## 3 Results and Discussion  
### Flow Characteristics of the Bileaflet Mechanical Heart Valve  
Figure 4 shows the motion of the leaflets. Initially, leaflets of the valve are in a closing stage. When the inlet pressure increases rapidly and is higher than the outlet pressure at about 0.155 s, leaflets begin to open. When the time reaches about 0.219 s, the leaflet reaches the fully opened stage. When the time reaches about 0.35 s, the leaflet starts to close because the outlet pressure is higher than the inlet pressure. These four stages, respectively, make up of 8.5%, 16.1%, 4.7% and 70.7% of the total period. It can be found that the closing time of the valve is shorter than opening time. It is caused by the difference between the inlet pressure and outlet pressure. The pressure difference is getting larger and larger and leads to the high-speed of valve leaflets during the closing process. Figure 3: Velocity distribution with different kinds of mesh regimes. Figure 5 shows the velocity distribution on the middle plane at different times during the motion of valve leaflets. Time \(a\) indicates that leaflets are in the opening process; time \(b\) indicates that the valve has just reaches the fully opening stage; time \(c\) indicates that the inlet pressure just equals to the outlet pressure; time \(d\) indicates that the valve starts to close; time \(e\) indicates that leaflet is about to close fully. From Figure 5, the flow inside the model likes three orifice flows, owing to the existence of the two leaflets. At the beginning of leaflets rotating, the velocity of orifice flows on both sides is higher than  
Figure 4: The motion of the leaflets in a cycle and streamlines. Figure 5: The variation of velocity in the middle of the channel. that in the middle orifice. As leaflets approach the fully opening stage, the fluid velocity in the middle orifice increases significantly and is larger than that in side orifices. In the meantime, the force acting on the leaflets decreases, so the movement speed of the leaflets decreases. When the outlet pressure is larger than the inlet pressure, the mechanical heart valve starts to close and the flow velocity in the blood vessel starts to decrease. When the leaflets are in the closing stage, the fluid behind the valve is basically blocked by leaflets with a strong leakage flow between the leaflets and the valve housing. Figure 6 shows the pressure distribution on the middle surface at different times, where time \(f\) indicates the valve just reaches the fully closing stage. As can be seen from the Figure 6, during the opening and closing processes of the valve, the pressure is larger than the saturated vapor pressure of blood, indicating that there is no cavitation in the opening stage. When the leaflet just reaches the fully closing stage, as shown in moment \(f\) in Figure 6, the pressure has a dramatical variation at the tip of leaflets. The downstream pressure of the valve increases to near 1 MPa, which is about 10 times that of the normal pressure in the model, while the upstream pressure of the valve is significantly reduced to the saturated vapor pressure. The sharp increase of downstream pressure due to valve closing is a common phenomenon of water hammer in hydrodynamics. It indicates that the occurrence of water hammer may be the cause of cavitation in the bileaflet mechanical heart valve. Figure 7 shows the pressure distribution near the valve leaflet at four different times after the valve is closed. It can be found that after the valve closing, the downstream pressure of the valve leaflet back to normal level, which means the effect of water hammer decreases rapidly in a short time. However, the minimum upstream pressure of the valve is still the saturated vapor pressure, indicating that the occurrence of cavitation is also affected by other factors. From the pressure distribution near the leaflet at 230 microseconds after the valve closing, it can be found that the low-pressure area inside the valve decreases gradually and disappears eventually.