Optimization of Fluid-Structure Interaction Using the Sensitivity Equation Approach

Abstract

A methodology for the optimization of coupled fluid-structure systems that couples flow and structural analysis codes without requiring iteration between the two codes is presented here. This method is valid in the nonlinear transonic and high-alpha regimes. It requires the sensitivity of the flow solution to perturbations in the geometry, in addition to the flow solution for the undeformed configuration. The flow solution for the base configuration and its sensitivity to geometric parameters are generated and transferred to the finite-element structural code. The structural code then solves the direct and sensitivity problems for the coupled fluid-structure system using a modified stiffness matrix. Results for the direct problem axe presented for the static aeroelastic effects on a wing section in inviscid transonic flow. The wing section is mounted through a torsion spring, in which case the geometry variation is due to deformation as well as rotation about the hinge point. The displacements show the expected aeroelastic relief effect due to the flexible loads increment. Both the flow sensitivity and the sensitivity of the coupled fluid-structure system are calculated using the sensitivity equation or direct differentiation approach. The flow sensitivity calculation is implemented by altering an existing flow code, CFL3D from NASA Langley. Implementation of optimization of the coupled system is being performed using the commercial C++ class library, PDESolve. Code snippets are presented to illustrate that an object-oriented library like PDESolve significantly reduces the effort in implementing the direct and sensitivity solutions.