The drainage cannula in a venoarterial extracorporeal membrane oxygenation (VA ECMO) circuit transfers venous blood from the patient to a pump. However, drainage cannulas are prone to thrombosis, leading to significant morbidity in patients. Therefore, this study aimed to evaluate the effects of cannula size, design, and flow rate on flow dynamics and risk of flow-induced thrombosis in different patient geometries using computational fluid dynamics (CFD). Four cannulas (21 Fr and 23 Fr Bio-Medicus and Maquet models) were modeled in three patient-specific venous vasculatures. These were simulated at 2, 3, 4, and 5 L/min drainage flow rates (N = 48 simulations). To assess potential thrombosis risk, a platelet activation model was implemented along with measurement of prothrombotic flow markers. Increasing drainage flow rates worsened washout rates and increased blood residence times and platelet activation rates. The 21 Fr Bio-Medicus cannula had greater activated platelet distributions and higher tip velocities than the 21 Fr Maquet model. Lastly, patient geometry altered blood residence times, washout rates, and activated platelet distributions, but not flow within the cannulas themselves. These findings will be beneficial for clinicians in their cannula selection and cannulation strategy for VA ECMO, as well as engineers in the development of future drainage cannulas.