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I wanted to know that there have been a handful of literature that mentions vent openings in the rocket payload fairings. However, none specify the kind of valves used in those fairings? does anyone know what valves are used in such fairings and how do they operate?

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Answer: Butterfly Valves.

I found references to both valved and unvalved payload fairing (PLF) vents. Apparently the valves (if used) control the rate of pressure drop. Within the PLF are a number of compartments. If the rate of pressure drop exceeds their ability to vent, it places stress on those compartments. Consider honeycomb panels. Every cell in the honeycomb has its own vent hole. The payload may also have limits on pressure drop rate.

The Falcon9 limits PLF pressure drop rate. From the User's Manual:

Inside the Falcon launch vehicle, the payload fairing internal pressure will decay at a rate no larger than 0.40 psi/sec (2.8 kPa/sec) from liftoff through immediately prior to fairing separation, except for brief periods during flight, where the payload fairing internal pressure will decay at a rate no larger than 0.65 psi/sec (4.5 kPa/sec), for no more than 5 seconds.

https://www.spacex.com/media/falcon-users-guide-2021-09.pdf p38

At the same time, the PLF vent rate needs to be high enough to keep the pressure differential on the PLF within design limits. Butterfly valves are used to keep pressure drop rates within specified limits.

The performance characteristics of a vent valve with a spring-loaded door has been evaluated for Korea space launch vehicle-II by Oh et al., [18]. Singh [19] https://www.researchgate.net/publication/324163616_Vent_Valve_for_Test_Launch_Vehicle_of_Korea_Space_Launch_Vehicle_II

https://saspublishers.com/article/6033/download Scholars Journal of Engineering and Technology Review of Vent Systems of Space Vehicle, Spacecraft and Aircraft Fig 17 shows housing and butterfly valve

enter image description here

This spring-loaded butterfly valve bears a striking resemblance to the common barometric damper found on boiler chimneys. These are designed to self-regulate the pressure difference across the wall of the flue pipe. In PLF, the butterfly valve serves the same function: it maintains a constant pressure difference across the wall of the PLF as the ambient pressure falls.

enter image description here

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