Aerodynamic Shape Optimization Research Articles

Data-driven constraint approach to ensure low-speed performance in transonic aerodynamic shape optimization

Aerodynamic shape optimization based on computational fluid dynamics has the potential to become more widely used in the industry; however, the optimized shapes are often criticized for not being practical. Techniques seeking more practical results, such as multipoint optimization and geometric constraints, are either ineffective or too time consuming because they require trial and error. We propose a data-driven constraint for the aerodynamic shape optimization of aircraft wings that ensures the overall practicality of the optimum shape, with a focus on achieving a good low-speed performance. The constraint is formulated by extracting the relevant features from an airfoil database via modal analysis, correlation analysis, and Gaussian mixture models. The optimization results demonstrated that this approach addresses the thin leading edge issue that had plagued previous optimization results, and further analysis demonstrated that this data-driven constraint ensures good low-speed off-design performance without sacrificing the transonic on-design performance. The proposed approach can use other airfoil databases and can even be generalized to other shape optimization and engineering design problems.

Efficient aerodynamic shape optimization using variable-fidelity surrogate models and multilevel computational grids

A variable-fidelity method can remarkably improve the efficiency of a design optimization based on a high-fidelity and expensive numerical simulation, with assistance of lower-fidelity and cheaper simulation(s). However, most existing works only incorporate “two” levels of fidelity, and thus efficiency improvement is very limited. In order to reduce the number of high-fidelity simulations as many as possible, there is a strong need to extend it to three or more fidelities. This article proposes a novel variable-fidelity optimization approach with application to aerodynamic design. Its key ingredient is the theory and algorithm of a Multi-level Hierarchical Kriging (MHK), which is referred to as a surrogate model that can incorporate simulation data with arbitrary levels of fidelity. The high-fidelity model is defined as a CFD simulation using a fine grid and the lower-fidelity models are defined as the same CFD model but with coarser grids, which are determined through a grid convergence study. First, sampling shapes are selected for each level of fidelity via technique of Design of Experiments (DoE). Then, CFD simulations are conducted and the output data of varying fidelity is used to build initial MHK models for objective (e.g. CD) and constraint (e.g. CL, Cm) functions. Next, new samples are selected through infill-sampling criteria and the surrogate models are repetitively updated until a global optimum is found. The proposed method is validated by analytical test cases and applied to aerodynamic shape optimization of a NACA0012 airfoil and an ONERA M6 wing in transonic flows. The results confirm that the proposed method can significantly improve the optimization efficiency and apparently outperforms the existing single-fidelity or two-level-fidelity method.

Morphing control of a new bionic morphing UAV with deep reinforcement learning

With rapid development of aviation technology, materials science and artificial intelligence, aircraft design is pursuing higher requirements both in civil and military fields. The new generation of aircraft should have the autonomous capable of performing a variety of tasks (such as take-off and landing, cruising, maneuvering, hover, attack, etc.) under a highly variable flight environment (height, Mach number, etc.) and meanwhile maintaining good performance. Morphing aircraft can use smart materials and actuators to autonomously deform the shape according to the changes in flight environment and mission, and always maintain an optimal aerodynamic shape, therefore get flourished developments. Based on the ability of birds to stretch wings when flying at low speed and to constrict wings at high speed, a new bionic morphing UAV has been designed and developed as the study model by our team. In order to make this new aircraft be able to complete rapid autonomous morphing and aerodynamic performance optimization under different missions and flight conditions, we developed deep neural networks and reinforcement learning techniques as a control strategy. Considering the continuity of the state and action spaces for model, the Deep Deterministic Policy Gradient (DDPG) algorithm based on the actor-critic, model-free algorithm was adopted and verified on the classic nonlinear Pendulum model and Cart Pole game. After the feasibility was verified, morphing aircraft model was controlled to complete prescribed deformation using DDPG algorithm. Furthermore, on the condition that the DDPG algorithm can control morphing well, through training and testing on model using simulation data from wind tunnel tests and actual flight, the autonomous morphing control for the shape optimization of the bionic morphing UAV model could be realized.

