Bihs, Hans

Chella, Mayilvahanan Alagan

Muskulus, Michael

English

Hydraulic Engineering Repository

Conference Paper, Published VersionChella, Mayilvahanan Alagan; Bihs, Hans; Muskulus, MichaelNumerical Simulation of Breaking Waves on a Plane Slopewith a Parallel Level Set SolverZur Verfügung gestellt in Kooperation mit/Provided in Cooperation with:Kuratorium für Forschung im Küsteningenieurwesen (KFKI)Verfügbar unter/Available at: https://hdl.handle.net/20.500.11970/99455Vorgeschlagene Zitierweise/Suggested citation:Chella, Mayilvahanan Alagan; Bihs, Hans; Muskulus, Michael (2014): Numerical Simulationof Breaking Waves on a Plane Slope with a Parallel Level Set Solver. In: Lehfeldt, Rainer;Kopmann, Rebekka (Hg.): ICHE 2014. Proceedings of the 11th International Conference onHydroscience & Engineering. Karlsruhe: Bundesanstalt für Wasserbau. S. 391-398.Standardnutzungsbedingungen/Terms of Use:Die Dokumente in HENRY stehen unter der Creative Commons Lizenz CC BY 4.0, sofern keine abweichendenNutzungsbedingungen getroffen wurden. Damit ist sowohl die kommerzielle Nutzung als auch das Teilen, dieWeiterbearbeitung und Speicherung erlaubt. Das Verwenden und das Bearbeiten stehen unter der Bedingung derNamensnennung. Im Einzelfall kann eine restriktivere Lizenz gelten; dann gelten abweichend von den obigenNutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte.Documents in HENRY are made available under the Creative Commons License CC BY 4.0, if no other license isapplicable. Under CC BY 4.0 commercial use and sharing, remixing, transforming, and building upon the materialof the work is permitted. In some cases a different, more restrictive license may apply; if applicable the terms ofthe restrictive license will be binding. 1 INTRODUCTION Breaking is initiated when the wave topography becomes steep then the wave becomes unstable and dis-sipates the energy in the form of turbulence, while a significant amount of air is trapped. Breaker types can be classified into four different types, namely spilling, plunging, surging and collapsing (Galvin, 1968). The breaking process is strongly influenced by the local water depth, wave steepness and sea bed slope. An exact numerical modeling of wave breaking process is intricate due to the strong non-linear air-sea interaction at the free surface, air entrainment and turbulent production, transport and dissipation pro-cess. Since there are many challenges to model the breaking process numerically, most of the studies on breaking waves are limited to field and experimental research. Ting and Kirby (1996) investigated the turbulent structures spilling breakers in the surf zone. Further, they studied the different wave breaking process between different types of breaking waves.  Longuet-Higgins and Cokelet (1976) first proposed a mixed Eulerian-Lagrangian formulation (MEL) based on potential theory to simulate breaking waves in deep water. Later, the method was modified the application to finite water depth by Vinje and Brevig (1981). However, most of the numerical models based on potential theory can describe the breaking process until breaking, but these model cannot model the impingement of the water jet during breaking (Chen et al., 1999). Wave breaking process can be de-scribed numerically with a model based on computational fluid dynamics (CFD) method without specify-ing breaking criteria. In addition to that most of the physical flow properties such as interface defor-mation, velocities and turbulence can be evaluated in detail. Numerous studies have attempted to simulate the breaking waves with a single phase viscous model which does not account the role of the air and the Numerical Simulation of Breaking Waves on a Plane Slope with a Parallel Level Set Solver M. Alagan Chella, H. Bihs & M. Muskulus Department of Civil and Transport Engineering, Norwegian University of Science and Technology, Trondheim, Norway  ABSTRACT: In the present study, spilling breaking waves are simulated using a numerical model with interface capturing technique. The numerical model solves the Reynolds-Averaged Navier-Stokes (RANS) equations on a uniform Cartesian grid and complex geometry is modeled with a ghost cell im-mersed boundary method. The flow problem is solved as a two-phase flow of air and water with the free-surface is represented by the interface between the two phases. Thus, the level set method (LSM) is used to capture the complex free-surface changes. The temporal and spatial turbulent kinetic energy in the breaking waves is described by k-ω model. The conservative 5th order weighted essentially non-oscillatory (WENO) scheme is employed for the convective discretization. A much stronger coupling be-tween velocity and pressure is obtained by using a staggered grid which is essential for a two phase mod-el. The present model is fully parallelized using the message processing interface (MPI) library routines. The main focus of the present study is to investigate the wave breaking wave process over a sloping bed. The paper discusses the changes in the free surface profile, water surface envelope, and horizontal veloci-ty in different regimes during the breaking process. Numerical experiments are carried out with the 5th order cnoidal waves on a plane slope 1/35. The present numerical model is validated and compared with the experimental data. The results from the numerical model are in good agreement with the experimental data concerning water surface envelope and horizontal velocity.  