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

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

Robust optimization of 2D airfoils driven by full Navier–Stokes computations

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.

An efficient computational-fluid-dynamics-driven approach to multipoint constrained aerodynamic wing design for business jet aircraft is proposed. This method significantly extends the capabilities of the optimization tool OPTIMAS, previously developed by the authors, for aerodynamic design of three-dimensional isolated wings. In the framework of the method, the total drag of an optimized aircraft configuration is minimized at fixed lift values subject to numerous geometrical and aerodynamical constraints. The optimum search is driven by genetic algorithms and is based on full Navier-Stokes computations supported by massive multilevel parallelization. The applications include a series of single- and multipoint aerodynamic design optimizations for a generic business jet. For the considered class of shape optimizations, significant drag reduction in on- and off-design conditions has been achieved.

We present an approach for shape optimization of large-scale aerodynamic problems, combining free-form deformation and POD based reduced-order modeling. An extension of the classical Free-Form Deformation techniques is derived in order to handle efficiently constraints regarding fixed and deformable portions of the geometry and to impose the smoothness at the interface between the two different regions. The second aspect concerns the development of a hybrid model, combining a POD-based reduced order model and a industrial CFD solver using a domain-decomposition approach. A method on how determining automatically a suitable domain decomposition is discussed. The effectiveness and drawback of the above techniques are highlighted on a large-scale aerodynamic shape optimization and control problem, i.e. the mainsail thrust optimization of a sailing boat.

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

Aerodynamic Shape Optimization and Parallel Computing Applied to Industrial Problems

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.

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.

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.

The study of reactive silencers by shape and parametric optimization techniques

An optimal shape of two-dimensional asymmetric diffuser with maximum pressure recovery at the exit is numerically obtained using a mathematical theory based on the variational calculus and gradient algorithm. The initial diffuser is taken to be a two-dimensional asymmetric diffuser for which much experimental and numerical data are available. The Reynolds number based on the bulk mean velocity and the channel height at the diffuser entrance is 1.8 × × 10 4 .F rom this initial shape, optimal diffuser shapes are designed for six different geometric constraints, such as the streamwise length and height of the diffuser. The optimality condition for maximum pressure recovery is obtained to be zero skin friction along the diffuser wall. The turbulent flow inside the diffuser is predicted using the k‐� ‐v2‐f model, and optimal shapes are obtained through iterative procedures to satisfy the optimality condition. With the shape design, flow separation that appeared in the initial diffuser is completely removed or significantly reduced. For one of the optimal diffuser shapes obtained, large-eddy simulation is carried out to validate the result of the shape design. The wall shear stress, wall pressure, mean velocity, and turbulence quantities obtained from large-eddy simulation are in good agreement with those from the simulation using the turbulence model.

Efficient global optimization of aerodynamic shapes with the high-fidelity method is of great importance in the design process of modern aircrafts. In this study, modifications are made to the particle swarm optimization (PSO) algorithm and the radial basis function (RBF) model for further improvements of efficiency and accuracy of optimization. Specifically, a PSO algorithm with randomly distributed cognitive and social parameters, exponential decrease of maximum velocity and inertia weight, and periodic mutation of particle position is proposed. Furthermore, a nonuniform shape parameters strategy is introduced for the RBF surrogate model. Validations on test functions show that the new PSO has remarkable speed of convergence, and the new RBF model has superior approximation accuracy. The PSO algorithm and RBF model are then combined to construct the computational fluid dynamics (CFD)–based optimization framework. Finally, optimizations of transonic airfoil and supersonic launch vehicle are perfo...

In aerodynamic shape optimization, the convergence and computational cost are greatly affected by the representation capacity and compactness of the design space. Previous research has demonstrated that using a deep generative model to parameterize two-dimensional (2D) airfoils achieves high representation capacity/compactness, which significantly benefits shape optimization. In this paper, we propose a deep generative model, Free-Form Deformation Generative Adversarial Networks (FFD-GAN), that provides an efficient parameterization for three-dimensional (3D) aerodynamic/hydrodynamic shapes like aircraft wings, turbine blades, car bodies, and hulls. The learned model maps a compact set of design variables to 3D surface points representing the shape. We ensure the surface smoothness and continuity of generated geometries by incorporating an FFD layer into the generative model. We demonstrate FFD-GAN's performance using a wing shape design example. The results show that FFD-GAN can generate realistic designs and form a reasonable parameterization. We further demonstrate FFD-GAN's high representation compactness and capacity by testing its design space coverage, the feasibility ratio of the design space, and its performance in design optimization. We demonstrate that over 94% feasibility ratio is achieved among wings randomly generated by the FFD-GAN, while FFD and B-spline only achieve less than 31%. We also show that the FFD-GAN leads to an order of magnitude faster convergence in a wing shape optimization problem, compared to the FFD and the B-spline parameterizations.

This paper presents design data defining optimal freeform notch shapes for use in tensile loading conditions for a range of geometries, notably the notch aspect ratio and plate widths. Here, an iterative two-dimensional finite element gradientless shape optimization procedure was used to obtain the optimal shapes, which offer the lowest possible stress concentration, subject to the geometric constraints. Precise non-dimensional coordinates are given, for a range of notch aspect ratios and plate widths, and are presented in a tabular form that allows them to be easily used by designers. All cases have been solved with a minimum radius of curvature constraint, which results in a ‘robust’ optimal shape that has no sharp corners. The optimal shapes were found to provide up to a 26 per cent reduction in local peak stress over circular shapes of the same aspect ratio. Optimal geometries are also given for limiting notches that provide a net section stress equal to unity, at a finite notch aspect ratio. The results obtained are applicable to both the initial design of notched components and the shape reworking of existing components to remove damage.