Response characteristics of probe-transducer systems for pressure measurements in gas-solid fluidized beds: how to prevent pitfalls in dynamic pressure measurements

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.