Granular Matter (2008) 10:63–73 DOI 10.1007/s10035-007-0077-8 Granular temperature in a gas fluidized bed Mark J. Biggs · Don Glass · L. Xie · Vladimir Zivkovic · Alex Buts · M. A. Curt Kounders Received: 25 February 2007 / Published online: 6 November 2007 © Springer-Verlag 2007 Abstract The mean square of particle velocity fluctuations, δv 2 , which is directly related to the so-called granular tem- perature, plays an important role in the flow, mixing, segre- gation and attrition phenomena of particulate systems and associated theories. It is, therefore, important to be able to measure this quantity. We report here in detail our use of diffusing wave spectroscopy (DWS) to measure the mean square particle velocity fluctuations for a 2D non-circulating gas fluidized bed of hollow glass particles whose mean dia- meter and effective density are 60 μm and 200 kg/m 3 , res- pectively. Mean square particle velocity fluctuations were observed to increase with superficial velocity, U s , beyond the minimum fluidization velocity. Following the uniform fluidization theory of Batchelor (1988), the function f (φ) in the expression δv 2 = f (φ)U 2 s was also determined and shown to increase from zero at a solids loading of φ ≈ 0.33 to a maximum at φ ≈ 0.4 before decreasing again to zero at φ ≈ 0.53. The spatial variation of the mean square particle velocity fluctuations was also determined and shown to be approximately symmetrical about the centreline where it is also maximal, and to increase with height above the distri- butor. Keywords Granular temperature · Velocity fluctuations · Kinetic theory · Erosion · Heat transfer · Granulation · Diffusing wave spectroscopy · Fluidized bed M. J. Biggs (B ) · D. Glass · L. Xie · V. Zivkovic · A. Buts Institute for Materials and Processes, University of Edinburgh, King’s Buildings, Mayfield Road, Edinburgh EH9 3JL, Scotland, UK e-mail: M.Biggs@ed.ac.uk M. A. Curt Kounders School of Mathematics, Kingston University, Penrhyn Road, Kingston-on-Thames, KT1 2EE Surrey, England, UK 1 Introduction Granular flows in which the particulate motion involves successive ballistic flights between predominately binary col- lisions occur widely—just two examples are fluidization and pneumatic conveying of powders. The similarity between such “rapid granular flow” and the behaviour of dense gases has lead to the development of inelastic kinetic theories [1–4] akin to those established for the former many years ago [5, 6]. There are a number of key fundamental quantities required for the evaluation of the constitutive parameters of these theo- ries. One of them is the so-called “granular temperature”, which is a quantity that is proportional to the square of the particle velocity fluctuations about the mean [1, 2]. The cen- tral role played by this quantity in the kinetic theories of rapid granular flow [7] and models for other phenomena (e.g. heat transfer [8], granulation [9] and erosion [10]) in such flows means the validation of these theories requires its measure- ment. A range of methods have been used over the past 15 or more years to measure the granular temperature for a variety of systems. The first attempts involved use of fibre optic probes to measure streamwise velocity fluctuations in 3D chute flows [11, 12], a method also used later to study gra- nular flow in a rotating drum [13]. The intrusive nature of this method and its restriction to a single direction means it has seen limited application. Computer-aided analysis of video images is the most widely used non-intrusive means of determining granular temperature—it has been used to study granular flows down chutes [14–19], granular mate- rials undergoing slow shear [20–26] and a variety of fluidi- zed beds [27–37]. The restriction of the video image analysis approach and other optical methods such as laser Doppler velocimetry [38] to dilute systems or the surfaces of dense systems has motivated some to develop the application of 123