Optimizing the design of ship propellers is of key importance for the marine industry, as it has a direct impact on operational costs through its influence on fuel consumption and ship performance. Even the smallest improvement in the design of the propellers can save ship operators millions of dollars across an entire fleet. The same is true, be it at a smaller scale, for the super yacht and pleasure boat industries for example.   

Today propeller designs can be simulated meticulously with powerful tools that take into account a broad range of physics, from fluid flow to structural integrity to even acoustics behavior. And those designs can be optimized for optimal performance in a fully automated way. 

The question that arises though, is whether we are sure that this ‘optimal’ design corresponds to the optimal design under realworld conditions, where uncertainties are an inevitable part of life. Uncertainties for example that are embedded in operating conditions such as ship speed and rotational speed of the shaft, or uncertainties in the manufacturing process, which lead to geometrical variations in the propeller shape that can have a significant impact on the final performance of the propellers.

To find a response to this question, robust optimization should be considered. Robust Design Optimization (RDO) takes into account a series of these uncertainties that can influence the performance of products. It allows for designs to be optimized in a ‘robust’ way, for example by making them less sensitive to inevitable variations in operating conditions or to small differences in geometries due to manufacturing variability.

To illustrate this, the below described customer case presents the optimization under uncertainties of a ducted ship propeller. The goal of this case was to reduce the impact of manufacturing variability on the ship’s open water efficiency.

Methodology

Two optimization studies of a ducted ship propeller were performed. First, a standard (deterministic) design optimization was used to maximize the open water efficiency of the propeller. Then, in a second step, robust design optimization was performed to maximize the mean value of the open water efficiency and minimize standard deviation of this efficiency. 

Uncertainty Quantification

A total of 12 uncertainties were identified and characterized for this case: 11 manufacturing uncertainties and 1 operational uncertainty (axialvelocity). The manufacturing uncertainties were deduced from the technical norm ISO-484-2, which specifies all the manufacturing tolerances for this particular case. The manufacturing variability of every propeller has to respect these imposed manufacturing tolerances.

Cadence’s optimization software FINE™/Design3D is equipped with a unique Uncertainty Quantification (UQ) analysis module. It enables designers to easily assess the effects of uncertainties on performance by carrying out several CFD simulations in a fully automated way. In this study, the 12 defined uncertainties resulted in 35 individual CFD simulations.

Scaled sensitivities

To gain physical insight into the influence of uncertainties on performance and to reduce computational cost, Cadence developed an intelligent post-processing tool, called “scaled sensitivities”. This tool measures the sensitivity of a performance, in this case open water efficiency, to specific uncertainties. Exploiting these sensitivity derivatives enables designers to reduce the number of uncertainties to be analyzed to the minimum relevant ones, and thus minimize computational cost. For this study Figure 1 shows that open water efficiency is very sensitive to propeller chord length and ship velocity, while thickness plays only a minor role. Knowing this allows us to merge all thickness sections together for this study, forming one single uncertainty control for the thickness at 70% of the span height. This enables us to reduce the total number of uncertainties to be taken into account from 12 to 5, even though the total impact of all uncertainties is maintained in the analysis.

Figure 1: Scale sensitivity on open water efficiency

Deterministic vs robust optimal design

UQ analysis was performed on the standard deterministic design, in order to be able to compare its results with the robust optimal version. Figure 2 shows a characteristic Pareto plot where the standard deviation of the open water efficiency is shown over its mean value.

Figure 2 : Pareto plot showing the standard and robust optimal design together with the baseline design in the two objective spaces.

Standard design optimization

The baseline design that the study started from is indicated in the graph by the red dot and the UQ results of the standard optimal design (not taking into account uncertainties) by the blue square. The plot shows that the open water efficiency has increased quite significantly by 8.5%, but that there is also an increase of 2.6% in its standard deviation. This means that this design is slightly more sensitive to the influence of manufacturing variability and axial velocity than the original design. »

Robust design optimization

Robust optimal design 3 plotted in fig. 2 shows that the mean value of the open water efficiency increased by the same amount as for the standard optimal design, namely 8.5%. However, its variability is reduced by -17.7%. That means that this design is less sensitive to the influence of manufacturing variability and axial velocity than the original design and that it provides more stable performances.

Propeller shape

Figure 3 compares the shapes of the standard optimized design and the best robust optimized result with the original propeller shape. Even though performance is the samefor both designs, their shapes are significantly different!

Figure 3 : Resulting propeller shape

Conclusions

Robust Design Optimization enables engineers to create designs that are less sensitive to existing and unavoidable manufacturing and operational variabilities. Comparing standard and robust design optimization clearly showed that a comparable performance increase can be achieved with both strategies in this marine propeller case, but only the robust optimization allows for reduction of performance variability, making it less sensitive to uncertainties originating from the manufacturing process or from operational variability.

Posted by Dirk Wunsch

Dirk Wunsch is head of the Robust Design group at Numeca International in Brussels, Belgium. He holds an aerospace engineering degree from the University of Stuttgart, Germany and a doctorate from the Institut National Polytechnique in Toulouse, France. He has a background in multiphase flow modelling and simulation. After he joined Numeca he had been working as development engineer on spray and particle flow modelling for turbo-machinery applications, spray combustion and multi-purpose multiphase flow simulation capabilities for a few years. Later he has been in charge of uncertainty quantification (UQ) modelling within Numeca and is now leading the Robust Design group focusing on UQ and robust and reliable design optimization