Three model problems associated with aerodynamic drag minimizations are studied. These test cases have been proposed by the aerodynamic design optimization discussion group, and they include an inviscid NACA0012 nonlifting airfoil, a viscous RAE2822 lifting airfoil, and a viscous lifting wing based on the NASA Common Research Model. Various optimization methods are used, including MDOPT, TRANAIR, SYN83, and SYN107. The resulting designed and associated baseline geometries are cross analyzed by several computational fluid dynamics codes, including OVERFLOW, TRANAIR, GGNS, and FLO82. Pathological issues are unveiled in both of the simple airfoil model problems. Designed geometries for the inviscid symmetric test case exhibit strong tendencies to permit nonsymmetric flow solutions. Designed airfoils for the viscous lifting case also support nonunique solutions and hysteresis loops at or near the design point in Reynolds-averaged Navier-Stokes and integral boundary-layer method simulations. These results provide further evidence that single-point aerodynamic optimization is often ill posed. In extreme cases, it can yield designs with very undesirable aerodynamic characteristics, at least as analyzed by Reynolds-averaged Navier-Stokes and integral boundary-layer methods occurring at offdesign, and even ondesign, conditions. These examples are used to further document the multiple-solution and pseudosolution phenomena for steady-state Reynolds-averaged Navier-Stokes. This provides evidence that, even in practical engineering settings, numerical methods to assess stability and uniqueness of steady-state solutions and/or predict the bifurcations of these solutions have value. The single-point wing design problem is likewise ill posed in the spanwise direction. A multipoint design with a potentially large number of points or the inclusion of inequality constraints can regularize the problem.wing reference chord, which is approximately equal to the mean aerodynamic chord M = Mach number; V∕a P 0 = total pressure q = dynamic pressure; 1 2 ρV 2 Re = Reynolds number; ρ ∞ V ∞ C ref ∕μ ∞ S ref = reference area t = thickness of an airfoil α = angle of attack Δ = difference in quantity (new-baseline) η = fraction of wing semispan κ = curvature ρ = radius of curvature τ = trailing-edge-included angle ∞ = freestream conditions

A Multidisciplinary Design Optimization (MDOPT) framework has been developed for air vehicle design and analysis. The developed MDOPT system contains a collection of technology modules for performing optimization studies by means of a Graphical User Interface (GUI), and combining robust numerical optimization schemes with higher order computational analysis. A variety of multidisciplinary objective and constraint functions are available, including aerodynamic, weight, mission performance, and stability and control characteristics. This paper is intended to provide an overview of the MDOPT development and test case results for a generic fighter configuration, funded under an Air Force Contract, F33615-98-2-3014, with Boeing cost match funds. The period of development was established with contract activity beginning in September 1998 and ending April 2002. Continued MDOPT development and design applications are being pursued within Boeing using internal funding. I.

The fourth model problem from the AIAA Aerodynamic Design Optimization Discussion Group is studied, referred to below as the ADODG CRM wing test case. Two optimization software packages are utilized, TRANAIR design and MDOPT (using both Design of Experiments methods as well as gradient based methods) with OVERFLOW. The resulting designed and associated baseline geometries are cross-analyzed using OVERFLOW and TRANAIR. Previous results using TRANAIR design were run using standard engineering practices and resulted in somewhat non-optimal wings. New results generated using more cycles of design have significantly lower drag and are closer to optimal. In addition, we examine using gradients from an adjoint method in OVERFLOW with the MDOPT tool. Nomenclature a = Local speed of sound b = Wing Span CF D = Computational Fluid Dynamics C D = Drag Coefficient = Drag q∞S ref C L = Lift Coefficient = Lif t q∞S ref C M = Pitching-Moment Coefficient C P = Pressure Coefficient = P −P∞ q∞ C ref = Wing Reference Chord MAC C f = Local Coefficient of Skin Friction count = Drag Coefficient Unit = 0.0001 DP W = Drag Prediction Workshop IBL = Integral Boundary Layer Method M = Mach Number = V a P 0 = Total Pressure q = Dynamic Pressure = 1 2 ρV 2 RAN S = Reynolds-Averaged Navier-Stokes Re = Reynolds number = ρ∞ V∞ C ref µ∞ S ref = Reference Area α = Angle-of-Attack ∆ = Difference in Quantity (New -Baseline) η = Fraction of Wing Semi-Span ∞ = Signifies Freestream Conditions

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