Shape Optimization Research Articles

Comprehensive investigation of optimal vortex generator shape and position for heat transfer enhancement in a rectangular passage to cool electronic appliances: A numerical analysis

Comprehensive investigation of optimal vortex generator shape and position for heat transfer enhancement in a rectangular passage to cool electronic appliances: A numerical analysis

A simultaneous shape and topology optimization approach of shell structures based on isogeometric analysis and density distribution field

This paper presents a novel simultaneous shape and topology optimization approach of shell structures based on isogeometric analysis and density distribution field. In the optimization approach, Non-Uniform Rational B-Splines (NURBS) technology is utilized to describe the geometry and material distribution of the shell structures. The coordinates and densities of the NURBS control points are utilized as design variables to simultaneously optimize the shape and topology of shell structures. The proposed approach offers significant advantages, including ease of implementation, seamless integration with CAD models, high efficiency, and smooth, clear boundaries. Two representative examples are performed to demonstrate the effectiveness of the proposed approach. The optimized configurations are compared with other works and commercial software results.

Better than linear strength scaling of multifunctional ceramic truss lattice materials

Driven by the goal of creating exceptionally strong and lightweight thermal insulators to enable the operation of a vacuum airship on Venus, conditions where ceramic truss lattice materials provide better than linear scaling of strength with respect to variations in relative density have been found. This enhanced scaling relationship is a consequence of the pressure sensitive shear strength of ceramic materials. A new Gibson-Ashby type scaling relationship is developed between strength and relative density. Elementary analysis is used to formulate theoretical limits for the compressive strength, minimum density, and minimum thermal conductivity for truss lattice materials subjected to hydrostatic pressure loads. Shape optimization using the covariance matrix adopted evolutionary strategy (CMA-ES) and highly resolved finite element models is conducted on silicon carbide Kelvin cells with variable cross-section axisymmetric struts considering three failure modes: buckling, tensile rupture, and shear failure. The optimized designs closely adhere to and validate the newly developed analytical scaling relationship with better than linear strength scaling. These optimized designs are found to withstand the extreme loading conditions on Venus while providing up to 43 kgm3 of buoyancy. The thermal conductivity of the optimized designs are computed and found to be less than 0.5 WmK, with one design outperforming silica aerogels at elevated temperature.

Hand drill shape optimization using Open CASCADE library and the steepest descent method

In this article, compliance optimization with the steepest descent method of the hand drill bits shapes for metal drilling is presented. The analysis of stress, displacements and compliance of the solid with random shape can be performed using the finite element method. In the case of a high number of optimization iterations, each analysis needs automatic modifications of geometry, mesh and boundary conditions. The Open CASCADE library can be used in the fast and automatic construction of modified models. It allows for fast reanalysis for each derivative of the objective function in the optimization process. The motivation of this research is to fill the gap in the literature on drilling technology. Most of the contemporary research is devoted to the oil and gas industry, while optimization of the hand drill bits used in metal drilling is rare. Compliance optimization allows us to find the shape which guarantees a greater stiffness for the specified loading conditions and a given amount of material. Although the obtained compliance was low, further experimental research would be needed to apply new solutions in drilling practice. This will involve the construction of the drill bit tips and the development of a heat treatment process

Automatic Differentiation Accelerated Shape Optimization Approaches to Photonic Inverse Design in FDFD/FDTD

AbstractShape optimization approaches to inverse design offer low‐dimensional, physically‐guided parameterizations of structures by representing them as combinations of primitives. However, on fixed grids, computing the gradient of a user objective via the adjoint variables method requires a product of forward/adjoint field solutions and the Jacobian of the simulation material distribution with respect to the structural shape parameters. Shape parameters often perturb global parts of the simulation grid resulting in many non‐zero Jacobian entries. These are often computed by finite‐difference (FD) in practice, and hence can be non‐trivial. In this work, the gradient calculation is accelerated by invoking automatic differentiation (AD) in instantiations of structural material distributions, enabled by the development of extensible differentiable feature‐mappings from parameters to primitives and differentiable effective logic operations (denoted AutoDiffGeo or ADG). ADG can also be used to accelerate FD‐based shape optimization by efficient boundary selection. AD‐enhanced shape optimization is demonstrated using three integrated photonic examples: a blazed grating coupler, a waveguide transition taper, and a polarization‐splitting grating coupler. The accelerations of the gradient calculation by AD relative to FD with boundary selection exceed 10, resulting in total optimization wall time accelerations of – on the same hardware with no compromise to device figure‐of‐merit.

