Viscous Aerodynamic Shape Optimization of Wings Including Planform Variables

This paper presents an aerodynamic shape optimization method based on a genetic algorithm with the compressible Euler or Navier-Stokes equations. A new algorithm to represent aerodynamic configurations is proposed to find optimum aerodynamic configurations efficiently. We solve three aerodynamic shape optimization problems. First, an inverse problem is solved to understand a basic character and to examine the possibility of the genetic algorithm. Second, a drag minimization problem is solved to find a streamlined body. Finally, L/D(ratio of lift to drag) maximization problem in a transonic flow is solved and the optimized configuration is compared with a supercritical airfoil. The results show that genetic algorithm is powerful and robust in solving aerodynamic shape optimization problems.

Optimization of aerodynamic shapes using numerical methods has always been of engineering interest. This paper presents a highly efficient aerodynamic optimization method for hypersonic wings based on local piston theory. The objective of the optimization is to improve the aerodynamic characteristics of original airfoils or wings generated from NACA0012 while satisfying constraints on structure requirements. In the optimization procedure, a genetic algorithm is employed for optimum search, the Hicks–Henne bump function is used for airfoil geometrical modification, and local piston theory is used for unsteady pressure perturbations caused by geometrical modification from the baseline. Because unsteady pressure perturbations at supersonic or hypersonic conditions could be calculated by local piston theory based on initial flowfield results in the optimum searching process, only one steady-state solution without any use of moving or deforming grids is required. Therefore, the optimization method described in this paper is an extremely efficient technique that combines the advantages of steady computational fluid dynamics and the local piston theory and thus has very low computational cost in an optimum search process. Optimization results of airfoils and wings, including single and multipoint optimization for a flat wing without any sweep, and backswept wing, demonstrate the effectiveness and efficiency of the aerodynamic optimization method for hypersonic wings.

Surrogate models are used to dramatically improve the design efficiency of numerical aerodynamic shape optimization, where high-fidelity, expensive computational fluid dynamics (CFD) is often employed. Traditionally, in adaptation, only one single sample point is chosen to update the surrogate model during each updating cycle, after the initial surrogate model is built. To enable the selection of multiple new samples at each updating cycle, a few parallel infilling strategies have been developed in recent years, in order to reduce the optimization wall clock time. In this article, an alternative parallel infilling strategy for surrogate-based constrained optimization is presented and demonstrated by the aerodynamic shape optimization of transonic wings. Different from existing methods in which multiple sample points are chosen by a single infill criterion, this article uses a combination of multiple infill criteria, with each criterion choosing a different sample point. Constrained drag minimizations of the ONERA-M6 and DLR-F4 wings are exercised to demonstrate the proposed method, including low-dimensional (6 design variables) and higher-dimensional problems (up to 48 design variables). The results show that, for surrogate-based optimization of transonic wings, the proposed method is more effective than the existing parallel infilling strategies, when the number of initial sample points are in the range from Nv to 8Nv (Nv here denotes the number of design variables). Each case is repeated 50 times to eliminate the effect of randomness in our results.

We present a new continuous adjoint method for aerodynamic shape optimization using the Euler equations, which reduces the computational cost of the gradients by reducing the volume integral part of the adjoint gradient formula to a surface integral. The savings are particularly significant for three-dimensional aerodynamic shape optimization problems on general unstructured and overset meshes. In order to validate the concept, the new gradient equations have been tested for various aerodynamic shape optimization problems, including an inverse problem for threedimensional wing configurations, and drag minimization problems of a single-element airfoil and a three-dimensional wing-fuselage configuration. In order to assess their accuracy, the results are compared with finite-difference gradients, complex-step gradients, and gradients calculated by the previous adjoint method which includes a volume integral. ∗Thomas V. Jones Professor of Engineering, Department of Aeronautics and Astronautics, Stanford University, AIAA Fellow †Postdoctoral Fellow, Department of Aeronautics and Astronautics, Stanford University, AIAA Member

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.

