Extension of Hill–Koch–Ladd drag correlation over all ranges of Reynolds number and solids volume fraction

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.