Modeling of Hydroelastic Response of Closed Flexible Fish Cages due to Sea Loads

Norway is presently the worlds biggest producer of Atlantic salmon. The traditionally used open-net-structures are probably the most important reason for the Norwegian success.The very nature of aquaculture, where fish is grown at a much higher density than appear naturally, makes it likely to affect the existing surrounding environment. Views on weaknesses related to the traditional technology have been stated. These weaknesses concern sustainability challenges related to escapes, sea-lice, diseases and pollution. Closed Flexible Fish Cages are proposed used in the sea, to meet with ecological challenges in the aquaculture industry. In a closed fish production system, the farmer has increased control of how the fish are exposed to the environment, by controlling the flow and quality of the water entering and leaving the bag.A closed flexible floating system is not far from the currently used net cage fish farm systems, and may therefore be easier to put directly into operation. Even though a CFC seems to be an attractive solution, the existing knowledge about how the CFC will respond to external sea loads are limited. More knowledge is needed to understand the response of the cage if this technology are to be utilized in an industrial scale. Experimental data from towing experiments conducted in the summer of 2012, are analysed to better understand the current forces with connected deformations on the bag for different filling levels. The analysed bag showed an increased tendency to deform for decreasing filling levels, leading to an increase in drag coefficient.A new method for mathematical modelling of the increase in drag, by a filling-level-dependent drag coefficient is proposed. Earlier experiences with structural collapse of a similarconcept have shown that it is crucial to secure the cage against raptures and escapes. To assure this, a method to detect leakage and pump failure at an early stage must be developed. To detectleakages it is important to know how the bag deforms under static conditions for lower filling levels. Experimental data from experiments conducted in the spring of 2013 was analysed related to deformations on the bag for different filling levels, with and without applied passive control by braces, under static conditions. A new method for modelling the deformed shape of the bag for decreasing filling levels is proposed

Linear wave-induced dynamic structural stress analysis of a 2D semi-flexible closed fish cage

Closed fish cages in the sea are proposed as a new concept in marine aquaculture, replacing the conventional net cages in order to meet ecological challenges related to fish lice and escapes. A closed fish cage can be compared to a floating tank structure with an internal free surface. Several types of closed cages have been suggested, and they are categorised according to structural properties as flexible membrane structures (fabric), semi-flexible structures (glass fibre) and rigid structures (steel or concrete). To be able to develop safe and reliable structures, more knowledge is required on the seakeeping behaviour of closed cages in waves and the structural response to the wave loads. This paper builds on a theory presented in Strand and Faltinsen (2019) on the linear wave loads on a 2D closed flexible fish cage. A modelling error has been found in Strand and Faltinsen (2019), however, all the main conclusions are in hold. The error has been corrected in the model in the present paper. The present paper extends the model to include bending in the structural model to be able to handle semi-flexible structures where bending stiffness is significant. In this paper, the linear theory of a 2D semi-flexible closed fish cage in waves is developed and analysed to investigate the structural response of the semi-flexible closed cage in waves. We have compared a quasi-static analysis with a fully coupled hydroelastic analysis to investigate if it is a valid and conservative assumption to assume that the stresses in the structure can be assumed quasi-static. If a hydroelastic analysis is necessary or not, is dependent on the stiffness of the structure. We have investigated what happens with the stress in the curved beam part of the closed fish cage for increasing and decreasing stiffness relative to a reference composite structure. One stiffer and two softer cases have been analysed. One major concern for the structural stresses in a closed cage is the effect of sloshing. Sloshing is internal wave motion inside the cage and have multiple resonance periods. The results indicate that to use the quasi-static assumption in structural stress calculation is conservative within the given frequency range for all examined stiffnesses and frequencies, except the frequencies very close to the second sloshing frequency. Close to the second sloshing frequency for all the examined stiffnesses, a localised peak can be observed in the coupled hydroelastic results. The second sloshing frequency is a frequency connected to a symmetric sloshing mode. Rigid body motion is not affected at the symmetric sloshing frequency for an assumed rigid structure, and are therefore also not visible in the stress results from the quasi-static analysis. The structural stress in irregular sea was calculated. These results show no indication of increased stress close to the second sloshing frequency. However, this is not a surprising result since the stress peak is very localised in frequency, and the accumulated effect on the stress standard deviation is therefore small

