Descending Thoracic Aortic Aneurysm (DTAA) is a life-threatening disorder, defined as a localized enlargement of the descending portion of the thoracic aorta. In this context, we develop a Fluid-Structure Interaction (FSI) computational framework, with the inclusion of a turbulence model and different material properties for the healthy and the aneurysmatic portions of the vessel, to study the hemodynamics and its relationship with DTAA. We first provide an analysis on nine ideal scenarios, accounting for different aortic arch types and DTAA ubications, to study changes in blood pressure, flow patterns, turbulence, wall shear stress, drag forces and internal wall stresses. Our findings demonstrate that the hemodynamics in DTAA is profoundly disturbed, with the presence of flow recirculation, formation of vortices and transition to turbulence. In particular, configurations with a more steep aortic arch exhibit a more chaotic hemodynamics. We notice also an increase of pressure values for configurations with less steep aortic arch and of drag forces for configurations with distal DTAA. Secondly, we replicate our analysis for three patient-specific cases (one for type of arch) obtaining conforting results in terms of accordance with the ideal scenarios. Finally, in a very preliminary way, we try to relate our findings to possible stent-graft migrations after TEVAR procedure to provide predictions on the post-operative state.