Grid generation for three-dimensional turbomachinery geometries including tip clearance

An efficient technique for the generation of structured grids for viscous flow computations in turbomachinery blade rows (two- and three-dimensional), and a specialized embedded //-grid for application, particularly to tip clearance flows, are presented. The grid generation technique uses a combination of algebraic and elliptic methods to obtain smooth grids while maintaining strict control over grid spacing and orthogonality at domain boundaries. A geometric series scheme is used to distribute boundary points. Algebraically generated layers next to boundaries are used, thus excluding highly clustered regions from the elliptic generation procedure's domain. The computational efficiency of the elliptic generation procedure is greatly enhanced by the application of the minimal residual method. The embedded //-grid topology provides good resolution of tip clearance effects. This topology requires only minor modifications to flow solvers developed for conventional //-grids. The results obtained with an embedded //-grid are compared to those obtained using a thin-tip approximation. A linear compressor cascade with tip clearance was used as a test case. Both grid topologies capture the dominant flow structures associated with the leakage flow. The embedded //-grid provided better quantitative agreement with the experimental results.