Aerodynamic shape optimisation technology is presented, comprising an efficient variable fidelity shape parameterisation method, an efficient andhigh quality mesh deformation scheme, and a parallel optimisation algorithm. The objective of the research presented here is the comparison of truly three-dimensional optimisations of aircraft wings in both aerodynamic and aeroelastic environments. The novel shape parameterisation technique allows various fidelities of design parameters, ranging from detailed surface changes to novel truly three-dimensional planform adjustments. An efficient interpolation scheme, using radial basis functions, transfers domain element movements into direct deformations of the design surface and corresponding CFD mesh, thus allowing total independence from the grid generation package and type (structured or unstructured). Optimisation is independent from the CFD flow solver by obtaining sensitivity information for an advanced parallel gradient-based optimiser by finite-differences. This ‘wrap-around’ optimisation technique is applied to a modern large transport aircraft wing in the cruise flight condition for minimum drag with stringent constraints in lift, volume, and two root moments. The objective of all optimisations is aerodynamic, however the static aeroelastic deflection provided by an aeroelastic solver will give that particular optimisation increased accuracy and real world relevance. The result of a constrained inviscid aerodynamic optimisation is presented and has a significant reduction in drag when compared to the initial wing with no violation of any constraints. The shape parameterisation method demonstrates that only a low number of design variables are necessary to achieve innovative planform and surface geometries with dramatically improved performance. Computational fluid dynamics (CFD) methods are now commonplace in aerospace industries, and at the forefront of analysis capabilities, providing a fast and effective method of predicting a design’s aerodynamic performance. However, with ever increasing complexity of designs, engineers can often struggle to interpret the intricacies of the CFD results sufficiently to be able to manually alter the geometry to improve performance. Hence, there has been an increase in demand for intelligent and automatic shape optimisation schemes. This requires combining geometry control methods with numerical optimisation algorithms, to provide a mechanism to mathematically seek improved and optimum designs, using CFD as the analysis tool. Optimisation requires consideration of three issues, each of which have numerous solutions: shape parameterisation including CFD surface and volume mesh deformation, computation of design variable derivatives, and effective use of these derivatives to improve design. Geometry parameterisation is critical for effective shape optimisation. This is the method of representing the design surface, and defines the degrees of freedom in which the geometry can be altered and, ideally, this should be linked with an effective method of deforming the CFD surface and volume mesh in a corresponding fashion. Parameterising complex shapes is a problem that remains a serious obstacle to both manual and automatic CFD-based optimisation. A wide variety of shape control and morphing methods have been developed, but many do not allow sufficiently

In the aerodynamic shape design, the drag prediction has always been an extremely challenging mission for the exploration of a configuration. As for the more complex configurations, it is especially desired to the availability of a highly accurate and reliable aerodynamic numerical solution. For improving the drag prediction accuracy and promoting the aerodynamic shape designs, firstly, the characteristics of drag prediction based on far-field drag method and near-field drag method is analyzed and compared. Also, the merits and demerits of defining axial velocity defect with the current main far-field drag prediction approaches is summarized, which promotes the building of the improved method of axial velocity defect and the improved far-field drag prediction and decomposition approach. Moreover, during the establishment of the drag decomposition method, it is necessary to judge and decide on the selection of the drag region. Therefore, the discussions on the sensitivity of the relevant parameters are fulfilled. Furthermore, based on the far-field drag prediction and decomposition method constructed, the aerodynamic performance research of Common Research Model wing-body configuration is launched. The results show that it can effectively observe and analyze the changes in drag components, their impact on the total drag and the contribution percentage. Finally, combining the far-field drag prediction and decomposition method proposed in this paper with a gradient-based aerodynamic shape optimization design system, the aerodynamic shape optimization designs are studied with CRM wing-body configuration. The results can not only directly analyze the detailed change of the visualized drag region, but also can obtain the more accurate total drag and lift-to-drag ratio of the optimized configuration by removing the spurious drag.

