Pro­peller Opti­miza­tion with Machine Learning

Achiev­ing optimal effi­ciency and per­for­mance is crucial for the design of pro­pellers. A com­bi­na­tion of AI and CFD helped win a recent online pro­peller design com­pe­ti­tion hosted by Daniel Riley, a maker and popular YouTube creator (RCTest­flight). Using CAESES and Air­Shaper, we gen­er­ated two high-per­for­mance pro­pellers that demon­strated remark­able efficiency.

Objec­tive

The primary goal of the com­pe­ti­tion was to design pro­pellers that could achieve maximum effi­ciency across a wide range of oper­at­ing speeds. Using an exper­i­men­tal approach to evaluate the per­for­mance, Daniel from RCTest­flight 3D-printed the pro­pellers and attached them to a test vessel. He came up with a unique effi­ciency para­me­ter that con­sisted in mea­sur­ing the (grams of) thrust per Watt of each pro­peller from 2 m/​s to whatever speed the boat reaches at full throttle (mostly around 3.5 m/​s). The pro­peller with the largest integral, i.e., area under the curve, wins. This com­pre­hen­sive approach provided a more thorough eval­u­a­tion of pro­peller per­for­mance compared to tra­di­tional single-point objec­tives, making the chal­lenge both complex and rewarding.

As toroidal pro­pellers have become a popular topic, we decided to run separate opti­miza­tions for a toroidal and a con­ven­tional design, so that we could bench­mark these two types against each other.

Pro­peller Opti­miza­tion Approach

In short, a large number of geometry variants were gen­er­ated by CAESES and analyzed by Air­Shaper. The results were fed into a machine learning model, which was then used to predict the best possible design.

This process involved several key steps:

1. Para­met­ric Model: We devel­oped a para­met­ric model for each the con­ven­tional and toroidal pro­peller using the CAESES CAD modeling environment.
2. Design Space Explo­ration: We sampled the design space using a Design of Exper­i­ments (DoE) approach uti­liz­ing a Sobol sequence.
3. CFD Sim­u­la­tions: Using Air­Shaper’s API, which seam­lessly connects CAESES to the CFD tool, we ran the sim­u­la­tions at dif­fer­ent speeds for each design
4. Machine Learning: We used the CFD results (torque and thrust) within CAESES to train sur­ro­gate models. With these sur­ro­gate models, we are able to generate the open-water diagram for any design variant in the con­sid­ered design space.
5. Opti­miza­tion and Val­i­da­tion: With the infor­ma­tion from the open-water diagram, each design can be eval­u­ated over the whole oper­at­ing range and the single objec­tive function can be eval­u­ated. A gradient-based opti­miza­tion was used to find the optimal design.

Para­met­ric Models of the Propellers

Two separate para­met­ric models were created for the toroidal and con­ven­tional pro­peller. Of course, several para­me­ters can be used to control their shape. For the design explo­ration, 6 para­me­ters for each of the pro­pellers were selected, shown in the fol­low­ing ani­ma­tions (click on the images to see them in higher resolution).

The ranges for these para­me­ters were deter­mined by real­is­tic oper­a­tional ranges (e.g., avoiding pitch angles that would lead to stall) and physical con­straints (e.g., struc­tural integrity, geo­met­ri­cal inter­fer­ences between blades, and maximum diameter).

Toroidal Pro­peller

Con­ven­tional Propeller

CFD Con­nec­tion and Optimization

Through the provided API, CAESES was able to com­mu­ni­cate directly with Air­Shaper to launch sim­u­la­tions for each design variant and obtain the result­ing torque and thrust values. This inte­gra­tion greatly improved the effi­ciency, stream­lin­ing the process of upload­ing models, defining para­me­ters, and retriev­ing results.

The results from Air­Shaper were read back into CAESES to create sur­ro­gate models for thrust and torque at three dif­fer­ent speeds. By inter­po­lat­ing the output of the sur­ro­gate models, we were able to create the curves for the thrust and the torque coef­fi­cient over the advance ratio. Having this infor­ma­tion, and knowing the vessel’s resis­tance for any speed, we were now able to easily cal­cu­late the pro­peller effi­ciency over the whole oper­at­ing range for any design in the design space without running a CFD sim­u­la­tion. There­fore, the actual opti­miza­tion runs could be carried out in just a few minutes instead of hours or days, which is the case for a direct opti­miza­tion approach where each design has to be eval­u­ated by a CFD simulation.

Results

For the toroidal pro­peller the opti­miza­tion resulted in a 21% improve­ment over the baseline pro­peller, which was loosely based on FRIEND­SHIP SYSTEMS’ Wagenin­gen B‑Series App.

For the con­ven­tional pro­peller the opti­miza­tion resulted in a stag­ger­ing 58% improve­ment over the baseline pro­peller! And even as new and improved designs from the com­mu­nity came in, this design still had a 7% higher effi­ciency compared to the second best 3D printed design in the competition.

Toroidal vs. Con­ven­tional Propeller

The opti­mized con­ven­tional pro­peller, fea­tur­ing slender blades and a max­i­mized diameter, out­per­formed the opti­mized toroidal pro­peller by 24%. However, this is not nec­es­sar­ily a con­clu­sive assess­ment about whether con­ven­tional or toroidal pro­pellers are better and we believe this is very much depen­dent on the specific appli­ca­tion case and require­ments a design is tar­get­ing. But it does show that the design of a good con­ven­tional pro­peller is easier than the design of a good toroidal pro­peller. Espe­cially, when limiting the sim­u­la­tion resources, the apparent advan­tage of having more degrees of freedom with the toroidal pro­peller might become a dis­ad­van­tage, as the number of variable para­me­ters has a direct influ­ence on the number of sim­u­la­tions needed to achieve a suf­fi­cient explo­ration of the design space.

Build a Toroidal Pro­peller Model

To learn how to design your own fully-para­met­ric toroidal pro­peller model, follow the tutorial in our CAESES user guide documentation.