Multiphase flows are frequently encountered in various industries, such as oil, nuclear, and refrigeration, among others. In numerical simulations of flows with more than one phase, one of the major challenges is tracking the phases in the domain, which can be distributed in different patterns depending on the operational conditions of the flow, fluid properties, and pipe geometry. The focus of this study is on the vertical annular pattern, which is characterized by a central gas core flowing at high velocity, surrounded by a thin liquid film. The One-Dimensional Two-Fluid Model is used to predict the behavior of two-phase flows and is obtained by averaging processes over the cross-sectional areas. This requires defining closure relationships to render the system well-posed. The objective of the present work is to analyze turbulent viscosity models in vertical annular flow using the 1D Two-Fluid Model. Three models have been proposed for investigation. The first is based on the universal logarithmic wall profile, the second on the velocity profile proposed by Castello Branco (2022), and the third model considers the characteristic length to be proportional to the pipe diameter. The obtained results were compared with the literature and showed that the additional diffusion due to turbulence is beneficial for rendering the system well-posed and improving agreement with experimental data regarding film thickness and pressure gradient. However, turbulent viscosity alone is not sufficient to stabilize all combinations of superficial velocities, recommending the inclusion of the momentum flux parameter.