1455 de Maisonneuve, West
MIE Dept., EV 4.151
Montreal, QC, H3G 1M8, CANADA
Shape representation is an integral part of any shape optimization problem. This representation is usually
used in generating the geometric model, referred to as the CAD model that is used later on for generating
the computational mesh used in e.g. aerodynamic, thermodynamic or structure simulations. Geometry
representation can be feature-based, design parameter-based, global or local, parametric or point-wise.
This paper presents and assesses different geometric representations of axial turbine and compressor
blades used in gas turbines, and their effect on the design space and the optimization process.
The shape representation that is used in a given application should be accurate, flexible and robust; it
should involve the minimum number of design parameters (unless an adjoint-based optimization method
is used), these parameters are lately used as design variables. Such representation should also be suitable
for the intended application, i.e. it should relate to the design parameters and should preferably use a
CAD-native parameterization either directly or through e.g. an Application Programming Interface (API).
In this paper, we will demonstrate that the geometric representation can make the optimization approach
more efficient, moreover it can reduce the complexity of a given design problem.
The applications that are considered in this work are at the component level optimization, e.g. a single or
multi-stage turbine or compressor with single or multi-objective. Shapes include airfoils in two-
dimensional (2D) flows and complete blades in three-dimensional (3D) flows. The representations vary
from a global low fidelity to a local/global high fidelity representation.
Shape representations take almost as many different forms as the number of researchers using automatic
shape optimization. They vary from very simplistic ones to fairly complex ones; these representations vary
in flexibility, accuracy, smoothness and generality. One way to categorize them is as follows:
Point-wise representation of geometries, where the surface mesh (on e.g. the blade in internal flow
or the wing in external flow) or a geometric representation thereof [1, 2] are taken as the design
variables. This approach is used typically in conjunction with adjoint-based optimization methods
since the number of design variables does not affect the complexity of the optimization method.
The geometry is smoothed out during the optimization process and, in cases where a geometric
representation is used, the modified surface mesh is propagated into that geometric representation
using a basis space of independent perturbation functions of the Hicks Henne type. Examples of
this approach are given in Reuther and Jameson  for external flow and in Wang