An Adaptive Parameterisation Method for Shape Optimisation Using Adjoint Sensitivities.

Abstract

Adjoint methods are the most e cient approach to compute the design sensitivities as the entire gradient vector of a single objective function is obtained in a single adjoint system solve. This in turn opens up a wide range of possibilities to parameterise the shape. Most shape parameterisation methods require manual set-up which typically results in a restricted design space. In this work, two parameterisation methods that can be derived automatically from existing information are extended to include adaptive design space in shape optimisation. The node-based method derives parameterisation directly from the computational mesh employed for simulation and normal displacements of the surface grid nodes are taken as design variables. This method o ers the richest design space for shape optimisation. However, this method requires an additional surface regularization method to annihilate high-frequency shape modes. Hence the best achievable design depends on the amount of smoothing applied on the design surface. An improved adaptive explicit surface regularization method is proposed in this thesis to capture superior shape modes in the design process. The NSPCC approach takes CAD descriptions as input and perturbs the control points of the NURBS boundary representation to modify the shape. The adaptive NSPCC method is proposed where the optimisation begins with a coarser design space and adapts to ner parameterisation during the design process. Driven by adjoint sensitivity information the control points on the design surfaces are adaptively enriched using knot insertion algorithm without modifying the shape. Both parameterisation methods are coupled in the adjoint-based shape optimisation process to reduce the total pressure loss of a turbine blade internal cooling channel. Based on analyses regarding the quality of the optima and the rate of convergence of the design process the adaptive NSPCC method outperforms both adaptive node-based and the static NSPCC approach.