A methodology to implement non-reflecting boundary conditions for turbomachinery applications, based on characteristic analysis is described in this paper. For these simulations, inlet conditions usually corre- spond to imposed total pressure, total temperature, flow angles and species composition. While directly imposing these quantities on the inlet boundary condition works correctly for steady RANS simulations, this approach is not adapted for compressible unsteady Large Eddy Simulations because it is fully re- flecting in terms of acoustics. Deriving non-reflecting conditions in this situation requires to construct characteristic relations for the incoming wave amplitudes. These relations must impose total pressure, total temperature, flow angle and species composition, and simultaneously identify acoustic waves reach- ing the inlet to let them propagate without reflection. This treatment must also be compatible with the injection of turbulence at the inlet. The proposed approach shows how characteristic equations can be derived to satisfy all these criteria. It is tested on several cases, ranging from a simple inviscid 2D duct to a rotor/stator stage with turbulence injection.