Aerodynamic and flutter performance of the bridge deck with various countermeasures using computational fluid dynamics

Aerodynamic layouts of bridge decks considerably affect aerostatic torsional divergence and flutter for bridges. The crucial operation is choosing the optimal bridge deck shape considering the aerodynamic effect. The present study intends to provide a better solution for the flutter control scheme by changing five aspect ratios and four passive aerodynamic countermeasures. The countermeasures are an eccentric wing, inspection rail, down vertical central stabilizer and wind barrier, which have been used for three deck shapes: streamlined, semi-streamline and bluff body sections with large angles of attack. Nowadays, wind barriers are frequently installed on bridges to shield vehicles from the harmful effects of crosswinds, which can influence the flutter characteristics of the bridge. Therefore, the present study contemplates reducing the flutter effect with countermeasures. These countermeasures adversely affect the deck’s dynamic stability, mainly manifested in the different divergence forms of the structure. Finally, the eccentric wing, which runs parallel to the bridge deck, increases the critical flutter speed. However, the flow that passes through the eccentric wing extracts considerable energy from the flow field of the countermeasure. Therefore, the framework and solution of the present investigation are sustainable and safe for bridge design.

An in-depth analysis of the Radial Point Interpolation Method’s parameters in relation to the accuracy of fracture problem

The fracture problem has been modeled using Radial Point Interpolation Method (RPIM) to examine the effects of support domain size and shape parameter value on the calculation of Stress Intensity Factor (SIF). The study focuses on an edge crack problem subjected to normal load and shear loads, determining that the support domain size of ‘ α ≥ 3.5 and shape parameter value between ‘ n = 1.9 -2.1’ yield results of accuracy with error % ≤ 3 % . Additionally, research extended by varying the problem domain size and crack location to verify consistency. The findings indicate that selecting the optimal shape parameter value will ensure better accuracy over the enrichment techniques with lesser computational cost.

Experimental Investigation on the Effect of Coil Shape on Planar Eddy Current Sensor Characteristic for Blade Tip Clearance.

Given the increasing application of eddy current sensors for measuring turbine tip clearance in aero engines, enhancing the performance of these sensors is essential for improving measurement accuracy. This study investigates the influence of coil shape on the measurement performance of planar eddy current sensors and identifies an optimal coil shape to enhance sensing capabilities. To achieve this, various coil shapes-specifically circular, square, rectangular wave, and triangular wave-were designed and fabricated, featuring different numbers of turns for the experiment at room temperature. By employing a method for calculating coil inductance, the performance of each sensor was evaluated based on key metrics: measurement range, sensitivity, and linearity. Experimental results reveal that the square coil configuration outperforms other shapes in overall measurement performance. Notably, the square coil demonstrated a measurement range of 0 mm to 8 mm, a sensitivity of 0.115685 μH/mm, and an impressive linearity of 98.41% within the range of 0 mm to 2 mm. These findings indicate that the square coil configuration enhances measurement capabilities. The conclusions drawn from this study provide valuable insights for selecting coil shapes and optimizing the performance of planar eddy current sensors, thereby contributing to the advancement of turbine tip clearance measurement techniques in aero engines.

Preliminary Techno-Economic Study of Optimized Floating Offshore Wind Turbine Substructure

Floating offshore wind turbines (FOWTs) are still in the pre-commercial stage and, although different concepts of FOWTs are being developed, cost is a main barrier to commercializing the FOWT system. This article aims to use a shape parameterization technique within a multidisciplinary design analysis and optimization framework to alter the shape of the FOWT platform with the objective of reducing cost. This cost reduction is then implemented in 30 MW and 60 MW floating offshore wind farms (FOWFs) designed based on the static pitch angle constraints (5 degrees, 7 degrees and 10 degrees) used within the optimization framework to estimate the reduction in the levelized cost of energy (LCOE) in comparison to a FOWT platform without any shape alteration–OC3 spar platform design. Key findings in this work show that an optimal shape alteration of the platform design that satisfies the design requirements, objectives and constraints set within the optimization framework contributes to significantly reducing the CAPEX cost and the LCOE in the floating wind farms considered. This is due to the reduction in the required platform mass for hydrostatic stability when the static pitch angle is increased. The FOWF designed with a 10 degree static pitch angle constraint provided the lowest LCOE value, while the FOWF designed with a 5 degree static pitch angle constraint provided the largest LCOE value, barring the FOWT designed with the OC3 dimension, which is considered to have no inclination.

