What is the force on a poppet valve due to expanding air?

[tommy101]

I need help with the following problem. I have attached a rough sketch showing what I'm looking at. Basically a popppet valve is closed over a vent. It is then pushed open by a force applied to the valve by the pushing rod. Their is a spring on the rod resisting this and providing a force labeled Fspring. The air inside the container at P1 is then expanding from rest through the valve to Pa (atmospheric). What i am trying to work out, and can't find a formula anywhere for, is what the force on the poppet valve will be due to the expanding air (Ffluid). I'm trying to model this system and currently the valve won't stay open as i can't compute the force on the poppet valve accuratley.

 

[Cyrus]

The spring force, equal and opposite.

 

[tommy101]

The spring force, equal and opposite.

Yes it will be when the valve initially opens. But the pressure in the bag (P1) then decreases, the mass flow through the poppet will decrease, so the force on the poppet will decrease. Thats what I'm trying to work out. I need to know the force on the poppet to work out when the valve closes again.

 

[Cyrus]

The valve will close when the pressure force is less than the force needed to deflect the spring.

 

[Q_Goest]

In designs like you show, the velocity of the fluid increases as it aproaches the curtain area, so the pressure across the face of the poppet drops (think Bernoulli's principal) even though you may not measure a decrease in pressure directly upstream of the poppet. The result is the force on the poppet will decrease with increased flow.

Things can be done to change this. Relief valves for example, have a 'huddling chamber' downstream of the curtain area which effectively increases the area, resulting in a higher force on the poppet from the fluid which pops the valve open (even though the spring load also increases per k*dx). Similarly, adjusting poppet and valve geometry can provide different pressure forces on the poppet as the valve opens. Careful control of the geometry can change the pressure load as a function of lift.