Shape Optimization of Blended-Wing-Body Configuration- An Experimental Approach

In the recent years alternative aircraft configurations, such as Blended – Wing- Body(BWB) aircraft, are being studied and researched with the intention to develop more effectual aircraft configurations, in particular for very large transport that are more efficient and environmental friendly. In addition to the removal of the tail for this specific kind of aircraft and the substantial decline in equivalent weight, drag force, and radar cross-section, the accessible space for mounting equipment inside the wing and the operational range have also been augmented. Regardless of all these stated advantages, instability is the negative outcome of removing the tail. Revising this imperfection requires designing a combination of control surfaces and reflexed wing sections and using complex computer control systems. Hence, the aerodynamic shape optimization of BWBs, along with the need to meet the design necessities, has encouraged numerous investigators to overwhelm its challenges. In this project an experimental approach was adopted to optimize the shape of a basic design of a BWB using an experimental approach. The flow simulation using wind tunnel was carried out for a basic model of BWB. Then the aerodynamic efficiency of the basic design was compared with a conventional aircraft B747 using the same experimental conditions. The three models such as the basic BWB, B747 and the 787 were compared in terms of their (CL)max, (CD)min and (L/D)max values. The results were presented with the BWB with 45% efficient shape when the above-mentioned parameters are compared.

Efficient Design Optimization Assisted by Sequential Surrogate Models

The paper proposes a global optimization algorithm employing surrogate modeling and adaptive infill criteria. The surrogates are exploited to screen the design space and provide lower-fidelity predictions across it; on the other hand, specific criteria are designed to suggest new points for high-fidelity evaluation so as to enrich the optimizer database. Both Kriging and radial basis function network are used as surrogates with different training strategies. Sequential design is achieved by introducing several infill criteria according to the realization of the exploration-exploitation trade-off. Optimization results are provided both for scalable and analytical test functions and for a practical aerodynamic shape optimization problem.

Aerodynamic shape optimization of airfoils at ultra-low Reynolds numbers

The flow over NACA 0008 airfoil is studied computationally in the ultra-low Reynolds number regime Re ∈ [1000, 10000] for various angles of attack α ∈ [0°, 8°]. The laminar flow separation occurs even at low angles of attack in this Reynolds number regime. The lift curve slope is far reduced from the inviscid thin airfoil theory value of Cl,α = 2π. Significant increase in the values of drag coefficient is seen with a decrease in Re. Lift-to-drag ratios are consequently very low. An adjoint-based aerodynamic shape optimization methodology is employed to obtain improved aerodynamic characteristics in the ultra-low Re regime. Three different objective functions are considered, namely, (i) minimization of drag coefficient, Cd, (ii) maximization of lift coefficient, Cl, and (iii) maximization of lift-to-drag ratio, (Cl/Cd). Significant improvement in each of the objective functions is obtained.

Performance impact of flow and geometric variations for a turbine blade using an adaptive NIPC method

Geometric variations of the realistic blades due to the limited machining precision and flow variations at the outlet boundary due to the operational condition changes for turbomachinery blades cannot be totally eliminated, the significant effects of which require to be taken into account in the aerodynamic shape design and optimization. The present paper investigates the performance impact of flow and geometric variations by using the polynomial chaos. The adaptive non-intrusive polynomial chaos (NIPC) model based on an adaptive sparse grid technique is firstly introduced, the response performance of which is validated through function experiments and uncertainty quantification of performance change for a three-dimensional turbine blade. Then the adaptive NIPC is used to statistically evaluate the adiabatic efficiency change of the turbine blade due to the geometric and back pressure variations separately. The performance change exhibits nonlinear dependence on the geometric and back pressure variations. Moreover, the geometric variations induce more performance deteriorations to the turbine blade in the present study. Finally, the simultaneous performance impact of geometric and back pressure variations are investigated. The results are presented in detail and compared with those obtained from the uncoupled studies, demonstrating that these two kinds of uncertain effects to the performance change are nonlinearly dependent.

