Homogeneous detached composite breakwater

CFD study of the design sensitivities in the 2D geometrical layout using a detached homogeneous low-crested structure to reduce sea wall overtopping

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In this research OpenFOAM is used to model and determine the complex hydrodynamic behaviour of a Homogeneous low-crested structure (HLCS) consisting of cubipod artificial concrete elements. The validated model is used to gain insight in the design sensitivities of a two dimensional cross sectional layout to reduce sea wall overtopping.

HLCS and Low-crested structure (LCS) in general dissipate energy from the incoming wave field by wave breaking over the crest of the structure and porous flow through the structure. By energy dissipation milder wave conditions are created inside the basin between the HLCS and the sea wall. Milder wave conditions result in reduced hydrodynamic loads on the sea wall and reduced flood risk. However not only the milder wave conditions determine the amount of sea wall overtopping. Additionally wave-induced water level set-up and basin hydrodynamics (i.e. seiching and resonance) contribute to the amount of overtopping. The relative importance of these different hydrodynamic interactions on sea wall overtopping depend on the main geometrical layout parameters of the system. The main geometrical layout parameters that are analysed in this research are the crest height of the HLCS (푅c ), the crest width of the HLCS (퐵) and the basin length between the HLCS and the sea wall (퐿pool). These geometrical layout parameters can be used by the engineer to steer the hydrodynamic behaviour towards the most cost effective design to reduce sea wall overtopping. However, due to the complexity of physical processes involved and their interactions, theoretical analysis is cumbersome. Therefore advanced OpenFOAM Computational Fluid Dynamics (CFD) simulations are performed in this research. These simulations are used to capture the complex hydrodynamics and gain more insight in the design sensitivities of these types of hydrodynamic systems.

A coupled numerical model using both OceanWave3D and OpenFOAM has been set-up in this research. Model dimensions are based on conducted physical model experiments to assess the amount of wave transmission over HLCS as described in J. Medina et al. (2019). No raw data was available from these physical model experiments. Therefore the wave flume hydrodynamics (i.e. irregular wave characteristics) have been calibrated using a grid resolution study. In this study also simulations with varying courant numbers have been performed. Both extracted statistical wave parameters of the coupled model and a standalone OceanWave3D model have been compared. Additionally the separate output of OceanWave3D and OpenFOAM within the coupled model have been compared. Grid convergence has been found for increasing OpenFOAM grid resolution. The measured mean overtopping discharges from the OpenFOAM model are validated against Eurotop 2018 prediction guidelines. The grid which showed the most accurate results in comparison to the required computational time has been selected for the remainder of the study. This OpenFOAM grid is characterized a grid resolution of Δx = Δy= 퐻s/10.

In order to assess the hydrodynamic behaviour related to wave transmission for HLCS, the van Gent (1995) parameterization of the extended Darcy Forchheimer equation has been used to model the amount of flow resistance that is exerted on the flow by the HLCS. Based on the differences between conventional rubble mound low-crested structures and HLCS a detailed analysis on the input parameters of the van Gent (1995) parameterization (i.e. the 퐷n , 퐾퐶, np and the closure coefficients 훼 and 훽) has been conducted. Large porosity gradients are found near the boundaries of the artificial cubipod elements. This effect has been implemented in the numerical model using two numerical layers with different porosity values resulting from the derived porosity distribution for artificial cubipod concrete elements. Additionally the effect of numerical outer layer schematization has been addressed. Both numerical additions only show to have minor effect on the modelled wave transmission behaviour (i.e. < 2% on 퐾t ). The closure coefficients 훼 and 훽 have been calibrated and validated based on the conducted physical model experiments J. Medina et al. (2019). Additionally a sensitivity analysis is included which can be used for the calibration of different artificial concrete elements. The best agreement between the modelled transmission coefficient and the experimental transmission coefficient is v vi Summary found for 훼 = 500 and 훽 = 1.0.

A parametric study is performed using the validated OpenFOAM model including the HLCS and sea wall to describe the complex hydrodynamic interactions within the hydrodynamic system and assess the design sensitivities. For this parametric study multiple simulations on 6 parallel processors were performed with a duration of 500 waves. Each simulation took approximately 48 hours to complete.

The most important findings and implications of the parametric study are in summary:

• For all varying geometrical parameters a decay in the form of an exponential function of the mean overtopping discharge is found. The most influence on the overtopping reduction is found for varying crest height of the HLCS.
• Wave transmission is found to be the dominant over the water level set-up, seiching and resonance inside the basin for the overtopping assessment of varying crest height and crest width of the HLCS. The most striking result for wave transmission over HLCS is that HLCS shows a constant trend in wave transmission for emergent structures (i.e. 푅c > 0). A further increase of crest height does not result in reduced wave transmission, contrary to conventional rubble mound LCS where a further reduction is observed.
• Furthermore a large dependency is found for varying basin length. The propagation of broken waves (i.e. hydraulic bores) due to wave breaking over the crest of the HLCS result in a significant increase in mean overtopping discharge. It is observed that these hydraulic bores die out for larger basin length. Additionally low-frequency wave motion (i.e. seiching and resonance) is observed for varying basin length. However this effect is smaller compared to the dissipating bores.
• By comparing the estimated overtopping discharge using the Eurotop guidelines solely based on the amount of wave transmission and the obtained overtopping discharge from the OpenFOAM model a mean underestimation of 69% is found by only using the transmission coefficient for the assessment of the amount of mean overtopping discharge. This concludes that the water level set-up cannot be neglected for overtopping assessments. Furthermore the use of advanced CFD modelling (e.g. using OpenFOAM) or physical modelling is of added value for the assessment of the amount of overtopping for these complex hydrodynamic systems due to the influence of dissipating bores, seiching and resonance inside the basin.

The ability of OpenFOAM to gain insight and to study the interactions for complex hydrodynamic systems has been demonstrated. Moreover design sensitivities of the hydrodynamic system under consideration are presented. These results can be used during early design stages for the assessment of the most cost effective design for these types of hydrodynamic systems. Additionally the sensitivity of the geometrical layout parameters can be used by the engineer to make targeted adjustments. Furthermore for comparable hydraulic boundary conditions (i.e. the same order of 퐻s , 퐻s/ℎ, ℎ/퐿p) and the use of low-crested structures (i.e. 푅c/퐻s,i ≈ 0) this OpenFOAM model can be used during design stages without further calibration.