• axial turbine stage
• computational fluid dynamics
• dimensional analysis
• Harmonic Balance method
• Mixing Plane method
• similitude
• Turbomachinery
• unsteady losses
• unsteady performance

This thesis discusses the importance of the unsteady flow phenomena in bi-dimensional axial turbine stages. Although the flow in a turbomachine is inherently unsteady, most of the optimization methods for turbomachinery are mostly based on the assumption of steady flow. The unsteadiness significantly can affect the overall stage efficiency and have other important consequences such as blade flutter or forced response, as well as noise and thermal stresses. The aim is to evaluate the difference between steady and unsteady flow predictions in order to investigate the impact of unsteady effects on the performance of the axial turbine stage. By dimensional analysis, the meaningful dimensionless numbers based on input parameters for the two-dimensional (2D) axial cascade, are derived as a similarity criterion. These non-dimensional numbers are used to estimate the field measurement of turbine performance. Three blade designs are studied by varying the expansion ratio, the working fluid, and the non-dimensional axial gap. The steady calculations are performed by using a mixing plane approach (MP), whereas the unsteady calculations are solved with the harmonic balance approach (HB). These two methods are implemented in the open-source SU2 software. In this work, several cases are discussed in which significant differences are found between steady and unsteady results.