Research Fellows
Rejish Jesudasan
Early Stage Researcher 1 at Queen Mary University of London
Adjoint based aerodynamic shape optimisation methods have recently become very popular in the
aerospace, automotive and marine industries. The adjoint method is essential for gradient based optimi-
sation with many design variables since the gradient of the objective function is computed at a cost that
is independent of the number of design variables. This method reduces the computational complexity in
sensitivity evaluation for each design variable. Various methods for parametrisation of the geometry have
been proposed.
Two well-known 3D geometry parametrisation methodologies are focused upon here
as they offer rich design spaces: a) the CAD-free node based approach and b) the CAD-based NURBS.
The CAD/NURBS approach works with the generic boundary representation using NURBS patches
as typically given in the STEP file format. The control points and weights of the NURBS patches are used
as design variables, offering the richest design space the geometric representation can express. Additional
constraints have to be introduced to maintain continuity between the patches, thickness, radius or box
constraints during the optimisation.
In the node-based parametrisation the positions of the grid nodes on the shape are taken as the design
variables. This is the richest design space the grid can express, and is typically too rich as it allows high-
frequency oscillations that the flow solver does not adequately resolve, regularisation of the gradients or
smoothing of the shape is required.
Comparison between the initial and optimised velocity magnitude at design iteration 5 obtained
using node based parametrisation method is shown in the Fig. 1. The goal is to deform the 180 ◦ joints
connecting the adjacent channel passages to minimise the mass averaged total pressure loss at a Reynolds
number of 40, 000. The node-based method uses the displacement of 2000 surface nodes regularised with
implicit smoothing.
