Evaluation of boundary conditions used to model dilute, turbulent gas/solids flows in a pipe

Abstract A turbulent gas/solids model, based on the work of Simonin [1] [Simonin, O., 1996. Continuum modeling of dispersed two-phase flows, in Combustion and Turbulence in Two-Phase Flows, Von Karman Institute of Fluid Dynamics Lecture Series 1996-2], has been recently implemented in the MFIX computational fluid dynamic (CFD) code. This theory includes the effects of turbulence in the gas phase as well as inter-particle collisions. The extension of this theory [2] [Balzer, G., Simonin, O., Boelle, A., Lavieville, J., 1996. A unifying modelling approach for the numerical prediction of dilute and dense gas-solid two phase flow, CFB5, 5th Int. Conf. on Circulating Fluidized Beds , Beijing, China] to dense gas/solids systems was made possible by including the kinetic theory of granular material to describe the solids stresses. The turbulence model and boundary conditions were evaluated by simulating the gas/solids flow experiments of Jones [3] [N.E. Jones, An experimental investigation of particle size distribution effect in dilute phase gas–solid flow, Ph.D. thesis, Purdue University (2001)]. Their experimental results included velocity and turbulence measurements for fully developed flows for a range of particle loading from very dilute to relatively dense. Our numerical calculations were conducted by imposing periodic boundary conditions as well as in a long pipe with different length-to-diameter ratios to achieve a fully developed condition. We propose modifications to the single-phase wall functions, to include the effect of the particulate phase. However, these modifications had only a minor effect on the predictions of gas turbulent kinetic energy due to the dilute nature of the flow considered in this study. The turbulent gas/solids flow model based on the work of Simonin [1] [Simonin, O., 1996. Continuum modeling of dispersed two-phase flows, in Combustion and Turbulence in Two-Phase Flows, Von Karman Institute of Fluid Dynamics Lecture Series 1996-2] is able to predict reasonably well dilute gas/solids flows with appropriate boundary conditions (BC). Four different types of boundary conditions were investigated to assess their sensitivity. The experimental data fall between the large-friction/no-sliding and small-friction/all-sliding limits of Jenkins and Louge [4] [J.T. Jenkins, M.Y. Louge, On the flux of fluctuating energy in a collisional grain flow at a flat frictional wall, Phys. Fluids 9 (10), (1997) 2835–2840] BC. However, the physical behavior of the particle–wall interactions is close to the small-friction/all-sliding limit of Jenkins and Louge BC or the Johnson and Jackson [5] [P.C. Johnson, R. Jackson, Frictional-collisional constitutive relations for granular materials, with application to plane shearing. J. Fluid Mech. 176 (1987) 67–93]BC with a small specularity coefficient or simply the free-slip BC.