Keywords: Breaking waves, Wave breaking, CFD modelling, Free surface ICHE 2014, Hamburg - Lehfeldt & Kopmann (eds) - © 2014 Bundesanstalt für Wasserbau ISBN 978-3-939230-32-8391density variation at the interface such as Bradford (2000); Lin and Liu (1998); Zhao et al. (2004). Further, it has been demonstrated that the importance of a two phase viscous flow models in the simulation of the breaking waves (Chen et al., 1999; Christensen, 2006; Hieu et al., 2004; Jacobsen et al., 2012). Moreover, these studies investigated turbulent characteristics and the undertow profiles. The present numerical mod-el was utilized to study the wave transformation over a submerged reef with a slope of 1/10 with the 5th order Stokes waves and the main focus was to investigate the wave breaking process. The results from the numerical model showed a reasonable agreement with experimental data (Alagan Chella et al., 2013). The main focus of the present study is to investigate the breaking process with the changes in the free surface profile, wave surface elevation and the horizontal velocity. Moreover, the intention of the paper is to in-vestigate the wave breaking process of spilling breakers over a sloping seabed using a two-phase flow three dimensional (3D) CFD model. The present 3D numerical model is utilized in a two dimensional (2D) setup to simulate the breaking waves over a sloping bed. To validate the present numerical model, the numerical results are compared with the experimental data by Ting and Kirby (1996). The changes in the free surface profile and velocity in different regimes are studied in the surf zone. The results from the numerical model are in good agreement with the experimental data concerning instantaneous free surface elevation, instantaneous horizontal velocity and wave group envelope. 2 NUMERICAL MODEL 2.1 Governing Equations In the present study, the incompressible Reynolds-Averaged Navier-Stokes (RANS) equations are solved together with the continuity equation that describes the conservation of mass and the momentum. The governing equations are:  0iiUx∂ =∂   (1) 1( ) ji i ij t ij i j j iUU U UPU gt x x x x xν νρ  ∂∂ ∂ ∂∂ ∂+ = − + + + +   ∂ ∂ ∂ ∂ ∂ ∂    (2)  U is the velocity averaged over the time t, x is the spatial geometrical scale, ρ is the water density, ν is the kinematic viscosity, νt is the eddy viscosity, P is the pressure, and g is the gravitational constant. A stag-gered uniform Cartesian grid is used in the model in order to make the computational domain simple which enables the direct implementation of finite difference numerical schemes. Discretization of the convective term of the RANS equations is accomplished by the 5th order Weighted Essentially Non-Oscillatory (WENO) scheme (Jiang and Shu, 1996). This scheme has 3rd order accuracy for discontinu-ous solutions and has 5th order accuracy for a smooth solution. A 3rd order total variance diminishing (TVD) Runge-Kutta scheme, a three-step scheme is adopted for the time discretization (Shu and Osher, 1988).  The temporal and spatial turbulent kinetic energy in the breaking waves is described by the k-ω model (Wilcox, 1994). The two-equation model has two transport equations for the turbulent kinetic energy, k, and the specific turbulence dissipation, ω:  tj k kj j k jk k kU P kt x x xνν β ωσ  ∂ ∂ ∂ ∂+ = + + −  ∂ ∂ ∂ ∂     (3) 2tj kj j jU Pt x x x kωνω ω ω ων α βωσ  ∂ ∂ ∂ ∂+ = + + −  ∂ ∂ ∂ ∂    (4) where Pk is the production rate, and closure coefficients α = 5/9, βk = 9/100 and β = 3/40.  A ghost cell immersed boundary method is implemented to describe the solid boundaries in the fluid domain and the algorithm is based on the local directional approach by Berthelsen and Faltinsen (2008). This methods avoids the explicit boundary conditions for the numerical discretization.  392ACKNOWLEDGEMENTS The authors would like to thank Dr. James Kirby and Dr. Ting Francis for sharing the experimental data. The authors wish to acknowledge support from the Norwegian Research Center for Offshore Wind Tech-nology (NOWITECH), Research council of Norway contract no.193823. The authors gratefully acknowledge the computing time granted by NOTUR (NN9240K) and provided on the Vilje system at the super computing facilities at NTNU.  REFERENCES Alagan Chella, M., Bihs, H., Kamath, A., Muskulus, M., (2013). Numerical modeling of breaking waves over a reef with a level set based numerical wave tank, Proceedings of 32nd International Conference on Offshore Mechanics and Arctic En-gineering. 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Numerical Simulation of Breaking Waves on a Plane Slope with a Parallel Level Set Solver

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Numerical Simulation of Breaking Waves on a Plane Slope with a Parallel Level Set Solver

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