A coupled adjoint formulation for non-cooled and internally cooled turbine blade optimization

Most researches on the application of the adjoint method in turbine blade design are concentrated on the aerodynamic shape optimization without considering the heat transfer to/from the blade material. In this study, the adjoint method is extended to the conjugate heat transfer problems in which the viscous flow field is coupled to heat transfer in the solid region. Introducing a new adjoint variable in the solid domain, a heat adjoint equation is derived which is coupled with the energy adjoint equation in the fluid zone at the fluid/solid interface. The detailed mathematical description associated with the derivation of the heat adjoint equation with corresponding boundary conditions are presented. The applicability of the proposed adjoint system is assessed via aerodynamic redesign of a well-known benchmark, NASA GRC linear turbine cascade for cooled and non-cooled cases.