We previously developed an inverted frusto-conical shaking bioreactor (IFSB) which had high mammalian cell culture performance when compared with a mechanically stirred tank reactor (STR) or a flat-bottom shaking bioreactor (FBSB). Here, we determined the mixing time (t) and volumetric oxygen transfer coefficient ($k_La$) of this IFSB at various speeds, and simulated the fluid hydrodynamics, including the shear stress and specific surface area, by computational fluid dynamics. The shortest mixing time was observed in a STR. The maximum $k_La$ value of 12/h was achieved in the IFSB at an aeration rate of 4 L/h, demonstrating that our IFSB has enhanced oxygen transfer capabilities needed to meet the demands of mammalian cells. Simulation studies revealed a 3% greater specific surface area and a 21% lower shear strain in the IFSB compared to an FBSB under the same conditions. Additionally, the conical angle of the vessel, which significantly affected cell growth and recombinant protein production, was tested here. We conclude that, compared to the STR and FBSB, the IFSB has an increased liquid surface area for oxygen uptake and exhaust $CO_2$ stripping, an enhanced $k_La$ for cell robust growth to a high cell density, and a lower shear stress to alleviate cell damage.