Method For Aerodynamic Shape Optimization Research Articles

Adaptive Free-Form Deformation Parameterization Based on Spring Analogy Method for Aerodynamic Shape Optimization

An adaptive Free-Form Deformation parameterization method based on a spring analogy is presented for aerodynamic shape optimization problems. The proposed method effectively incorporates the gradients of the objective and constraint functions, achieving automatic control point adjustment based on variances in design variable components. To evaluate the performance of the adaptive FFD parameterization method, two 2D airfoil optimization design problems are examined. The optimization of the RAE2822 airfoil with 12, 18 and 24 design variables demonstrates superior results for the adaptive method compared to uniform parameterization. The adaptive method requires fewer iterations and achieves lower objective function values. Additionally, the optimization design from NACA0012 to RAE2822 airfoil with 18 design variables shows that the adaptive parameterization method achieves a lower drag coefficient while satisfying the optimization objective. This validates the method’s capability to finely adjust airfoil shapes and capture more optimal design points by exerting stronger control over local shapes. The proposed adaptive FFD parameterization method proves highly effective for optimizing aerodynamic shapes, offering stability and efficiency in the early stages of optimization, even with a limited number of design variables.

Efficient aerodynamic shape optimization by using unsupervised manifold learning to filter geometric features

Many aerodynamic shape optimization methods often focus on utilizing the end-to-end relationship between design variables and aerodynamic performance to find the optimal design, while overlooking the exploration of geometric knowledge of the shape itself. To fully use geometric knowledge to improve optimization efficiency, this paper proposes an efficient method by exploring the potential correlation between geometric features and aerodynamic performance at a low cost. We use unsupervised isometric feature mapping in manifold learning to capture geometric features that can distinguish the aerodynamic performance of different airfoils without embedding any tags. Then a filter criterion is establish based on the geometric features. During the optimization process, airfoils that deliver poor aerodynamic performance can be filtered out with a high probability before being precisely evaluated through computational fluid dynamics simulations. This helps improve samples quality to enhance the optimization efficiency. We applied the proposed method to the unconstrained and constrained optimizations of the Royal Aircraft Establishment (RAE) 2822 airfoil to validate its performance. The results demonstrate that the proposed method can improve the efficiency of optimization by over 50% compared with the original evolutionary optimization algorithm. It performs well across various optimization problems, demonstrating high engineering practical value.

A mid-range approximation method assisted by trust region strategy for aerodynamic shape optimization

This paper presents an efficient solution for high-fidelity large-scale aerodynamic shape optimization problems based on several developments in the mid-range approximation method within a trust region optimization framework. The mid-range approximation method is an iterative optimization technique that utilizes mid-range approximations to replace the physical experiments or simulations during the optimization based on the selected trust region strategy. It could transform the original optimization problem into a sequence of approximate sub-optimization problems. In this work, an improved trust region strategy is proposed to contain more optimization states with a flexible and controllable performance to suit different types of problems. A metamodel assembly technique and its gradient-enhanced version are developed to further relax the requirements of computational costs in the mid-range approximation method. Its performance is discussed through a detailed comparison of metamodel performance using a mathematical benchmark case named Vanderplaats scalable beam. The wing only of the Common Research Model is offered to the proposed method for aerodynamic shape optimization. The optimization has 1 design objective, 232 design variables, and 135 design constraints. With all constraints satisfied, the optimized configuration has a 4.85 % improvement in wing drag performance. The shock region is greatly reduced and the wing pressure distribution is smooth and nearly parallel. These results show that the proposed method could achieve the design goal successfully within a reasonable computational cost for large-scale problems.