Linear wave response of a 2D closed flexible fish cage

Closed flexible fish cages (CFFC) are proposed as a new concept in marine aquaculture, replacing the conventional net cages in order to meet ecological challenges related to fish lice and escapes. A linear mathematical model of a freely floating 2D CFFC in waves have been developed. It was found that the wave induced rigid body motion responses of a flexible CFFC in sway, heave and roll are significantly different from the responses of a rigid CFFC. Large ratios between free-surface elevation amplitudes and incident wave amplitude are predicted inside the tank at the first and third natural sloshing frequencies. It implies that non-linear free surface effects must be accounted for inside the tank in realistic sea conditions. The dynamic tension in the membrane of the CFFC must be smaller than the static tension in the applied structural method. For the analysed case with 25 m between the centre of the floaters, the most probable largest dynamic tension is larger than the static tension, for significant wave heights larger than 0.5 meter. The effect of scaling of elasticity on the rigid body motion have also been investigated. The non-dimensional response of the CFFC versus non-dimensional frequency, and based on Froude scaling using an elasticity available in model scale have been compared to the response of the CFFC using the elasticity for full scale. These responses were found to deviate to a large extent, showing limitations of model tests of a CFFC

Linear sloshing in a 2D rectangular tank with a flexible sidewall

A 2D rectangular sloshing tank with a flexible sidewall have been studied analytically and numerically, with a focus on the coupling between sloshing and the flexible wall. This analysis introduces new knowledge of the effect of internal motions and flow in a membrane structure with a free surface, such as closed flexible fish cages. A framework for analyzing coupled fluid–membrane interaction in the time, and frequency domain in 2D have been developed. The analytical solution gives new knowledge about the effect of the deformations on the linear pressure inside the tank. Coupled eigenfrequencies and the transfer functions for two different membrane lengths due to sway excitation have been found both analytically and numerically. The analytical and numerical results agree. The eigenfrequencies of the system are highly dependent on both the tension and the 2D membrane length. If we consider a given value of tension, then the eigenfrequency of the coupled system is smaller than the sloshing frequency of the rigid tank for any given n. If the tension is small, and we consider a given sloshing frequency of the rigid tank, then there can be more than n eigenfrequencies of the coupled system that is lower than the sloshing frequency of the rigid tank. For large tensions, the eigenfrequencies of the system become the sloshing frequency of a rigid tank. For low tensions, numerical challenges for the direct numerical solution for frequencies close to the natural sloshing frequencies were pointed out

Experimental study of current forces and deformations on a half ellipsoidal closed flexible fish cage

Closed flexible fish cages are proposed as a new concept in marine aquaculture, replacing the conventional net cages in order to meet ecological challenges related to fish lice and escapes. It is important to understand the response of the cage exposed to current loads. Then more knowledge about forces and deformations on the closed flexible fish cage for different filling levels is needed. A scaled model of a closed flexible fish cage shaped like a half ellipsoid was tested in a towing-tank. Global drag forces and bag deformations were measured for four different filling levels between 70% and 100%, and steady current velocities between 0.04 m/s and 0.22 m/s in model scale, corresponding to Reynolds numbers in the range Re=3–17×104Re=3–17×104. Findings from the experiments showed that the drag force increased for decreasing filling levels. This increase was caused by a large deformation of the front of the bag affecting the drag coefficient.Norges forskningsrådacceptedVersio

Wave response of closed flexible bags

Recent environmental considerations, as salmon lice, escape of farmed fish and release of nutrients, have prompted the aquaculture industry to consider the use of closed fish production systems. The use of such systems is considered as one potential way of expanding the salmon production in Norway. To better understand the response in waves of such bags, experiments were conducted with a series of 1:30 scaled models of closed flexible bags. The bags and floater were moored in a wave tank and subjected to series of regular waves (wave period between 0.5 and 1.5s and wave steepness 1/15, 1/30 and 1/60). Three different geometries were investigated; cylindrical, spherical and elliptical, and the models was both tested deflated (70% filling level) and inflated (100% filling level). Incident waves were measured together with the horizontal and vertical motion of the floater in two points (front and aft). Visual observations of the response were also done using cameras. The main finding from the experiments were that a deflated bag was more wave compliant than an inflated bag, and that the integrity (whether water entered or left the bag over the floater) was challenged for the inflated bags even for smaller waves (identified as wave condition B (1.0macceptedVersio