Adaptive modeling strategy for constrained global optimization with application to aerodynamic wing design

Surrogate models are often used to reduce the cost of design optimization problems that involve computationally costly models, such as computational fluid dynamics simulations. However, the number of evaluations required by surrogate models usually scales poorly with the number of design variables, and there is a need for both better constraint formulations and multimodal function handling. To address this issue, we developed a surrogate-based gradient-free optimization algorithm that can handle cases where the function evaluations are expensive, the computational budget is limited, the functions are multimodal, and the optimization problem includes nonlinear equality or inequality constraints. The proposed algorithm—super efficient global optimization coupled with mixture of experts (SEGOMOE)—can tackle complex constrained design optimization problems through the use of an enrichment strategy based on a mixture of experts coupled with adaptive surrogate models. The performance of this approach was evaluated for analytic constrained and unconstrained problems, as well as for a multimodal aerodynamic shape optimization problem with 17 design variables and an equality constraint. Our results showed that the method is efficient and that the optimum is much less dependent on the starting point than the conventional gradient-based optimization.

Artificial Intelligence to Enhance Aerodynamic Shape Optimisation of the Aegis UAV

This article presents an optimisation framework that uses stochastic multi-objective optimisation, combined with an Artificial Neural Network (ANN), and describes its application to the aerodynamic design of aircraft shapes. The framework uses the Multi-Objective Particle Swarm Optimisation (MOPSO) algorithm and the obtained results confirm that the proposed technique provides highly optimal solutions in less computational time than other approaches to the same design problem. The main idea was to focus computational effort on worthwhile design solutions rather than exploring and evaluating all possible solutions in the design space. It is shown that the number of valid solutions obtained using ANN-MOPSO compared to MOPSO for 3000 evaluations grew from 529 to 1006 (90% improvement) with a penalty of only 8.3% (11 min) in computational time. It is demonstrated that including an ANN, the ANN-MOPSO with 3000 evaluations produced a larger number of valid solutions than the MOPSO with 5500 evaluations, and in 33% less computational time (64 min). This is taken as confirmation of the potential power of ANNs when applied to this type of design problem.

Solving Stackelberg equilibrium for multi objective aerodynamic shape optimization

• The Stackelberg game is introduced into multi-objective aerodynamic shape optimization . • Numerical methods coupled (EAs) and/or adjoint method with a Stackelberg game are Presented. • Virtual Nash and virtual Stackelberg problems are equivalent, and their solutions are the same. • Final equilibrium solutions are only related to what information is exchanged. • The equilibrium of the weak form Stackelberg problem is as the same as the Nash equilibrium. Numerical methods coupling evolutionary algorithms and/or adjoint methods with a two level hierarchical game between leader and follower, called the Stackelberg game, are presented for solving multi objective aerodynamic shape optimization problems in this paper, in which both leader and follower can be a Nash sub-game with multiple players. The decision making process of leader and follower is hierarchically and non-cooperatively in numerical implementation, more accurately they are alternate. The leader enounces a decision (a Nash sub-game solution), and the follower takes into account this decision and solves the other Nash sub-game optimization problem. The elitist information that follower passes to leader is the response function of follower to leader’s decision, instead of its response only. Then, the leader optimizes his objective based on elitist information accepted from follower depending on his behavior. The approximate response function is obtained by recalculating the follower’s Nash sub-game with a small perturbation on leader’s decision. Finally, a multi-objective shape optimization problem of hypersonic air-breathing vehicle is solved by using the optimization algorithm presented in this paper, and the converged result of the algorithm is proved to be a Stackelberg equilibrium.

