Response characteristics of probe-transducer systems for pressure measurements in gas-solid fluidized beds: how to prevent pitfalls in dynamic pressure measurements
Jr. Van Ommen et al., Response characteristics of probe-transducer systems for pressure measurements in gas-solid fluidized beds: how to prevent pitfalls in dynamic pressure measurements, POWD TECH, 106(3), 1999, pp. 199-218
It is long known already that the pressure probe-transducer systems applied
in gas-solid fluidized beds can distort the measured pressure fluctuations
. Several rules of thumb have been proposed to determine probe length and i
nternal diameter required to prevent this. Recently, Xie and Geldart [H.-Y.
Xie, D. Geldart, Powder Technol. 90 (1997) 149] proposed 4 mm i.d. probes
as a panacea for all practical situations encountered. However, almost no i
nformation is available in the literature that relates possible distortions
to characteristics to be extracted from the pressure signal. This paper re
ports the influence of probe dimensions on the outcomes of different data a
nalysis methods for fluidized bed pressure signals (spectral analysis, stat
istical analysis, and chaos analysis). It reviews the most important probe-
transducer models and compares them on the basis of experiments with both n
oisy (i.e., highly turbulent gas phase) pressure time-series, and pressure
time-series measured in a bench-scale fluidized bed. The comparison is carr
ied out by determining the frequency response function in the frequency dom
ain. It is shown, that the Bergh and Tijdeman model [H. Bergh, H. Tijdeman,
Theoretical and experimental results for the dynamic response of pressure
measuring systems, Report NLR-TR F.238, National Aero- and Astronautical Re
search Institute, Amsterdam, the Netherlands, 1965] is superior to all othe
r models reported in literature. The Bergh and Tijdeman model, originally d
eveloped for wind-tunnel testing, is the only model that gives a good predi
ction of the frequency response characteristics of a probe-transducer syste
m for a wide range of probe dimensions. In this paper, rules of the thumb s
upported by this model will be given. It is found that for statistical anal
ysis and chaos analysis, probes up to 2.5 m length with an internal diamete
r ranging from 2 to 5 mm do not severely effect the analysis results, since
these are mainly focused on frequencies up to about 20 Hz. However, in gen
eral, it is preferable to keep the probe length as short as possible. in th
e case of spectral analysis, the demands on the probe dimensions depend on
the frequency range of interest: if one is interested in a frequency range
up to 200 Hz (e.g., when studying the power-law fall-off in the power spect
ral density), the probe length should be limited to about 20 cm. The result
s reported in this paper are obtained using a transducer with an internal v
olume of 1500 mm(3), but it is shown that the conclusions on the probe dime
nsions are valid for a wide range of transducer volumes. The experiments ar
e carried out in an 80-cm i.d. bench-scale fluidized bed of sand (median di
ameter 470 mu m, Geldart type B); for smaller particles and smaller scale i
nstallations, the frequency range of interest will shift to higher frequenc
ies. In that case, the optimal probe diameter stays in the range from 2 to
5 mm, but it will become even more important to keep the probe length limit
ed; this can be calculated with the Bergh and Tijdeman model [H. Bergh, H.
Tijdeman, Theoretical and experimental results for the dynamic response of
pressure measuring systems, Report NLR-TR F.238, National Aero- and Astrona
utical Research Institute, Amsterdam, the Netherlands, 1965]. The experimen
ts presented in this paper are carried out at ambient pressure and temperat
ure. However, since the Bergh and Tijdeman model contains no fitted paramet
ers, it is expected to give a reliable estimate for the probe-transducer ch
aracteristics at other operating conditions as well; the effect of the temp
erature is shown in this paper. (C) 1999 Elsevier Science S.A. All rights r
eserved.