Abstract: The Lagrangian vortex method is applied to direct description of the unsteady flow due to rotor-stator interaction in turbomachinery by tracing the trajectory of vortices.The Baldwin-Lomax turbulence model adapted for wakes overcomes the short comes of other numerical methods,that they cannot continuously monitor the moving wake centerlines and give the computed viscosity in the outer region much higher than in the boundary regions.The agreement between the computational and experimental results is generally good,which shows that the present method is feasible.The result also show that the development of wakes and other vortices can be correctly predicted with the help of the presented turbulence model.So this method can be used as a new tool for analyzing unsteady flow and complicated phenomena in turbomachinery.