Harmonic Analysis: Elementary Pipe and Collar Models - Measurement While Drilling Signal Analysis, Optimization and Design - page 91

It is important that we understand how different sources of experimental
error may arise in our use of Case (d) results. In particular:
(1) We have mathematically assumed that “x = 0” was our dipole source.
In practice, the siren stator-rotor and electric drive system may be as much
as 1 foot long and is not “x = 0.” To minimize measurement error, the use
of a longer wind tunnel is preferred, say 100-200 feet. It is not necessary
to use the very long, 2,000 ft wind tunnel described later for evaluating
many telemetry concepts - a simple 100-200 ft pipe with a blower and a
piezoelectric pressure transducer suffices.
(2) If the dipole source were an electric speaker, the pressures p 1 and p 2
will be perfectly antisymmetric because there are no other sources of noise.
However, when a mud siren is used, there is turbulent flow noise upstream
of the stator, and downstream of the rotor, there exists turbulence noise
plus strong pressure oscillations due to a swirling vortex motion imparted
by the turning rotor. Measured pressures will be acoustic ones calculated
in this topic, plus these additional sources of noise. In order to measure
acoustic 'p's properly, the noise on each side of the siren should ideally be
filtered. The noise upstream of the stator is probably simpler to filter out -
one might attempt a white noise or a Gaussian noise filter. The noise
downstream of the rotor is more challenging. There is a periodic
component due to the acoustics, but also a periodic component of the same
frequency due to vortex motions (to visualize these motions, one might use
the “ball in cage” method described in Chapter 9). This vortex component
can be removed by placing flow straighteners just downstream of the rotor.
These straighteners might occupy an axial distance of, say, 3-4 inches. A
differential pressure transducer can be used to obtain 'p directly, with one
end of the transducer placed just upstream of the stator and the other
downstream of the flow straighteners. Of course, the method of Case (d)
assumes that a differential transducer is not used, and that p s is to be
calculated from “p” obtained at a location “x.”
(3) Again, the recommendation is to use piezoelectric pressure data
upstream of the stator as it is less noisy and does not contain the swirling
effects of the flow downstream of the rotor. However, it should not be
located at the ends x = ± L because acoustic pressure vanishes at this
locations; it is preferable, for example, to select an upstream location
midway to the blower, say, x = - ½ L, in order to avoid downstream noise
associated with the swirling rotor vortex flow having the same frequency.
Turbulence noise may need to be filtered before calculating p s from
Equation 3.A.14.