A continuous adjoint method for

This paper describes the formulation of optimization techniques based on control theory for wing section and planform design in viscous compressible flow modeled by the Reynolds Averaged Navier-Stokes equations. Because the two disciplines that are relevant to this problem are aerodynamics and structures, an extension of a single to a multiple objective cost function is considered. A realistic model for the structural weight, which is sensitive to both planform variations and wing loading, is implemented. Results of optimizing a wing-fuselage of a commercial transport aircraft show a successful trade-off between the aerodynamic and structural cost functions, leading to meaningful wing planform designs. Results also indicate that large improvements in lift-to-drag ratio can be achieved without any penalty on the structural weight by stretching the span along with decreasing the sweep angle, thickening the wing-sections, and modifying the airfoil sections. Furthermore, by varying the weighting constants in the cost function, the “Pareto front ” can be captured, broadening the design range of optimal shapes. I.

This paper focuses on aero-structural optimization of wing for long range transport aircraft, using Adjoint based optimization. The paper explores and compares attainable limit such as attainable L/D vs. Mach number, which may be appreciable higher than the historical trend typically used in conceptual design. It also seeks to identify a discernable trend in the planform variables such as sweep, thickness-to-chord ratio, aspect ratio, and chords for optimum wings. Results form wing-fuselage and complete-aircraft-configuration optimizations indicate that by stretching the span together with decreasing sweep and thickening the wing sections the lift-to-drag ratio can be increased without any penalty on the structure weight. I.

The performance of an aerodynamic shape optimization routine is greatly dependent on its geometry control system. This system must accurately parameterize the initial geometry and generate a flexible set of design variables for the optimization cycle. It must also generate new instances of the geometry based on the changes to the design variables dictated by the optimization routine. In response to changes in the geometry, it is also desirable to generate a new surface grid with the same topology as the original grid. This new surface grid can be used to perturb the associated volume grid. This paper presents two geometry control systems, a CAD-free system, and a CATIA V5 CAD-based system. The two systems provide practical tools for aerodynamic optimization. They also provide a basis for comparing CAD-free and CAD-based systems and understanding additional issues that need to be addressed in order to develop reliable optimization systems.

Since the present author first became involved in computational fluid dynamics, around 1970, the landscape has changed dramatically. At that time, panel methods had just come into use, and the world’s fastest super computer, the Control data 6600, had only 131000 words of memory (about 1 megabyte). Prior to the break-through of Murman and Cole [1970], no viable algorithms for computing transonic flow with shock

in the calculation of the complete gradient is e#ectively independent of the number of design variables. In the control theory approach the necessary gradients are obtained via the solution of the adjoint equations of the governing equations of interest. The only cost involved is the calculation of one flow solution and one adjoint solution whose complexity is similar to that of the flow solution. The present work builds on the foundation of control theory for systems governed by partial di#erential equations originally laid out by J.L. Lions and first used in transonic flow by Jameson. In fact, the method has even been successfully used for the aerodynamic design of complete aircraft configurations. Recently the authors have also included wing planform as design variables and have successfully designed a wing of the aircraft configuration which produces a specified lift with minimum drag, while meeting other criteria such as low structure weight, su#cient fuel volume, and st

this paper we outline the adjoint approach to shape optimization, the formulation of design procedure for the Euler equations, the reduced gradient formulations, the mesh deformation procedure we use and some results from using this design procedure on complete aircraft configurations. The details of the numerical discretization of the flow and adjoint systems can be obtained from Jameson et.al

This paper discusses the role that computational fluid dynamics (CFD) plays in the design of aircraft. An overview of the design process is provided, covering some of the typical decisions that a design team addresses within a multi-disciplinary environment. On a very regular basis trade-offs between disciplines have to be made where a set of conflicting requirements exists. Within an aircraft development project, we focus on the aerodynamic design problem and review how this process has been advanced, first with the improving capabilities of traditional computational fluid dynamics analyses, and then with aerodynamic optimizations based on these increasingly accurate methods. 1 Background The past 25 years have seen a revolution in the entire engineering design process as computational simulation has come to play an increasingly dominant role. Most notably, computer aided design (CAD) methods have essentially replaced the drawing board as the basic tool for the definition and control of the configuration. Computer visualization techniques enable the designer to verify that no interferences exist between different parts in the layout.

This paper describes the formulation of optimization techniques based on control theory for aerodynamic shape design in inviscid compressible flow modeled by the Euler equations. The design methodology has been expanded to include wing planform optimization. It extends the previous work on wing planform optimization based on simple wing weight estimation. A more realistic model for the structural weight, which is sensitive to both planform variations and wing loading, is included in the design cost function to provide a meaningful design. A practical method to combine the structural weight into the design cost function is studied. An extension of a single to a multiple objective cost function is also considered. Results of optimizing a wing-fuselage of a commercial transport aircraft show a successful trade-o# between the aerodynamic and structural cost functions, leading to meaningful wing planform designs. The results also support the necessity of including the structural weight in the cost function. Furthermore, by varying the weighting constant in the cost function, an optimal set called "Pareto front" can be captured, broadening the design range of optimal shapes

Introduction The focus of CFD applications has shifted to aerodynamic design. This shift has been mainly motivated by the availability of high performance computing platforms and by the development of new and e#cient analysis and design algorithms. In particular automatic design procedures, which use CFD combined with gradient-based optimization techniques, have had a significant impact on the design process by removing di#culties in the decision making process faced by the aerodynamicist. A fast way of calculating the accurate gradient information is essential since the gradient calculation can be the most time consuming portion of the design algorithm. The computational cost of gradient calculation can be dramatically reduced by the control theory approach since the computational expense incurred in the calculation of the complete gradient is e#ectively independent of the number of design variables. The foundation of control theory for systems governed by partial di#erential equat