High-dimensional aerodynamic shape optimization framework using geometric domain decomposition and data-driven support strategy for wing design

Traditional aerodynamic shape optimization methods usually suffer from difficulties in optimization and modeling for high-dimensional aerodynamic optimization problems. To overcome these difficulties, a new high-dimensional aerodynamic shape optimization framework is proposed from the perspectives of geometric domain decomposition for dimensionality reduction and a data-driven model support strategy for changing the role of surrogate model and assisting the optimizer. Geometric domain decomposition uses proper orthogonal decomposition to transform the high-dimensional Class-Shape Function Transformation method into low-dimensional geometric modes to reduce design dimensions for parameterizing the geometric shape, which reduces optimization and modeling difficulties. Also, a data-driven support strategy is proposed to improve the effectiveness and efficiency of the optimizer by learning from historical aerodynamic data; this strategy modifies the role of surrogate model in the optimization framework to assist the optimizer; the surrogate model, serving as an auxiliary role, can reduce the dependence on model accuracy, which overcomes the difficulty of high-dimensional modeling to some extent. We applied the developed framework to transonic drag reduction of wings to validate its performance. The optimization results show that the developed framework converges faster and offers better designs compared to direct optimization and state-of-the-art surrogate-based optimization frameworks for high-dimensional aerodynamic shape optimization.

Aerodynamic shape optimization of the vortex-shock integrated waverider over a wide speed range

The vortex-shock integrated waverider over a wide speed range could significantly improve the aerodynamic performance of traditional waveriders by introducing the vortex effect at subsonic speeds. Therefore, it is promising to be widely used in the design of wide-speed-range aerospace vehicles. However, the design of the vortex-shock integrated waverider ignores the three-dimensional effect, the subsonic effect, and the viscous effect in the establishment of the reference flow field, which fails to obtain the expected ideal performance. Therefore, it is necessary to further improve the wide-speed-range performance of the vortex-shock integrated waverider by employing the aerodynamic shape optimization method. In this study, the wide-speed-range multipoint optimization of the vortex-shock integrated waverider is carried out using a gradient-based optimizer combined with adjoint gradient evaluations. The results show that the optimum configuration increases the subsonic lift and lift-to-drag ratio by 6.7 % and 7.1 %, while increasing the hypersonic lift-to-drag ratio by 1.4 %. The improvement of the aerodynamic performance at subsonic speeds is attributed to the enhancement of the leeward vortex effect. Also, the leeward surface near the leading edge is optimized to an inner concave region to further enhance the vortex lift, while guaranteeing against the volume decline. Furthermore, the Detached Eddy Simulation (DES) method and the Dynamic Mode Decomposition (DMD) method are used to analyze the vortex dynamic characteristics at subsonic speeds. By analyzing the first three modes, it is observed that the aerodynamic performance of the optimum configuration is improved mainly by the frequency reduction and the increase of the pressure difference between the windward and the leeward surface, which enhance the stability and strength of the vortex.

Effects of Static Stability Margin on Aerodynamic Design Optimization of Truss-Braced Wing Aircraft

Currently, the aviation industry is facing an oil and energy crisis and is contributing much more greenhouse gas emissions to the environment. Aircraft design approaches, such as aerodynamic shape optimization, new configuration concepts, and active control technology, have been the primary and effective means of achieving goals concerning fuel burn, noise, and emissions. For now, the design problems of relaxed static stability (RSS, an active control technique) and truss-braced wing (TBW) configurations with high-fidelity aerodynamic shape optimization methods have been investigated widely to promote aerodynamic performance. Nevertheless, they are studied almost always separately, and the combination of exploration and refined design is rarely presented. Therefore, the purposes of this work are to evaluate the benefits of RSS on a full TBW wing–body–tail configuration under various flight conditions and the effects on multi-components and to further explore the potential and analyze the aerodynamic features with the combination of shape optimization and RSS. To address these issues, on the one hand, a range of seven static stability margins are adopted to evaluate its effects with a high-fidelity Reynolds-averaged Navier–Stokes solver. On the other hand, seven cases of drag minimization multipoint aerodynamic design optimization are performed, which are with 600 shape variables and 13 twist variables, subject to lift coefficient, trim, and thickness constraints. The results indicate that with RSS only, the initial configuration has a 2.39% drag reduction under cruise conditions and a 3.01% and a 5.24% drag reduction under two off-design conditions. Additionally, the effects on the multi-components are observed and analyzed. Moreover, all of the optimized configurations with RSS have 2.13%, 2.42%, and 2.12% drag reductions under cruise conditions, drag divergence conditions, and near-buffet-onset conditions, respectively. The most promising optimized configuration has a lift-to-drag ratio of 24.48 with an aerodynamic efficiency of 17.14. The evaluations with a series of off-design points also present high-level aerodynamic efficiency.

