Extension of Hill–Koch–Ladd drag correlation over all ranges of Reynolds number and solids volume fraction Sofiane Benyahia a, ⁎ , Madhava Syamlal b,1 , Thomas J. O'Brien b,1 a Fluent Incorporated, 3647 Collins Ferry Road, Suite A, Morgantown, WV 26505, United States b US Department of Energy, MS-N04, 3610, Collins Ferry Road, Morgantown, WV 26505, United States Received 27 April 2005; received in revised form 15 November 2005; accepted 12 December 2005 Abstract Hill et al. [R. J. Hill, D.L. Koch, J.C. Ladd, J. Fluid Mech. (2001), 448, pp. 213–241 and 243–278] proposed a set of drag correlations, based on data from Lattice–Boltzmann simulations. These correlations, while very accurate within the range of void fractions and Reynolds numbers used in the Lattice–Boltzmann simulations, do not cover the full range of void fractions and Reynolds numbers encountered in fluidized bed simulations. In this paper a drag correlation applicable to the full range of void fractions and Reynolds numbers is developed by blending the Hill– Koch–Ladd (HKL) drag correlation with known limiting forms of the gas–solids drag function such that the blended function is continuous with respect to Reynolds number and void fraction. This study also corrects a misinterpretation of the HKL drag correlation that was published in the literature, which makes the drag function discontinuous with respect to the Reynolds number. Two examples of gas/solids flows in a bubbling fluidized bed and a one-dimensional channel flow are used to illustrate differences between the proposed extension of HKL drag correlation and another form published in the literature. © 2005 Elsevier B.V. All rights reserved. Keywords: Drag correlation; LBM simulation; Gas/solids fluidization 1. Introduction Due to the recent advances in computational resources and software development, it has become possible to perform detailed calculations of heavily loaded, gas-particle flows based on two-fluids or DEM-fluid methods [1,2]. Both of these approaches are based on fundamental physical laws, which imply that they can be used as predictive methods. However, they require the knowledge of several constitutive closure laws the most important of which describes the momentum exchange between the fluid and the particles. Such a correlation is dependent on many parameters of the system, the foremost of which are the Reynolds number of the flow and the solids volume fraction. Other features, such as particle shape, roughness, and the packing “fabric”, may also be important but are seldom considered. Until recently, this closure law could only be determined by the analysis of experimental data, which leads to empirical correlations with limited theoretical under- pinnings ([3] and references therein). Because of the empirical nature of this principal closure law, the two-fluids or DEM-fluid methods cannot truly be called ab initio methods. Ironically, closure formulations for secondary constitutive law, the granular stress, are much more firmly based in theory, thanks to the kinetic theory of granular materials ([4] and references therein). However, recent articles [5–9] have used the Lattice– Boltzmann method (LBM) to calculate the drag exerted by a fluid flow on a collection of randomly dispersed, fixed particles. Such calculations, repeated for different values of the Reynolds number and the solids volume fraction, can be used to derive a drag law. Thus, this essential constitutive law of two-fluids and discrete element models of multiphase flow can now be determined from first principles. The most extensive numerical-experimental (a terminology justified by the fact that LBM uses first principles calculations) data Powder Technology 162 (2006) 166 – 174 + MODEL PTEC-06446; No of Pages 9 www.elsevier.com/locate/powtec ⁎ Corresponding author. Tel.: +1 304 285 1373; fax: +1 304 598 7185. E-mail addresses: sof@fluent.com (S. Benyahia), tobrie@netl.doe.gov (T.J. O'Brien). 1 Tel.: +1 304 285 4571. 0032-5910/$ - see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2005.12.014 ARTICLE IN PRESS