Hydrodynamic study of a moored fish farming cage with fish influence
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- Institutt for marin teknikk 
The thesis deals with the influences of all components of the fish farming cage on the mooring loads, focusing on the influences of the fish school. First, the net cages with and without closed bottom were studied in current only. The numerical method developed by Kristiansen and Faltinsen  was used to simulate the hydrodynamic behavior of the net cage. The net was divided into many trusses with an equivalent solidity ratio Sn, which is one minus the open area ratio of the net. The mass of trusses of the model was lumped into the nodes connecting the trusses. The tension in the trusses were solved at each time step, and the viscous hydrodynamic forces were calculated by using a screen-type empirical model. The node positions were time stepped according to Newton’s second law. A screen-type hydrodynamic model implied that both normal and tangential loading on a net panel were considered. It involved pressure loss coefficients, which were functions of the Reynolds number of individual twines and the solidity ratio Sn. The cross-sectional shape of twines was approximated by a circular section. Then, a horizontally moored fish farm cage with a flexible two-tori floater, a closed bottom net, and a bottom ring was studied experimentally and numerically. The model scale was 1:16. For current-only cases, the total drag forces from the numerical calculation and the experimental results were compared. For combined waves and current cases, the mooring forces from the two side mooring lines and longitudinal mooring lines were compared separately. The comparisons showed that the numerical model gave satisfactory predictions of the mooring loads. The comparisons of the mooring forces between the models with and without the bottom ring were performed under a combined wave and current. The simulated results demonstrated that the main differences between the two models were the amplitude of the front mooring forces. The most front part of the bottom ring was lifted up higher than the relevant bottom weights, while the two sides right after the most front part of the bottom ring had lower positions than the relevant bottom weights due to the hydroelastic effects of the ring. These resulted in a less vertical restoring forces on the front part of the floater, which was the reason for the larger amplitudes of the front mooring forces and some influences on the amplitudes of the two side mooring forces. The VIV of a realistic full scale bottom ring (refer to Nygaard ) were discussed and recommendations for the study were made in different exposure areas according to Norwegian Standard NS9415:2009 . Higher order VIV might occur for all the exposure areas. For heavy exposure area, the order of the VIV could be from the 3rd up to the 7th order. In order to study the influence of the Vortex Induced Vibrations (VIV) of the bottom ring of a fish farming cage, a plastic ring with a ring diameter of 1.5m, cross-sectional diameter D=32mm, bending stiffness EI=23.23Nm2, and mass per unit length m=0.6kg/m was used as the experimental model. The model was tested in current speed range from 0.04 m/s to 2.0 m/s. The natural frequency of the model was calculated using a beam equation for a quarter of the ring with two clamped ends. The VIV were observed when the towing speed was larger than 0.8 m/s corresponding to the reduced velocity of 2.33. The vortex shedding frequencies were estimated by setting the Strouhal number to be 0.21. The oscillation frequencies of the ring were estimated by counting the images extracted from the videos. The drag forces on the bottom ring with and without VIV were estimated based on existing empirical formulas and guidelines for a circular straight cylinder. The drag forces were well predicted when there was no VIV, while overpredicted when VIV occurred. For the study of the influences of the fish, the experimental and numerical studies with artificial fish and live fish were performed. For the fish school simulations, the slender body theory was adopted. For the rigid fish group, a far-field solution was applied. The transverse dipole and source distributions along the fish body were discussed. It was found that the effects of the transverse dipole distribution were negligible when calculating the far-field flow generated by the fish body. The interaction of the horizontal flow between the fish was concluded to be nonnegligible. The numerical and experimental studies of the influences of the artificial fish were performed in current only. The bottomless net cage with approximately inelastic floater was used. Nine equivalent artificial fish models with total volume of 2.5% of the volume of the net cage with imaginary flat bottom were used, which was a typical volume occupation of the fish in real fish farming cage. The numerical and experimental results showed that the influences of the nine artificial fish models to the drag forces on the net cage were around 3% of the no-fish case. The influences of the live fish on the drag forces of the net in waves and current were further discussed experimentally and numerically. More than 800 salmons of length 16 cm occupied about 2.5% of the fish-cage volume at rest. The fish were found to swim in a circular path along the net cage in calm water and to keep station against the current speed in current only. The measured mooring loads with live fish in current were between 10% and 28% larger than without fish. The reason was contact between the fish and the net cage. The contact effects were documented with the numerical model by changing the local solidity ratio of the net in the contact area so that the net configurations in the numerical simulations and experiments agreed. The experiments in waves, and combined waves and current also showed a non-negligible influence of the fish on the mooring loads. The waves influenced the behavior of the fish, and some of the fish went to the net bottom possibly due to that they were uncomfortable in the wave zone.