Aerodynamic shape optimization using a real-number-encoded genetic algorithm

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

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.

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 direct method for aerodynamic shape optimization based on the use of Bezier spline approximation is proposed. The method is tested as applied to the optimization of the supersonic part of an axisymmetric de Laval nozzle. The optimization results are compared with the exact solution obtained by the control contour method (variational nozzle) and with nozzles constructed using another direct method, namely, local linearization. It is shown that both direct optimization methods can be used on rather coarse grids without degrading the accuracy of the solution. The optimization procedure involves the isoperimetric condition that the surface area of the nozzle is given and fixed, which prevents the use of the control contour method. Optimization with allowance for viscosity is performed using the method. For fairly short maximum possible nozzle lengths in the range of Reynolds numbers under consideration, it is shown that allowance for viscosity does not improve the nozzle shape produced by optimization based on the Euler equations. The role of viscosity is reduced to the determination of an optimal length.

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.

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.

Research on POD-based CST airfoil parameterization method for aerodynamic shape optimization

Ar obust and efficient approach to the multiobjective constrained design, previously developed by the authors, is extended to optimization of three-dimensional aerodynamic wings. The objective is to minimize the total drag at fixed lift subject to various geometrical and aerodynamical constraints. The approach employs genetic algorithms (GAs) as an optimization tool in combination with a reduced-order-models (ROM) method, based on linked local databases obtained by full Navier‐Stokes computations. The work focuses on the following issues: geometrical representation of three-dimensional shapes, handling of sensitive nonlinear constraints such as pitching moment, and the influence of flight conditions on the results of optimization. The method, implemented in the computer code OPTIMAS (Optimization of Aerodynamic Shapes), was applied to the problem of multipoint transonic threedimensional wing optimization with nonlinear constraints. The results include a variety of optimization cases for two wings: a classical test case of ONERA M6 wing and a generic cranked transport-type wing. For the investigated class of problems, significant aerodynamic gains have been obtained. Nomenclature C D = total drag coefficient CL = total lift coefficient C M = total pitching-moment coefficient C p = pressure coefficient M = freestream Mach number N D = dimension of the search space Nws = number of sectional airfoils Q = objective function R/c = relative radius of the airfoil leading edge Re = freestream Reynolds number t/c = relative thickness of airfoil α = angle of attack θ = trailing-edge angle of airfoil

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.

Chapter 4 - Massive Parallelization as Prinicipal Technology for Constrained Optimization of Aerodynamic Shapes

A computational approach is presented for evaluating shape sensitivities using an innovative embedded boundary method for computational fluid dynamics that mitigates the well-known difficulties associated with meshing, mesh updating and/or re-meshing. It is based on the analytical derivation of relevant semi-discrete gradients of the underlying comprehensive flow solver and associated computational geometry support. The proposed approach is integrated in a gradient-based optimization procedure and exploited to perform aerodynamic shape optimization of complex rigid and aeroelastic configurations. It demonstrates the potential of embedded boundary methods for the multi-disciplinary shape optimization of complex aerodynamic systems, and highlights their practical advantages in terms of flexibility, robustness, and performance.

Optimization and design of an aircraft’s morphing wing-tip demonstrator for drag reduction at low speed, Part I – Aerodynamic optimization using genetic, bee colony and gradient descent algorithms

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.

Aerodynamic shape optimization of aircraft configurations often ignores stability considerations. To address this, a method for the computation of static, dynamic, and transient aircraft stability derivatives and their sensitivities for use in gradient-based optimization is introduced and evaluated. Computational fluid dynamics in the form of a three-dimensional structured-grid multiblock flow solver with both Euler and Reynolds-averaged Navier–Stokes equations is used. To compute the stability derivatives, a time-spectral formulation is used to compute an oscillating solution for the configuration of interest. From this oscillating solution, a series of linear regressions is performed to calculate the various stability derivatives. Because the solution is time dependent, it contains the information required to compute the transient, or “dot,” derivatives for the configuration. An adjoint method is used to compute the gradients of the stability derivatives of interest, enabling gradient-based stability-constrained aerodynamic shape optimization with respect to a large number of design variables. The computed stability derivatives are verified for an airfoil and validated for a generic unmanned combat aerial vehicle. The stability-constrained optimization of a wing demonstrates the viability and usefulness of the method for aircraft design optimization.

☞Introduction and Motivation➣While aerodynamic prediction methods based on CFD are now well established,accurate, and robust, the ultimate need in the design process is to find theoptimum shape which maximizes the aerodynamic performance.➣During the last decade aerodynamic shape optimization methods based oncontrol theory have been perfected for rigid wings with fixed planforms.➣Example: Redesign of the wing of a Boeing 747 with fuselage.