Aerostructural Optimization Research Articles

Aerostructural wing shape optimization assisted by algorithmic differentiation

With more efficient structures, last trends in aeronautics have witnessed an increased flexibility of wings, calling for adequate design and optimization approaches. To correctly model the coupled physics, aerostructural optimization has progressively become more important, being nowadays performed also considering higher-fidelity discipline methods, i.e., CFD for aerodynamics and FEM for structures. In this paper a methodology for high-fidelity gradient-based aerostructural optimization of wings, including aerodynamic and structural nonlinearities, is presented. The main key feature of the method is its modularity: each discipline solver, independently employing algorithmic differentiation for the evaluation of adjoint-based sensitivities, is interfaced at high-level by means of a wrapper to both solve the aerostructural primal problem and evaluate exact discrete gradients of the coupled problem. The implemented capability, ad-hoc created to demonstrate the methodology, and freely available within the open-source SU2 multiphysics suite, is applied to perform aerostructural optimization of aeroelastic test cases based on the ONERA M6 and NASA CRM wings. Single-point optimizations, employing Euler or RANS flow models, are carried out to find wing optimal outer mold line in terms of aerodynamic efficiency. Results remark the importance of taking into account the aerostructural coupling when performing wing shape optimization.

Aero-structural Optimization of Streamlined Twin-Box Deck Bridges with Short Gap Considering Flutter

Abstract Shape and size design of twin-box decks involves managing a number of highly sensitive deck features, including aerodynamic, stiffness, and mass properties, which leads to important and co...

Aero-structural optimization of supersonic wing under thermal environment using adjoint-based optimization algorithm

For solving the problems of jig-shape design and aerodynamic shape design at the same time, based on the aero-thermo-structural (ATS) analysis model, the paper presents a coupling optimization method, in which the adjoint equations of coupling system are developed. In order to demonstrate this methodology, a supersonic wing is optimized, and its objective function is the lift-to-drag ratio considering the elastic deformation of the wing structure induced by aerodynamic load and aerodynamic heating. And independent variables are the geometric twist angles of wing sections along the span, the thickness of skin, and the cross-sectional geometrical parameters of spar and stringer. The constraint is the strength of the wing structure. When the maximum allowable mass is 700 kg, the results show that the lift-to-drag ratio is increased from 6.0505 to 6.2875, and all constraints are satisfied. Therefore, the coupling optimization method is effective. And this method can control the increment of structural mass through the maximum mass constraint.

Supersonic Turbulent Boundary-Layer Separation Control Using a Morphing Surface

Separated flows arising due to shock-wave/turbulent boundary-layer interactions can cause problematic low-frequency unsteadiness with potentially severe structural response. High-fidelity large-eddy simulations are employed to examine surface morphing as a way to reduce the size of the separation region, and thus favorably alter the unsteadiness characteristics. The configuration considers a turbulent Mach 2.7 flow at a Reynolds number of subjected to an impinging shock system with a pressure ratio of , which results in separation and the presence of structurally relevant low-frequency unsteadiness. The control surface, centered about the shock impingement location and extending over the separation region, is allowed to deform under material property-based realizability constraints until an asymptotic state is achieved. The criterion for deformation uses a measure proportional to the directional surface shear stress. At an asymptotic state, the deformed surface reveals a shape consistent with aerostructural optimization and a maximum height of . Control mitigates the sharp initial pressure gradient of the uncontrolled flow to delay and reduce separation extent (by 50%) with diminution of low-frequency content and turbulent kinetic energy. Modal decomposition highlights these effects in the energy content of the prominent modes. Morphing may thus provide a means to adjust the local surface deflection in a manner that reduces some of the problems associated with turbulent separation.

Optimization of bridges with short gap streamlined twin-box decks considering structural, flutter and buffeting performance

While it is well known that the gap between twin-box decks is a key design variable that impacts the onset flutter velocity of a bridge, further research is required to ascertain how modifications in several bridge design variables affect other aeroelastic responses. This paper utilizes aero-structural optimization techniques for the design of long-span bridges with short gap twin-box decks considering simultaneously structural, flutter and buffeting constraints. The optimization helps to reduce the material volume of the structure while maintaining all the performance and safety requirements below the imposed thresholds. It has been found that the geometry of the individual box cross-section is an important feature for the control of the buffeting response, particularly the vertical acceleration. On the other hand, flutter and torsional buffeting constraints require designs with larger gap distance and alternative box geometries, leading to a trade-off between conflicting design demands. Hence, depending on the expected wind load conditions and the specific requirements of a particular project, an optimum aero-structural bridge design with a particular deck shape can be identified. The framework presented in this study is an effective tool to achieve sustainable and safe bridge designs that seeks a most efficient balance between all the design constraints.

