A three-dimensional inviscid flow solver is developed for turbomachinery components using unstructured meshes. The numerical scheme is based on the Roe``s flux-difference splitting with an explicit Runge-Kutta time integration. To accelerate the convergence to steady state, local time stepping and implicit residual smoothing are applied. Three-dimensional unstructured tetrahedral meshes are obtained using an advancing-front technique. To better resolve the flow at the periodic boundaries between blades, the grid periodicity is strictly enforced. The numerical method is applied for flows through a turbine annular cascade, advanced turbine rotor blade rows with the tip clearance gap, and a turbine volute. The results are compared with analytical and experimental data for validation.