SUMMARYA numerical continuation method for the compressible Reynolds-Averaged Navier-Stokes equation with the Spalart-Allmaras turbulence model is presented and applied to the flow around a 2D airfoil. Using continuation methods it is possible to study the steady flow states of a system as a parameter such as angle of attack is varied. This approach allows unstable solutions to be calculated, which are important for understanding the nonlinear dynamics of the system. Furthermore, this method can be used to find any multivalued solutions that exist at a single parameter value. The eigenvalues of the system are calculated using the Cayley transform to precondition the eigenvalue solver ARPACK. The eigenvalues are important as they show the stability of the solutions as well as accurately detect parameter values at which bifurcations take place.

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An initial design of a morphing wingtip for a regional jet aircraft is developed and evaluated. The adaptive wingtip concept is based upon a chiral-type internal structure, enabling controlled cant angle orientation, camber, and twist throughout the flight envelope. A baseline turbofan aircraft configuration model is used as the benchmark to assess the device. Computational fluid dynamics based aerodynamics are used to evaluate the required design configurations for the device at different points across the flight envelope in terms of lift/drag and bending moment distribution along the span, complemented by panel-method-based gust load computations. Detailed studies are performed to show how the chiral structure can facilitate the required shape changes in twist, camber, and cant. Actuator requirements and limitations are assessed, along with an evaluation of the aerodynamic gains from the inclusion of the device versus power and weight penalties. For a typical mission, it was found that savings of around 2% in fuel weight are possible using the morphing wingtip device. A similar reduction in weight due to passive gust load alleviation is also possible with a slight change of configuration.