Aero-structural design of bridges focusing on the buffeting response: Formulation, parametric studies and deck shape tailoring

The design of long-span bridges under wind places multiple demands that are frequently contradictory in regard to the resulting deck configuration. The structural demand requires that the deck contributes to the bridge stiffness, which results in bluff geometry. Conversely, aeroelastic aspects demand that the deck shape be more streamlined to reduce the aerodynamic and aeroelastic load effects. This requires that the design of long-span bridges be carried out as an aero-structural design problem, where the goal is to obtain designs with the lowest cost that simultaneously fulfill the structural and aeroelastic constraints. This study presents a numerical framework for the aero-structural design of long-span bridges under buffeting focusing on the deck shape. In this paper, the relationship between the buffeting response of a cable-stayed bridge and its deck shape is analyzed by means of parametric studies that help to better understand the role played by each involved parameter. This information is used to tailor the deck shape aiming at keeping the buffeting response under a given threshold. By building upon this framework, the design problem can be recast as an aero-structural optimization problem.

ADflow: An Open-Source Computational Fluid Dynamics Solver for Aerodynamic and Multidisciplinary Optimization

Computational fluid dynamics through the solution of the Navier–Stokes equations with turbulence models has become commonplace. However, simply solving these equations is not sufficient to be able to perform efficient design optimization with a flow solver in the loop. This paper discusses the recommendations for developing a flow solver that is suitable for efficient aerodynamic and multidisciplinary design optimization. One of the major recommendations is to be able to load the flow solver as a library that provides direct memory access to the relevant data. Other recommendations are to use a higher-level language for scripting and to pay special attention to solution warm starting, code efficiency, flow solver robustness, and solution failure handling. As an example of a flow solver that follows these recommendations, the open-source flow solver ADflow is presented. Results from aerodynamic optimization, aerostructural analysis, and aerostructural optimization using ADflow demonstrate the performance advantages claimed in the recommendations. The publication of these recommendations and the availability of the source code open the door for other solvers to adopt the same application programming interface. ADflow is part of a wider aerodynamic shape optimization tool suite that is also available under an open-source license.

Control Authority of a Camber Morphing Flying Wing

Flying wings achieve their roll, pitch, and yaw controllability exclusively through spanwise variations of lift and drag due to the lack of an empennage. Instead of using conventional control surfaces, which increase the aerodynamic drag due to gaps and discontinuities, a morphing structure can be employed. This work considers a previously developed camber morphing flying wing, which uses 10 electromechanical actuators to achieve spanwise-varying trailing edge deflections, resulting in variations of the lift and drag distributions and generating moments around the roll, pitch, and yaw axes. To investigate the control authority of the aircraft across all flight maneuvers, a series of multi-objective aerostructural optimizations is carried out. The performance for the individual maneuvers, as well as the interaction of simultaneous roll, pitch, and yaw moments and the resulting control authority, is assessed. Because the same actuators are used for all maneuvers, a high degree of interaction has been found between the achieved rolling and yawing moments. By minimizing the additional drag with the morphing actuation, the undesired effect of adverse yaw is minimized. The results describe a possible control strategy for flying wing aircraft with optimal drag performance.

DAFoam: An Open-Source Adjoint Framework for Multidisciplinary Design Optimization with OpenFOAM

