Shape Optimization Research Articles

Design optimization of phononic-fluidic resonator systems

Phononic-fluidic resonators utilize an acoustic fluid domain as a defect inside a solid metamaterial lattice, which can be used used to precisely measure acoustic properties of liquids. The design goal is to offer ideal boundary conditions for the acoustic resonator by matching defect resonance with phononic band gap. The design space of metamaterial or phononic crystal and fluidic resonator is nearly unlimited, especially when utilizing fully three-dimensional structures. In this work, we explore numerical shape and topology optimization to focus acoustic energy into the fluid domain and maximize the quality factor of the defect resonance. This requires the use of complex multi-frequency objective functions, while taking into account practical limits such as finite size and losses in the fluid and solid domains. Results highlight notable but limited improvements of quality factor with shape optimization starting from an initial design constrained by the maximum deformation possible. On the other hand, topology optimization results offer unique and unexpected ideas, and thus a deeper dive into the design space.

Testing Pellets Fuel Production from Sewage Sludge of Palm Oil Industry

The wastes from the palm oil production process were used in this study, such as wastewater sludge and cake decenter or decanter waste. That moisture was less than 40% and increased density by the cold pelletizing process. The aim is to use pellet fuel for heating. Analysis of pellet fuel consists of physical properties, proximate (moisture, ash, volatile matter and fixed carbon) and heating value. The results showed that cake decenter and wastewater sludge had similar high volatile matter. The decenter cake had a higher heating value than the wastewater sludge at 26.649 and 14.965 MJ/kg, respectively. The ash of decenter cake was lower than wastewater at 11.71% and 22.34%, respectively. Blending both raw materials for pelletization increased the volatile matter that did not mix with another material. Therefore, both materials can be used to produce pellet fuel that has an optimal shape and size. That was hard to break. The results of chemical property testing show that it is within acceptable limits and can be used as pellet fuel.

Numerical Evaluation of Wave Dissipation on a Breakwater Slope Covered by Precast Blocks with Different Geometrical Characteristics

Slopes suffer damage from waves in coastal environments. Precast blocks with well-designed geometrical characteristics can benefit the construction of revetments by mitigating the issue of wave overtopping and dissipating wave energy. In this study, we numerically studied the effect of the geometrical characteristics of precast blocks on wave overtopping by carrying out a numerical simulation of wave overtopping on a slope covered with precast blocks. A total of three different types of blocks were considered in this study to determine the optimal geometric shape using a validated numerical model. Our numerical investigation demonstrated that the roughness of the precast block plays an important role in lessening the height of the wave run-up. Concave and embedded regular hexagons could reduce the wave run-up height by 44.6% compared with smooth slopes within a 2 s wave period. Herein, we evaluate and discuss the influence of the geometrical characteristics of a given precast block, such as thickness, aperture, and wave dissipation notch, on wave run-up. We also present an empirical formula for predicting wave run-up on a slope covered by a concave and embedded regular hexagon-type prefabricated block. This study provides valuable insights into the design of prefabricated revetment blocks.

Shape Optimization by Constrained First-Order System Least Mean Approximation

Shape Optimization by Constrained First-Order System Least Mean Approximation

Shape optimization with level set-based method using a reaction diffusion equation for 2D sound barrier

A level set-based method using a reaction diffusion equation is applied for optimization problems of two dimensional (2D) sound barriers. The level set method is employed to implicitly represent the sound barrier structure, which distinguishes the material and void domains by the value of the level set function. The boundary element method is employed to solve acoustic problems governed by Helmholtz equation. Topological derivatives are computed by the boundary integral equation combined with the adjoint variable method. The distribution of level set function is iteratively updated based on the reaction diffusion equation to find the optimal structure. For the existent floating scatterers in the optimization process and the sharp and narrow parts on the surface of the sound barrier, we propose a filtering algorithm to remove floating scatterers and develop a method to achieve a smooth surface of the sound barrier. The shape optimization of sound barriers is achieved using these techniques, integrating the level set-based topology optimization method. Numerical tests are provided to demonstrate the validity and effectiveness of the proposed methods.

