Design optimization for self-propulsion of a bulk carrier hull using a discrete adjoint method
Introduction
Hull hydrodynamic performance is an important aspect of ship design because it determines their economic viability. Traditional hull shape designs rely heavily on the designers’ experience. The process typically involves manual geometry modification followed by performance evaluation. With advances in computing techniques, however, the hull design process can be automated using the computational fluid dynamics (CFD) method integrated with an optimization algorithm [1]. The main benefit of using automated design optimization is that it reduces the length of the design cycle while achieving satisfactory design quality compared with human-supervised design tools. This advantage has been quantitatively demonstrated for aerospace applications [2], and it is plausible that the same benefit applies to ship designs.
Owing to this advantage, CFD-based hull shape optimization has received increasing interest in recent years. Optimization algorithms can be divided into two categories: gradient-free and gradient-based. Gradient-free methods (e.g., genetic algorithm, particle swarm algorithm, and differential evolution) require only the values of the objective and constraint functions. Therefore, they can treat the CFD code as a black-box and are generally easy to implement. In addition, some gradient-free algorithms perform global exploration of the design space and have a higher chance of finding a point close to the global minimum compared with gradient-based algorithms; a favorable feature for handling multimodal problems. Gradient-free methods have been used in various hull shape optimization studies [3], [4], [5], [6], [7], [8], [9]. To further improve optimization efficiency, hybrid optimization strategies were developed using both global and local explorations [1], [10], [11], variable-fidelity methods were used that involved high- and low-fidelity CFD models [1], [10], and Karhunen–Loève expansion method was proposed to reduce the dimension of design space [12], [13].
Gradient-based methods require not only the values but also the derivatives of objective functions and constraints. Gradient-based methods typically perform local exploration of design space by starting from the baseline design and using the gradient (derivative) information to find the most promising direction for improvement. To efficiently compute the derivatives, one can use the adjoint method, the computational cost of which is independent of the number of design variables [14], [15], [16]. This salient feature allows a gradient-based method to handle complex design problems with a large amount of freedom for geometric modification. In addition, the derivatives provide extra information on the function behavior, which allows an optimizer to converge to the optimum more efficiently. Although gradient-based methods are only guaranteed to converge to local minima, we have found that the design space in aerodynamic shape optimization is for the most part unimodal [17], [18]. Because unimodality is impossible to prove but easy to disprove, we assume that the design space is unimodal until we find multiple local minima. Therefore, we opt to use gradient-based optimization for hull shape design, because of its ability to handle large-scale complex design problems.
The combination of gradient-based optimization and adjoint derivative computation has been widely used in aircraft [19], [20], [21], [22], [23], ground vehicles [24], [25], hydrofoil [26], [27], and turbomachinery [28], [29] design optimization, as well as in hydrodynamic optimization of ship hulls [30], [31], [32], [33], [34], [35], [36]. The challenges of adjoint-based hull shape optimization include handling the naturally unsteady nonlinear interaction of ship waves and wave breaking, formulating the optimization problems with the relevant design considerations (e.g., drag, wake distortion) as well as imposing appropriate geometric and physical constraints [31]. To handle the free surface, early adjoint-based hull optimization focused on potential flow [30], [32]. Recently, Kröger et al. [35] used the volume-of-fluid method to handle the free surface in an adjoint-based hull shape optimization framework, and imposed geometric constraints to maintain the main dimension and displacement of the hull. In terms of formulating design considerations, drag [30], [31], [32], [33] and propeller-wake distortion [34], [37] have been individually used as the objective function in hull design optimization.
Nelson et al. [38] used a low-fidelity, multidisciplinary design optimization model to optimize a hull-propeller system, and concluded that simultaneously considering multiple objectives is critical due to their tight coupling. This is because a low drag design can cause high wake distortion, which is characterized by alternate low- and high-speed wake regions in the circumferential direction at the propeller plane. When the propeller blades pass through the low-speed-wake region, blade loading decreases and cavitation can occur [37], [39]. Similarly, a low-wake-distortion design can induce a large penalty in drag. Thus, there is a need to consider both drag and wake distortion in hull design optimization.
