Automatic differentiation based nonlinear reduced-order model with geometric gradient computation capability
Presented is an automatic differentiation based nonlinear reduced-order modeling technique which includes geometric variation computation capability. The method is based on a Taylor series expansion of a nonlinear frequency-domain harmonic balance based computational fluid dynamic solver residual. In our original development of the methodology, the harmonic balance flow solver residual is Taylor series expanded in terms of the harmonic balance dependent flow solution variables and the harmonic balance flow solver input variables, e.g., Mach number, Reynolds number, angle-of-attack, unsteady structural motion modal coordinates, unsteady frequency, etc. We have now expanded the methodology to include the variables which governing the geometric design of given configuration in the Taylor series expansion. The Taylor series expansion consists of first, second, and possibly higher-order gradients of harmonic balance solution residual with respect to the harmonic balance flow solution, the harmonic balance flow solver input variables, and now also the geometric design variables, as well as linear, quadratic, and possibly higher powers of the changes of the harmonic balance flow solution, changes of the harmonic balance flow solver inputs, and changes of the design variables. Once constructed, the nonlinear reduced-order model allows one to rapidly compute alternate harmonic balance flow solutions based on alternate values for the harmonic balance flow solver inputs, as well as alternate values for the geometric design variables. Adding the capability to model geometric design changes will allow the nonlinear reduced-order model to be used for adjoint based design optimization at a significant cost reduction as compared to when computing adjoint solutions for the full harmonic balance flow solver. In this paper, we present the theory for the methodology along with aerodynamic reduced-order modeling results for a cylinder in cross-flow configuration as well as aeroelastic reduced-order modeling results for a benchmark NLR 7301 airfoil aeroelastic configuration.