Hull shape optimization of autonomous underwater vehicles using a full turbulent continuous adjoint solver

The present study aims at simultaneously optimizing the nose and tail of two distinct Autonomous Underwater Vehicles (AUVs) using a full turbulent continuous adjoint solver. The entire procedure is carried out utilizing two open-source software: Salome (CAD and mesh generator) and OpenFOAM v2206 (CFD solver and optimizer). Reynolds-Averaged Navier–Stokes (RANS) equations closed by the k-ω SST model are employed to simulate the turbulent flow around AUV hulls. Besides, adjointOptimisationFoam solver is used to perform the shape optimization. Two different unconstrained and constrained optimizations of AUV hulls are conducted at an angle of attack (α) equal to 0°. In the unconstrained optimization, the drag force is chosen as an objective function to be minimized while a partial volume is considered as a geometric constraint in the constrained optimization. The predicted drag force is validated against experimental results from the literature, indicating a mere 0.58% discrepancy. In the unconstrained optimizations, the first and second AUV hulls reveal a 4.17% and 3.66% reduction in the drag force, respectively. In the constrained optimizations of the first and second AUV hulls, drag force is reduced by 3.25% and 2.63%, respectively.

The continuous adjoint to the incompressible (D)DES Spalart-Allmaras turbulence models

This article formulates the continuous adjoint method for the gradient-based shape optimization of fluid flows governed by the incompressible Detached Eddy Simulation (DES) and Delayed-DES (DDES) models, based on the Spalart-Allmaras turbulence model. As both flow models are inherently unsteady, challenges arise regarding the availability of flow fields during the backward in time integration of the unsteady adjoint equations. To minimize both the computational cost and the memory demands, the computed flow fields are compressed using the iPGDZ+ lossy compression technique, recently developed by the authors. Its application in the context of turbulence-resolving flows, where the compression of flow fields poses an intricate challenge, is a second original contribution of this article. Everything is implemented as an extension to the publicly available adjointOptimisation library of OpenFOAM, which is used to solve the flow and adjoint equations and conduct the optimization. Using two shape optimization problems in external aerodynamics, it is demonstrated that including the adjoint to the turbulence model equation is crucial for the computation of accurate sensitivity derivatives. In contrast to sensitivities computed under the “frozen turbulence” assumption, which neglects variations in turbulent viscosity due to changes in the design variables, the proposed adjoint method yields sensitivities that align with those obtained using Finite Differences. This is due to the Think-Discrete Do-Continuous adjoint method which, inspired by hand-differentiated discrete adjoint, gives rise to consistent discretization schemes of the terms involved in the equations derived by continuous adjoint. Furthermore, it is demonstrated that the proposed adjoint method can significantly benefit from the iPGDZ+ algorithm, by reducing memory requirements by more than two orders of magnitude, eliminating the need for flow recomputations, while maintaining the accuracy of the computed derivatives. Ways to handle large integration windows of the objective function with this type of flow models are beyond the scope of this article.

Combined parameter and shape optimization of electric machines with isogeometric analysis

Combined parameter and shape optimization of electric machines with isogeometric analysis

Shape and topology optimization method with generalized topological derivatives

This paper introduces a novel method for shape and topology optimization based on a generalized approach for evaluating topological derivatives, which are essential for the integration of shape and topology optimization. Traditionally, evaluating these derivatives presents significant mathematical challenges due to the discontinuity introduced by the insertion of a hole within the domain of interest. To overcome this issue, the study employs Helmholtz-type partial differential equations (PDEs) to construct a filtered objective functional. This approach ensures differentiability across the material and void phases and continuity over the fixed design domain while maintaining the same evaluation value as the original objective functional. By considering differentiability, continuity conditions, and the relationship between shape and topological derivatives during asymptotic analysis, generalized topological derivatives are obtained through established mathematical procedures. These topological derivatives exhibit a direct correlation with the PDE solutions and demonstrate satisfactory smoothness, thereby facilitating refined shapes in optimization strategies. Furthermore, an effective shape update algorithm is proposed, which directly integrates topological derivatives into structural optimization problems, simplifying their implementation and improving efficiency. Finally, the efficacy of the proposed methodology is demonstrated through its application to various optimal design problems, including stiffness maximization, compliant mechanisms, and eigenfrequency maximization. Verification results further highlight its potential to enhance existing methods for addressing more practical and complex optimization challenges.

