We're working with a vibrating system driven by high velocity flow through a valve. CAESAR Tech Reference, page 5-4, discusses acoustic vibration: “For example, Strouhal’s equation predicts that the developed frequency (Hz) of vibration caused by flow through an orifice will be somewhere between 0.2 V/D and 0.3 V/D, where V is the fluid velocity (ft./sec.) and D is the diameter of the orifice (ft)”. Is there a further reference for this statement?

In which direction does this vibration act; axially or laterally?

For magnitude of force, we have acceleration in g's and frequency of 2400Hz. Can we use F=ma using mass of the valve?

How do we combine static and dynamic analyses to look at forces if we anchor the valve?

We're using version 4.40.

The Strouhal number is a function of geometry and Reynolds number for low Mach number. It will vary from 0.2 to 0.5 with the pipe system flow. You may get more detail information in the references. An old memory comes back to my mind is Blevins,R.D., “Vortex-Induced Vibration” in Flow Induced Vibration, Chapter 3, NewYork, Van Nostrand Reinhold, 1977.

Where vortex shedding is a potential source of pipe vibration, the wide range of Strouhal number makes exact prediction of vortex shedding frequencies difficult. My understanding is the vortex shedding normally results in low-amplitude pressure pulsations, and no problem occurs unless these pulsations coincide with a piping acoustical and/or piping natural (structural frequency) resonance. The vortex tends to lock into a close piping acoustical frequency, and the pressure pulsation can then be greatly amplified. In my past experience, which is limited to the fields of nuclear power plant and petrochemical plants, this type of resonance has been encountered rarely in steam relief and safety relief valve installation. The symptoms of this type resonance are excessive vibration and noise near the relief valve. Eliminating or reducing vortex shedding pulsations is accomplished by modifying the flow restriction or changing the piping acoustical frequency.
In the absence of pressure pulsation, the pressure acting on each elbow produces opposite and equal to the pressure(P) times the piping inside area(A). These pressure loadings cause longitudinal pressure stress in the piping but do not result in unbalanced pressure force. When the pressure pulsations induced by vortex shedding travel through the piping at any instant in time, the pressure on one elbow may not equal the the pressure on the other elbow of the pipe segment leg. This results in an unbalanced force in the pipe leg. This Unbalanced force(F) can be roughly determined as below;

F=differential pressure of each pipe segment(delta P) x pipe inside area(A).

These forces act at each elbow and resultant loading on a particular pipe segment or straight length of piping is equal to the vector addition of these loadinga. The resultant unbalanced loading on straight leg of piping can be considered to act along the axial direction of piping. That is, these forces can be applied at each elbow as the pipe axial force in Caesar II static analysis(with DLF) or dynamic analysis(as harmonic term).

In the piping system with control valve/or restriction orifice, I think, cavitation and flashing are more commonly experienced than vortex shedding. My practice is always to add guide/anchor supports to the downstream of control valve manifold.

I hope that other members can give better idea and advice with his/her experience in the vortex shedding in your valve system.

Sun Wee

From your initial question I am not sure it this is an existing piping system or is this a design problem. Your available approaches to this problem are quite different.

I do not believe that the rules for predicting vortex shedding hold true for the noise in control valves. From my memory vortex shedding requires laminar flow. Control valve flow will be anything but laminar.

I have yet to come across any methods for predicting forces from control valves. The common methods all start with predicting the noise in the fluid just downstream of the control valve. This can generate two different types of stress problems; 1/ local stress, particularly on large diameter thin wall pipe or small bore branch connections; 2/ acoustic waves coupling with piping system natural frequencies causing piping to vibrate (the type of thing that Caesar calculates).

Hope this has helped.

To clarify - this is a problem with an existing piping system that has existed for several years. It was revealed when we installed electronic position feedback sensors on the valve to replace old mechanical feedback potentiometers. We first attempted to reduce pressure drop across the valve by adding a longer run of pipe downstream along with expansions from 12" to 18" and 18" to 24". We reduced the downstream vibrations, but still have the high vibration at the valve.