, Port, Coastal and Ocean Engineering Division, ASCE, vol. 121, no. 6, pp , Shu CW, Osher S., Efficient implementation of essentially non-oscillatory shock capturing schemes, Journal of Computational Physics, vol. 77, no. 2, pp , Subba Rao and N. B. S. Rao, Laboratory investigation on wave transmission through suspended perforated pipes, ISH Journal of Hydraulic Engineering, Taylor & Francis Publication, The Indian Society for Hydraulics, CWPRS, Pune., vol. 7, no. 1, pp , Subba Rao and N.B.S. Rao, Laboratory investigation on wave reflection characteristics of suspended perforated pipe breakwater, ISH Journal of Hydraulic Engineering, Taylor & Francis Publication, The Indian Society for Hydraulics, Subba Rao, N.B.S. Rao, and V.S. Sathyanarayana, Wave transmission and reflection for two rows of perforated hollow piles, Indian Journal of Marine Sciences, vol. 31, no. 4, pp ,

11 Suh, K., Ji, C., and Kim, B. H., Closed-form solutions for wave reflection and transmission by vertical slotted barrier, Coastal Engineering, vol. 58, pp. 12, pp , Truitt, C. L., and Herbich, J. B., Transmission of random waves through pile breakwaters, Proceedings of 20 th Coastal Engineering Conference, Taipei, Taiwan, pp , Van Weele, J., and Herbich, J.B., Wave reflection and transmission for pile arrays, Proceedings of the 13 th Coastal Engineering Conference, Vancouver, B.C., Canada, pp , Biographies Pradeep Suryanarayana Barimar Rao currently serves as transportation engineering consultant for an infrastructure solution consulting firm. Mr. Rao holds a Bachelors of Engineering in Civil Engineering from National institute of technology, Karnataka and a Master of Science degree in transportation engineering from Auburn University. He is a civil engineering Professional Engineer (PE) with more than 15 years of experience successfully developing, designing, implementing and managing Intelligent Transportation Systems (ITS) projects as part of multi-agency and consultant teams designing and managing freeway management systems, virtual weigh-in-motion systems, truck parking systems, High Occupancy Toll (HOT) and traveler information systems. He is interests are design, planning, modelling and simulation. He is a member of Institute of Transportation Engineers. Sheryl Elizabeth Mathew has recently completed her Master of Technology degree in Marine structures from National Institute of Technology Surathkal, India. She holds a Bachelor of Technology degree in Civil Engineering from National Institute of Technology, Calicut. Her research interests include computational fluid dynamics, simulation and wave hydrodynamics. Praveen Suvarna is a PhD scholar of National Institute of Technology, Karnataka, India. Completed his Masters from National Institute of Technology, Karnataka. His research interests include computational fluid dynamics and wave hydrodynamics. He is member of ACCE, AMIE and IIV. Arunakumar Hunasanahally Sathyanarayana has completed his Master of Technology degree in Marine structures from National Institute of Technology, Karnataka and Bachelor of Engineering in Civil Engineering from National Institute of Engineering, Mysore, India. His research interests include computational fluid dynamics, Wave structure interaction and wave hydrodynamics. Dr. Pruthviraj Umesh currently serves as Assistant Professor in Department of Applied Mechanics and Hydraulics, National Institute of Technology (NITK), Karnataka, India. He did PhD in flow through perforated plates which had extensive CFD analysis and experimental studies using wind tunnel. His Research interest includes wind engineering, GIS, open source product development, Engineering applications in wildlife conservation. He has experience in design and development of open source unmanned systems for civilian applications. He has presented his research work in technical conferences in Netherlands, Oman, Germany, Japan, USA, and Switzerland. He has been mentor for student technical teams which won prizes in National Level competitions. He has guided many Ph. D. scholars and M. Tech students. He is the coordinator for RT Lab of Strength of Materials and coordinator of Computer for System Designs (CSD), NITK, Surathkal. He actively pursues aerial photography, Unmanned Aerial Vehicles (UAV) and Videography. 1628