Multipoint high-fidelity CFD-based aerodynamic shape optimization of a 10 MW wind turbine

Abstract. The wind energy industry relies heavily on computational fluid dynamics (CFD) to analyze new turbine designs. To utilize CFD earlier in the design process, where lower-fidelity methods such as blade element momentum (BEM) are more common, requires the development of new tools. Tools that utilize numerical optimization are particularly valuable because they reduce the reliance on design by trial and error. We present the first comprehensive 3-D CFD adjoint-based shape optimization of a modern 10 MW offshore wind turbine. The optimization problem is aligned with a case study from International Energy Agency (IEA) Wind Task 37, making it possible to compare our findings with the BEM results from this case study and therefore allowing us to determine the value of design optimization based on high-fidelity models. The comparison shows that the overall design trends suggested by the two models do agree, and that it is particularly valuable to consult the high-fidelity model in areas such as root and tip where BEM is inaccurate. In addition, we compare two different CFD solvers to quantify the effect of modeling compressibility and to estimate the accuracy of the chosen grid resolution and order of convergence of the solver. Meshes up to 14×106 cells are used in the optimization whereby flow details are resolved. The present work shows that it is now possible to successfully optimize modern wind turbines aerodynamically under normal operating conditions using Reynolds-averaged Navier–Stokes (RANS) models. The key benefit of a 3-D RANS approach is that it is possible to optimize the blade planform and cross-sectional shape simultaneously, thus tailoring the shape to the actual 3-D flow over the rotor. This work does not address evaluation of extreme loads used for structural sizing, where BEM-based methods have proven very accurate, and therefore will likely remain the method of choice.

Aerodynamic Shape Design and Validation of an Advanced High-Lift Device for a Regional Aircraft with Morphing Droop Nose

In the present work, the aerodynamic shape design of an advanced high-lift system for a natural laminar flow (NLF) wing, based on the combination of a morphing droop nose and a single slot trailing edge flap, is presented. The paper presents both the aerodynamic design and optimization of the NLF wing and the high-lift configuration considering the mutual effects of both flap devices. Concerning the morphing droop nose (DN), after defining the parameterization techniques adopted to describe the geometry in terms of morphing shape and flap settings, the external configuration is obtained by an aerodynamic shape optimization procedure able to meet geometrical constraints and the skin structural requirements due to the morphing. The final performance assessment of the three-dimensional high-lift configurations is performed by high-fidelity aerodynamic analyses. The design procedure is applied to a twin-prop regional aircraft equipped with a natural laminar flow wing. The morphing droop nose is compatible with an NLF wing that requires the continuity of the skin and, at the same time, extends the possibilities to improve the performances of the class of regional aircraft which usually are not equipped with conventional leading edge devices. Additionally, the morphing technology applied to the flap allows the design of a tracking system fully integrated inside the airfoil geometry, leading to a solution without external fairings and so with no extra friction drag penalty for the aircraft.

Multi-level Hybridized Optimization Methods Coupling Local Search Deterministic and Global Search Evolutionary Algorithms

Efficient optimization methods coupling a stochastic evolutionary algorithm with a gradient based deterministic method are presented in this paper. Two kinds of hybridization are compared: one is a stochastic/deterministic alternate algorithm, the other is a stochastic/deterministic embedded algorithm. In the alternating algorithm, stochastic and deterministic optimizers are performed alternately as follows: some individuals are selected from the previous population, and sent to the deterministic algorithms for further optimization, then the improved individuals are inserted into the above population to form a new one for the stochastic algorithm. In the embedded hybridized algorithm, stochastic and deterministic optimization software are run in parallel and independently, the coupling between them is that the deterministic optimizer operates on a randomly selected individual (or the best individual) from the non evaluated population of the stochastic algorithm, then its outcome (new individual) is re-injected into the evaluated population. Moreover, a multilevel approximation (e.g. variable fidelity modeling, analysis and hierarchical approximated parameterization) is introduced in the algorithm, via a low fidelity modeling and rough parameterization to perform a search on large population at lower level, and a high fidelity modeling with detailed parameterization used at higher level. After a theoretical validation of the methods on mathematical test cases, the hybridized methods are successfully applied to the aerodynamic shape optimization of a fore-body of an hypersonic air breathing vehicle, providing both a significant acceleration in terms of parallel HPC performance and improved quality of the design.