Driven by the above motivation, we conduct a hull-shape optimization in towed and self-propelled modes using a high-fidelity, gradient-based hydrodynamic shape optimization framework. We simultaneously consider drag and wake distortion in the hull shape designs and use the adjoint method to efficiently compute the derivatives; this allows a large number of design variables to parameterize the complex hull shape and provides correspondingly broad freedom in geometric modifications. We use the discrete adjoint method because its derivatives are fully consistent with flow solutions, as discussed in our previous studies [25]. We impose geometric constraints on the hull surface (volume, thickness, and curvature) to ensure that the final designs are practical.
The baseline geometry is the Japan bulk carrier (JBC) [40] at model scale, and we focus on optimizing the stern region of the hull. This design is a capesize bulk carrier that has been the focus of propulsive efficiency improvement studies [41], [42], [43], [44]. The design Froude number is relatively low, and our focus is hull-propeller interaction. Free-surface effects are not included; while the wave field can influence propulsive performance (it certainly alters the flow near the water surface), our objective is to demonstrate the ability to consider a large number of design variables for hull-propeller interaction with the discrete-adjoint method and RANS-based CFD. Another important focus of this work is to demonstrate the importance of optimization in self-propulsion configuration, rather than in the towed condition. To this end, we use the actuator disk method to mimic the effect of the propeller. This simplification introduces simulation errors compared with unsteady simulations using dynamic meshes for the propeller. However, it enables RANS-based optimization and significantly reduces the computational cost compared with an unsteady adjoint approach.
The rest of the paper is organized as follows. In Section 2, we introduce the optimization framework and its components. The hull shape optimization results are presented and discussed in Section 3 and we summarize our findings in Section 4.
Section snippets
Methods
In this study, we adapt our aerodynamic optimization framework [25] to perform hydrodynamic design of ship hulls. We use the gradient-based optimization approach coupled with the adjoint method to efficiently compute the total derivative where f is the function of interest (drag, wake distortion, or a combination of both), and x represents the design variables that control the design surface geometry. In this section, we first introduce the overall optimization framework, followed by a
Results and discussion
In this section, we present the optimization results, in terms of both drag and wake distortion at the propeller plane. We construct a Pareto front using five optimizations with different combinations of weights for drag and distortion. We analyze and interpret the optimization results by comparing shapes and flow structures between the single- and multi-objective cases. We use the JBC hull as our baseline geometry, and both towed and self-propulsion configurations are considered. We also
Conclusions
In this paper, we have conducted hydrodynamic design optimization for a model-scale JBC hull, simultaneously considering drag and wake distortion. We used a gradient-based optimization framework coupled with an efficient discrete adjoint solver to compute derivatives. We used 32 design variables to parameterize the complex hull surface, which allowed us to have great freedom for geometric modification. In addition, we imposed geometric constraints (volume, thickness, and curvature) to ensure
Acknowledgment
The computations were done in the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant No. ACI-1548562.
References (67)
- et al.
Shape optimization in ship hydrodynamics using computational fluid dynamics
Comput Methods Appl MechEng
(2006) - et al.
Comparison between aerodynamic designs obtained by human driven and automatic procedures
Aerosp Sci Technol
(2018) - et al.
A new surface modification approach for CFD-based hull form optimization
J Hydrodyn Ser-B
(2010) - et al.
Design optimization of the lines of the bulbous bow of a hull based on parametric modeling and computational fluid dynamics calculation
Math Comput Appl
(2017) - et al.
High-fidelity global optimization of shape design by dimensionality reduction, metamodels and deterministic particle swarm
Eng Optim
(2015) Aerodynamic design via control theory
J Sci Comput
(1988)- et al.
Optimum aerodynamic design using the Navier–Stokes equations
Theor Comput Fluid Dyn
(1998) - et al.
Aerodynamic shape optimization investigations of the Common Research Model wing benchmark
AIAA J
(2015) - et al.
High-fidelity multipoint hydrostructural optimization of a 3-D hydrofoil
J Fluids Struct
(2017) - et al.