An efficient geometric constraint handling method for surrogate-based aerodynamic shape optimization

Handling a large number of geometric constraints brings a big challenge to the surrogate-based aerodynamic shape optimization (ASO) driven by computational fluid dynamics (CFD). It is not feasible to calculate the geometric constraint functions directly during the sub-optimization of a surrogate-based optimization, as the geometric constraint functions are to be evaluated thousands of times for each updating cycle and the total cost of a number of cycles can be prohibitive. This article proposes an efficient method of handling geometric constraints within the framework of a surrogate-based optimization to address this problem. The core idea is to use the Kreisselmeier-Steinhauser (KS) method to aggregate all geometric constraints into one that can be approximated by a cheap surrogate model, in order to avoid the large computational cost associated with tremendous calculation of geometric constraint values. The proposed method is verified by an analytical test case. Then, the proposed method is demonstrated and compared with the methods of building surrogate models of all geometric constraints and calculating all geometric constraints directly during each sub-optimization by drag minimizations of NACA0012 air foil and ONERA M6 wing in transonic flows. To investigate the ability of the proposed method for handling various geometric constraints, drag minimization of CRM wing in viscous transonic flow driven by CFD is performed. Results show that the proposed method can dramatically improve the optimization efficiency of ASO with the number of geometric constraints ranging from 15 to 1429 and the number of types of geometric constraints up to 3, which offers great potential for handling a larger number and more types of geometric constraints.

Generic Modal Design Variables for Efficient Aerodynamic Optimization

Orthogonal modes are an effective method for aerodynamic shape optimization due to their excellent design space compactness; however, all existing methods are generated from a database of representative geometry. Moreover, application to high-fidelity design spaces is not possible because high-frequency shape components are insufficiently bounded, leading to nonsmooth and oscillatory geometries. In this work, a new generic methodology for generating orthogonal shape modes is presented based on a purely geometric derivation, eliminating the need for geometric training data. The new method is a further development of the gradient-limiting method developed previously for constraining the design space in a geometrically meaningful way to reduce the effective degrees of freedom and improve optimization convergence rate and final result. Here, the gradient-limiting methodology is reformulated by transforming the constraints directly onto design variables to produce orthogonal shape modes with equivalent constraints for ensuring smooth and valid iterates. The new generic methodology requires no training data, can be applied to arbitrary topologies using different boundary conditions, and naturally includes translational modes as part of the orthogonal basis. When applied to two standard aerodynamic test cases, the new method has superior performance compared to library-derived modes. Importantly, the optimization convergence rate is independent of the number of design variables, and the optimized objective at high design fidelities is greatly improved by avoiding local minima corresponding to spurious geometries. A nonstandard test case is demonstrated, for which traditional library modes are not useable due to nontrivial topology, and it is shown to benefit from the high-fidelity design space and translational mode made possible with the novel methodology.

Aerodynamic Efficiency Enhancement of Delta Wings for Micro Air Vehicles Using Shape-Optimization

The performance of fixed-wing micro air vehicles (MAVs) is impaired due to their small size, operating speeds, and altitude leading to limited lift, aerodynamic efficiency (lift-to-drag ratio), and low gust resilience. Nonslender delta wings have high stall angle and maneuverability, which are desirable features for MAVs. However, the aerodynamic efficiency of delta-winged MAVs is low, thus impacting the overall performance. We optimize the aerodynamic efficiency of a flat-plate delta wing using the adjoint-based aerodynamic shape optimization method coupled with incompressible Reynolds-averaged Navier–Stokes equations. The optimization improves the aerodynamic efficiency from 6.2 to 10.2 at 5° angle of attack while satisfying lift and moment constraints. The optimized wing is significantly cambered, and the axial cross section reveals that a circular arc can approximate the optimized wing airfoil. A parametric study of the circular camber delta wings with a 0–7.5% camber-to-chord ratio reveals that an increase in camber leads to linear growth in the lift, whereas the drag shows a quadratic growth. Consequently, an optimum camber exists at 2.5% for maximizing the aerodynamic efficiency (9.3); the wing has aerodynamic characteristics closely resembling the optimized wing, thus revealing that the essence of the efficiency optimization process is to identify the optimal camber distribution.

