# CFD Estimation of a Resistance Coefficient for an Egg-Shaped Geometric Dome
## 1 Introduction  
Aquaculture is growing and new production technologies are under development and testing. While open net pens are the standard equipment, one opportunity for controlling the environment and reduce the risk of fish escape is to close the fish farm unit from the surroundings using firm walls. Egget(r) is an example of this, which utilizes a fiber composite structure. Cylindrical closed fish farms have lately received much focus, for example, in [1, 2], where the researchers have carried out experiments and numerical analysis with a particular emphasis on the sloshing behavior. While Egget(r) has certain similarities to the structure studied, it has the shape of an Egg with a cylindrical buoyancy collar attached to it. To establish the hydrodynamic response and loads, precise estimates of the hydrodynamic properties are crucial. The total resistance includes all contributions, including wave making resistance. The resistance coefficient is used to estimate force from wind and current or, together with the inertia coefficient, to calculate wave loads, for example, by applying the well known Morison equation [3] for estimates of wave forces on slender structures. [PERSON] [4] studied the pressures and skin friction on the surface of cylinders with different surface roughness exposed to a constant flow in an air duct. He published data for skin friction, drag coefficients and separation points for a range of Reynolds numbers between \(4\times 10^{4}\) and \(3\times 10^{6}\). The study showed that the Reynolds number at which the critical flow sets in, as well as the level of drag in a certain flow regime, is impacted by the surface roughness. [PERSON] further published a study for smooth spheres, where drag coefficients are documented for the Reynolds numbers between \(5\times 10^{4}\) and \(6\times 10^{6}\)[5]. [PERSON] [6] published results from experiments in an u-shaped tube filled with water and different cylinders mounted on force measurement devices in the middle section. By oscillating the water and measuring the force, the drag and inertia coefficientsfor different cylinders was established for Reynolds numbers up to \(7\times 10^{5}\). His results demonstrated that the drag and inertia coefficients depend on velocity and wave period as well as viscosity and diameter. [PERSON] et al. provided experimental results for the flow around a sphere towed at the water surface in a conference paper [7] at Reynolds numbers between \(2\times 10^{5}\) and \(4.5\times 10^{5}\), where drag coefficients are reported. [PERSON] and [PERSON] [8] reported on experiments on a standing tube instrumented with pressure transducers and towed through a basin. The results demonstrated that the resistance coefficient depends on the proximity to the waterline as a function of the Froude number. They provide resistance coefficients for a vertical tube extending 2 diameters into the water volume. [PERSON] et al. [9] focused on hydrodynamic forces on partially submerged horizontal cylinders with Reynolds numbers ranging from \(5\times 10^{4}\) to \(9\times 10^{5}\). Their experimental results showed that when the cylinder protrudes the surface, the drag crisis did not occur as for completely submerged cylinders. They observed a reduction in drag coefficient as the depth decreased, which is not linear to the change in cross section area. This is indicative of a surface effect on the force measurement. Further they observed a dependence of the Froude number on the drag force. Although it is common to study flow problems based on similarity in Reynolds number, resistance tests for ships are usually carried out by Froude scaling, since this enables calculation of the wave making resistance [10]. To validate the experimental results and for analysis of similar and complex shapes, proper numerical models are important. [PERSON] et al. applied the finite difference method to estimate the drag force and drag coefficient [11].