A developed surrogate-based optimization framework combining HDMR-based modeling technique and TLBO algorithm for high-dimensional engineering problems

The traditional surrogate-based optimization techniques are facing severe challenges for high-dimensional engineering optimization problems. The main challenges are how to overcome metamodeling and optimization difficulties in high-dimensional design space. To solve the above difficulties, a developed surrogate-based optimization framework combining high-dimensional model representation (HDMR)-based modeling technique and teaching-learning-based optimization (TLBO) algorithm is developed. A high-dimensional model can be decomposed into a series of low-dimensional models by HDMR-based modeling technique, which can greatly reduce the difficulty of building high-dimensional model. The TLBO algorithm which has strong optimization ability and non-parameter setting characteristic is introduced to optimize the HDMR-based model to overcome the difficulty of optimization. Several representative functions are selected as examples to verify the developed optimization method for high-dimensional problems. In addition, The developed surrogate-based optimization is applied to solve a typical engineering optimization problem: high-dimensional aerodynamic shape optimization. It can be concluded that the optimization ability of the traditional surrogate-based optimization framework can be improved with assistance of HDMR-based modeling technique and TLBO algorithm for high-dimensional engineering problems.

Discretization error control for constrained aerodynamic shape optimization

In this paper, we present a method to control the discretization error in constrained aerodynamic shape optimization problems using meshes adapted via adjoint-based error estimates. The optimization constraints may involve outputs that are not directly targeted for optimization, and hence also not for error estimation and mesh adaptation. However, discretization errors in these outputs often indirectly affect the calculation of the objective function. The proposed method takes this effect into account, so that the mesh is adapted and itself optimized to predict both objective outputs and constraint outputs with appropriate accuracy. We use unstructured mesh optimization to maximize accuracy of the results for a given number of degrees of freedom. The error estimates drive a multifidelity optimization process, preventing over-optimization on a coarse mesh and over-refinement on an undesired design. We demonstrate the accuracy and efficiency of our proposed method on several airfoil shape optimization problems governed by the compressible Navier-Stokes equations. The framework is expected to be even more important for optimization problems with complex systems, dramatic design changes, or high-accuracy requirements.

NERONE: An Open-Source Based Tool for Aerodynamic Transonic Optimization of Nonplanar Wings

Transonic shape optimization of nonplanar wings is a relevant topic in current aeronautical world. Although widely studied, an appropriate level of robustness and automation is still lacking for the inclusion of aerodynamic shape optimization in a Multi-Disciplinary Optimization (MDO) process. In this paper, a new framework, opeNsource-mEsh-geneRation-fOr-aerodyNamic-Evaluations (NERONE), is presented that allows for an automatic transonic shape optimization process within an MDO loop design using open-source libraries, namely OpenCasCade (OCC) for the geometric description, GMSH for grid generation and SU2 multi-physics for aerodynamic analysis and optimization. Wing geometry is defined in the CPACS standard, converted to a mathematical continuous description (NURBS) and passed to the mesher. Grid generation process is driven by user-defined mesh dimensions defined on wing regions and on support domain boundary surfaces. The aerodynamic analysis and optimization are then launched on the obtained grid. SU2 software has been augmented to overcome robustness issues regarding point-inversion algorithm and to control geometric quality during optimization of nonplanar wings. Capability of NERONE is first demonstrated for 2D Euler and RANS simulations (on the RAE2822 airfoil) and on a 3D Euler case (ONERA M6). With very few user-specified parameters, high-quality grids are obtained providing results that correlate well with the literature data. Finally, NERONE is applied to the local shape optimization of a wing–winglet configuration in transonic flight conditions.