Experimental analysis and optimization of a concentrated thermo-photovoltaic collector with bi-facial receiver

In this study, a concentrated thermo-photovoltaic collector is examined experimentally and numerically, while it was geometrically optimized. The main objective is the collector's thermal performance evaluation and optical optimization for operation in Greece. Experiments were conducted in Athens, Greece, from July 10th to 17th, 2023, investigating the thermal operation of the collector in a temperature range of approximately 40–80 °C. The collector's slope was set to 12.3° for maximum solar irradiance utilization during the specified dates, considering south orientation. A numerical model was created using SolidWorks Flow Simulation and COMSOL Multiphysics, The model was validated with the experimental data, achieving mean deviation less than 6.5 % and a maximum deviation of 9.6 %. Various geometries were optically examined using Tonatiuh software. By applying a performance evaluation criterion, a new design is proposed and compared to the initial design across four different months, considering constant tilt angle. A maximum thermal efficiency of 49.19 % at the lower inlet temperature was found experimentally. The temperature of the PV cells was found to be highest where the solar rays are concentrated. Shape optimization revealed significant enhancements in optical efficiency, particularly at negative incident angles. The new geometry showed substantial improvement, with enhancements exceeding 20 % considering daily operation.

Flow induced form: Shape optimization of bridge piers using CFD analyses and adjoint method

This study investigates the optimization of cylindrical bridge pier geometry using a relatively new technique involving Computational Fluid Dynamics (CFD) and adjoint shape optimization methods. Initially, Reynolds Averaged Navier-Stokes (RANS) equations were used in CFD models, integrated with an adjoint algorithm to reshape the pier and reduce bed shear stress. This approach is hereinafter called the “Flow induced Form”, FiF, aiming to minimize shear stress on the bed while maintaining the pier's cross-sectional and projected areas in the flow direction. Subsequently, Large Eddy Simulation (LES) transient analyses assessed the performance of the optimized geometry. Results show a reduction of approximately 5% in the time average of maximum shear stresses on the bed and a reduction of around 50% in instantaneous maximum values compared to the original pier design. These improvements were achieved with minimal changes to the cross-sectional area and projected area of the original geometry (∼2%), considering that the load-bearing capacity of the bridge pier.

Shape optimization of a non-uniform piezoelectric bending beam for human knee energy harvester

Abstract Scavenging energy from the human body to provide a sustainable source for electronic devices has gained significant attention. Recently, scientists have focused on harnessing biomechanical energy from human motion. This study was dedicated to developing and optimizing a non-uniform piezoelectric bending beam-based human knee energy harvester. The bimorph non-uniform piezoelectric bending beam consisted of a non-uniform carbon fiber substrate and piezoelectric macro fiber composites. Compared to the uniform piezoelectric bending beam, the non-uniform piezoelectric beam can optimize the shape to improve the average strain, thus improving the energy harvesting efficiency. In this study, eight shape functions, including ellipse, sin, tanh, exponential function, parabola, trigonometric line, and bell curves, were investigated and optimized. The bell curve bending beam was selected and fabricated due to its good performance. Then, a benchmark platform was developed to test the deflection curve and reaction force when the nonuniform bending beam was compressed. Finally, to validate the design, experimental testing on three subjects was conducted when they were equipped with the harvester and walked on a treadmill. Testing results indicated that the non-uniform bending beam-based energy harvester can improve the energy harvesting efficiency by 28.57% compared to the uniform beam-based energy harvester. The output power can reach 18.94 mW when walking at 7.0 km h−1.

