Discrete Adjoint Approach for Nonlinear Unsteady Aeroelastic Design Optimization
Abstract
Presented is a discrete adjoint approach for computing nonlinear unsteady aeroelastic geometric design sensitivities, which can subsequently be used for nonlinear unsteady aeroelastic geometric design optimization. The methodology is applicable to compressible Reynolds-averaged Navier–Stokes computational-fluid-dynamics solvers and is based on a harmonic balance nonlinear frequency-domain technique for modeling nonlinear aerodynamics in the frequency domain. Automatic differentiation is used to derive the computer code representing the adjoint gradient of the harmonic balance computational-fluid-dynamics solver. Discrete adjoint method airfoil geometric design nonlinear unsteady aerodynamic sensitivities are first computed for a benchmark NLR 7301 airfoil transonic aeroelastic configuration, and results are compared with finite difference computations to demonstrate the accuracy of the methodology. The airfoil surface is mathematically curve-fit using an airfoil parameterization technique, and the discrete adjoint methodology provides the gradient of the flutter onset or limit-cycle oscillation reduced velocity with respect to changes in each of the parameters of the airfoil curve-fit methodology for the cost of a single adjoint solution. This gradient information is supplied to a limited memory Broyden–Fletcher–Goldfarb–Shanno (BFGS) optimization solver, which then determines values for the curve-fit parameters that maximize flutter onset or limit-cycle oscillation reduced velocity. The discrete adjoint nonlinear unsteady aeroelastic geometric design sensitivity computation methodology is then used to redesign the shape of the benchmark NLR 7301 airfoil aeroelastic configuration to optimize the aeroelastic flutter onset reduced velocity or the reduced velocity for a specified limit-cycle oscillation response amplitude.
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