Objective Function and Constraints for Robust Transonic Aerofoil Optimization

Construction of the aerodynamic optimization problem is considered within the context of robustness. The most common aerodynamic optimization problem considered is a lift-constrained drag minimization problem (also subject to geometric constraints), however, point-design at transonic flow conditions can produce shock-free solutions and therefore the result is highly localised, where the gains obtained at the design point are outweighed by the losses at off-design conditions. As such, a range optimization problem subject to a constraint on fixed non-dimensional lift with a varying design point is considered to mitigate this issue. It is shown, first from an analytical treatment of the problem, and second from inviscid optimizations, that more robust solutions are obtainable when considering range optimization against drag minimization. Furthermore, to effectively capture the trade-offs that exist in three-dimensional aircraft design between range, lift, drag and speed, it is shown that an induced drag factor is required and this is suffcient to produce optimal solutions exhibiting shocks.