Aerodynamic Shape Optimization Method of Non-Smooth Surfaces for Aerodynamic Drag Reduction on A Minivan

To reduce aerodynamic drag of a minivan, non-smooth surfaces are applied to the minivan’s roof panel design. A steady computational fluid dynamics (CFD) method is used to investigate the aerodynamic drag characteristics. The accuracy of the numerical method is validated by wind tunnel test. The drag reduction effects of rectangle, rhombus and arithmetic progression arrangement for circular concaves are investigated numerically, and then the aerodynamic drag coefficient of the rectangle arrangement with a better drag reduction effect is chosen as the optimization objective. Three parameters, that is, the diameter D of the circular concave, the width W and the longitudinal distance L among the circular concaves, are selected as design variables. A 20-level design of an experimental study using a Latin Hypercube scheme is conducted. The responses of 20 groups of sample points are obtained by CFD simulation, based on which a Kriging model is chosen to create the surrogate-model. The multi-island genetic algorithm is employed to find the optimum solution. The result shows that maximum drag reduction effects up to 7.71% can be achieved with a rectangle circular concaves arrangement. The reduction mechanism of the roof with the circular concaves was discussed. The circular concaves decrease friction resistance of the roof and change the flow characteristics of the recirculation area in the wake of the minivan. The roof with the circular concaves reduces the differential pressure drag of the front and rear of the minivan.

Aerodynamic shape optimization of wind turbine blades for minimizing power production losses due to icing

Ice formation on a wind turbine alters the airfoil profiles of the blades and causes degradation in the aerodynamic performance of the wind turbine and the resulting power production losses. Since the blade profile plays a significant role in the icing of a blade, power production losses due to icing can be minimized by optimizing the blade profile against icing. In this study, blade profiles are optimized in order to minimize power production losses. A Gradient based aerodynamic shape optimization method is developed together with the Blade Element Momentum method and an ice accretion prediction tool in order to minimize the power production losses of horizontal axis wind turbines under various icing conditions. In an optimization study performed for the Aeolos-H 30 kW and NREL 5 MW wind turbines exposed to icing conditions up to 1 h, the power loss due to icing is reduced by about 4%.

Rapid Aerodynamic Shape Optimization With Payload Size Constraints for Hypersonic Vehicle

Nowadays, aerodynamic shape optimization of the hypersonic vehicle is mostly optimized for local details such as the wing. In the overall shape optimization, the conceptual design of the vehicle is more common, in which the shape is described in fewer parameters and optimized roughly. Meanwhile, in the optimization, the capacity is considered only by the volumetric ratio, and it can hardly meet the actual payload size constraints, which is difficult to apply to engineer practice. In this paper, a rapid aerodynamic shape optimization method with payload size constraints is proposed. The analytic method combined with a clamped cubic spline curve is used to establish the parametric model with the payload size constraints. In order to ensure the accuracy and improve the optimization efficiency, the aerodynamic characteristics of the vehicle are quickly obtained based on the adaptive Cartesian grid generation method and viscosity modified Euler equations. The lift-to-drag ratio is used as the objective, and a sequence iteration method with multi-point selecting strategy is adopted to make convergence faster. In order to compare and verify the effectiveness of the proposed method, the optimal solution is compared with a reference shape obtained through a conventional multi-objective aerodynamic shape optimization with lift-to-drag ratio and the volumetric ratio as objectives. Through comparative analysis, the method proposed in this paper can find the optimal shape that satisfies the payload size constraints quickly, which can effectively improve the aerodynamic performance of the hypersonic vehicle and can be better applied to practical engineering optimization problems.