Deep Reinforcement Learning for Fluid Mechanics: Control, Optimization, and Automation

A comprehensive review of recent advancements in applying deep reinforcement learning (DRL) to fluid dynamics problems is presented. Applications in flow control and shape optimization, the primary fields where DRL is currently utilized, are thoroughly examined. Moreover, the review introduces emerging research trends in automation within computational fluid dynamics, a promising field for enhancing the efficiency and reliability of numerical analysis. Emphasis is placed on strategies developed to overcome challenges in applying DRL to complex, real-world engineering problems, such as data efficiency, turbulence, and partial observability. Specifically, the implementations of transfer learning, multi-agent reinforcement learning, and the partially observable Markov decision process are discussed, illustrating how these techniques can provide solutions to such issues. Finally, future research directions that could further advance the integration of DRL in fluid dynamics research are highlighted.

An experimental acoustofluidic system for analyzing boundary-driven acoustic streaming generated by flat and curved walls

While boundary-driven acoustic streaming in fluids surrounded by flat walls has been extensively studied in the literature, theoretical studies on boundary-driven acoustic streaming generated by curved walls have recently emerged. This paper aims to present a quantitative analysis of acoustic streaming fields driven by forces induced by both flat and curved walls. A semi-circular channel made of stainless steel was designed to serve as a model channel with both flat and curved boundaries. A multi-layered glass-steel-glass device, actuated by a piezoelectric transducer, was assembled for experimental characterization of boundary-driven acoustic streaming in such scenarios. First, the various standing acoustic modes in the semi-circular channel were measured through the acoustophoretic patterning of 20 µm polystyrene particles. Next, the acoustic radiation force fields and boundary-driven acoustic streaming patterns under various resonant acoustic modes were characterized through micro-particle-image-velocimetry measurements of the motion of 20 µm and 1 µm polystyrene particles, respectively. Finally, the experimental results were explained using efficient finite element simulations of acoustofluidics and acoustophoresis in a semi-circular reduced-fluid model, with a focus on analyzing the streaming velocities driven by the flat and curved walls. Both experimental and numerical results demonstrated that the ratio of streaming velocities induced by the flat wall and the curved wall in this semi-circular channel depends on the resonant acoustic modes. This research highlights the diverse boundary-driven acoustic streaming patterns that arise in irregular channels and provides a theoretical foundation for choosing strategies for shape optimization to suppress acoustic streaming in acoustofluidic devices.

Preform cross-section shape optimization design for tube hydroforming with low pressure

Preform design refers to the intermediate geometric design between the initial tube blank and the desired product. A proper preform design can improve the formability of the tubular structure with small fillets. It is difficult to obtain a reasonable preform design based on engineering experience or trial-and-error methods. In this work, a Non-Uniform Rational B-Splines (NURBS) curve control point inversion algorithm-based approach is introduced to define and parameterize the preform cross-section profiles. The corresponding mathematical optimization model of preform cross-section shape design for tube hydroforming with low pressure is established, and an optimization procedure was accordingly proposed. In this procedure, the relationships between the design variables and responses are formulated by combining the DoE techniques with multiple surrogate models. The k-fold cross-validation strategy is adopted to quantify the performance of the candidate surrogate models on fresh datasets. The selected and verified surrogate models are integrated with the heuristic algorithm to determine the optimal preform shape. Compared to the direct hydroforming process, the optimized preform designs decreased the forming pressure of square, trapezoidal, and irregular polygonal tubes by 89.29%, 70.29%, and 32.67%, respectively. The validity of the proposed method is thus verified.

Concurrent and sequential coupled optimization design of a transonic compressor blade with axial slot casing treatment

This paper explores the optimization of the interaction between the rotor and axial slot casing treatment (ASCT) to enhance both efficiency and stability margins. Previous studies primarily focused on rotor tip optimization, often compromising flow in non-tip regions and reducing overall rotor performance. To address these limitations, this study introduces a new optimization framework integrating full-span 3D blade design with a semicircular axial slot, utilizing both sequential and concurrent optimization strategies. The sequential approach first optimizes blade geometries, followed by ASCT adjustments, while the concurrent approach treats the blade and ASCT as a unified aerodynamic system. Compared to prior studies focusing exclusively on tip-only 3D shape optimization, results indicate that sequential coupled optimization improves the stall margin by 13.32% and efficiency by 0.05%, whereas the concurrent strategy further enhances performance, shaping the blades into an inverse S form, reducing efficiency losses from 0.12% to 0.02%, and increasing the stall margin increment from 14.88% to 21.83%. These findings demonstrate the significant performance gains achievable through coordinated rotor and ASCT design.