Design and analysis of propeller blade geometry using the PDE method

This thesis aims to incorporate geometric and functional design of surfaces using a method known as the PDE method. In particular, it will be demonstrated how the PDE method
can be extended to represent an existing marine propeller geometry. Conventionally a propeller surface representation is generated by fitting a B-spline surface through a collection of given propeller blade sections. The PDE method is applied as a boundary-valued problem and consequently it will be demonstrated how a single patch of surface can be used to represent each propeller blade. This is achieved through the parametrisation of the base section of the blade, which can then be altered along the span of the blade. The advantages gained from this technique are firstly that a fair surface is automatically generated,
due to the nature of the PDE method. This would not be automatically achieved using a B-spline representation and hence manipulation of the surface would be required.
Secondly, the emphasis is on the fact that we can produce a surface representation which is controlled by a small parameter set. This will be fundamental to the final stage of the thesis.

In the second part it will be shown that the PDE generated surface is of a form which makes the hydrodynamic analysis of the propeller feasible using methods referred to as
panel methods. In this section the pressure distribution over the propeller surface will be calculated, along with the performance of the propeller, which can be compared with the predicted performance from other techniques.

The compatibility between the panel method and the PDE generated surface, along with the small parameter set lays the foundations for the final part of the thesis in which
the propeller performance will be improved by searching through various parameter subspaces. The emphasis will be on improvement of efficiency. However, to maintain feasible
geometries, constraints will be included based on the cavitation numbers of propellers, which will ensure that the final propeller design is non-cavitating.