The adjoint method is an efficient approach for computing derivatives that allow gradient-based optimization to handle systems parameterized with a large number of design variables. Despite this advantage, implementing the adjoint method for a partial-differential-equation-based primal solver is a time-consuming task. To lower the barrier for adjoint implementations, an object-oriented framework (DAFoam) is proposed to rapidly implement the discrete adjoint method for any steady-state OpenFOAM primal solver by adding or modifying only a few hundred lines of source code. In this paper, the DAFoam framework is introduced and the proposed object-oriented adjoint development process is illustrated. Using this strategy, the adjoint method is implemented for eight primal solvers, five turbulence models, and one radiation model in OpenFOAM. Excellent adjoint speed and scalability, with up to 10 million cells and 1536 CPU cores, and an average error in the adjoint derivatives of less than 0.1% are achieved. Finally, the implemented adjoint solvers and models are integrated into a gradient-based optimization framework, and four distinct design optimizations (multipoint aerodynamic optimization of a low-speed unmanned-aerial-vehicle wing, aerodynamic optimization of a transonic aircraft configuration, aerothermal optimization of a turbine internal cooling passage, and aerostructural optimization of a compressor rotor) are shown. DAFoam is available under an open-source license and is a powerful tool for the high-fidelity multidisciplinary design optimization of engineering systems, such as aircraft, ground vehicles, marine vessels, and turbomachinery.

High-fidelity aerostructural optimization of tow-steered composite wings

Over the past several decades, composites have increasingly become the material of choice in modern aircraft structural design. This is primarily due to the high stiffness- and strength-to-weight ratios offered by conventional composites when compared to metals. Unconventional composite designs, such as tow-steered composites, have demonstrated potential for further expanding these advantages. Unlike their conventional composite counterparts, tow-steered composites feature layers with spatially varying fiber orientations. When applied to wing design, tow-steered composites offer an increase in design freedom at the cost of higher design complexity, making them ideal candidates for design optimization. We develop a methodology for the aerostructural design optimization of tow-steered composite wings using high-fidelity physics models. We also quantify the benefits of this new technology by performing a fuel burn minimization for both a tow-steered and a conventional composite wing design. This assessment is done for the undeflected Common Research Model, which is representative of a twin-aisle transport aircraft. We find improvements of up to 2.4% in fuel burn and 24% in wing weight relative to the optimized conventional composite design. We show that this improvement is due to a combination of improved passive aeroelastic tailoring and local strength tailoring in high-stress regions in the tow-steered structure. For a higher-aspect-ratio (13.5) wing design, we find improvements of up to 1.5% and 14% in fuel savings and wing weight, respectively. To better understand the effect of aspect ratio on tow-steered wing design, we perform an optimization study where the aspect ratio is varied between 7.5 and 13.5. We found that there are diminishing returns in the benefit of tow steering as the aspect ratio is increased because less passive load alleviation is possible.

Aero-structural optimization and analysis of a camber-morphing flying wing: Structural and wind tunnel testing

This article presents the design, optimization and performance assessment of a novel structure-actuation morphing concept for a flying wing, enabling the flight control for straight flight and around the pitch and roll axes. The applied camber-morphing concept utilizes an optimized selectively compliant internal structure, combined with electromechanical actuators to achieve a trailing edge deflection. These deflections lead to variations of the local and global lift, permitting to control the flight of the aircraft. The aero-structural behaviour of the wing is analysed using a coupled three-dimensional aerodynamic and structural simulation tool. An optimization of the planform, aerodynamic shape, internal structure and actuation parameters is performed to attain a longitudinally stable and aerodynamically efficient flying wing. The drag increment caused by morphing is minimized through the numerical optimization, resulting in high aerodynamic efficiency across a range of flight speeds. The stiffness and morphing capabilities of the manufactured wing are characterized experimentally and are compared with the numerical predictions, and the aerodynamic and aeroelastic behaviour of the wing is investigated through wind tunnel tests. The test results indicate the ability of the flying wing to achieve sufficient variations in lift, roll and pitch to control the flight completely through camber morphing.

Wing aerostructural optimization with an analytical fuel consumption sensitivity model

Based on a quasi-steady mission in a vertical plane, this paper presents an analytical derivation to compute the fuel consumption sensitivity. Within the mission analysis simplifications required by this method, a wing aerostructural design problem that accounts for multiple flight conditions is proposed. Such graequdient-based optimization problem is presented for an Airbus A320 as a test case application. This test case efficiently couples the mission analysis to the aerostructural FEMWET analysis code via an online-generated parabolic drag polar. FEMWET uses a quasi-three-dimensional wing aerodynamic analysis coupled with a finite beam element method. The optimized solution yields a large-span wing in agreement with aerostructural design optimization literature.

