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Concluding remarks

As brief conclusions, we would like to offer reflections on the practical application of wave propagation models to generate incoming waves in wave-structure interaction calculations. It. is obvious that the application of a fast but accurate numerical model in a large domain to generate a wave input for a CFD wave-structure interaction solver operating in a much smaller domain offers considerable savings in computational resources. There are two ways to implement this approach. The first involves modelling a random sea state over a large area and a long period of time. Surface elevation and kinematics of selected events, e.g., extreme waves, are then used as input for a CFD solver. HOS models have a clear advantage for such an approach. The benefits of this method are recognised by the industry. See, for example, the recent feature article from DNV-GL where an application of a HOS model is reported to provide a realistic nonlinear wave input for the CFD wave-structure interaction code (Bitner-Gregersen, 2017).

In the second approach, a NWT is used in a manner similar to an experimental wave tank for generating a preselected wave event or for replicating a physical wave tank experiment. Any computationally efficient NWT based on an appropriate wave model can be used for this purpose, including the models described in this chapter. None of them seems to have obvious advantages except for the Lagrangian model in the case of waves on sheared currents. For this method, accurate generation of a desired wave event or reconstruction of experimental conditions are important because the errors due to incorrect wave input may be larger than the errors of a numerical scheme. The application of an iterative wave generation technique may be recommended as an effective solution to this problem. Such techniques are common in wave tank experiments and can be similarly applied in numerical wave tanks (e.g., Fernandez et ah, 2014; Buldakov et ah, 2017; Stagonas et ah, 2018b). An example of an accurate reconstruction of the experimental wave conditions by an advanced iterative technique in a Lagrangian NWT with an application as input to a wave-structure interaction CFD model can be found in Higuera et ah (2018).

The methods described above use the so called one-way coupling between the wave- propagation and CFD models. This means that the wave propagation model is used independently and is not influenced by the CFD model. We believe that for wave-structure interaction problems, this method of communication between models is preferable to real-time two-way coupling, especially when iterative wave generation is used. The computationally demanding CFD component is not executed during the iterative wave generation phase, and the wave propagation component is not executed when the wave interaction with a structure is simulated. Moreover, once generated, wave input can be used in different CFD models using different numerical methods and applied to different structures. One of the technical problems to be solved when applying the one-way coupling approach is to not allow the waves reflected by the structure to be reflected back to the domain by external domain boundaries. At the same time, the precise transition of the wave kinematics generated by the propagation model to the CFD domain must be ensured. This can be done in different ways.

For example, Higuera et al. (2018) used Lagrangian kinematics and surface elevation to specify the boundary condition for velocity on a front boundary of a rectangular CFD domain. Active dissipation was applied at the rear boundary and passive dissipation at the side boundaries of the domain. Another approach is using a cylindrical grid with a ring- shaped relaxation zone. This mesh type provides better resolution around a structure. The equations within the relaxation zone are modified to introduce a dissipation of disturbances of the incoming wave solution with a dissipation coefficient gradually increasing from zero at the inner edge of the relaxation zone to a high value at its outer edge. In this way, the incoming wave is generated at an outer boundary of the computational domain and propagates freely into the domain interior. At the same time, the waves reflected by the structure propagate freely in the field and dissipate inside the relaxation zone without being reflected back. The size of the computational domain is proportional to the wavelength of the incoming wave and the width of the relaxation zone to the length of the wave reflected or radiated by the structure. Normally, the reflected wave has the same length as the incoming wave, but in certain situations, e.g., for slender structures, the peak of the reflected spectrum is shifted towards higher frequencies. For such structures the width of the relaxation zone can be reduced. This is also the case for waves radiated by ringing structures. The optimal sizes of the main computation domain and the relaxation zone depend on a particular wave and structure. Practical recommendations on their selection for different types of structures and waves should be developed as a result of the convergence study with respect to these parameters.

Acknowledgments

The work on wave over sheared currents presented in this chapter is supported by EPSRC within the Supergen Marine Technology Challenge (Grant EP/J010316/1). The author also thanks Dr. Dimitris Stagonas for performing experiments on wave propagation over currents used in this work and for analysis of experimental data.

 
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