# Check-Valve Design in Enhancing Aerodynamic Performance of Flapping Wings
## 4 Discussion
### The Driving Force for Opening the Check-Valve  
The check-valve is passive and it need not require external power for opening. In the conceptual design stage, shown in Figure 11a,b, it was initially considered to be the aerodynamic pressure difference that pushed the valve disc-cap open. The direction of air flowing through the valve is designed to flow from the central orifice to the outside of the valve disc-cap, and it opens in during the upstroke period. For this reason, the valve is positioned upside down on the back of the wing membrane, and the inlet air flows from top to bottom during the upstroke. Hence, the valve disc-cap is pushed (open) to adjust the lift. In addition, the valve disc-cap is attached upside down; the assistance of gravity helps with valve opening.  
Figure 10: A 2D quasi steady COMSOL flow simulation of flapping wings according to the 30\({}^{\circ}\) inclined fuselage, and with an upstream velocity of 1.6 m/s and flapping frequency of 14 Hz (the total incident velocity is 4.68 m/s): (**a**) flow field of wing membrane with check-valve closing during downstroke, producing a lift of 9.83 gf; (**b**) flow field of wing membrane with check-valve opening during upstroke, producing a lift of \(-\)4.43 gf; (**c**) flow field of 90\({}^{\circ}\)-inclined wing membrane with check-valve opening during upstroke, producing a lift of 3.15 gf.  
The following are the major observations during valve opening: (1) during the upstroke of the flapping wing, the horizontal free stream and the vertical downward airflow, due to flapping, are combined into a total incident velocity, which blows obliquely downward from the head top and it stops flowing in a purely vertical direction; (2) considering the inclined angle of the wing membrane during the upstroke, the inclined angle of the fuselage during the downstroke is no longer effective, but it is instead a nearly vertical pull-up movement. This can be also verified by high-speed photography. Combining the above two considerations (1) and (2), the position of the valve disc-cap is no longer facing back to the inlet airflow, but instead facing forward to the inlet airflow. The direction of the airflow through the valve in Figure 11b, on the contrary, flows from outside of the valve disc-cap into the central orifice as shown in Figure 11c. It is opened in accordance with the time of upstroke. In turn, this causes the leading-edge vortex (LEV) of the wing to be impacted and broken, reducing the lift value during the upstroke. The flow field is also changed in Figure 11c. An interesting observation is that it was originally thought that the lift of the upstroke should be negative, but the instantaneous angle of attack (AOA) of the wing, relative to the inlet airflow, was positive in Figure 11c. As the LEV intensity is reduced by the orifice jet, there is only a slight positive value. Due to this phenomenon, the lift during the upstroke shows a positive trend instead of a negative one, as shown in Figure 7(a2,b2,c2), which explains the first question.  
Due to this, the dominant driving force for opening the check-valve is no longer the aerodynamic pressure difference, but it is the mass inertia of the valve disc-cap itself. When the upstroke starts, the majority of the wing moves upward, but the central valve disc-cap temporarily remains in place due to its mass inertia. The valve is opened until it is largely deformed and pulled up by three S-shaped support beams, and the upstroke ends. When it returned to its reset position, the valve was closed.