A numerical scheme based on the compressible Navier-Stokes equation has been developed for three-dimensional turbulent flows inside turbine blade rows. The numerical scheme is based on a fully conservative control volume formulation and solves the governing equations in fully elliptic form. Higher order discretizations are used for the convection term to reduce the numerical diffusion. An algebraic Reynolds stress model modified for the effects of the streamline curvature and the rotation is used for the closure of the governing equations. General coordinate transformations are used to represent the complex blade geometry accurately, and a grid generation technique based on elliptic partial differential equations is employed. Comparisons with the experimental data show that various complex three-dimensional viscous flow phenomena (three-dimensional flow separation near the leading edge, formation of the horseshoe vortex, etc.) are well predicted with the present method.

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