Adjoint-Based Two-Step Optimization Method Using Proper Orthogonal Decomposition and Domain Decomposition

A modified two-step method for aerodynamic shape optimization is proposed, where proper orthogonal decomposition and automatic domain-decomposition techniques are adopted to accelerate flow and adjoint solutions in the second-step optimization. As the first step in this method, the initial optimization is first performed by a genetic algorithm coupled with a kriging model. Next, a reduced-order model is set up via proper orthogonal decomposition with the reuse of ready-made flow snapshots in the first-step optimization. A proper-orthogonal-decomposition Petrov-Galerkin method is investigated to provide fast flow predictions in the second-step optimization. With the assistance of an error estimation method and an automatic domain-decomposition method that are presented in this paper, the sensitive domain in the computational grid is split out. To improve the accuracy, predictions provided by proper orthogonal decomposition in the sensitive domain are further corrected by computational fluid dynamics modifications. Meanwhile, in order to accelerate gradient solutions, the adjoint equation of this proper orthogonal decomposition and domain-decomposition-based flow analysis method is derived and discussed. The optimization results of a two-dimensional airfoil design test and a three-dimensional wing design test highlight the efficiency of the proposed method when compared with results of either a gradient-free optimization method or a traditional two-step method.

Virtual Stackelberg game coupled with the adjoint method for aerodynamic shape optimization

ABSTRACTIn this article, a Virtual Stackelberg Game (VSG) is proposed for aerodynamic shape optimization, where the design variables are divided into two categories to optimize the same objective function, one acts as a leader, and the other ones as followers react independently and selfishly relative to the leader's strategy. During each Stackelberg strategy cycle, the Gradient-Based Method (GBM) with the adjoint method in Stanford University Unstructured (SU2) is applied in the optimization of each player. Firstly, parametric studies of VSG by two simple cases are conducted to assess the impact of critical parameters on aerodynamic shape optimization, including the design cycle, the split of design variables and role (leader and follower) assignment. Based on the criterion from parametric studies, two typical numerical cases under transonic flow are applied—the drag reduction design of a 2D airfoil and a 3D wing. It is found that, compared to the original GBM method, VSG can provide better optimization results with less computational cost.

A novel surrogate-based aerodynamic optimization method using field approximate model

An efficient surrogate-based aerodynamic shape optimization method is developed to improve the optimization efficiency. In this method, the field approximate model is presented firstly to predict the flow field parameters of interest for specific aerodynamic optimization problems with respect to the design variables and sequentially updated. The differential evolution is used to locate the optimum of field approximate model coupled with the analytical post-processing to calculate the objective and constraints for aerodynamic optimization. This optimal point is calculated by time-consuming computational fluid dynamics simulation and the result is added to the sampling set to update the sampling points and field approximate model. The proposed method is compared with conventional sequential approximate optimization and shows great advantages in accuracy and efficiency. Two shape optimization test cases are provided to verify the efficacy and efficiency of the proposed method.

Automatic Optimization of Wing–Body–Under-the-Wing-Mounted-Nacelle Configurations

A robust and accurate method for aerodynamic shape optimization, previously developed by the authors, is extended to automatic multipoint design of aircraft configurations with under-the-wing-mounted nacelle. The shape is optimized for minimum drag at fixed lift subject to numerous geometrical and aerodynamic constraints. The method is driven by genetic algorithms and full Navier–Stokes computations combined with reduced-order-models approach. A recently developed optimization software based on the proposed method is applied to the design of a wing combined with fuselage and under-the-wing-mounted nacelle in a close coupling installation. A multipoint multiconstrained optimization carried out in a fully automatic mode achieved significant drag reduction within and beyond industry-realistic design conditions. The results indicate the ability of the developed automatic techniques to provide industrial-strength solutions that are not easily found through a traditional process of intelligent trial and error.

