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Fundamentals of Computational Fluid Dynamics
Published in Mohammed M. Farid, Mathematical Modeling of Food Processing, 2010
Gordon D. Mallinson, Stuart E. Norris
If there is no through flow through a boundary and the shear stress is zero then the boundary is called a symmetry boundary. A symmetry boundary has the useful property that there is no propagation of flow kinematics across the boundary and the flows on either side can be modeled separately.
A study of the impact of plunging waves on the inverted L-shaped breakwater structure based on SPH method
Published in Ships and Offshore Structures, 2022
Zhe Ma, Yefeng Yang, Gangjun Zhai, Jianyu Bao, Hee-Min Teh
Over the past decades, major studies concerning four breaking waves impacting the vertical breakwaters have been conducted by relevant scholars. Carried out experiments to investigate the interaction of breaking waves and vertical walls in different slopes, Kirkgoz (1982); Kirkgoz (1995) found that the slamming pressure is the largest when the wave front is parallel to the vertical wall, but the duration of the high pressure state is very short. Through the liquid sloshing experiment, Lugni et al. (2006) showed that the jets generated after impacting the wall are 10 times faster than that of the incident wave when waves in the shape of ‘flip-through’ (‘flip-through’ is situated between type (d) and type (c)) impacted the wall. So in the problem of the interaction between waves and the inverted L-shaped breakwater, the jets slam up against the horizontal cantilevered slab at high speeds again, resulting in large slamming pressures which cannot be ignored appearing at the corner of the structure. Another breaker type is that air will be entrapped between wave tongue and wall when waves flip before impacting the wall. And this breaker type can finely be divided into a well-developed plunging wave and plunging wave (see type (b) and type (c) in Figure 2) based on the amount of air. In the meantime, Chan and Melville (1988); Hattori et al. (1994) found that the peak slamming pressures decrease with the increase of the air content, while the pressure rising time is the opposite. Bullock et al. (2001) concluded that the presence of a huge cavitation would play a ‘buffering effect', in his experiment model, which could reduce the peak slamming pressure and increase the duration of pressure rising time. Although the presence of cavitation reduced the peak slamming pressure compared to the case without cavitation, Obhrai et al. (2005) observed that the duration of the high pressure state increased, which would cause the entire structure to be subjected to enormous wave forces. Bullock et al. (2007) conducted detailed discussions on the stress of the structure under different wave breaking conditions through experiments, and found that the slamming pressures are very huge in both ‘flip-through' and plunging waves conditions, while in the condition of plunging waves, the duration of the huge pressure state would be longer and the structure could be under great wave force. Meanwhile, a similar conclusion is drawn by Liu et al. (2019). Therefore, the structure would be subjected to local damages under the action of ‘flip-through', while plunging waves made the structure under high pressure for a long time so that it would suffer from overall damage. Combining the researches of the above scholars, it is highlighted that when plunging waves interact with the vertical structure, not only could it cause huge slamming pressures, but also it would be accompanied by a massive wave force, which would make the structure vulnerable to great damages.