This paper describes the implementation of various transition models used in conjunction with a single-equation turbulence model for predicting transitional flow over single and multiple element airfoil configurations. The analysis problem is formulated as well as the corresponding adjoint problem of the fully coupled flow-turbulence-transition equations. Test problems are shown for the computation of transitional airfoil cases, and the design optimization of a transitional airfoil using the adjoint-derived sensitivities is also demonstrated.
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