Composite materials can be used to fabricate flexible marine propellers, which can improve efficiency and reduce underwater radiated noise. Since the hydrodynamic performance of flexible propellers is determined by their deformation under fluid loading, similarity laws for flexible propeller scaling should account for the deformation in model experiments. This study introduces a non-dimensional parameter to characterise the deformation of flexible propellers and evaluates it through time-domain fluid–structure interaction simulations. A coupled solver combines unsteady Reynolds-Averaged Navier–Stokes equations with a finite-element structural solver. The study focuses on the Wageningen C4-40 propeller geometry under uniform inflow and is limited to isotropic materials.

A set of non-dimensional relations is derived through dimensional analysis, with a form of the Cauchy number expressing deformation amplitude. Validation using a Reynolds–Cauchy similarity approach on two geometrically similar propellers of different diameters confirms consistent deformation and less than 5\% difference in thrust and torque coefficients between model and full-scale propeller. The disparities in performance results are attributed to numerical artefacts in the fluid solver, as the results indicate that the $k-\omega$ SST turbulence model is sensitive to near-wall resolution.

Achieving full-scale Reynolds numbers in propeller test facilities is not feasible, yet simulations demonstrate that flexible propellers are sensitive to viscous forces. The study observes disparities in deformation extent across Reynolds numbers. The deformation of flexible propellers improves flow attachment over the blades. The overall Reynolds-number trends remain similar to the rigid results: thrust coefficients increase and torque coefficients decrease as Reynolds numbers increase. The open-water efficiency depends on both coefficients, and larger Reynolds numbers result in higher efficiencies.

The Froude–Cauchy scaling approach proves suitable for model experiments; however, material availability limits practical implementation. This study indicates that the steady-state deformation is primarily governed by stiffness, with negligible impact from the structural-to-fluid density ratio. In contrast, in unsteady conditions, the structural-to-fluid density ratio affects the modal frequencies, which describe the dynamic behaviour of propeller blades. Particularly, propellers with high skew, rake, or with anisotropic material properties are affected by structural-to-fluid density. Furthermore, this analysis observes that the first blade mode of a zero-skew angle propeller is pure bending, and a 30\% variation in structural density does not alter the natural frequency of this blade. However, coupled bend-twist modes are sensitive to the structural density, which therefore affects blade deformation in unsteady conditions.

In conclusion, the extent of propeller deformation can be controlled by a non-dimensional parameter expressing the ratio of elastic to hydrodynamic forces. For steady open-water conditions, deformation is additionally a function of Reynolds number. In unsteady conditions, the structural-to-fluid density ratio becomes relevant, as it alters coupled bend-twist modal frequencies. Thus, the deformation extent in this regime is, in addition to the Reynolds number, a function of fluid damping and the ratio of natural frequency to revolution rate. This study offers a basis for accurate scaling of flexible propellers in both experimental and computational studies.

Propellers are used to propel the vast majority of ships. They are most commonly made out of Nickel-Aluminum-Bronze alloys. This is due to their superior characteristics over other metals in terms of strength and corrosion resistance. Metal propellers are assumed to be rigid and undeformable. Current research opts to construct propellers out of more flexible materials such as composites. The potential of this material lies in the theory that this results in propellers which could unload themselves in the wake peak, which should lead to significant improvements in the cavitation- and noise behaviour of the propeller.
Since the material is much less stiff, the deformation can no longer be neglected and must be computed simultaneously with the hydrodynamic solution. This is done in a branch of fluid dynamics known as Fluid-Structure Interaction (FSI). Maritime Research Institute Netherlands (MARIN) is involved in the development of a program known as the ComPropApp.

The first goal of this thesis is to validate the unsteady FSI module of the ComPropApp which uses a coupled BEM-FEM code to calculate the hydrodynamic and structural performance of marine propellers in non-uniform inflow conditions. The numerical simulations are validated by comparison with conducted experiments at MARIN. It shows that the average deformation of the experiment and simulation are in good agreement but the ComPropApp overestimates the wake peak deformation. This is most likely the effect of divergence issues which do not allow for sufficiently small step sizes. This step size also does not allow for analysis of vibrations happening within a revolution as much more points should be considered. The most important recommendation, therefore, is to improve the numerical stability of the application.

The second goal is the exploration of the design space of flexible propellers. By altering propeller geometry parameters it is investigated which parameters have the potential to design adequate flexible propellers in the future. To quickly assess the cavitation risk of the propellers, the amount of negative pressure coefficients on the blade is used to quantify the cavitation risk in the initial propeller design stage. Through this method, it is shown that suction side cavitation risk is decreased easily by altering pitch, skew, chord length and camber. Pressure side cavitation risk is however much harder to relieve, mostly because of the deformation of flexible propellers. Yet, cavitation risk can be decreased with a combination of skew and camber. It is also shown that unfavourable tip pressures (thus risk of tip vortices) can be further decreased by applying a positive tip rake.
All these propellers were simulated in open water (because of the above-mentioned divergence issues in the unsteady FSI module). Thus it is no conclusion that these propellers also perform adequately in non-uniform inflow conditions. It is shown with a demonstration that two of the three most potential propellers of the open water study do indeed unload themselves and maintain better cavitation behaviour at the velocity in the wake peak compared to a metal reference propeller.