•Flow inside a ducted axial fan is computed by highly resolved LES.•The effect of tip-gap size and flow rate on the flow field are analyzed in detail.•The diameter and strength of the tip vortex increase with the tip gap.•The largest tip gap at the design condition shows breakdown of the main tip vortex.•The increase of tip-gap size resulted in more intense turbulent mixing and higher losses. Detailed and comprehensive analyses of the tip vortex system of a ducted axial fan are performed based on highly resolved large-eddy simulations. Various tip gap sizes, which are typically found in technical fans, and two operating conditions are considered. The Reynolds number based on the tip speed of the blade and the diameter of the fan D0 is Re=9.36×105, the Mach number is M=0.136, and the rotational speed Ω=3000 rpm. The chosen tip clearances s are s/Do=0.001,0.005,0.01 and the design and off-design operating conditions are defined by the flow rate coefficients Φ=0.195 and Φ=0.165, respectively. The conservation equations of a compressible, viscous fluid are integrated on a multi-block structured mesh with 140 × 106 grid points in a rotating frame of reference for a single out of five blades using periodic boundary conditions in the circumferential direction and prescribed undisturbed inflow conditions based on experimental data. The results show that increasing the tip-gap size results in several vortices in the tip-gap region, i.e., tip leakage, separation and induced vortices, which enlarge the diameter and the strength of the main tip vortex and decrease the efficiency of the fan. For the off-design operating condition, the tip-gap vortex for the smallest tip-gap size decays faster than for the design operating condition. Increasing the tip-gap width, changes the direction of the tip-leakage vortex trajectory. The angle between the blade chord and the tip-leakage vortex is decreased at design condition, while the opposite behavior is observed for the off-design condition, in which the tip-leakage vortex moves further away from the suction side of the blade. Furthermore, the interaction between the axial flow and the main tip leakage vortex convecting downstream of the blade leads to an enhanced turbulent mixing at larger tip-gap size. For the largest tip clearance, i.e., s/Do=0.01, spiral vortex breakdown occurs at the design operating condition caused by the interaction of the main tip vortex with the secondary vortex generated in the tip-gap region. At off-design operating conditions, a larger tip-leakage-loss coefficient is obtained due to a more intensive turbulent mixing, where the maximum loss coefficient occurs at around midchord.