A numerical analysis has been performed to investigate the characteristics of two-dimensional transient blood flows interacting with the leaflet motion in a bileaflet mechanical heart valve with different maximum opening angles, located in the aortic position. Here, for one cycle of heartbeat the analysis has been carried out in the light of fluid-structure interaction since the blood flow and the leaflet motion are coupled with each other. Blood has been assumed to be a Newtonian and non-Newtonian fluid, where the Carreau model has been used for the simulation of non-Newtonian fluid. Physiologic ventricular and aortic pressure waveforms have been used as flow boundary conditions at the ventricle and the aorta. A finite volume computational fluid dynamics code and a finite element structure dynamics code have been used concurrently to solve the flow and the structure equations, respectively, where the two equations are strongly coupled. Flow fields, leaflet behavior, and shear stresses with time have been obtained. Also the discharge and the regurgitation flow rates have been calculated. The maximum shear stress, an important issue for valve hemodynamic analysis, has been found in the vicinity of the contact point where a leaflet contacts with housing in the final stage of the closing phase.