Shape controlled synthesis and crystal facet dependent gas sensitivity of tungsten oxide

Gas sensors can achieve remarkable functionality through the optimization of particle size, shapes, crystal facets, and oxygen defects, resulting in unsaturated coordination atoms, high charge densities, and enhanced bond energies. In this study, WO2.72 nanourchins, WO3-x nanowires, and WO3 nanorods/nanocube with (010), (001), (200), and (002) dominant crystal facets were synthesized and used as gas sensing materials. It was found that WO2.72 nanourchins exhibit an excellent response of Ra/Rg=21 to 100 ppm acetone with good selectivity among other sensors as-fabricated. First-principle calculations of Density Functional Theory were performed on acetone's adsorption on different crystal planes of tungsten oxide. The results verify spontaneous and fast adsorption on the (010) crystal plane than on the (001) and (200) planes. Further characterizations indicate that WO2.72 nanourchins with (010) crystal facets contain more reactive sites with high surface energy, facilitating charge separation, increasing charge carrier mobility, and enabling the redox reactions to occur independently at different rates. Moreover, their richer electron-donor surface oxygen defects, smaller feature sizes, and higher surface area (SBET) with hierarchical porous structures, all contribute to the enhanced acetone sensing. Our work provides a strategy for improved acetone sensing based on optimizing the particle shape with different crystal facets and oxygen vacancy density. We further expect our strategy to be applicable in designing other sensor materials with efficient charge separation and fast surface redox reactions to detect toxic gases.

Emerging cost-time Pareto front for diffusion with stochastic return

Abstract Resetting, in which a system is regularly returned to a given state after a fixed or random duration, has become a useful strategy to optimize the search performance of a system. While earlier theoretical frameworks focused on instantaneous resetting, wherein the system is directly teleported to a given state, there is a growing interest in physical resetting mechanisms that involve a finite return time. However employing such a mechanism involves cost and the effect of this cost on the search time remains largely unexplored. Yet answering this is important in order to design cost-efficient resetting strategies. Motivated from this, we present a thermodynamic analysis of a diffusing particle whose position is intermittently reset to a specific site by employing a stochastic return protocol with external confining trap. We show for a family of potentials U R ( x ) ∼ | x | m with m > 0, it is possible to find optimal potential shape that minimises the expected first-passage time for a given value of the thermodynamic cost, i.e. mean work. By varying this value, we then obtain the Pareto optimal front, and demonstrate a trade-off relation between the first-passage time and the work done.

Evaluation of Clogging Potential Prediction Methods in Axial Flow Waterjet Pumps with CFD-DEM

Abstract Axial flow waterjet pumps propel high-speed passenger vessels by energizing and expelling fluid. In operation, foreign objects may enter, especially in shallow waters, potentially leading to performance decline and damage. Evaluating passage performance is crucial but primarily experimental and computationally costly. Limited research exists on deliberately introducing solids into axial flow pumps due to visualization challenges. Hence, experiments simulated solid substance entry into axial flow pumps, varying particle conditions. High-speed cameras visualized particle behaviour, exploring retention and optimal pump shapes. Additionally, simulations using the Discrete Element Method (DEM) confirmed its utility in predicting foreign object passage, with variations in particle retention across regions noted.

