Aerodynamic design optimization with constraints for turbomachinery based on control theory

In this paper, an approach of the adjoint system deduction based on the variation in grid node coordinates was applied. The minimization of entropy generation rate with a mass flow rate constraint was considered as the cost function of the optimization, and was applied in the direct design process. The adjoint partial differential equation (P.D.E) of the 2D N-S equation, as well as its boundary conditions, and the finial expression of sensitivity gradient were deduced in detail. An aerodynamic shape design optimization algorithm based on viscous adjoint method and N-S equation for 2D turbine blades was developed. Finally, to validate the present optimization algorithm, the aerodynamic design cases of a transonic turbine blade with and without mass flow rate restriction were performed and analyzed.