INVERSE METHOD FOR AXISYMMETRIC NAVIER-STOKES COMPUTATIONS IN TURBOMACHINERY AERODESIGN

Each blade row is replaced by a hub-to-tip streamsurface and its effects on the flow are modeled by inviscid and viscous blade forces. The inverse method seeks the axisymmetric flow field and hub-to-tip geometry for a specified distribution of swirl i.e. specific work in bladed regions. Navier-Stokes equations with a compressible Spalart-Allmaras turbulence model are solved in the meridional plane by means of an upwind finite-volume scheme. The time-marching procedure includes an evolutionary equation for each hub-to-tip surface, which is solved by upwind finite differences. In the annulus wall regions, since specification of swirl becomes unpractical, the method extrapolates the relative flow angle from the core flow region and computes the corresponding swirl and geometry. As a test case, an already designed turbine stage is re-obtained from a traditional throughflow solution. The test stresses around 1% overestimation of overall performances compared to this solution and a three-dimensional CFD analysis, with a satisfactory description of annulus wall flows.