Discrete adjoint approach for aeroelastic design optimization
Using aeroelastic flutter geometric design sensitivities provided by a recently developed discrete adjoint aeroelastic solver, the shape of a NLR 7301 airfoil section is optimized to increase flutter onset velocity for a benchmark transonic aeroelastic configuration. Two optimization approaches have been tested. In the first approach, the individual coordinates of the airfoil shape profile definition are allowed to move. The discrete adjoint aeroelastic solver provides the gradient of the flutter reduced velocity with respect to changes in the position of each point of the airfoil definition for the cost of a single adjoint solution. This gradient information is supplied to a limited memory BFGS optimization solver, which then determines new airfoil coordinates that maximize flutter reduced velocity. We have found this approach leads to wavy shaped airfoil profiles that exhibit nonphysical flow solutions. For the second approach to optimization, the airfoil surface is mathematically curve fit using a recently developed airfoil parameterization technique referred to as the intuitive class/shape function transformation (iCST) method. The aeroelastic adjoint solver then provides the gradient of the flutter reduced velocity with respect to the parameters ofiCST method, which the limited memory BFGS solver then uses for airfoil shape optimization. We have found this approach to optimization leads to much smoother airfoil shape profiles. A 17% percent increase in flutter onset velocity is demonstrated for one configuration.
