One of the goals of computational fluid dynamics for Turbomachinery is the prediction of their performance such as the ratio of pressure, efficiency, and the nature of the flow. In this research, which consists of two parts, in the first part were performed steady and unsteady simulation methods on stage of the axial flow Turbomachinery and results validated. In this regard, two numerical steady methods including a frozen rotor and stage, and three transitional numerical methods including standard transitions, time transformation, and profile transformation were used. Transient methods provided a more accurate prediction. In transient methods, it was observed that transient effects including wake, stator leading edge bubble and flow separation can be obtained more clearly, which were found to be weaker in other methods. In order to solve the numerical flow field used of structured grid and SST turbulence model was used for modeling turbulence. In the second part of the paper, 9 changes were investigated to the geometric changes, such as roughness in the blade surfaces, clockwise and counter-clockwise rotation of the foil sections, the creation of radius in the roots of the blades, and create of the axial distance between the blades.