Robust aerodynamic shape optimization—From a circle to an airfoil

Aerodynamic design optimization currently lacks robustness with respect to the starting design and requires trial and error in the flow solver and optimization algorithm settings to get a converged optimal design. We address need issue by developing ways to overcome robustness issues arising from shape parametrization, mesh deformation, and flow solver convergence. Our approach is demonstrated on the Aerodynamic Design Optimization Discussion Group (ADODG) airfoil optimization benchmarks to show the factors that dominate the robustness and efficiency. In the ADODG NACA 0012 benchmark, we address the additional issue of non-unique solutions. In the ADODG RAE 2822 case, we address solver failure due to shock waves, separation, and gradient accuracies due to the frozen turbulence model. Finally, we create a new, challenging aerodynamic shape optimization case that starts with a circle to test the robustness of our aerodynamic shape optimization framework. We use both fixed and adaptive parametrization methods to tackle this problem and show how we can exploit the advantages of adaptive parametrization methods to improve both robustness and efficiency. The combination of flow solver robustness, precision of gradient information, robust mesh deformation, and adaptive parametrization brings us closer to a “push-button” solution for airfoil design.

Restricted snakes volume of solid (RSVS): A parameterisation method for topology optimisation of external aerodynamics

An approach for aerodynamic shape optimisation is derived which is capable of handling topological design changes as well as detailed surface control. The technique applies a material distribution, or volume of solid approach where design variables specify a volume fraction of solid on a fixed mesh. To convert this data to a solid surface, a contour is constructed around the volumes by moving points on the surface until the final shape satisfies those specified volumes. The objective of this construction procedure is to minimise the surface length, subject to the preset volume constraints. As a result, the method reproduces circular arcs exactly. Shape function analysis is then used to explore the theoretical behaviour of the parameterisation, and to prevent oscillatory surfaces from forming, thereby ensuring good optimiser convergence. The method is extended to allow for anisotropic refinement of the parameter mesh. Final test cases include geometric fitting of arbitrary shapes, as well as drag minimisation of topologies in supersonic flow, and show the parameterisation is able to explore single and multi-body aerodynamic design problems.

Aerodynamic shape optimization using a novel optimizer based on machine learning techniques

Aerodynamic shape optimization is usually a loop of an optimization model, an optimizer and an evaluation workflow. A new optimizer is proposed and tested for a typical aerodynamic shape optimization of missile control surfaces with computational fluid dynamics (CFD). The new optimizer emphasizes the use of machine learning techniques, reinforcement learning and transfer learning, to improve performance and efficiency. Reinforcement learning is applied to extract the optimization experience from the semi-empirical method DATCOM using deep neural networks. Transfer learning is implemented to reuse the experience as priori knowledge in the CFD-based optimization by sharing neural network parameters. For the considered aerodynamic shape optimization problem of missile control surfaces, a remarkable reduction in the computational time has been accomplished. The new approach significantly decreases the required CFD calls by over 62.5%. Meanwhile, the time spent in the experience extraction and parameter transfer process is negligible.

Multimodality in Aerodynamic Wing Design Optimization

The application of gradient-based optimization to wing design could potentially reveal revolutionary new wing concepts. Giving the optimizer the freedom to discover novel wing designs may increase the likelihood of multimodality in the design space. To address this issue, this study investigates the existence and possible sources of multimodality in the aerodynamic shape optimization of a rectangular wing. Our test case, specified by the ADODG Case 6, has a high dimensionality design space and a large degree of flexibility within that design space. Several subproblems of this benchmark test case are studied, and the multimodality introduced by each set of variables is analyzed considering both inviscid and viscous analysis. This methodical approach allows us to isolate a few instances where certain parametrizations create a multimodal design space. However, this study demonstrates that these occurrences of multimodality are due to modeling inaccuracies or can be curbed by the application of practical design constraints. Additionally, it is found that the shape of the optimized wing is highly dependent on the interplay between induced and parasite drag, providing more incentive to consider viscous effects in the analysis. As an example, when minimizing drag with respect to chord distribution, there are multiple local minima at low , but a single global minimum (the elliptical planform) at high . These results will help other researchers avoid some of the pitfalls that could lead to multimodality in wing optimization.