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PIPEWALL TRANSMISSION LOSS AS USED IN VALVENOISE PREDICTION
Allen Fagerlund
Fisher Controls International205 South Center Street
Marshalltown, IA 50158
INTRODUCTION
It has become increasingly important in recent years to develop
methods for controlling thenoise which is produced in fluid
transmission systems. The acoustic energy which propagates
throughout the fluid/structural system will radiate from the
surface of the pipe. To evaluate,from external measurements, the
source levels which are present inside the pipe it is necessary
to
have an accurate description of the transmission loss
characteristics of the pipe wall.
DISCUSSION
On a worldwide basis thousands of pipewall transmission loss
(TL) calculations are madedaily as a part of the prediction of
control valve noise. Therefore, it has become necessary to
develop a model, which is easy to apply to the wide variety of
piping systems found in industry.
Transmission loss is typically defined as either the difference
in decibels between the inputpower to the pipe and the power
radiated by the pipe or between the internal and external
meansquare pressures. The two definitions yield identical values
when the internal and external fluids
are the same and a reference length is defined such that the
radiating area is equal to the crosssectional area of the pipe.
The current IEC Control Valve Aerodynamic Noise Prediction
Standard [1] utilizes anapproximate form of the mean square
pressure transmission loss as a function of frequency.
Total internal acoustic power is determined, converted to
pressure, and associated with a peakfrequency which follows from
[2]. Transmission loss is calculated at that peak frequency to
gain
the required external level. There are four important
frequencies that establish approximate ranges for various types
of
transmission loss behavior. 1) Ring frequency - fr - the
frequency at which the longitudinal wavelength is equal to the
circumference of the pipe. 2) Acoustic cut-off frequency - the
lowest frequency at which transverse modes of
propagation can exist in the internal fluid. 3) Internal
coincidence frequency - fo - the frequency at which the internal
acoustic and
structural axial wavenumbers are equal for a given
circumferential mode. 4) External coincidence frequency - fg - the
frequency at which the external acoustic
wavespeed is equal to the velocity of a bending wave in the pipe
wall.
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8/12/2019 Pipewall Transmission Loss as Used in Valve_allen
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As previously mentioned the relationship of the peak frequency
(fp) of the internal source to
the above frequencies determines the TL of the application.
Early work [3] established that above the ring frequency the pipe
responds as a flat plate of
the same thickness as the pipe wall with the effects of
curvature predominant below this point.These results allowed later
research to concentrate below the ring frequency. For most
industrial
piping the frequencies of maximum radiation are dictated by
strong coupling between higherorder internal acoustic modes and
bending modes of the pipe. This is referred to as coincidence
and is of primary interest between the acoustic cut-off
frequency and the ring frequency. Amethod was developed [4] to
calculate the frequencies at which minima occur in the TL
spectrum and incorporated into a TL estimation procedure, which
formed the basis for thetransmission loss terms in the German VDI
Document on piping noise [5]. Due to an
assumption that the ring frequency was less than the external
coincidence frequency, this workwas primarily suitable for
cylinders with low wall thickness to diameter ratios. This results
in a
linear dependence of TL on this ratio. While it is possible to
obtain a direct solution to the equations of motion for each
structural
mode interacting with an acoustic field, this becomes unwieldy
at high frequencies where the
number of modes is very high. An advantage in using a
statistical method for analyzing thisinteraction is that the
response and forcing function parameters are averaged over a
frequencyband. Since detailed characteristics of the structure are
essentially averaged, only the gross
physical parameters are necessary for analysis. This approach
was carried over into large-radius,thin-walled, externally [6],
[7], and internally [8] excited cylinders. The modal interaction
work
was further studied [9], [10], [11], [12], and in all of these
studies the importance of the internalcoincident frequencies was
brought out in regards to the pipe wall response. Experimental
results were presented [13] showing the effects of flow velocity
on transmission loss throughpipe walls commonly used in industry.
An analysis of the effects of uniform flow velocity as
well as internal pressure was developed [11], which in a very
approximate form, is the basis forthe TL terms in the IEC Standard
[1]. This approximate form showed that the TL varied as the
square of the thickness to diameter ratio.
IMPLEMENTATION
Below the cut-off frequency sound propagates only as a plane
wave moving through the fluid,however, above this frequency sound
can propagate in more complex higher order modes which
tend to travel with a spiral or helical motion. At the cut-off
frequency the sound wave spinscircumferentially and as frequency
increases an axial component is added which causes
propagation through the fluid in a spiral motion. The same
circumferential modes are present in the pipewall and also develop
an axial
component as frequency increases. These propagate as bending
waves at a velocity which isfrequency dependent. For each mode
order there is a frequency at which the axial bending
wavespeed in the pipe is equal to the axial propagation velocity
in the fluid which is called thecoincidence frequency.
The first internal coincidence frequency was calculated in
50mm(2in) through 600mm(24in)pipe with a variety of wall thickness
and air as the internal fluid. Also, the ring frequency using
the mean diameter was calculated for each pipe. The ratio of the
ring frequency (R) to the firstinternal coincidence frequency ( fo
) was consistently close to 4, which yields the approximate
expression ( fo= R /4 ) in the IEC standard. This frequency is
multiplied by ( c2 /343 ) as an
approximate correction for internal fluids other than air.
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