An inverse blade design method for subsonic and transonic viscous flow in compressors and turbines

Abstract

An inverse blade design method applicable to two- and three-dimensional inviscid and viscous flow in turbomachinery cascades is presented and is applied to design cascades in two-dimensional viscous flow. The pressure distribution along the blade surfaces is prescribed and is reached by modifying the initial guess of the blade geometry. The geometry modification is computed from a virtual velocity distribution derived from the difference between the current and the target pressure along the blade surfaces. The inverse method is implemented into and is consistent with the unsteady Reynolds-averaged Navier-Stokes (RANS) equations where an arbitrary Lagrangian–Eulerian (ALE) formulation on a moving and deforming grid is used. The grid velocities are determined from the space conservation law (SCL), which ensures a fully conservative computational procedure. The unsteady RANS equations are discretized using a cell-vertex finite volume method and the time accuracy is achieved using a dual time stepping scheme. An algebraic Baldwin–Lomax model is used for turbulence closure. The design method is first validated, and then its robustness, flexibility and usefulness are demonstrated on the redesign of recent compressor and turbine blade geometries used in modern gas turbine engines.