The continuous adjoint method for shape optimization in Conjugate Heat Transfer problems with turbulent incompressible flows

In this paper, the development of the continuous adjoint method for shape optimization in Conjugate Heat Transfer (CHT) problems with incompressible flows is presented. The main focus of this study is to develop a continuous adjoint method which computes accurate sensitivity derivatives by (a) extending the adjoint to the Spalart-Allmaras turbulence model, by taking into consideration additional contributions arising from the differentiation of the heat transfer equation valid in the flow domain and (b) extending the Enhanced-Surface Integral adjoint formulation, recently introduced by the authors' group for single-disciplinary problems, to CHT ones. The so-computed sensitivities are compared to the outcome of finite differences and alternative adjoint formulations in 2D turbulent flows. The proposed method is firstly validated in two simple cases and, then, used to perform the CHT optimization of a 2D internally cooled turbine blade and a 3D car piston-engine cylinder head.