Impact of Morphing Trailing Edges on Mission Performance for the Common Research Model

Nonmorphing, conventional aircraft wings are designed for a compromise of good performance at a variety of flight conditions. Accordingly, such wings perform suboptimally when considered at a single flight condition. Morphing trailing-edge devices offer an opportunity to change this wing design paradigm by allowing wings to adapt to varying flight conditions. This adaptability weakens the correlation between performance at various flight conditions and increases the robustness of the wing’s performance, providing closer-to-optimal performance at each flight condition. To study the isolated aerodynamic effects of this increased robustness, we perform a number of aerodynamic and aerostructural shape optimizations of a morphing trailing-edge device that can change the shape of the rear 10% of the wing at a variety of flight conditions on the Common Research Model aircraft configuration. The aerodynamically optimized morphing configuration yields a 1.0% fuel burn reduction for a long-range mission. When performing aerostructural optimization, which considers structural deformations and structural weight reductions enabled by active load alleviation, the fuel burn reduction is 2.7%.

High-Fidelity Aerostructural Gradient Computation Techniques with Application to a Realistic Wing Sizing

Aerostructural optimization is a keystone process to concurrently improve aerodynamic performance and reduce the structural mass of an aircraft. However, gradient-based multidisciplinary design optimization is efficient only if the computation of gradients is fast and accurate. To this end, two high-fidelity aerostructural gradient computation techniques are proposed for strongly coupled aeroelastic systems. In the specific context of this work, the focus is on design variables affecting structural stiffness only. Scalar objective functions like aerodynamic performance criteria are considered as well as a field of structural grid forces. The most intrusive technique includes well-established direct and adjoint formulations that require substantial implementation effort. In contrast, an alternative uncoupled nonintrusive approach is proposed that is easier to implement and yet capable of providing accurate gradient approximations. The accuracy of these methods is first demonstrated on the ONERA M6 wing test case. Their efficiency and applicability are then illustrated via a mass minimization problem applied to the Common Research Model. Both methods lead to very similar optimal designs, and the detailed analysis of results promotes the nonintrusive approach as a promising gradient computation alternative.

A new aero-structural optimization method for wind turbine blades used in low wind speed areas

The wind turbine blades used in lower quality wind resources have been recently designed. The designed blades for low wind speed areas are scaled version of blades used in high wind speed sites with longer blade lengths, same chord length and same airfoils series. A discrete optimization method for wind turbine blade used in low wind speed sites is proposed. In the optimization process, both aerodynamic and structural parameters are considered as design variables. The airfoil design is also considered in the optimization process to improve the aerodynamic and structural performance by the method of airfoil integrated theory. The Blade Element Momentum theory is used to evaluate the blade aerodynamic performance and the Classical Laminate Theory is used to estimate the stiffness and mass per unit of each blade section. Finally, a Finite Element Method structural analysis is used to verify the strength under the extreme loading conditions. To prove the efficiency and robustness of the design, a commercial 2.1 megawatt HAWT blade is used as a case study. The results show that the aerodynamic and structural performance of the new blade is improved compared with that of the original one.

Constraint aggregation for large number of constraints in wing surrogate-based optimization

The method of aggregating a large number of constraints into one or few constraints has been successfully applied to wing structural design using gradient-based local optimization. However, numerical difficulties may occur in the case that the local curvatures of the aggregated constraint become extremely large and then ill-conditioned Hessian matrix may be yielded. This paper aims to test different methods of constraint aggregation within the framework of a gradient-free optimization, which makes use of cheap-to-evaluate surrogate models to find the global optimum. Three constraint aggregation approaches are investigated: the maximum constraint approach, the constant parameter Kreisselmeier-Steinhauser (KS) function, and the adaptive KS function. We also explore methods of aggregating constraints over the entire structure and within sub-domains. Examples of structural optimization and aero-structural optimization for a transport aircraft wing are employed and the results show that (1) the KS function with a larger constant parameter ρ can lead to better optimization results than the adaptive method, as the active constraints are approximated more accurately; (2) lumping the constraints within sub-domains instead of all together can improve the accuracy of the aggregated constraint and therefore helps find a better design. Finally, it is concluded from current test cases that the most efficient way of handling large-scale constraints for wing surrogate-based optimization is to aggregate constraints within sub-domains and with a relatively large constant parameter.

