To use a sector of annulus for turbomachinery fluid/structure interaction (FSI) simulation, a time shifted phase lag (TSPL) is implemented at the circumferential boundaries where a phase lag condition exits based on a certain number of nodal diameters. A traveling wave initial condition to trigger the phase difference in blade vibration is also developed. For validation and comparison purpose for the phase-lag boundary conditions, full annulus flutter simulations of NASA Rotor 67 with backward traveling wave (BTW) of nodal diameter (ND) of 1 and 2 are conducted using a fully coupled FSI methodology, in which time accurate Reynolds averaged 3D Navier-Stokes equations are solved with a system of 5-decoupled structure modal equations in a fully coupled manner. The predicted blade vibration behavior from the single passage FSI using the TSPL shows good agreement with the full annulus FSI simulation. The traveling wave initial condition captures very well the effect of the phase angle difference for turbomachinery FSI simulation in the present study.