This paper describes the work performed by ONERA and Airbus to solve several aerodynamic optimization problems proposed in 2013 by the AIAA Optimization Discussion Group (ADODG). Three of the four test cases defined by this group have been addressed, respectively a 2D invicid, non-lifting, transonic airfoil optimization problem, a 2D RANS transonic airfoil optimization problem and a 3D RANS transonic wing optimization problem. All three problems have been investigated using local, gradient-based, optimization techniques and the elsA[1][2] CFD software and its adjoint capability. Through these three optimization exercises, several generic issues introduced by aerodynamic gradient-based optimization have been investigated. Among the investigated aspects are the impact of the geometry parameterization (nature and dimension), of the accuracy of the gradient calculation method, optimization algorithm and presence of constraints in the optimization problem. NomenclatureC p = pressure coefficient CD = total drag coefficient CDp = pressure drag coefficient CDf = friction drag coefficient CDw = wave drag coefficient CDvp = viscous pressure drag coefficient CL = lift coefficient CM = pitching moment coefficient c ref = chord reference d.c. = drag counts (0.0001) Ma = Mach number Re = Reynolds number AoA = Angle of attack f = objective function g = inequality constraint 1

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Cooperation and competition are natural laws that regulate the interactions between agents in numerous physical, or social phenomena. By analogy, we transpose these laws to devise efficient multi-objective algorithms applied to shape optimization problems involving two or more disciplines. Two efficient strategies are presented in this paper: a multiple gradient descent algorithm (MGDA) and a Nash game strategy based on an original split of territories between disciplines. MGDA is a multi-objective extension of the steepest descent method. The use of a gradient-based algorithm that exploits the cooperation principle aims at reducing the number of iterations required for classical multi-objective evolutionary algorithms to converge to a Pareto optimal design. On the other hand side, the Nash game strategy is well adapted to typical aeronautical optimization problems, when, after having optimized a preponderant or fragile discipline (e.g. aerodynamics), by the minimization of a primary objective-function, one then wishes to reduce a secondary objective-function, representative of another discipline, in a process that avoids degrading excessively the original optimum. Presently, the combination of the two approaches is exploited, in a method that explores the entire Pareto front. Both algorithms are first analyzed on analytical test cases to demonstrate their main features and then applied to the optimum-shape design of a low-boom/low-drag supersonic business jet design problem. Indeed, sonic boom is one of the main limiting factors to the development of civil supersonic transportation. As the driving design for low-boom is not compliant with the low-drag one, our goal is to provide a trade-off between aerodynamics and acoustics. Thus Nash games are adopted to define a low-boom configuration close to aerodynamic optimality w.r.t. wave drag.

A conceptual study is here presented and discussed on the possibility to transport 200 passengers over a distance of about 7000km in a nominal point-to-point mission through the Atlantic (either London-New York or London-Rio) at a cruise Mach number of 6 and an altitude about 30km. The aim of the study is not to design a specific airplane but to explore today's state of the art technology limits to realize such kind of concept, i.e. to identify if such a mission could succeed today. Because of the challenge the mission poses, its is being optimised with the major disciplines involved by means of MultiDisciplinary Optimisation (MDO) tools as a way to realize an optimum integrated airframe/propulsion aircraft. The environmental impact is being analysed in terms of the resulting sonic boom. No experimental data but CFD results by means of independent assessments has been generated. The study indicates that today the available technology provides with sufficient maturity to accomplish with the mission in areas like aerodynamic and thermal resistance materials but in others like sonic boom mitigation it is required a deeper insight in the physics. Finally while the present investigation clear identify that complex designs involving large amount of variables from different disciplines could be only possible via MDO/MDA strategies, today such processes still suffer on lack of robustness of the involved tools.

The shaped sonic boom theory is a valuable, efficient, computationally economical and robust tool in preliminary design of low-boom aircraft configurations. Instead of introducing a new F-function parameterization, as it has been investigated already in the past, the paper adopts a more general formulation proposed in the literature and focuses on reducing the limitations of the inverse method in the design process. Three main contributions are proposed: 1) a revisited procedure based on optimization to solve the coefficients of the F-function that enables to switch between different parameterizations; 2) a definition of the geometry corresponding to the equivalent area distribution combined with a fuselage tailoring process based on direct shape optimization; 3) a strategy to introduce a generic acoustic metrics in the definition of an optimum F-function. The proposed strategy enables the designer to evaluate the geometry of a low-boom configuration that corresponds to a desired F-function in a complete inverse design approach. In this way, the usual limits of the inverse method are significantly alleviated by the present method.