Viscous flow around a simplified model of a Christmas tree
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- Institutt for marin teknikk 
In the petroleum industry, a Christmas tree is a structure consisting of valves and spools that sits atop an oil well. In order to better understand the forces acting on a Christmas tree during and after installation, numerical simulations of steady flow past a simplified model at the sea floor have been performed and, where possible, compared to relevant literature. Both 2D and 3D simulations have been undertaken. The 2D simulations themselves do not say much about the forces experienced by a full scale model, but were performed to see if they could give any indication as to how the 3D model would scale with higher Reynolds numbers. The model is based on a previous model by Kjemperud (2011), and consists of three cylinders in a triangular arrangement, fixed between two horizontal plates and with a vertical plate on their downstream side. All simulations were performed with the open source Computational Fluid Dynamics (CFD)software OpenFOAM. They were run in parallel on the super computer Vilje at NTNU. TheReynolds-Averaged Navier-Stokes (RANS) approach to turbulence modelling was used, employing the k−ω SST model in 2D and the RNG k−epsilon model in 3D. Emphasis was put on making a high quality mesh and finding a numerical setup that was the best compromise between accuracy, stability and efficiency. Near-wall treatment was done using wall functions for all simulations. In 2D, simulations were run for current velocities of 0.1, 0.2, 0.3, 0.5 and 1 m/s, so that the Reynolds number was in the range 2.31 ∗ 10^5 < Re < 2.31 ∗ 10^6. Two simulations were carried out in 3D, at Re = 5.49 ∗ 10^3 and at Re = 2.31 ∗ 10^5. No previous research has been performed on the geometry and flow direction of the present study. To the extent that it is possible to compare with reference literature, the results obtained in 2D seem reasonable. They experience vortex shedding from the plate and a Strouhal number that is stable up to and including a current velocity of 0.5 m/s. The forces experienced by the plate and cylinders seem reasonable, but the simulations at current velocities of 0.3 and 0.5 m/s did not scale with Reynolds numbers as one would expect. They should not be used to make assumptions on the Reynolds number dependence in 3D or should be used with great care. Neither of the 3D models exhibited vortex shedding. The low Reynolds number model didhowever exhibit another plausible flow pattern with a large, stationary, vertical vortex in its immediate near-wake. As such, the results obtained in that simulation might have been correct and might be used for low current velocities. Further research needs to be carried out to validate the simulation.The high Reynolds number model did not converge because vortex shedding did not start. It might have worked to have run the simulation with the flow approaching it at an oblique angle so as to help the vortex shedding initiate.