Non-intrusive determination of bubble and slug length scales in fluidized beds by decomposition of the power spectral density of pressure time series J. van der Schaaf a,b,* , J.C. Schouten b , F. Johnsson c , C.M. van den Bleek a a Chemical Reactor Engineering Section, Department of Chemical Process Technology, J.M. Burgers Centre for Fluid Mechanics, Delft University of Technology, Julianalaan 136, 2628 BL Delft, Netherlands b Laboratory of Chemical Reactor Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands c Department of Energy Conversion, Chalmers University of Technology, S-412 96 G€ oteborg, Sweden Received 30 November 1999; received in revised form 29 November 2001 Abstract In this paper we show that spectral analysis of non-intrusive time dependent pressure measurements in bubbling and circulating gas–solid fluidized beds permits to obtain the first estimates of bubble, gas slug, and solids cluster length scales from pressure fluctuation data. These length scales are calculated from the incoherent cross power spectra of pressure signals measured in the bubbling or circulating bed and in the plenum. Remarkable quantitative agreement with bubble diameter data is found, and equally remarkable agreement is obtained with independent estimates of gas slug lengths by others in circulating fluidized beds. These results demonstrate the possibility of greatly expanding the information that can be obtained non- intrusively from gas–solid fluidized beds. Ó 2002 Published by Elsevier Science Ltd. Keywords: Fluidization; Bubble size; Slug size; Pressure; Power spectral density; Coherence 1. Introduction A gas–solid fluidized bed is a commonly encountered reactor type in chemical industries for, e.g., efficiently contacting gaseous reactants with catalyst particles. Because the performance of a fluidized bed is highly dependent on the hydrodynamic state of fluidization, fluidized bed hy- drodynamics have been the subject of study for many years now. International Journal of Multiphase Flow 28 (2002) 865–880 www.elsevier.com/locate/ijmulflow * Corresponding author. Address: Laboratory of Chemical Reactor Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands. Tel.: +31-40-247-4712; fax: +31-40-244-6653. E-mail address: j.vanderschaaf@tue.nl (J. van der Schaaf). 0301-9322/02/$ - see front matter Ó 2002 Published by Elsevier Science Ltd. PII:S0301-9322(01)00090-8