Building shape optimization based on interconnected embodied and operational energy and carbon impacts

Strategic building design decisions informed by a comprehensive life cycle impact assessment hold substantial potential in addressing global energy consumption and carbon emissions, with buildings accounting for 40% of energy consumption and 37% of emissions. While building operational energy (OE) has traditionally received greater attention, the dynamic trade-offs between OE and embodied energy (EE) in building design are often overlooked. Design decisions, such material selection and building shape, can present conflicting considerations between OE and EE. Addressing these impacts in isolation may fail to achieve comprehensive reductions in energy consumption and carbon emissions. This study highlights the necessity of a holistic approach to design decisions such as building shape and material selection, emphasizing the importance of considering both OE and EE simultaneously. Our literature review confirms a gap in studies that consider these factors together in the context of building shape optimization. To analyze the interconnectivity of building shape design, material choice, and the trade-offs between OE and EE, we devised two parametric test cases with identical features but using two different insulation materials: hemp-based and glass wool. The analysis allows us to (1) evaluate the impact of integrating total lifecycle impact on building shape design optimization, in comparison to designs that focus solely on OE; (2) assess how the selection of materials, specifically hemp-based versus glass wool insulation, influences optimized building shape and carbon emissions reduction; and explore the benefits of bio-based materials by analyzing performance variations in the two insulations case studies. Our findings reveal that although OE typically has a larger impact over a building’s lifetime, the optimal building shape can still vary significantly based on the EE contribution. The benefit of bio-based material is context-dependent, varying with factors such as the building shape discussed in this paper, as well as other factors such as climate. In our test cases, we observed that shape variations resulted in up to a 17.9% change in OE due to different building shapes, and a 60.7% variation in the envelope’s surface area, while the building area remained unchanged. This expanded understanding will facilitate more informed and sustainable decision-making in the construction and design industries, addressing the often-overlooked interconnectivity of OE and EE.

A guidance of solid element application in predicting the ultimate strength of flat plates in compression

With the increasing demand in ocean engineering field for the ultimate limit state (ULS) analysis of thick plates, the solid (3D) element has been more frequently used in the ULS analysis. Compared to 2D element, 3D element can better consider the transverse shearing effect during the analysis which usually occurs on thick plates, due to its reliable reflection of geometrical characteristics and kinematic equations of the structures. Besides, 3D element can also facilitate the introduction of influencing factors into the ULS analysis, such as the erosions, cracks and residual stress. This may improve the simulation precision of ULS analysis of thick plate models. Until now, there is a lack of 3D element modelling technique in the ULS analysis of flat/stiffened plates. The present study aims to provide helpful information on 3D elements in the ULS analysis of flat plates under axial compression load. A total of 350 plate scenarios were adopted in the parametric study to consider the effects of 3D element shape (αyz). It is found that the element shape significantly influences the ULS analysis of flat plates, where planar-like 3D element is not recommended. An empirical formula for determining the optimal 3D element shape of the finite element (FE) model is proposed based on the parametric results. A guidance for implementing the 3D elements is then documented, which may help engineers further understand the ultimate strength characteristic of very thick flat plates.

Enhancing Heat Storage Capacity: Nanoparticle and Shape Optimization for PCM Systems

ABSTRACTPhase change material (PCM)‐based heat storage systems utilize the absorption or release of latent heat during a phase change of the storage material to store thermal energy. Nevertheless, the effectiveness of these systems is restricted by the shape and structure of their confinement, as well as the heat conductivity of the storage material. This work investigates a novel method to enhance the effectiveness of PCM systems by concurrently utilizing two techniques: the inclusion of nanoparticles and the alteration of the system's geometry. Introducing nanoparticles enhances the thermal conductivity of the storage medium while altering the shape, which improves heat transfer efficiency by adjusting the surface area available for heat exchange. RT‐35 was tested for use in latent heat thermal energy storage systems for space heating and cooling. With a melting point of 35°C, RT‐35 was chosen to moderate building temperatures by storing and releasing thermal energy for space heating and cooling. The results indicate that using nanoparticles and adjusting shape can greatly enhance the effectiveness of PCM systems. By incorporating Al2O3 nanoparticles, the melting time of the PCM was reduced by 20% compared to the pure PCM, and it is more efficient than the best case of shape modification. These findings indicate that including nanoparticles and modifying the shape are effective methods to improve the performance of heat storage devices. This technology's potential surpasses this study's limits and can be utilized in diverse applications, including solar thermal energy storage, district heating and cooling, and industrial process heat.

