Shape optimisation of naval propellers: towards a suitable marine environment
How to design propeller blades to reduce seawater vibrations exploiting a model order reduction technique by Anna Ivagnes
Nowadays we hear the word “sustainability” in many contexts, most of the time linked to climate change and air pollution. But sustainability is also correlated to another type of pollution: acoustic pollution in seawater.
Noises and vibrations caused by the ships’ engines and by the maritime traffic can directly affect the lives of our marine friends…
What can we do to preserve life in seawater? Design more sustainable ships!
And how can we do this? Well, back to the basics… Let’s start with the study of a fundamental component of a ship’s engine: the propeller.
The propeller is an extremely important body and, if not well designed, it can end up being unfeasible. This can lead to poor performance, cavitation, and vibrations both in seawater and for people on the ship.
For this reason, it is crucial to design propellers with blades of improved shape and optimised efficiency.
Let’s go deeper into the topic, analysing each step of the project pipeline, fully described in [3].
Geometrical parametrisation of propellers
The first step of our shape optimisation is blade parametrisation.
Each blade has different geometrical features which can be modified to obtain a deformed blade. We distinguish global parameters (pitch, rake, skew, chord length) and local parameters (thickness, camber), that refer to each selected cylindrical section. But how can we extract and deform the geometrical features from the CAD file of a blade? The Python library BladeX[1] makes this operation very easy.
First of all, the parameters extracted from the CAD file are stored in a Blade object, encapsulating both the global and the local data. The power of BladeX is the ability to extract the geometrical features starting from the blade cylindrical coordinates and to modify them to obtain deformed blades.
This is the way we adopted to explore a very large number of shapes.
The offline stage: expensive simulations
What’s next? The simulation of the water flow. Computational Fluid Dynamics (CFD) helped us to simulate an open-water test: this step is commonly called the offline stage. Here, the open-source software OpenFOAM is used to approximately solve the Navier-Stokes equations to simulate the water flow accelerated by a rotating propeller into a cylindrical domain.
The setup of the offline simulation is built such that the accuracy in terms of the thrust and torque forces acting on the blades is below 3 percent if compared to the experimental open-water results. Not bad!
The next step in the offline stage is to repeat the same simulation for all the deformed propellers. So, for each shape one has to:
- Deform the mesh using an interpolation technique, named Radial Basis Functions (RBF) which learns how to deform the points of the mesh from the deformation of a reduced number of points, named control points.
- Run the offline simulation with the deformed mesh in the original setup. We obtained in this way the flow fields for each deformed propeller.
But there is an issue: these kinds of simulations need millions of degrees of freedom to be sufficiently accurate (in our case about 6 millions), which traduces in a long computational time … running an optimisation algorithm in this framework would last a decade!
How can we reduce the computational cost? With data-driven Reduced Order Models (ROMs).
The online stage: towards optimised shapes with fast computation
Data-driven ROMs are a powerful tool that exploits the data information coming from expensive high-fidelity simulations to build a model which predicts the flow fields of interest in a reduced amount of time.
The Python library used to develop the ROM is an extremely intuitive and user-friendly package: EZyRB[2].
The flow fields obtained for each offline simulation, our snapshots, and the corresponding blade deformation, our parameters, are used to construct the non-intrusive POD-based ROM.
But where is the real computational gain? In the optimisation step!
But let’s start with the basics of optimisation theory. We followed a genetic algorithm, that is inspired by natural selection. Basically, we start initializing the population: in our case, each individual of the population corresponds to a deformed blade, and the genes of the individual are the deformations imposed on the geometrical parameters of the blade. We then choose a fitness that has to be maximized, the propeller efficiency in our case.
The aim of the algorithm is to explore new individuals and finally find the individual(s) able to optimise the fitness. To do so, the algorithm iteratively performs 3 main steps (selection, crossover and mutation) until it finds the optimal blade shape.
Where do ROMs come into play? The answer is: in the fitness (efficiency) evaluation. Indeed, for each individual the FOM would last 24–48 hours, whereas the ROM evaluation takes only a few seconds.
The entire optimisation algorithm takes less than one hour, obtaining a propeller of efficiency improved by 1%. Yeah, I know it can sound like a poor result, but, trust me, it is a really good achievement in this field!
Conclusions: more ROMs for sustainability
Now we can definitely say that reduced order models help in improving the sustainability, not only for dolphins and seawater life but also because of the exceptional speed-up they guarantee, leading to minor energy consumption. So, more ROMs for everyone!
[1] M. Gadalla, M. Tezzele, A. Mola, and G. Rozza. BladeX: python blade morphing. Journal of Open Source Software, 4(34), 1203 (2019).
[2] N. Demo, M. Tezzele, and G. Rozza. EZyRB: Easy reduced basis method. Journal of Open Source Software, 3(24), 661 (2018).
[3] A. Ivagnes, N. Demo, G. Gustin, G. Lavini, G. Rozza. “A shape optimisation pipeline for propeller blades in naval applications”, in preparation.
