A Computational Fluid Dynamics Investigation of a Numerically Simulated Wave Tank

Mohammad Nasim Uddin¹, Michael Atkinson^1, and Frimpong Opoku¹

¹Department of Mechanical Engineering, North Carolina A&T State University, Greensboro, NC, USA

Cite this paper:
Mohammad Nasim Uddin, Michael Atkinson and Frimpong Opoku. A Computational Fluid Dynamics Investigation of a Numerically Simulated Wave Tank. American Journal of Mechanical Engineering. 2020; 8(1):40-49. doi: 10.12691/ajme-8-1-5

Abstract

In this paper, a two-dimensional Numerical Wave Tank (NWT) is proposed to calculate the static pressure variation along the lower wall of an experimental wave-flume. The experimental setup was a 4.72m long wave flume with a flap-type wave-maker. The experiments were carried out at various water heights of 100mm, 80mm, and 60mm, with a motor speed of 60 rpm. The numerical simulations were completed using ANSYS™ Fluent, with two sets solutions: 1) the unsteady, three-dimensional Reynolds Averaged Navier-Stokes (URANS) equations coupled with a k-ε turbulence model; 2) unsteady 3-D Euler equations. In both computations, the volume of fluid (VOF) method was used to capture the free surface and a grid independence study was completed. The unsteady Euler simulations showed the best agreement to the experimental results. Several cases were run to complete validation and verification of the numerical model, and the CFD results are in good agreement with the experiment. Thus, for small two-dimensional experimental wave flumes, the unsteady inviscid, volume of fluid method can accurately predict surface pressure distribution.

Keywords:
numerical wave tank flap-type wavemaker volume of fluid Reynolds averaged Navier Stokes

