Application of simulated annealing to inverse design of transonic turbomachinery cascades

In turbomachinery blade design, inverse methods and optimization techniques are often applied independently to produce high performance blade shapes. The idea of using an optimization algorithm to seek the optimal target distribution for an inverse design methodology has been explored. However, these efforts have been made mainly in the design of single aerofoils. In this paper, a new inverse design method is coupled with a simulated annealing algorithm to search for the optimum turbomachinery cascade shape. In order to speed up the algorithm, a database of generated designs is set up and the nearest match is selected to initialize subsequent calculation. The proposed computational procedure equips engineers with an automatic design tool with which the inverse method may be applied in isolation or combined with the optimization algorithm to produce the optimum. The inverse methodology is based on a cell vertex, finite volume time-marching flow solver that gives the viscous cascade flow solution in both the subsonic and the transonic flow regimes. The cascade shape is computed subject to an imposed distribution of the mass-averaged tangential velocity and a specified tangential thickness profile. The solver code is validated using experimental data and the accuracy of the inverse method is verified by regenerating a known cascade geometry starting from a different one using its mass-averaged tangential velocity distribution. In combining the inverse methodology with the optimization algorithm, the mass-averaged tangential velocity distribution is parametrized using a cubic B-spline curve and the proposed simulated annealing algorithm is applied to predict the optimal distribution by minimizing loss. The overall procedure is demonstrated to produce optimum shapes of a transonic axial turbine and an axial compressor rotor.