Abstract

An inverse blade design method, applicable to 2D and 3D flow in turbomachinery blading is developed and is implemented for the design of 2D cascades in compressible viscous flow. The prescribed design quantities are either the pressure distributions on the blade suction and pressure surfaces or the blade pressure loading and its thickness distribution. The design scheme is based on a wall movement approach where the blade walls are modified based on a virtual velocity distribution that would make the current and target momentum fluxes balance on the blade suction and pressure surfaces. The virtual velocity is used to drive the blade geometry towards a steady state shape corresponding to the prescribed quantities. The design method is implemented in a consistent manner into the unsteady Reynolds Averaged Navier-Stokes (RANS) equations, where an arbitrary Lagrangian-Eulerian (ALE) formulation is used and the boundaries of the computational domain can move and deform in any prescribed time-varying fashion to accommodate the blade movement. A cell vertex finite volume method is used for discretizing the governing equations in space and, at each physical time level, integration in pseudotime is performed using an explicit Runge-Kutta scheme, where local time stepping and residual smoothing are used for convergence acceleration. For design calculations, which are inherently unsteady due to blade movement, the time accuracy of the solution is achieved by means of a dual time stepping scheme. An algebraic Baldwin-Lomax model is used for turbulence closure. The flow analysis method is applied to several test cases for steady state internal flow in linear cascades and the results are compared to numerical and experimental data available in the literature. The inverse design method is first validated for three different configurations, namely a parabolic cascade, a subsonic compressor cascade and a transonic impulse turbine cascade, where different choices of the prescribed design variables are used. The usefulness, robustness, accuracy, and flexibility of this inverse method are then demonstrated on the design of an ONERA transonic compressor cascade, a NACA transonic compressor cascade, a highly cambered DFVLR subsonic turbine cascade, and a VKI transonic turbine cascade geometries, which are typical of gas turbine blades used in modern gas turbine engines