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]	R. G. Dean and R. A. Dalrymple, Water wave mechanics for engineers and scientists. 1984.
[2]	M. Horko, “CFD Optimisation of an Oscillating Water Column Wave Energy Converter,” M.Sc Thesis. Univ. West. Aust., pp. 1-159, 2007.
[3]	S. T. Grilli and J. Horrillo, “Numerical generation and absorption of fully nonlinear periodic waves,” J. Eng. Mech., vol. 123, no. 10, pp. 1060-1069, 1997.
[4]	D. B. Kothe, M. W. Williams, K. L. Lam, D. R. Korzekwa, P. K. Tubesing, and E. G. Puckett, “A second-order accurate, linearity-preserving volume tracking algorithm for free surface flows on 3-D unstructured meshes,” Proc. 1999 3rd ASME/JSME Jt. Fluids Eng. Conf. FEDSM’99, San Fr. California, USA, 18-23 July 1999, p. 1, 1999.
[5]	J. C. Park, M. H. Kim, H. Miyata, and H. H. Chun, “Fully nonlinear numerical wave tank (NWT) simulations and wave run-up prediction around 3-D structures,” Ocean Eng., vol. 30, no. 15, pp. 1969-1996, 2003.
[6]	V. R. Gopala and B. G. M. van Wachem, “Volume of fluid methods for immiscible-fluid and free-surface flows,” Chem. Eng. J., vol. 141, no. 1-3, pp. 204-221, 2008.
[7]	J. Maljaars, R. J. Labeur, M. Möller, and W. Uijttewaal, “A Numerical Wave Tank Using a Hybrid Particle-mesh Approach,” Procedia Eng., vol. 175, pp. 21-28, 2017.
[8]	Z. Sun, Y. Pang, and H. Li, “Two dimensional fully nonlinear numerical wave tank based on the BEM,” J. Mar. Sci. Appl., vol. 11, no. 4, pp. 437-446, 2012.
[9]	B. Engquist and A. Majdat, “Absorbing Boundary,” Encycl. Comput. Neurosci., vol. 74, no. 5, pp. 125-125, 2015.
[10]	Y. Gao, H. Song, J. Zhang, and Z. Yao, “Comparison of artificial absorbing boundaries for acoustic wave equation modelling,” Explor. Geophys., vol. 48, no. 1, pp. 76-93, 2017.
[11]	S. F. Baudic, A. N. Williams, and A. Kareem, “A two dimensional numerical wave flume - Part 1: Nonlinear wave generation, propagation, and absorption,” J. Offshore Mech. Arct. Eng., vol. 123, no. 2, pp. 70-75, 2001.
[12]	R. L. Higdon, “Radiation boundary conditions for elastic wave propagation,” SIAM J. Numer. Anal., vol. 27, no. 4, pp. 831-869, 1990.
[13]	Y. L. Chen and S. C. Hsiao, “Generation of 3D water waves using mass source wavemaker applied to Navier-Stokes model,” Coast. Eng., vol. 109, pp. 76-95, 2016.
[14]	M. Israeli and S. A. Orszag, “Approximation of radiation boundary conditions,” J. Comput. Phys., vol. 41, no. 1, pp. 115-135, 1981.
[15]	S. Boo, “A Numerical Wave Tank For Nonlinear Irregular Waves By 3-D Higher Order Boundary Element Method,” no. August, 2016.
[16]	T. Ohyama and K. Nadaoka, “Development of a numerical wave tank for analysis of nonlinear and irregular wave field,” Fluid Dyn. Res., vol. 8, no. 5-6, pp. 231-251, 1991.
[17]	S. Y. Boo and K. N. Academy, “f f,” vol. 111, 1996.
[18]	S. T. Grilli, S. Vogelmann, and P. Watts, “Development of a 3D numerical wave tank for modeling tsunami generation by underwater landslides,” Eng. Anal. Bound. Elem., vol. 26, no. 4, pp. 301-313, 2002.
[19]	Z. Ma, T. Zhou, J. Sun, and G. Zhai, “Simulation on tsunami-like solitary wave run-up around a conical island using a modified mass source method,” Eng. Appl. Comput. Fluid Mech., vol. 13, no. 1, pp. 849-859, 2019.
[20]	J. S. Zhang, Y. Zhang, D. S. Jeng, P. L. F. Liu, and C. Zhang, “Numerical simulation of wave-current interaction using a RANS solver,” Ocean Eng., vol. 75, pp. 157-164, 2014.
[21]	J. L. Lara, N. Garcia, and I. J. Losada, “RANS modelling applied to random wave interaction with submerged permeable structures,” Coast. Eng., vol. 53, no. 5-6, pp. 395-417, 2006.
[22]	H. L. Wu, S. C. Hsiao, W. Y. Hsu, R. Y. Yang, and H. H. Hwung, “Dynamic response of density-stratified fluid in a submarine rectangular trench,” J. Hydro-Environment Res., vol. 9, no. 1, pp. 61-80, 2015.
[23]	K. Iwata, K. Kawasaki, and D. S. Kim, “Breaking limit, breaking and post-breaking wave deformation due to submerged structures,” Proc. Coast. Eng. Conf., vol. 2, pp. 2338-2351, 1997.
[24]	X. Feng and W. Wu, “Generation of Water Waves Using Momentum Source Wave-Maker Applied to a RANS Solver,” Math. Probl. Eng., vol. 2019.
[25]	J. C. Park, M. H. Kim, and H. Miyata, “Fully non-linear free-surface simulations by a 3D viscous numerical wave tank,” Int. J. Numer. Methods Fluids, vol. 29, no. 6, pp. 685-703, 1999.
[26]	J. Bai, N. Ma, and X. Gu, “Numerical Simulation of Focused Wave and Its Uncertainty Analysis,” J. Shanghai Jiaotong Univ., vol. 23, no. 4, pp. 475-481, 2018.
[27]	X. Hu, Y. Jiang, and D. Cai, “Numerical Modeling and Simulation of Wave Impact of a Circular Cylinder during the Submergence Process,” Model. Simul. Eng., vol. 2017, 2017.
[28]	C. Jiang, X. Liu, Y. Yao, and B. Deng, “Numerical investigation of solitary wave interaction with a row of vertical slotted piles on a sloping beach,” Int. J. Nav. Archit. Ocean Eng., vol. 11, no. 1, pp. 530-541, 2019.
[29]	A. Elhanafi, A. Fleming, Z. Leong, and G. Macfarlane, “Effect of RANS-based turbulence models on nonlinear wave generation in a two-phase numerical wave tank,” Prog. Comput. Fluid Dyn., vol. 17, no. 3, pp. 141-158, 2017.
[30]	Z. Liu, B. S. Hyun, and K. Y. Hong, “Application of numerical wave tank to OWC air chamber for wave energy conversion,” Proc. Int. Offshore Polar Eng. Conf., vol. 8, pp. 350-356, 2008.
[31]	M. Zabihi, S. Mazaheri, and A. R. Mazyak, “Wave Generation in a Numerical Wave Tank,” 17th Mar. Ind. Conf. 22-25 December2015 - Kish Isl., vol. 2017, no. 2, p. 11, 2015.
[32]	A. Clément, “Coupling of two absorbing boundary conditions for 2D time-domain simulations of free surface gravity waves,” J. Comput. Phys., vol. 126, no. 1, pp. 139-151, 1996.
[33]	C. M. Dong and C. J. Huang, “On a 2-D numerical wave tank in viscous fluid,” Proc. Int. Offshore Polar Eng. Conf., vol. 3, pp. 148-155, 2001.
[34]	J. T. Batina, “Using Unstructured Dynamic Meshes,” AIAA J., vol. 28, no. 8, pp. 1381-1388, 1990.
[35]	J. F. Antaki, G. E. Blelloch, O. Ghattas, I. Malcevic, G. L. Miller, and N. J. Walkington, “a Parallel Dynamic-Mesh Lagrangian Method for Simulation of Flows With Dynamic Interfaces,” vol. 00, no. c, pp. 26-26, 2015.
[36]	M. Hasan, A. Kabir, and Y. M. Akib, “Dynamic stall investigation of two-dimensional vertical axis wind turbine blades using computational fluid dynamics,” 8Th Bsme Int. Conf. Therm. Eng., vol. 2121, p. 120003, 2019.
[37]	H. K. Esfeh, A. Azarafza, and M. K. A. Hamid, “On the computational fluid dynamics of PEM fuel cells (PEMFCs): An investigation on mesh independence analysis,” RSC Adv., vol. 7, no. 52, pp. 32893-32902.
[38]	S. B. Sarkar, Santanu, “I Nternational J Ournal of,” Int. J. Energy Environ., vol. 4, no. 3, pp. 449-458, 2013.
[39]	M. Anbarsooz, M. Passandideh-Fard, and M. Moghiman, “Fully nonlinear viscous wave generation in numerical wave tanks,” Ocean Eng., vol. 59, pp. 73-85.
[40]	C. Windt, J. Davidson, and J. V. Ringwood, “High-fidelity numerical modelling of ocean wave energy systems: A review of computational fluid dynamics-based numerical wave tanks,” Renew. Sustain. Energy Rev., vol. 93, no. May, pp. 610-630, 2018.
[41]	W. P. Jones and B. E. Launder, “The prediction of laminarization with a two-equation model of turbulence,” Int. J. Heat Mass Transf., 1972.
[42]	C. W. Hirt and B. D. Nichols, “Volume of fluid (VOF) method for the dynamics of free boundaries,” J. Comput. Phys., vol. 39, no. 1, pp. 201-225, 1981.