Abstract

Non-Uniform Rational B-Splines (NURBS) have become the industrial standard to represent and exchange a CAD geometry between CAD/CAE systems. CAD-based shape parameterisation uses parameters of a CAD model to modify the shape which allows to integrate a CAD model into the design loop. However, feature-trees of typical commercial CAD systems are not open and obtaining exact derivatives for gradient-based optimisation methods is not possible. Using the CAD-based NSPCC approach a designer can deform multiple NURBS patches in the design loop without violating geometric and/or thickness constraints. The NSPCC approach takes CAD descriptions as input and perturbs the control points of the NURBS boundary representation to modify the shape. In this work, an adaptive NSPCC method is proposed where the optimisation begins with a coarser design space and adapts to finer parametrisation during the design process where more shape control is needed. The refinement sensor is based on a comparison of smoothed node-based sensitivity compared to its projection onto the shape modes of the current parametrisation. Both static and adaptive parametrisation methods are coupled in the adjoint-based shape optimisation process to reduce the total pressure loss of a turbine blade internal cooling channel. The discrete adjoint flow solver STAMPS is used to compute the flow fields and their derivatives w.r.t. surface node displacements. The shape derivatives for gradient-based optimisation are obtained by application of reverse mode AD to the NSPCC CAD kernel. Since a CAD model is kept inside the design loop, the resulting optimal shape is directly available in CAD for further analysis or manufacturing. Based on the analysis regarding quality of the optima and rate of convergence of the design process adaptive NSPCC method outperforms static NSPCC approach.