Veno-arterial extra corporeal membrane oxygenation (VA-ECMO) is a modified heart lung machine used for patients with both heart and lung failure. This results in retrograde supply of oxygenated blood through the femoral artery in which the unsteady pulsating antegrade flow from the aorta interacts with a steady, uniform, and retrograde flow from the femoral artery, creating a mixing zone. This work aims to provide a mechanistic interpretation of VA-ECMO by developing an in-silico framework using computational fluid dynamics. We performed several numerical simulations to investigate the effects of aortic geometry on VA-ECMO by implementing two idealized full aorta models and studied the formation of secondary flow features and vortices. We used vortex identification methods to capture the three-dimensional vortical structures formed under various ECMO support levels. Our results show that under pulsatile aortic flow and 80% of ECMO support, the streamwise vorticity and aortic arch geometry strongly influence the mixing zone. Furthermore, we found that pulsatility at the aortic inlet causes oscillation in secondary flow structures at the abdominal aorta leading to unsteadiness in ECMO flow and differential wall shear stress. We also examined the effects of VA-ECMO flow rates on secondary flow and vortical structures. We show that the location and complexity of secondary flows and vortical structures are affected by ECMO support levels and geometry of aortic segments. Together, we believe that this computational framework is a crucial step in understanding flow features and vortical structures formed during VA-ECMO administration, which can improve patient care and ECMO management.