Native heart valves with limited functionality are commonly replaced by a bileaflet mechanical heart valve (BMHV). However, despite their widespread use, BMHVs still cause major complications, including hemolysis, platelet activation, and thromboembolic events. These complications are believed to be due to the non-physiologic hemodynamic stresses imposed on blood elements by the hinge flows. Three-dimensional characterization of the hinge flows is therefore crucial to ultimately design BMHVs with lower complication rates. This study aims at simulating the pulsatile 3D hinge flows of various BMHVs placed and estimating the thromboembolic potential associated with each hinge. The hinge and leaflet geometries of clinical BMHVs are reconstructed from micro-computed tomography scans. Simulations are conducted using a Cartesian sharp-interface immersed-boundary methodology combined with a second-order accurate fractional-step method. Physiologic flow boundary conditions and leaflet motion are extracted from the Fluid-Structure-Interaction simulations of the BMHV bulk flow. The accuracy of the solver is assessed by comparing the results with experimental data. The numerical results are analyzed using a particle tracking approach coupled with existing blood damage models to relate the flow structures to the risk for blood damage. Calculations reveal complex, unsteady, and highly 3D flow fields. Zones of flow stagnation and recirculation, favorable to thrombosis and regions of elevated shear stresses, which may induce platelet activation, are identified throughout the hinge and cardiac cycle. The hinge gap width and, more importantly, the shape of the hinge recess and leaflet are found to impact the flow distribution. Avoiding sharp corners or sudden shape transitions appear as key geometrical design parameters to minimize flow disturbances and thromboembolic potential. The computed flows underscore the need to perform full 3D pulsatile simulations throughout the cardiac cycle to fully capture the complexity and unsteadiness of the hinge flows. Though based only on three different designs, this study provides general guidelines to optimize the hinge design based on hemodynamic performance and thromboembolic potential. The developed framework enables rapid and cost-efficient pre-clinical evaluation of prototype BMHV designs prior to valve manufacturing. Application to a wide range of hinges with varying design parameters will eventually help in determining the optimal hinge design.