Abstract
PhD Theses.
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.