The present paper is concerned with numerical simulations of pneumatic conveying in pipes of circular cross-section. Based on an Euler-Lagrange approach relying on the large-eddy simulation technique for the fluid flow and a particle tracking scheme accounting for all relevant elementary processes (particle rotation, transverse lift forces, inter-particle collisions, particle-wall collisions with smooth and rough walls, coupling between phases) several cases are analyzed in detail to elucidate the origin of secondary flow structures in the pipe cross-section. A smooth glass pipe and a rough steel pipe are taken into account at two different mass loadings considering a polydisperse size distribution with a number mean diameter of about 40 mu m mimicking the corresponding reference experiment. After a detailed validation of the single-phase as well as the two-phase flow based on experimental and DNS data, the secondary flow structures are analyzed qualitatively and quantitatively. That confirms recently published experimental results that the secondary flow observed is of second kind. Finally, to prove that for another particle size distribution numerically investigated in the literature the secondary flow is still of second kind, rather large monodisperse inertial particles (134 mu m) hitting the pipe walls with two different roughnesses are additionally simulated. The strength of the secondary flow is found to be strongly reduced for these cases compared with the polydisperse smaller particles, but the mechanism responsible for the secondary flow is the same. (c) 2013 Elsevier Ltd. All rights reserved.