Automatic Design of Wing–Body–Nacelle Configurations for Minimum Drag

A computational-fluid-dynamics-driven robust and accurate method for aerodynamic shape optimization, previously developed by the authors, is further enhanced by extending it to automatic multipoint design of wing–body–nacelle configurations. The shape is optimized for minimum drag at fixed lift subject to numerous geometrical and aerodynamical constraints. The method, which is driven by genetic algorithms and full Navier–Stokes computations combined with reduced-order models approach, is supported by massive multilevel parallelization. The applications include single- and multipoint aerodynamic designs for a transport-type aircraft configuration. For the considered class of shape optimizations, significant drag reduction in on- and off-design conditions has been achieved. It was also shown that the optimizations, which start from markedly different initial shapes, ultimately converge to optimum shapes very close one to one another. The paper demonstrates how automated techniques based on the developed method have now matured and provide an industrial strength solution.

A design and optimization method for matching the torque of the wind turbines

An aerodynamic shape optimization method for a horizontal axis wind turbine is developed and verified through experimentation with a laboratory-scale wind turbine. Our method is based on matching the rotor's and the coupled generator's torque. Prior to shape optimization, an initial rotor design is established with a hybrid use of Schmitz and blade element momentum theories. The experimental verification of the developed method is conducted with a small-scale wind turbine; thus, the operating Reynolds number is one order of magnitude lower than large-scale wind turbines. Therefore, a high-lift low-Re airfoil, namely, SG6043, is selected for the blade along the whole span. The shape is optimized by determining the optimum chord and cumulative pitch angle distributions by manipulating the tapering and twisting of the blade. The objective of the optimization is to maximize the turbine's power coefficient Cp, while maintaining the torque equal to that of the generator. The generator's characteristics are found through experimentations which are conducted apart from the wind tunnel experiments. During the optimization process, the local aerodynamic forces on the blade are calculated by interfacing the optimization program with XFOIL; thus, the torque and power can be calculated for the rotor at each iteration step. The optimized turbine performance is evaluated under a design and off-design operating condition. The performance verification experiments are carried out in the wind tunnel with a specially designed setup. A comparison of the measured and computed performance shows good agreement.

Aerodynamic shape optimization by variable-fidelity computational fluid dynamics models: A review of recent progress

A brief review of some recent variable-fidelity aerodynamic shape optimization methods is presented. We discuss three techniques that—by exploiting information embedded in low-fidelity computational fluid dynamics (CFD) models—are able to yield a satisfactory design at a low computational cost, usually corresponding to a few evaluations of the original, high-fidelity CFD model to be optimized. The specific techniques considered here include multi-level design optimization, space mapping, and shape-preserving response prediction. All of them use the same prediction–correction scheme, however, they differ in the way the low-fidelity model information it utilized to construct the surrogate model. The presented techniques are illustrated using three specific cases of transonic airfoil design involving lift maximization and drag minimization.

Surrogate model for aerodynamic shape optimization of a tractor-trailer in crosswinds

A surrogate model-based aerodynamic shape optimization method applied to the wind deflector of a tractor-trailer is presented in this paper. The aerodynamic drag coefficient of the tractor-trailer with and without the wind deflector subjected to crosswinds is analyzed. The numerical results show that the wind deflector can decrease drag coefficient. Four parameters are used to describe the wind deflector geometry: width, length, height, and angle. A 30-level design of experiments study using the optimal Latin hypercube method was conducted to analyze the sensitivity of the design variables and build a database to set up the surrogate model. The surrogate model was constructed based on the Kriging interpolation technique. The fitting precision of the surrogate model was examined using computational fluid dynamics and certified using a surrogate model simulation. Finally, a multi-island genetic algorithm was used to optimize the shape of the wind deflector based on the surrogate model. The tolerance between the results of the computational fluid dynamics simulation and the surrogate model was only 0.92% when using the optimal design variables, and the aerodynamic drag coefficient decreased by 4.65% compared to the drag coefficient of the tractor-trailer installed with the original wind deflector. The effect of the optimal shape of the wind deflector was validated by computational fluid dynamics and wind tunnel experiment.