Design of a transonic wing with an adaptive morphing trailing edge via aerostructural optimization

Novel aircraft configurations and technologies like adaptive morphing trailing edges offer the potential to improve the fuel efficiency of commercial transport aircraft. To accurately quantify the benefits of morphing wing technology for commercial transport aircraft, high-fidelity design optimization that considers both aerodynamic and structural design with a large number of design variables is required. To address this need, we use a high fidelity aerostructural model that enables the detailed optimization of wing shape and sizing using hundreds of design variables. We perform a number of multipoint aerostructural optimizations to demonstrate the performance benefits offered by morphing technology and identify how those benefits are enabled. In a comparison of optimizations considering seven flight conditions, the addition of a morphing trailing edge device along the aft 40% of the wing can reduce cruise fuel burn by more than 5%. A large portion of fuel burn reduction due to morphing trailing edges results from a significant reduction in structural weight, enabled by adaptive maneuver load alleviation. We also show that a smaller morphing device along the aft 30% of the wing produces nearly as much fuel burn reduction as the larger morphing device, and that morphing technology is particularly effective for high aspect ratio wings.

An automated selection algorithm for nonlinear solvers in MDO

There are two major types of approaches that are used for the multidisciplinary analysis (MDA) of coupled systems: fixed-point-iteration-based approaches and coupled Newton-based approaches. Fixed-point-iteration approaches are easier to implement, but can require a large number of iterations or diverge for strongly coupled problems. On the other hand, coupled-Newton approaches have superior convergence orders, but generally require more effort to implement and have more expensive iterations. Additionally, these two major approaches have many variations, including hybrid approaches where the MDA begins with a fixed-point iteration and then switches to a coupled-Newton approach after a certain number of iterations. However, there is a lack of criteria to govern how to select between these approaches, and when to switch between them in a hybrid approach. This paper compares these approaches and provides an algorithm that can be used to automatically select and switch between them. The proposed algorithm is implemented using OpenMDAO, NASA’s open-source framework for multidisciplinary analysis and optimization, and is tested using OpenAeroStruct, an open-source low-fidelity tool for aerostructural optimization. The results show that the proposed algorithm provides a balance of improved robustness and speed.

Graph-based algorithms and data-driven documents for formulation and visualization of large MDO systems

A new system is presented that enables the visualization of large multidisciplinary design optimization (MDO) problems and their solution strategy. It was developed within the scope of the European project AGILE. In AGILE, collaborative MDO is performed in large, heterogeneous teams of experts by solving MDO problems using a collection of design and analysis tools. This paper focuses on the visualizations required to support the formulation phase of an MDO project. The Knowledge and graph-based AGILE Design for Multidisciplinary Optimization System (KADMOS), an open-source MDO support system developed by Delft University of Technology, uses graph-based analysis to formulate an MDO problem and its solution strategy, based on the disciplinary analyses available in a repository. The results of KADMOS are stored in the standardized format CMDOWS (Common MDO Workflow Schema), which comprises the entire information on an MDO system. Although, based on Extensible Markup Language, the readability of the CMDOWS file is quite poor also for MDO experts, especially for large MDO systems involving thousands of variables. Providing visualization capabilities to thoroughly inspect the outcome of the different MDO formulation steps becomes a key factor to enable the specification of large MDO systems in a heterogeneous team. Therefore, VISTOMS (VISualization TOol for MDO Systems), a dynamic visualization package, was developed by RWTH Aachen University to enable the visualization and inspection of the different MDO system specification steps, thereby removing one of the main hurdles for using MDO as a development process. The developed visualization capabilities are demonstrated by means of an aerostructural wing design optimization project.

Preliminary design and optimization of a 20MW reference wind turbine

We use the capabilities of a multi-disciplinary design tool to provide a definition of a 20 MW wind turbine. Starting from an aero-elastic model obtained through a classic scaling procedure, we conduct an aero-structural optimization of the rotor through a staged redesign process, in which we optimize primary characteristics of the rotor including the blade shape, the solidity and a certain amount of native structural tailoring. The process is based on a series of parametric analysis, in order to assess the impact of a variation of macro design parameters on the fundamental performance of the turbine. The redesign activity shows remarkable advantages in terms of blade mass reduction and load alleviation, highlighting directions for the development and optimization of very large rotors.