The plasma jet generated by a non-transferred plasma torch may appear steady and laminar, but it undergoes significant turbulence. Initially, within the plasma torch, the jet begins as laminar, but upon interaction with the surrounding atmosphere at the outlet, it transforms into a turbulent flow. As it exits, the jet extends into a long structure and evolves into a wavy, fully turbulent flow. This paper delves into the intricacies of computational modelling for non-transferred plasma torches, outlining the challenges associated with simulating multiphysics and multiphase interactions at the outlet, and detailing the development of the plasma jet. The computational analysis is executed using the COMSOL Multiphysics software. Steady-state computational analysis is conducted on a 2D axisymmetric geometry, employing various turbulent models. A comparative analysis of results from each turbulent model is presented. Additionally, a transient study is undertaken using the optimal turbulent model to capture the jet's structure and its evolution. The paper concludes by validating the computationally obtained jet structure through a comparison with experimental data, ensuring the accuracy and reliability of the simulation results.