A new method for aerodynamic shape optimization using a genetic algorithm with real number encoding is presented. The algorithm is used to optimize three different problems, a simple hill climbing problem, a quasi-one-dimensional nozzle problem using an Euler equation solver and a three-dimensional transonic wing problem using a nonlinear potential solver. Results indicate that the genetic algorithm is easy to implement and extremely reliable, being relatively insensitive to design space noise.

This paper presents an approach for the rapid implementation of an adjoint solver for the ReynoldsAveraged Navier–Stokes equations with a Spalart–Allmaras turbulence model. Automatic differentiation is used to construct the partial derivatives required in the adjoint formulation. The resulting adjoint implementation is computationally efficient and highly accurate. The assembly of each partial derivative in the adjoint formulation is discussed. In addition, a coloring acceleration technique is presented to improve the adjoint efficiency. The RANS adjoint is verified with complex-step method using a flow over a bump case. The RANS-based aerodynamic shape optimization of an ONERA M6 wing is also presented to demonstrate the aerodynamic shape optimization capability. The drag coefficient is reduced by 19% when subject to a lift coefficient constraint. The results are compared with Euler-based aerodynamic shape optimization and previous work. Finally, the effects of the frozenturbulence assumption on the accuracy and computational cost are assessed.

An efficient approach to optimization of real-life 3D aerodynamic shapes for minimum drag is presented. The method allows for substitution of fictitious surfaces for those parts of aircraft which are not subject to modification in the process of design. The approach essentially reduces the geometrical complexity of computational models thus making the optimization of complete aerodynamic configurations practically feasible and, eventually, increasing the accuracy and reliability of optimization. The optimization framework is that of OPTIMAS, the in-house IAI optimization tool based on Genetic Algorithms and full Navier-Stokes computations. The method is illustrated by example of wing shape optimization for the full configuration of generic business jet with close coupled wing-body-nacelle, and vertical/horisontal tails. The results indicate the applicability of the method to practical aerodynamic design.KeywordsAerodynamic PerformanceWing ShapeAerodynamic DesignAerodynamic ShapeMinimum DragThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In aerodynamic shape optimization, traditional static geometry control methods can produce suboptimal performance by introducing performance tradeoffs at various stages of optimization, enforcing arbitrary constraints on open-ended optimization, and necessitating foreknowledge of problem behavior to design an effective control scheme. These shortcomings can be mitigated through dynamic geometry control, which partly automates the geometry control design process by refining the geometry control topology throughout optimization. Such refinement can occur in a predetermined fashion (as in progressive control) or more automatically using sensitivity information to guide refinement (as in adaptive control). Both progressive control and adaptive control are implemented in the context of axial and free-form deformation geometry control, and novel contributions are made to the adaptive algorithm, including the treatment of active constraints and several novel “potential indicators” to rank candidate refinements. Application to a wide suite of aerodynamic shape optimization problems demonstrates that dynamic geometry control is effective, producing lower final drag than well-designed static schemes while reducing required iterations to convergence by 50% or more, and simultaneously reducing labor requirements on the user. These benefits are demonstrated across a wide variety of problems, representative of detailed and exploratory problems often encountered in both academia and industry.

Optimization problems in many industrial applications are very hard to solve. Many examples of them can be found in the design of aeronautical systems. In this field, the designer is frequently faced with the problem of considering not only a single design objective, but several of them, i.e., the designer needs to solve a Multi-Objective Optimization Problem (MOP). In aeronautical systems design, aerodynamics plays a key role in aircraft design, as well as in the design of propulsion system components, such as turbine engines. Thus, aerodynamic shape optimization is a crucial task, and has been extensively studied and developed. Multi-Objective Evolutionary Algorithms (MOEAs) have gained popularity in recent years as optimization methods in this area, mainly because of their simplicity, their ease of use and their suitability to be coupled to specialized numerical simulation tools. In this chapter, we will review some of the most relevant research on the use of MOEAs to solve multi-objective and/or multi-disciplinary aerodynamic shape optimization problems. In this review, we will highlight some of the benefits and drawbacks of the use of MOEAs, as compared to traditional design optimization methods. In the second part of the chapter, we will present a case study on the application of MOEAs for the solution of a multi-objective aerodynamic shape optimization problem.

