Focus on the dispersed phase boundary conditions at the wall for irregular particle bouncing A. Tani  ere, M. Khalij, B. Oesterl  e * LEMTA––UMR 7563 CNRS, ESSTIN, Universit e Henri Poincar e, 2 rue Jean Lamour, 54519 Vandoeuvre-l es-Nancy, France Received 31 July 2003; received in revised form 28 October 2003 Abstract The dispersed phase wall boundary conditions for gas–particle flows are investigated here accounting for the effects of wall roughness on frictional inelastic particle–wall collisions. Particle statistics at the wall are computed by simulating a large number of particle–wall impacts for a given distribution of the incident wall normal velocity. The collisions are treated by using an irregular bouncing model and avoiding unphysical impact or reflected angles, the so-called shadow effect. In this sense, the present study is a preliminary step towards improvement of the formulation of wall boundary conditions for the dispersed phase needed in two-fluid models. The current approaches which allow deriving the dispersed phase boundary conditions in the cases of smooth and rough wall are described and analyzed. By taking the zero mass flux condition and the shadow effect into account, the second- and third-order particle velocity correlations at the wall can be compared to the theoretical relations obtained in the smooth case. Equivalent friction and restitution coefficients are defined, making it possible to use the same formulation of the dispersed phase boundary conditions as established in the smooth wall case. The dependence of these equivalent coefficients upon the actual collision parameters and the wall roughness is illustrated by the results of the numerical simulation. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Gas–solid flow; Particle–wall collisions; Wall roughness; Boundary conditions 1. Introduction Generation and transport of powders in the chemical and pharmaceutical industries, in tur- bulent combustion sprays, sedimentation of dilute suspensions are all examples of particle–laden International Journal of Multiphase Flow 30 (2004) 327–345 www.elsevier.com/locate/ijmulflow * Corresponding author. Tel.: +33-383-685-080; fax: +33-383-685-085. E-mail addresses: taniere@esstin.uhp-nancy.fr (A. Tani ere), benoit.oesterle@esstin.uhp-nancy.fr (B. Oesterl e). 0301-9322/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmultiphaseflow.2003.11.013