Potential of specification of swirl in axisymmetric CFD methods for turbine blade aerodesign

A time-marching model for complete axial flow turbomachinery is adopted, which replaces the blades with hub-to-shroud streamsurfaces. The main effects of the real blades on the flow are modelled by blade forces. The inverse method seeks the hub-to-shroud geometry that produces a specified distribution of swirl in the blade regions. Swirl drives the spanwise distribution of specific rotor work. Euler equations are solved in the meridional plane using an upwind finite-volume scheme. The time-marching algorithm includes an evolutionary equation for each hub-to-shroud surface, which is solved by upwind finite differences. Since swirl is a monotonic function of the outflow angle, its specification allows the inverse method to converge more naturally and effectively than previous approaches to high-deflection solutions of the axisymmetric problem. A satisfactory agreement is found in comparing the numerical solution to (i) a theoretical solution for a linear turbine cascade and (ii) a conventional throughflow solution and a three-dimensional computational fluid dynamics (CFD) solution for a two-stage turbine.