Experiments to characterise vortices in hyperbolic shaped funnels are being conducted at the Water Application Centre (WAC) in Wetsus. These have demonstrated their higher gas transfer rates in comparison to the conventional aeration systems presently in use. Depending on the imposed flow conditions, different regimes of vortices are formed, among which the Twisted vortical structure is observed to have the highest gas dissolution rates. This has probed several questions on the physical mechanisms responsible on both micro-and macroscopic scales. The present research aims to numerically analyse the flow field organisation in these vortices to reason the observed high gas transfer rates using Computational Fluid Dynamics (CFD).  Transient simulations were performed on a three-dimensional radially structured hexahedral mesh. Multi-phase modelling was done using the Euler-Euler approach-based Volume-of-Fluid (VOF) method, while the turbulent flow was modelled using Shear Stress Transport (SST) based on k - ω equations with curvature correction. The choice of boundary conditions and their location is crucial for forming a stable vortex in the hyperbolic funnels. The position of the air-water interface from experimental results was used to validate the obtained numerical results. Two regimes of the vortex, namely the Twisted and Straight vortical structures, were evaluated for their gas transfer capabilities in terms of Hydraulic Retention Time (HRT), interfacial area and mixing in the bulk.  Instabilities arise in the secondary flow field of these vortical structures analogous to the Taylor-vortices that develop in the well known Taylor-Couette flow systems. In hyperbolic funnels, these instabilities aid in advecting the bulk of liquid to the air-water interfacial region and also enhance mixing within the bulk of water. The former enhances the gas transfer rates while the latter promotes uniform mixing. The strength of these instabilities is qualitatively analysed in terms of average vorticity per unit mass of water. This is found to be higher in the Twisted regime in comparison to other regimes. This is augmented by high air-water interfacial area making this regime possess superior gas transfer rates.  Although the gas transfer rates are high, water exiting the funnel is undersaturated at the given operating conditions. In order to further enhance the amount of gas dissolved few possibilities are qualitatively discussed at the end of this study.