Level-set based shape optimization for plane elastic structures using radial basis functions and Hilbertian descent direction

Structural optimization problems are often associated with the so-called shape functionals depending on a shape through its geometry and the state being a solution of given partial differential equation. In such a framework it is convenient to work with the gradient-like method based on a concept of a shape derivative and level set method. The key idea of level set method is to represent the structural boundary with zero level set of given function (level set function—LSF). Now, changing the shape of a structure under optimization is equivalent to transport the LSF in such a direction that ensures decreasing the value of the objective functional. To this end, we make use of coercive bilinear form taken from the weak formulation of elasticity problem to obtain descent direction at each iteration. This descent direction is a solution of an additional variational problem, involving the bilinear form mentioned above and the volumetric expression of the shape derivative plays the role of a linear form. In this paper, we combine level set method with radial basis functions (RBFs) used to approximate LSF. We focus on the so-called multiquadric RBFs, but other classes of RBFs are also briefly considered. This eventually leads to transformation of partial differential equation (linear transport equation governing the evolution of shapes) to a system of linear ordinary differential equations which admits analytical formula for the solution. We apply our method to compliance minimization of a cantilever problem as well as to total potential energy minimization of a structure with kinematic loading. To run all the numerical experiments, we wrote our own code in Wolfram Mathematica environment.

Data-driven airfoil shape optimization framework for enhanced flutter performance

Data-driven airfoil shape optimization framework for enhanced flutter performance

Improving Transonic Performance with Adjoint-Based NACA 0012 Airfoil Design Optimization

This study delves into the discrete adjoint method, a powerful tool in high-fidelity aerodynamic shape optimization that efficiently computes derivatives of a target function for different design variables. It offers a theoretical exploration of its implementation as an innovative tool for calculating partial derivatives (sensitivities) related to objective functions and design variables. It is implemented to a NACA0012 airfoil at a transonic speed. This designated test case is qualitatively evaluated, considering specified Mach number and Reynolds number values of 0.7 and 15.96 million, respectively. The standard Spalart-Allmaras turbulence model is adapted to improve computational cost efficiency. The results validate the efficiency of Discrete Adjoint with OpenFOAM, showcasing its capability to generate optimal configurations. The achieved optimized performance is evidenced by minimizing the drag coefficient value (CD) to an impressive value of 0.00871, 62.2% lower than the previous studies, thus securing a novelty. While this research does not consider the post-processing of sensitivity calculations, it enables the potential for future research. The primary target of this paper is to assess the educational and training needs of researchers, engineers, and graduate students, offering a comprehensive introduction to discrete adjoint aerodynamic design optimization, presenting a novel methodology, and contributing to future advancements in the design optimization field.

A new mesh deformation method using quaternion and displacement normal propagation for high quality and high efficiency

Mesh deformation technology is widely used in aerodynamic applications like unsteady flow, aeroelasticity, and aerodynamic shape optimization because of its low computational costs and consistent mesh connectivity. In order to raise deformed mesh quality and improve efficiency, a new mesh deformation method based on quaternion and displacement normal propagation (named QN method) is introduced in this paper. The boundary points propagate their displacements composed of translational vectors and quaternions to corresponding volume points along the normal direction under the control of the damping function, which preserves the mesh shape and guarantees the quality near boundaries, including orthogonality and normal size. It can also prevent the volume points from being interfered by other less relevant boundary points, so dealing with complex displacement fields effectively. In addition, it avoids complicated matrix and interpolation operations, thus saving lots of computational costs. For mesh with complex topology, a hybrid method combining the QN method and the radial basis function method (RBF method) is investigated to broaden application scenarios, which are applied to the mesh with normal correspondence inside the boundary layer and the mesh outside, respectively. Benefitting from effective handling for the near-wall elements by the QN method, the RBF interpolation part in the hybrid method requires minor support points to carry out valid large deformation, improving the deformation efficiency greatly compared to the individual RBF method. Five typical test cases with different deformation modes and mesh characteristics are implemented, showing better performance of the proposed method in deformed mesh quality and deformation efficiency.

