What is the frequency of axial flow induced vibration in bellows

[Shridhara12]

Fuel is flowing in a piping system passes through bellows. Does this induces any vibrations in the bellows?.If Yes what will be the frequency of the excitation. The bellows upstream has a valve and down stream is a T joint.The flow velocity is just around sonic speed.

Thanks

 

[EnglishMuffin]

Do you have a physical example of this ? If you stop the flow, and the vibration ceases, then you have your answer!
I would say that, if the vibration is caused by the fluid acting directly on the bellows, it would be a very difficult thing to calculate, especially if it involves turbulence. If you can identify the major mode shape using high speed photography, and its a relatively simple mode, the natural frequency might very roughly correspond to that of a beam with a distributed mass (the fuel fluid), where the axial and/or bending stiffness of the beam is equated to the matching stiffness of the empty bellows - but its a long shot.

 

[Shridhara12]

Hi Muffin,
Thanks for the reply, I have the test measured data.This is a problem faced in power system fuel line. The vibration definatly stops if the fuel is cut off. But I was curios to calculate the frequency,by some equations.


Thanks
Shridhara.G.H

 

[EnglishMuffin]

There's one caveat to the first part of my answer - if you happened to stop the flow by stopping a pump, and the vibration happened to be caused by mechanical vibration of the pump, you would be misled.

 

[Shridhara12]

There is no pump there !!!! Pump is somewhere away very away....

 

[EnglishMuffin]

Well, I would personally be reluctant to say how you could calculate the frequency without knowing exactly what the mode shape was, or even the static shape. Provide more details. Is it a concertina type ? Is it all metal ? How long ? Is it round ? What diameter ? Is it arranged in an offset or curved configuration ? If you excite the bellows with a light tap, when the flow is turned off but the bellows is full of fuel, does the frequency and/or mode of vibration (if any) correspond to the induced vibration during flow conditions ?

 

[EnglishMuffin]

One other thing you need to try and determine before proceeding is whether the vibration originates in the bellows itself. It seems certain that the vibration is caused by the fluid, from what you have said, but the bellows may be being excited by the adjacent pipes. Alternatively, it could be a "water hammer" effect.

 

[Franko]

This sounds like a class question - assume sonic velocity is for a fuel gas - no one I know would have such a high velocity in a pipe - unless it was venting. In any event high speed flows for gas should have an internal liner for a bellows. For suggested cautions (also contact expansion joint manufacturers) - see:

http://www.gramya.com/sample_JPEP.htm