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Abstract. This paper illustrates how surface curvature constraints are incorporated within a two-dimensional optimization method to control geometric oscillations along aerodynamically optimized airfoils. Two treatments were developed; each bounds the surface curvature of an airfoil with upper and lower limits. The first treatment maintains the overall shape of the airfoil while minimizing the local oscillations by applying symmetric curvature bounding. The second treatment bounds an airfoil within a prescribed curvature space. It strongly controls the geometric surface oscillations; however, it does allow an airfoil to be significantly altered from its original shape versus the first method. Both treatments are effective in reducing geometric oscillations along the airfoil surface while maintaining the overall aerodynamic performance.Résumé. Dans cet article, on montre comment les contraintes de la courbure de la surface sont intégrées dans le contexte d'une méthode d'optimisation à deux dimensions pour contrôler les oscillations géométriques le long des surfaces portantes optimisées pour l'aérodynamisme. Deux traitements ont été développés, chacun fixant la courbure du profil d'aile portante dans des limites supérieures et inférieures. Le premier traitement conserve la forme de la surface portante dans son ensemble tout en minimisant les oscillations locales en appliquant une limite de courbure symétrique. Le second traitement fixe les limites de la surface portante à l'intérieur d'un espace de courbure prescrit. Ce dernier contrôle fortement les oscillations géométriques de surface, tout en permettant de transformer de façon significative la surface portante par rapport à sa forme initiale contrairement à la première méthode. Les deux traitements sont efficaces pour réduire les oscillations géométriques le long de la surface portante tout en maintenant la performance aérodynamique dans son ensemble. [Traduit par la Rédaction] 7

Flow transition is important, in both practical and phenomenological terms. However, there is currently no method for identifying the spatial locations associated with transition, such as the start and end of intermittency. The concept of flow stability and experimental correlations have been used, however, flow stability only identifies the location where disturbances begin to grow in the laminar flow and experimental correlations can only give approximations as measuring the start and end of intermittency is diffcult. Therefore, the focus of this work is to construct a method to identify the start and end of intermittency, for a natural boundary layer transition and a separated flow transition. We obtain these locations by deriving a complex-lamellar description of the velocity field that exists between a fully laminar and fully turbulent boundary condition. Mathematically, this complex-lamellar decomposition, which is constructed from the classical Darwin-Lighthill-Hawthorne drift function and the transport of enstrophy, describes the flow that exists between the fully laminar Pohlhausen equations and Prandtl's fully turbulent one seventh power law. We approximate the difference in enstrophy density between the boundary conditions using a power series. The slope of the power series is scaled by using the shape of the universal intermittency distribution within the intermittency region. We solve the complex-lamellar decomposition of the velocity field along with the slope of the difference in enstrophy density function to determine the location of the laminar and turbulent boundary conditions. Then from the difference in enstrophy density function we calculate the start and end of intermittency. We perform this calculation on a natural boundary layer transition over a flat plate for zero pressure gradient flow and for separated shear flow over a separation bubble. We compare these results to existing experimental results and verify the accuracy of our transition model.

This research demonstrates the importance of including multi-disciplinary constraints within a two-dimensional aerodynamic optimization method. These constraints increase the methods flexibility and versatility by providing the aerodynamic designer with the latitude to expand the design envelope. The additional constraints include a global minimum thickness, a maximum point thickness, an area, two curvature functions and a stowability constraint. The global minimum thickness constraint is used to prevent airfoil surface crossovers. The maximum point thickness and area constraint address airfoil structural requirements. The curvature function constraints deal with the airfoils manufacturability. Finally, the stowability constraints combines flap trajectory, including the flap mechanics, together with the final airfoil shape, to ensure high-lift stowability

In this paper, we develop a complex-lamellar description of the incompressible flow that exists as a boundary layer transitions from a fully developed laminar to fully developed turbulent flow. This complex-lamellar description is coupled to the shape of the universal intermittency distribution and experimental correlations to obtain a boundary layer model of transition. This transition model is used to analyze the effects of several different freestream turbulence levels on the reattachment location and the length of the resulting separation bubbles. Furthermore, we show that at the separation bubble reattachment location, the resulting boundary layer flow is both turbulent and fully developed. Results obtained from this transition model are compared with, and verified by several different DNS simulations.