Numerical Simulation of Flow Around a Prolate Spheroid
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- Institutt for marin teknikk 
The concept of closed containment fish cages is promising when coping with sea lice andescaped fish challenges in the aquaculture industry. Unlike the traditional open net cages,the external flow caused by current and waves has to flow entirely around the fully closedwalls. Hence, the importance to consider the hydrodynamic loads, as well as the behavior ofthe disturbed flow. In the present study, a closed containment fish cage has been simplified as a (LR = L/D= 4/3) prolate spheroid. The model is assumed fully submerged in a steady current, andoriented with its major axis normal to the incoming flow. The flow has been simulated numericallyby a finite volume method in the software OpenFOAM for five different Reynoldsnumbers, Re = 100, 200, 250, 300 and 500. The resulting pressure, velocity and vorticityfields are presented using various visualization techniques, whereas quantities related to hydrodynamicforce coefficients, separation and vortex shedding frequencies are computed. Dueto the low aspect ratio, the main goal of the present study was to relate the present resultsto flow features appearing in the wake of a sphere. For the two lowest Reynolds numbers Re = 100 and 200, the flow was found to be steadyand symmetric in the major plane. At the former Re, a similar planar symmetry alignedwith the minor plane of the prolate spheroid was observed. The flow separates and rejoins acertain distance downstream. A maximum separation length equal to Ls = 1.26D and 1.75Dwas obtained for Re = 100 and 200, respectively. An unsteady wake flow was apparent for Reynolds numbers Re 250, with consequentoscillating hydrodynamic forces. At Re = 250, a pair of counter-rotating vortices were foundto twist around each other as they propagate downstream. The most striking discovery,relating the present results to the flow around a sphere, is the periodic shedding of hairpin-shapedvortices of constant orientation, at Re = 300. The topology of the vortical structures,as well as the associated shedding frequency, were found to coincide with the results of asphere. A planar symmetry is evident and aligned with the major axis of the LR = 4/3prolate spheroid. As a Reynolds number of Re = 500 is reached, the symmetry features ofthe wake are lost. Unlike the vortex structures of fixed orientation at Re = 300, the presentvisualizations at Re = 500 revealed a chaotic wake of alternately shed vortices. The dominantshedding frequency in terms of Strouhal number, St = 0.137 and 0.183, were found for Re= 300 and 500, respectively. The resemblance between the results of the LR = 4/3 prolate spheroid and the spherewas found to be strong concerning hydrodynamic force coefficients and separation. At Re =300 an averaged drag and lift coefficient of 0.664 and 0.052 were computed afterthe flow had reached a steady state. For increasing Re, the point of separation was found tomove upstream. The separation angle from the front stagnation point in the middle minorplane decreased from 121 at Re = 100 to 103 at Re = 500. The outline of the wake 1D behind the prolate spheroid was found to maintain its projectedarea at all Re. However, at the two highest tested Reynolds numbers, the major axisof the wake was found to rotate and align with the minor axis of the prolate spheroid, somewherebetween 4D and 7D downstream. A comparable axis switching phenomenon has beenreported for similar asymmetric bodies as a LR = 6 prolate spheroid and LR = 3 elliptic disk. Therefore, the present results indicate that flow features appearing in the wake of a sphere are maintained for the low aspect ratio (LR = 4/3) prolate spheroid, at the tested Re.However, the presence of an asymmetric cross-section is seen to introduce similarities towardresults of higher aspect ratio bluff bodies. For further work, it is recommended to increase the practical relevance of the numericalsimulations. This may be done by increasing the Reynolds number to simulate turbulentflow or change the boundary conditions to introduce e.g. a free surface or a shallow watercondition.