[Paper Review] Efficient Reduction in Shape Parameter Space Dimension for Ship Propeller Blade Design

Andrea Mola, Marco Tezzele+5 more|arXiv (Cornell University)|May 15, 2019

Cavitation Phenomena in Pumps4 citations

TL;DR

This paper presents a novel active subspaces (AS)-based dimensionality reduction approach for ship propeller blade design, enabling efficient optimization of 20 geometric parameters by identifying a single dominant linear combination that captures most performance variation. Using potential flow simulations with PROCAL, the method reduces computational cost, identifies key design influences (especially mid-to-tip pitch), and enables constrained optimization for reduced tip vortex pressure and improved efficiency without sacrificing thrust.

ABSTRACT

In this work, we present the results of a ship propeller design optimization campaign carried out in the framework of the research project PRELICA, funded by the Friuli Venezia Giulia regional government. The main idea of this work is to operate on a multidisciplinary level to identify propeller shapes that lead to reduced tip vortex-induced pressure and increased efficiency without altering the thrust. First, a specific tool for the bottom-up construction of parameterized propeller blade geometries has been developed. The algorithm proposed operates with a user defined number of arbitrary shaped or NACA airfoil sections, and employs arbitrary degree NURBS to represent the chord, pitch, skew and rake distribution as a function of the blade radial coordinate. The control points of such curves have been modified to generate, in a fully automated way, a family of blade geometries depending on as many as 20 shape parameters. Such geometries have then been used to carry out potential flow simulations with the Boundary Element Method based software PROCAL. Given the high number of parameters considered, such a preliminary stage allowed for a fast evaluation of the performance of several hundreds of shapes. In addition, the data obtained from the potential flow simulation allowed for the application of a parameter space reduction methodology based on active subspaces (AS) property, which suggested that the main propeller performance indices are, at a first but rather accurate approximation, only depending on a single parameter which is a linear combination of all the original geometric ones. AS analysis has also been used to carry out a constrained optimization exploiting response surface method in the reduced parameter space, and a sensitivity analysis based on such surrogate model. The few selected shapes were finally used to set up high fidelity RANS simulations and select an optimal shape.

Motivation & Objective

• Address the curse of dimensionality in multidisciplinary ship propeller design optimization with high-parameter spaces.
• Develop a parameterized blade geometry generator capable of creating hundreds of blade variants from 20 shape parameters using NURBS-based distributions.
• Apply active subspaces (AS) to identify a low-dimensional manifold in the parameter space that captures the dominant influence on performance metrics such as tip vortex pressure and efficiency.
• Enable constrained optimization in the reduced space to minimize acoustic pressure and maximize efficiency while preserving thrust.
• Reduce the number of high-fidelity RANS simulations by pre-selecting only the most promising candidates from the reduced space.

Proposed method

• Developed a bottom-up, automated blade parameterization tool using NURBS to represent chord, pitch, skew, and rake distributions as functions of radial position.
• Generated 1100 blade variants by varying 20 shape parameters derived from control points of NURBS curves for chord, pitch, skew, and rake.
• Performed potential flow simulations using the low-cost, high-accuracy boundary element method (BEM) solver PROCAL to evaluate performance across the design space.
• Applied active subspaces (AS) analysis to the simulation outputs, identifying a single dominant linear combination of the 20 original parameters that explains most of the variance in performance indices.
• Constructed one-dimensional response surfaces in the active subspace to enable constrained optimization for minimal tip vortex-induced pressure and maximal efficiency.
• Mapped optimal solutions in the reduced space back to the original parameter space and selected the top candidate for high-fidelity RANS validation.

Experimental results

Research questions

• RQ1 Can active subspaces effectively reduce the dimensionality of a 20-parameter ship propeller blade design space while preserving predictive accuracy for key performance metrics?
• RQ2 Which geometric parameters (e.g., pitch, camber, rake) have the highest influence on tip vortex-induced pressure and efficiency?
• RQ3 Can a low-dimensional surrogate model based on active subspaces enable effective constrained optimization for hydroacoustic performance without increasing computational cost?
• RQ4 To what extent can the use of potential flow simulations combined with active subspaces reduce the number of required high-fidelity RANS simulations in the optimization pipeline?
• RQ5 Can the identified active subspace be shared across multiple objectives (e.g., pressure, efficiency, thrust) to enable multi-objective optimization in a reduced space?

Key findings

• The active subspaces analysis revealed that all performance metrics (tip vortex pressure, efficiency, thrust) can be accurately approximated by a single linear combination of the 20 original shape parameters.
• The dominant active variable was found to be most sensitive to mid-to-tip region pitch modifications, with camber changes in the blade middle portion having a secondary but notable influence.
• The response surface for tip vortex-induced maximum pressure $P_{ ext{max}}$ achieved a prediction accuracy of 80% on the training set and 20% for validation, with a one-dimensional model capturing the essential behavior.
• The optimal blade shape identified via constrained optimization in the reduced space achieved minimal $P_{ ext{max}}$ while maintaining thrust and improving efficiency, and was selected for high-fidelity RANS simulation.
• The entire optimization pipeline reduced the number of high-fidelity simulations from potentially thousands to just one final candidate, significantly accelerating the design process.
• The method demonstrated that a 20-dimensional design space can be effectively reduced to a single dominant parameter, enabling efficient and interpretable optimization in engineering design.