Investigation of the particle–particle drag in a dense binary fluidized bed Zhongxi Chao a, ⁎, Yuefa Wang a , Jana P. Jakobsen b , Maria Fernandino c , Hugo A. Jakobsen a a Department of Chemical Engineering, 7491 Trondheim, Norway b SINTEF Energy, 7491 Trondheim, Norway c NTNU Department of Energy and Process Engineering, 7491 Trondheim, Norway abstract article info Article history: Received 14 June 2011 Received in revised form 5 March 2012 Accepted 10 March 2012 Available online 17 March 2012 Keywords: Size segregation Dense fluidized bed Binary particle drag Frictional drag Kinetic theory of granular flow The behavior of seven binary particle drag closures from the literatures which have been derived based on the kinetic theory of granular flows (KTGF) for the application to fluidized beds are investigated using a binary KTGF model. The dynamic size segregation experimental data from the literature is used to validate the simulation re- sults. The validations show that all of the seven binary particle drags under-predict the binary particle coupling in the dense fluidized bed, satisfactory results could be obtained if an extra semi-empirical frictional binary particle drag is included. The semi-empirical frictional binary particle drag considering the long term particle–particle con- tact effects is a correction of the short term collisional frictional binary particle drag from Syamlal. Furthermore, a group of comprehensive calculations shows that the model using the semi-empirical frictional binary particle drag can fairly well predict the particle segregation rates and the bed heights of the individual particles with a change of gas fluidization velocity, the initial bed height, and the small particle ratio with the same fixed correction coeffi- cient. Therefore, it is proposed that the frictional binary particle drag which represents the binary particle momen- tum exchange due to the long term particle contacts (sliding/rolling) must be included in order to model dense binary fluidized beds. © 2012 Elsevier B.V. All rights reserved. 1. Introduction Fluidized beds are widely used in many industrial processes. In some applications, there exist two types of particles with completely different physical properties (for example particle density and size). Previous experimental investigations [1–6] show that the binary particles could segregate due to the property differences under some operation conditions, the small, light particles called flotsam tend to rise, and the large, heavy particles called jetsam tend to sink. In order to describe the flow behaviors, some computational fluid dynamic models have been established. Among these models, the KTGF Eulerian–Eulerian multi-fluid models are often used. The KTGF is based on an analogy to the classical kinetic theory of gases. The basic particle billiard ball collision theory and some statistical methods are adopted to obtain continuity equations, Navier–Stokes-like momentum equations and other transport equations. Lun et al. [7], and Gidaspow [8] successfully applied the theory to a mono-particle system. Gidaspow et al. [9], Syamlal [10], Bell [11], Lathouwers and Bellan [12], Chao et al. [13], Lu et al. [14–16], Iddir et al. [17,18], Jenkins and Mancini[19], Gidaspow et al. [20], Manger [21] and Mathiesen et al. [22] put forth or applied some KTGF models for binary or poly- dispersed problems. The KTGF model constitutive equations consider based on the short term particle–particle collisions and translational motions. The- oretically, these constitutive equations are suitable for describing the rapid flows. In dense beds at low shear rates, the stress generation mechanism is more likely due to the long term particle–particle con- tacts such as sliding and rolling which cause large amount of energy being dissipated [23]. This effect should also be included in models describing dense fluidized bed behaviors. A common approach is to add a frictional term to the model [12,23,24] for both mono- and binary-particle systems. This treatment is thus adopted in the frictional KTGF model in the present paper. Compared with mono-particle models, the binary particle drag is a novel term which considers the binary particle momentum coupling. In the literature, seven binary particle drag expressions which are de- rived based on the KTGF are found [9–18]. The proposed expressions deviate somewhat as different integral methods are used, and various terms are neglected in the integral calculations. For example, the bi- nary drags from Gidaspow et al. [9], Syamlal [10] and Bell [11] neglect the effects of particle fluctuations, so no granular temperature occurs in these closures. On the other hand, the four binary drags from Lathouwers and Bellan [12], Chao et al. [13], Lu et al. [14–16] and Iddir et al. [17,18] include this effect. The particle sliding effect during the particle collisions is only considered in the expression given by Syamlal [10]. The binary particle coupling due to the differences of other properties than the velocities, are only considered by Lathouwers and Bellan [12], Lu et al. [14–16] and Iddir et al. [17,18]. Theoretically, these seven expressions are only valid for dilute binary Powder Technology 224 (2012) 311–322 ⁎ Corresponding author. E-mail addresses: realizedream@hotmail.com, chao@chemeng.ntnu.no (Z. Chao). 0032-5910/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2012.03.013 Contents lists available at SciVerse ScienceDirect Powder Technology journal homepage: www.elsevier.com/locate/powtec