Aerodynamic Shape Optimization for Natural Laminar Flow Using a Discrete-Adjoint Approach

A framework for the design of natural-laminar-flow airfoils is developed based on multipoint aerodynamic shape optimization capable of efficiently incorporating and exploiting laminar–turbulent transition. A two-dimensional Reynolds–averaged Navier–Stokes flow solver making use of the Spalart–Allmaras turbulence model is extended to incorporate an iterative laminar–turbulent transition prediction methodology. The natural transition locations due to Tollmien–Schlichting instabilities are predicted using a simplified eN method or the compressible form of the Arnal–Habiballah–Delcourt criterion. The Reynolds–averaged Navier–Stokes solver is subsequently used in a gradient-based sequential quadratic programming shape optimization framework. The transition criteria are tightly coupled into the objective and gradient evaluations. The gradients are obtained using an augmented discrete-adjoint formulation for nonlocal transition criteria. Robust design over a range of cruise flight conditions is demonstrated thro...

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