This work compared the suitability of the k-$ϵ$ standard, k-$ϵ$ RNG, k-$\omega$ SST, and k-$\omega$ standard turbulence models for simulating a gravitational water vortex hydraulic turbine using ANSYS Fluent. This study revealed significant discrepancies between the models, particularly in predicting vortex circulation. While the k-$ϵ$ RNG and standard k-$\omega$ models maintained relatively constant circulation values, the k-$ϵ$ standard model exhibited higher values, and the k-$\omega$ SST model showed irregular fluctuations. The mass flow rate stabilization also varied, with the k-$ϵ$ RNG, k-$\omega$ SST, and k-$\omega$ standard models being stabilized around 2.1 kg/s, whereas the k-$ϵ$ standard model fluctuated between 1.9 and 2.1 kg/s. Statistical analyses, including ANOVA and multiple comparison methods, confirmed the significant impact of the turbulence model choice on both the circulation and mass flow rate. Experimental validation further supported the numerical findings by demonstrating that the k-$\omega$ shear stress transport (SST) model most closely matched the real vortex profile, followed by the k-$ϵ$ RNG model. The primary contribution of this work is the comprehensive evaluation of these turbulence models, which provide clear guidance on their applicability to gravitational water vortex hydraulic turbine simulations.