Hydrodynamic coefficients of a dropper line in North Sea conditions

Abstract

Coastal communities around the world are facing significant challenges such as erosion, flooding, and storm surges. These issues highlight the need for nature-based coastal management solutions that can help mitigate the negative impacts of these events. Coastbusters Consortium developed such a solution in the North Sea. This solution is a system that utilizes a bivalve long line approach, where blue mussels are allowed to grow and eventually attach to the seabed, forming a reef structure that can help induce natural accretion of sand, attenuate storm waves, and reinforce the foreshore against coastal erosion. This reef structure can help to enhance coastal protection and reduce the impacts of these significant challenges on coastal communities.

To enhance the current long line system, it is imperative to develop numerical models that can accurately predict the forces acting on the slender cylinders in current and waves. One approach to this is to use the Morison equation, which accounts for both drag and inertia force. However, there is a lack of understanding regarding the drag and inertia coefficients in the literature that are used in the Morison equation. To address this issue, the present research conducts three experiments on a 3D-printed model of a dropper line, at a one-to-one scale, in a towing and wave tank. To treat the dropper line as a cylinder, a characteristic diameter is used. The 3D model is developed based on a thorough evaluation of the existing dropper lines at De Panne. These experiments aim to determine the drag and inertia coefficients for the dropper line in different steady and oscillatory flows, which can aid in the design of more efficient and effective bivalve aquaculture systems and integration into numerical models.

To determine the drag coefficient of the current towing experiments were conducted and forced oscillations and waves experiments were conducted to determine the drag and inertia coefficient in waves. The parameters used were based on the current and wave regimes at De Panne, and were expressed in terms of Reynolds and Keulegan-Carpenter numbers. The results showed that for continuous current, the drag coefficient of a dropper line containing blue mussels was determined to be $C_D$ = 1.2 for Reynolds numbers between $3.0*10^4$ and $1.0 *10^5$. In oscillatory flow, the drag coefficient varied between $C_D$ = 2.3 - 3.5, and the inertia coefficient varied between $C_M$ = 1 - 2.5 for Keulegan-Carpenter numbers between KC = 5 - 28.

The experiments conducted in this study included evaluations of the characteristic diameter and shape of the dropper line.
Results also showed that a difference existed between the coefficients obtained from the forced oscillation and wave experiments. Possible explanations for this difference were investigated, including free surface effects and flow differences. The results obtained from this study can be applied to the design of bivalve aquaculture systems and their integration into numerical models. These findings contribute to improving the efficiency and effectiveness of nature-based coastal management strategies for mitigating the effects of erosion, flooding, and storm surges on coastal communities. Further research is needed to fully understand the complex dynamics of the bivalve long line system and its interactions with the coastal environment.