Siren Design and Evaluation in Mud Flow Loops and Wind Tunnels - Measurement While Drilling Signal Analysis, Optimization and Design - page 250

reverberate continuously to develop the solutions above. It is easily verified that
p 1 = 0 at x = - L and p 2 = 0 at x = +L. Also, the acoustic pressure is
antisymmetric with respect to the x = 0, where the 'p is maintained. This is a
very important solution for wind tunnel testing determination of 'p. It allows
placement of a single (not differential) piezoelectric transducer anywhere, at any
position “x” for measurement of the “p,” which includes the effects of all
reflections needed to set up the standing wave. In wind tunnel applications,
standing waves are set up within seconds.
Then, depending on whether Equation 3-A-14 or 3-A-15 is used, we can
solve for the p s representing “delta-p” in “p 2 - p 1 = p s e i Zt ” directly. This is
repeated for different values of Z. It is important to understand that different
sources of experimental error and consideration will arise. In particular,
(1) We have mathematically assumed that “x = 0” was our dipole source.
In practice, the siren stator-rotor and electric motor drive may be as much
as 1 foot long and is not located at the point “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, very long wind tunnel - a
simple 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 associated with the blower, and also, turbulent flow noise plus
strong pressure oscillations due to a swirling vortex motion imparted by
the turning rotor in the downstream (the frequency of the downstream
vortex noise will be identical to that of the acoustic signal). In order to
measure acoustic 'p properly, the noise on each side of the siren may need
to be filtered. The noise upstream of the stator might be eliminated using
white noise or Gaussian noise filters. The noise downstream of the rotor,
associated with a rotating flow, is more challenging (this rotating flow is
easily observed using the flow visualization techniques described
previously). However, the analog use of flow straighteners should
satisfactorily filter this effect.
(3) Again, two means of acquiring 'p data are recommended although not
required, namely, single pressure transducer and differential transducer
methods. In either case, sensitive piezoelectric gauges should be used that
are connected to oscilloscopes, signal analyzers and data recorders. These
redundant measurements provide useful checks for experimental error and
also provide increased physical insight which is invaluable in research. In
the case of single pressure transducer testing, we recommend the use of
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.