Aerodinamics

Chapter 1 Introduction
1.1 Background
The aircraft industry, like others, is increasingly exposed to considerable commercial pressures: Boeing Company and Airbus Industrie are struggling for supremacy on the large-size civil airliner (seating more than 100 passengers) market, while many companies, such as Bombardier, Embraer, Dornier, Dasa, are fighting for a larger share of the expandingregional jet aircraft market. Since the success of such commercial products depends on cost and timeliness as well as quality, the design process is being reengineered to save cost and time scales. With advances in Computational Fluid Dynamics (CFD) and computer hardware, CFD has become an integral part of the aircraft design process. CFD has contributed to cut aerodynamic design cost and time scalesby reducing the number of required wind tunnel tests. However, it is just an instrument for estimating aerodynamic performance of a given aircraft configuration. On the whole, the basis of the design process is trial and error, and the success of the final design depends on the knowledge and intuition of the designer. CFD technology will be able to display its ability to the full when it is coupledwith numerical optimization methods by displacing any human interactions in the design procedure. Yet, despite the fact that numerical optimization methods have been successfully used for a countless number of design problems, an application of numerical optimization to aerodynamic design still remains as a formidable challenge because of the following difficulties: 1) Objective functionlandscape of an aerodynamic optimization is often multimodal and nonlinear: there are many local optima, plateaus, or ridges even in a simplified problem [1]. This is because the flow field is governed by a system of nonlinear partial differential equations expressing the conservation of mass, momentum, and energy. 2) Function evaluations using a CFD code, especially a three-dimensional Euler orNavier-Stokes code, are very expensive. An aerodynamic evaluation of a simple wing with a Navier-Stokes solver, for instance, can take more than an hour of CPU time even on a vector computer. Aerodynamic design problems with these properties require a numerical optimization tool to be very robust and efficient as well. The application of numerical optimization methods coupled with CFD to transonicaerodynamic shape designs was pioneered by Hicks et al., where airfoil shapes were designed using a gradient-based method coupled with a potential flow solver [2]. Since then, the gradient-based methods have been widely used for wing design [3], scramjet nozzle design [4], supersonic wing-body design [5], and more complex aircraft configurations [6,7]. These methods use the gradient of an objectivefunction with respect to changes in the design variables to calculate a search direction using the finite difference methods [8] or adjoint formulations [9]. These methods are efficient in searching optimums. Not only that, the optimum obtained from these methods will be a global one, if the objective and constraints are differentiable and convex (Kuhn-Tucker condition). Distribution of an objectivefunction of an aerodynamic design problem, however, is usually multimodal, and thus, one could only hope for a local optimum neighboring the initial design point by using the gradient-based method. Therefore, to find a global optimum, one must start the optimization process repeatedly from a number of initial points and check for consistency of the optima obtained. In this sense, the gradientbasedmethods are neither efficient nor robust for design automation. Evolutionary Algorithms (EAs) are emergent optimization algorithms mimicking mechanism of the natural evolution, where a biological population evolves over generations to adapt to an environment by selection, crossover and mutation. When EAs are applied to optimization problems, fitness, individual and genes usually correspond to an...