Adjoint Based Optimisation for Coupled Conjugate Heat Transfer.

Abstract

Conjugate Heat Transfer (CHT) problems are typically solved using a partitioned approach where separate solvers for the fluid and structure are loosely coupled through boundary conditions. These boundary conditions need to be updated iteratively until the temperature and heat flux are continuous between the two domains. In this thesis, CHT problems are solved by coupling the in-house flow solver with the open-source heat conduction solver, CalculiX. Three coupling algorithms are used, which involve a combination of Neumann, Dirichlet, and Robin boundary conditions. The interest in shape optimisation has increased the need for efficient optimisation techniques. Consequently, gradient based optimisation using adjoint methods are preferred due to the reduced computational cost of obtaining gradients. Currently, the use of adjoint methods in CHT shape optimisation problems mostly favours the continuous adjoint method which suffers from high developmental costs. This thesis advocates for the use of the discrete adjoint via Automatic Differentiation (AD) as a cost-effective alternative to the continuous adjoint. This is done by differentiating the fluid and solid solvers with respect to the coupling boundary conditions using AD. A fully differentiated partitioned coupling approach is achieved by differentiating the three coupling algorithms used. The differentiation of the Robin boundary conditions results in two new differentiated coupling algorithms and the accuracy of the differentiated coupling algorithms is demonstrated by comparing with gradients obtained through finite differences. The efficacy of the developed methods is then demonstrated on three CHT optimisation problems: An inverse design problem related to a flat plate and a thermal optimisation of the MarkII turbine blade and an internal cooling channel U-Bend. The gradient verification and optimisation results revealed that the use of Robin boundary conditions in the flow solver reduces computational runtime.