A tool was developed for optimizing 3D marine structures subjected to fluid forces and stresses. It was used to optimize a NACA 0009 hydrofoil, leading to a 12.4% efficiency increase, 7.3% weight reduction, and 45% higher cavitation inception speed, while satisfying stress and cavitation constraints. The tool can optimize complex marine propellers and turbines to reduce fuel use and emissions in maritime transport, responsible for 90% of world trade.

1. • A high-fidelity hydrostructural design optimization tool for 3-D lifting
bodies operating in dense, incompressible fluids with consideration for
cavitation and maximum stress, was developed.
• High-fidelity hydrostructural optimization of NACA 0009 hydrofoil can
lead to:
 Increase in efficiency by 12.4%
 Reduction in weight by 7.3%
 Increase in cavitation inception speed by 45%
• Systematic study of the design space of marine propulsors using the
state-of-art high-fidelity hydrostructural optimization tool has the
potential to drastically improve fuel efficiency and hence reduce CO2
emission, enhance agility, and reduce the structural weight, while
ensuring the structural integrity and delaying cavitation inception.
Support for this research was provided by the U.S. Office of Naval
Research (Contract N00014-13-1-0763), managed by Ms. Kelly Cooper.
The computations were performed on the Flux HPC cluster at the
University of Michigan Center of Advanced Computing.
1. G. A. Zarruk, P. A. Brandner, B. W. Pearce, and A. W. Phillips. (2014).
Experimental study of the steady fluid–structure interaction of flexible
hydrofoils. Journal of Fluids and Structures, 51, 326-343.
High-fidelity Hydrostructural Shape Optimization of
a 3-D Hydrofoil
Nitin Garg1, Gaetan K. W. Kenway2, Joaquim R. R. A. Martins2, Yin L. Young1
1Department of Naval Architecture and Marine Engineering, University of Michigan, AA, MI.
2Department of Aerospace Engineering, University of Michigan, AA, MI.
Overview
Methodology
Results and Discussion
Conclusions
Acknowledgements
References
With increasing focus on developing energy efficient marine propulsors
due to the increasing oil prices and desire to reduce the environmental
impacts of marine transportation. In the present research, a state-of-art,
efficient, high-fidelity hydrostructural design optimization tool, capable of
handling large number of design variables, with constraint on cavitation
and maximum stress is presented. Results show that coupled
hydrostructural optimization of the cantilevered Aluminum NACA 0009
hydrofoil can lead to increase in efficiency (i.e., ratio of lift to drag) of
12.4%, reduction in weight by 7.3%, and increase in cavitation inception
speed by 45%. The following method can be easily extended to solve for
more complex marine propulsors like propellers, turbines, and other
control surfaces, to improve the fuel efficiency and reduce CO2 emissions
of maritime transportation, which is responsible for 90% of the world trade.
0
400
800
1200
1600
0 2 4 6 8 10
LiftForce(N)
α
0
4
8
12
16
20
0 2 4 6 8 10
BendingDeformation(mm)
α
Exp. [1]
MACH
Figure 4: RANS-based coupled hydrostructural optimization results in 12.4% increase in efficiency, 7.3%
reduction in weight, and 45% increase in cavitation inception speed.
Figure 3: Good agreement was observed between the numerical predictions and the experimental
measurements [1].
Fluids and structure are tightly coupled disciplines in the design of
maritime platforms and propulsors. The focus of this research is to present
a state-of-art, high-fidelity, coupled hydrostructural optimization tool. In
Figure 3, the coupled hydrostructural validation with experimental
measurements from [1] is presented in terms of the lift force and maximum
tip bending deformation for the solid, unswept, cantilevered, tapered
Aluminum 3-D NACA 0009 hydrofoil. In Figure 4, detailed comparison of
the NACA 0009 hydrofoil and the hydrostructural optimized foil is
presented. A total of 210 design variables were used in the optimization
study, with constraint on lift coefficient (CL), cavitation number (σ), and
maximum von-Mises stress (based on fatigue strength of Aluminum). The
coupled hydrostructural optimized foil results in increase in efficiency of
12.4%, reduction in weight by 7.3%, and increase in cavitation inception
speed by 45% (assuming an operational depth of 1 m), over the original
NACA 0009 hydrofoil, while satisfying the cavitation constraint and the
maximum stress constraint.
Figure 2: Pictorial description of the problem setup used for the optimization study. The 200 shape
design variables (FFD control points) and 10 twist design variables are depicted on the right side.
Figure 1: Basic optimization workflow
To carry out coupled hydrostructural gradient-based optimization, the
modified Multi-disciplinary Design Optimization (MDO) of Aircraft
Configurations with High-fidelity (MACH) is used. Highly efficient and
accurate adjoint method is used to calculate gradients for carrying out
gradient-based optimization with large number of design variables
(greater than 100).