Aerothermal optimization of a ribbed U-bend cooling channel using the adjoint method
Int J Heat Mass Transf
(2019)
An adjoint-based design methodology for CFD optimization problems
41st Aerospace Sciences Meeting and Exhibit
Verification and validation of resistance and propulsion computation
Proceedings of Tokyo 2015 Workshop on CFD in Ship Hydrodynamics
A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows
Int J Heat Mass Transf
Efficient management of parallelism in object oriented numerical software libraries
Computational fluid dynamics-based multiobjective optimization of a surface combatant using a global optimization method
J Mar Sci Technol
Bulbous bow retrofit of a containership using an open source computational fluid dynamics (CFD) toolbox
SNAME Trans
An effective approximation modeling method for ship resistance in multidisciplinary ship design optimization
ASME 2014 33rd international conference on ocean, offshore and arctic engineering
Uncertainty quantification for a sailing yacht hull, using multi-fidelity Kriging
Comput Fluids
Computational fluid dynamics-based hull form optimization using approximation method
Eng Appl Comput Fluid Mech
High-fidelity models and multiobjective global optimization algorithms in simulation-based design
J Ship Res
Ship hydrodynamic optimization by local hybridization of deterministic derivative-free global algorithms
Appl Ocean Res
Design-space dimensionality reduction in shape optimization by Karhunen–Loève expansion
Comput Methods Appl Mech Eng
Multidisciplinary design optimization of aircraft configurations—Part 2: High-fidelity aerostructural optimization
Lecture Series
A laminate parametrization technique for discrete ply angle problems with manufacturing constraints
Struct Multidiscip Optim
On the influence of optimization algorithm and starting design on wing aerodynamic shape optimization
Aerosp Sci Technol
Multimodality in aerodynamic wing design optimization
AIAA J
Aerodynamic design optimization on unstructured meshes using the Navier–Stokes equations
AIAA J
Aerodynamic design optimization on unstructured grids with a continuous adjoint formulation
Comput Fluid
Multipoint high-fidelity aerostructural optimization of a transport aircraft configuration
J Aircr
Adjoint methods for car aerodynamics
J Math Indus
An aerodynamic design optimization framework using a discrete adjoint approach with OpenFOAM
Comput Fluids
High-fidelity hydrodynamic shape optimization of a 3-D hydrofoil
J Ship Res
Adjoint aerodynamic design optimization for blades in multistage turbomachines—part I: methodology and verification
J Turbomach
Cited by (22)
Analysis of partially cavitating hydrofoils under the free surface using BEM-based adjoint optimization
2022, Applied Mathematical ModellingCitation Excerpt :Among optimization methods, gradient-based methods can be more efficient when the optimum is nearby. Particularly, adjoint methods based on continuous [44] or discrete formulations [45] are of great interest due to their ability to efficiently handle large numbers of design variables. Notable is the introduction of continuous adjoint methods for fluid dynamic design, typically attributed to [46], who studied drag minimization for two-dimensional shapes in Stokes and Low-Reynolds number flows.
Simultaneous wing shape and actuator parameter optimization using the adjoint method
2022, Aerospace Science and TechnologyMultidisciplinary design analysis and optimisation frameworks for floating offshore wind turbines: State of the art
2022, Ocean EngineeringCitation Excerpt :However, the framework only supports optimisation algorithms available in the python library pyOptSparse, and the choice of physics solvers is limited to those implemented in OpenFOAM. An example of the application of DAFoam to engineering optimisation can be found in He et al. (2019). DAKOTA is a multilevel parallel object-oriented framework for sensitivity and uncertainty analysis, design optimisation and calibration, developed by the Sandia National Laboratory with contributions from the community.
Resistance and wake distortion optimization of JBC considering ship-propeller interaction
2022, Ocean EngineeringCitation Excerpt :Feng et al. (2018) optimized an offshore aquaculture vessel to improve the resistance performance and the wake field quality. He et al. (2019a) used the adjoint method and potential method to optimize the resistance and propeller wake under self-propulsion and towing conditions. Liu et al. (2021) improved the resistance and wake performance of Japan Bulk Carrier utilizing the Liutex-based centripetal force field.
A discrete adjoint method for pressure-based algorithms
2021, Computers and FluidsCitation Excerpt :A different interpolation for the interior mesh is usually chosen in order the preserve the boundary layer resolution and to prevent the optimizer from taking advantage of mesh effects. We adopt the use of inverse distance weighted (IDW) interpolation to deform the interior mesh [16,17]. For the surface mesh deformation, two methods are described in this paper.