The traditional multi-objective efficient global optimization (EGO) algorithms have been hybridized and adapted to solving the expensive aerodynamic shape optimization problems based on high-fidelity numerical simulations. Although the traditional EGO algorithms are highly efficient in solving some of the optimization problems with very complex landscape, it is not preferred to solve most of the aerodynamic shape optimization problems with relatively low-degree multi-modal design spaces. A new infill criterion encouraging more local exploitation has been proposed by hybridizing two traditional multi-objective expected improvements (EIs), namely, statistical multi-objective EI and expected hypervolume improvement, in order to improve their robustness and efficiency in aerodynamic shape optimization. Different analytical test problems and aerodynamic shape optimization problems have been investigated. In comparison with traditional multi-objective EI algorithms and a standard evolutionary multi-objective optimization algorithm, the proposed method is shown to be more robust and efficient in the tests due to its hybrid characteristics, easier handling of sub-optimization problems, and enhanced exploitation capability.

The present-day scenario of urbanization is mostly vertical densification that results in the building of super-tall structures in metropolitan areas with land shortage. In the process of going higher up, these buildings become part of the wind load rather than gravity acting on them. The combined action of turbulence wind flow and bluff bodies of high-rise buildings promotes the introduction of complex aerodynamic phenomena that include vortex shedding, buffeting, and galloping, all of which have a direct bearing on structural safety and occupant comfort. While traditional design techniques still focus on prismatic geometries, the recent architectural trends have moved to complex and irregular plan configurations, such as that of the Fish, Y, and Plus shapes, and also the globally twisted and tapered towers, which are mainly driven by aesthetic aspirations and functional optimization. Nevertheless, the current international design codes such as ASCE 7-16 and IS 875 (Part 3) do not provide many guidelines on these non-standard geometries and, consequently, performance-based wind engineering testing is commonly needed (ASCE, 2017; Bureau of Indian Standards, 2015). This is a review of the aerodynamic performance of complex plan-geometry high-rise buildings critically synthesized based on the peer-reviewed literature. It is conducted in a methodical assessment against the effectiveness of the Aerodynamic Shape Optimization (ASO) strategies by local geometric alterations including corner rounding, chamfering and recession against global morphological alterations including twisting and tapering. Additionally, the review examine the current analytical and numerical methods, find the drawbacks of Reynolds-Averaged Navier-Stokes (RANS) models regarding their inability to capture unsteady wake dynamics in comparison to Large Eddy Simulation (LES) and Delayed Detached Eddy Simulation (DDES) methods. The combined results illustrate the extent to which corner rounding and helical twisting lower the drag forces and the susceptibility to vibration caused by vortexes through disrupting the span-wise coherence of the vortices, while highly irregular configurations, like Fish-shaped plans, are very sensitive to the direction of the wind. Moreover, the review concludes with the identification of critical research gaps concerning the wind interference effects in dense urban clusters, and it positions the possible adoption of machine-learning-based surrogate models in the preliminary design phases as an attractive option to solve the problem of wind design codes currently having limitations.

Nowadays, one of the priorities of the European Commission is to reduce the environmental impact of aviation through the advanced design of novel aircraft configurations. This is of utmost importance in order to decrease the environmental footprint of aviation and to reduce fuel consumption and make airlines more profitable. This implies that new methods and tools for aerodynamic shape optimization will have to be developed, allowing aircraft configurations that cannot be obtained with traditional strategies. This paper focuses on the application of enhanced methods in aerodynamic shape design optimization to enable advanced aircraft configurations. In particular, this work aims to demonstrate the feasibility of the proposed strategy to reach optimal configurations that are far away from its baseline geometry. For this purpose, evolutionary algorithms are combined with support vector machines and applied to the optimization of a baseline geometry for different flow conditions. In particular, the selected application is based on the shape optimization problem of the landing gear master cylinder. Results pointed out the feasibility of the mentioned strategy to enable novel configurations within an aerodynamic shape optimization process.