Euler-based throughflow method for inverse design and optimization of turbomachinery blades

An inviscid model for complete axial flow turbomachinery is adopted, which replaces the blades with throughflow surfaces. The main effects of the real blades on the flow are modelled by blade forces. The inverse method predicts the axisymmetric flow field and throughflow surface geometry for a specified distribution of azimuthal inviscid force. This quantity drives the meridional distribution of rotor shaft power. Euler equations are solved by an implicit upwind finite-volume scheme. The time-marching computation includes an evolutionary equation for each throughflow surface, which is solved by implicit finite differences. Standard optimisation algorithms are used to find distributions of azimuthal force that minimise some sample cost functions. The optimal blade shapes are given by the corresponding geometrical solutions of the inverse problem. Since the cost function evaluation is reduced to an inviscid two-dimensional computation, the entire process is significantly less time-consuming than those based on three-dimensional CFD solvers