Sources
& Remedies of High Frequency Piping Vibration & Noise
S. M. Price and D. R. Smith, 28th Turbomachinery Symposium,
The Turbomachinery Laboratory, Texas A&M University, Houston,
TX, September 1999.
In large diameter piping, high-frequency energy can produce excessive
noise and vibration, and failures of thermowells, instrumentation,
and attached small-bore piping. In severe cases, the pipe itself
can fracture. Perhaps more precisely called “high wave number”
problems, these problems most often manifest themselves in centrifugal
compressors, screw compressors, heat exchangers, and silencers.
Two high-frequency
energy generation mechanisms predominate in most industrial processes;
flow induced (vortex shedding) and pulsation at multiples of running
speed (blade-pass in centrifugal compressors and pocket-passing
frequency in screw compressors). Once this energy is generated,
amplification may occur from acoustical and/or structural resonances,
resulting in high amplitude vibration and noise.
To resolve
these problems successfully, an understanding of the underlying
physics of two- and three-dimensional acoustics is necessary.
With these principles in mind, modifications to the piping system
can be considered for the particular application. The three-dimensional
wave equation is used to analyze the propagation of the high-order
(cross-wall) acoustical modes in the duct or pipe. These cross-wall
modes can be diametrical (m) modes, annular (n) modes, or combined
(m, n modes). By reformulating the resulting differential equations
into polar coordinates and applying the appropriate boundary conditions,
an equation for the “cut-on” frequencies, ƒ(m,
n), for cross-wall modes can be developed that incorporates zeros
of the first order Bessel function, ß(m, n), the speed of
sound, and pipe diameter. Several references provide lists of
the zeros of the Bessel function; however, most of these references
only provide solutions up to m, n = 6. Field tests have identified
cross-wall modes up to m = 30. Therefore, a table is provided
for zeros of ß(m, n) for m = 0 to 32 and n = 0 to 8.
This paper
discusses the excitation and amplification mechanisms relevant
to high-frequency energy generation in piping systems. Mechanisms
that allow efficient coupling of this energy with the surroundings
(either structural or acoustical) are discussed. Data from various
systems are presented, as well as design modifications that have
been shown to be effective at reducing the high-frequency energy.
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