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 internal 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 information is available in the literature that relates possible distortions to characteristics to be extracted from the pressure signal. This paper reports the influence of probe dimensions on the outcomes of different data analysis methods for fluidized bed pressure signals (spectral analysis, statistical analysis, and chaos analysis). It reviews the most important probe–transducer models and compares them on the basis of experiments with both noisy (i.e., highly turbulent gas phase) pressure time-series, and pressure time-series measured in a bench-scale fluidized bed. The comparison is carried out by determining the frequency response function in the frequency domain. 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 Research Institute, Amsterdam, the Netherlands, 1965] is superior to all other models reported in literature. The Bergh and Tijdeman model, originally developed for wind-tunnel testing, is the only model that gives a good prediction of the frequency response characteristics of a probe–transducer system for a wide range of probe dimensions. In this paper, rules of the thumb supported by this model will be given. It is found that for statistical analysis and chaos analysis, probes up to 2.5 m length with an internal diameter 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 general, it is preferable to keep the probe length as short as possible. In the 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 spectral density), the probe length should be limited to about 20 cm. The results reported in this paper are obtained using a transducer with an internal volume of 1500 mm3, but it is shown that the conclusions on the probe dimensions are valid for a wide range of transducer volumes. The experiments are carried out in an 80-cm i.d. bench-scale fluidized bed of sand (median diameter 470 µm, Geldart type B); for smaller particles and smaller scale installations, the frequency range of interest will shift to higher frequencies. 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 limited; 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 Astronautical Research Institute, Amsterdam, the Netherlands, 1965]. The experiments presented in this paper are carried out at ambient pressure and temperature. However, since the Bergh and Tijdeman model contains no fitted parameters, it is expected to give a reliable estimate for the probe–transducer characteristics at other operating conditions as well; the effect of the temperature is shown in this paper