Stress-based topological shape optimization for thick shells using the level set method and trimmed non-conforming multi-patch isogeometric analysis

Stress-based topological shape optimization for thick shells using the level set method and trimmed non-conforming multi-patch isogeometric analysis

Three-dimensional aerodynamic shape optimization with high-order direct discontinuous Galerkin schemes

Three-dimensional aerodynamic shape optimization with high-order direct discontinuous Galerkin schemes

Adjoint-based shape optimization for compressible flow based on volume penalization method

AbstractReducing the resistance of compressible flow around a blunt body is of great interest in engineering applications, while an efficient shape optimization method for compressible flows remains far from well established, especially for high Mach numbers. To this end, a volume penalization method for simulating compressible flows past a no-slip and isothermal solid is established by introducing an artificial body force and a heat sink into the governing equations. The level-set functions are introduced as design variables, and the cost functional is defined as the total drag acting on the solid. Then, a continuous adjoint-based shape optimization algorithm for drag reduction is developed by deriving the adjoint equations, the adjoint boundary conditions, and the shape update formula. Both the forward and adjoint simulations are verified by existing studies. The results show that the relative deviations of the drag coefficients obtained in the present study from those reported in the reference studies are around 5% at most, and also a comparable drag reduction rate and also optimal shapes can be reproduced by the present optimization scheme for benchmark problems at relatively low Mach numbers considered in previous studies. Finally, the present method is applied to shape optimization of an initially two-dimensional cylinder and also a three-dimensional sphere in the transonic regime of Ma∞ = 1.2. The drag reduction of over 20% is achieved for both two-dimensional and three-dimensional cases.

Aircraft Ducted Heat Exchanger Aerodynamic Shape and Thermal Optimization

Abstract Interest in aircraft electrification and hydrogen fuel cells is driving demand for efficient waste heat management systems. Ultimately, most of the heat must be rejected to the freestream air. Ducted heat exchangers, also called ducted radiators, are the most common and effective way to do this. Engineers manually design ducted heat exchangers by adjusting the duct's shape and heat exchanger's configuration to reduce drag and transfer sufficient heat. This manual approach misses potential performance improvements because engineers cannot simultaneously consider all of the complex interactions between the detailed duct shape, heat exchanger design, and operating conditions. To find these potential gains, we apply gradient-based optimization to a three-dimensional ducted heat exchanger computational fluid dynamics (CFD) model. The optimizer determines the duct shape, heat exchanger size, heater exchanger channel geometry, and coolant flowrate that minimize the ducted heat exchanger's power requirements while rejecting enough heat. Gradient-based optimization enables the use of nearly 100 shape design variables, creating a large design space and allowing fine-tuning of the optimal design. When applied to an arbitrary, poorly performing baseline, our method produces a nuanced and sophisticated ducted heat exchanger design with five times less cruise drag. Employing this method in the design of electric and fuel cell aircraft thermal management could uncover performance not achievable with manual design practices.

Numerical investigation on the behavior of thin concrete shells subjected to nonuniform and asymmetrical loads

AbstractConcrete shells, designed with near optimal shapes for uniform gravity loads, can be subjected to nonmembrane effects caused by nonuniform and asymmetrical loads. In this paper, a numerical study on the effect of normative loads on a thin triangular concrete shell with three supports is presented. Two actions were considered, wind and snow, which present high spatial variability in both intensity and direction, assuming the values established in Eurocode 1 for the worst possible location, in Portugal. Linear, nonlinear and stability analyses were performed using the ABAQUS software. Results suggest that the wind action, but especially the exceptional snow load in drifted arrangement, produce significant bending moments, leading to decompression, and eventually to the development of stresses above the tensile strength of current concrete classes. Therefore, the production of these shells by assembling prefabricated un‐reinforced modules, requires the use of ultrahigh‐performance fiber reinforced concrete, combined with prestressing.