A Fast Aeroelasticity Computational Technique for Aircraft Wing Structure Optimization

摘要

In the first stage of aircraft wing design, the variation of several parameters related to the structure surrounded by a flow requires numerical simulations in aeroelasticity which often takes a long computing time. Aeroelasticity can be defined as the study of mutual interactions between aerodynamic, iner-tial and elastic forces on flexible structures. There are several mathematical models governing transonic flows; however, some have limited applications such as the solution of the linearized compressible potential equation, or the solution of the small transonic disturbances (TSD) model. Higher order models such as solving the Euleur or the Navier-Stokes equations represent more accurately the physical phenomenon, but given the number of equations to be solved, they require a too large computing time to be used during a preliminary stage of design. The full potential equation (FP) combined with a boundary layer model, is able to reproduce the phenomena of shocks and gives a pressure field relatively precise with a sizeable computing time. This single equation is a very great simplification of the five equations of Euleur (three-dimensional field) and gives practically identical results for subsonic flows and transonic flows without separation. Over the last decade, considerable effort has been devoted to developing computational methods for modeling unsteady viscous flows. Although such investigations are very useful for gaining more physical accuracy they can become very prohibitive for routine parametric calculations. The major advantage of the simpler model using FP approach over those based on Euler and N-S formulations is the large reduction in computational cost requirements making them suitable for the preliminary design stage. For this reason the numerical method used for fast computational aeroelasticity is based on the resolution of the full potential equation. Our objective is to develop a fast and accurate tool for computing the aeroelastic behavior for a given wing structure. The main technical features of this approach are : 1. Flow solver : Unsteady full potential equation, combined with a boundary layer model, solved using an implicit time-accurate scheme and a finite difference space discretization. Viscous-inviscid interaction equation is performed by coupling a boundary-layer scheme with the inviscid code using algebraic turbulence model ; 2. Structure solver : The structure represented as a wing box model is discretized using a finite element model for linear elasticity. In the first stage of the project, modal analysis is performed. The modal extraction is achieved by subspace iteration. We use the modal superposition method with a Newmark's time integration scheme for aeroelastic response at each fluid time step. In the second stage, the structure is solved at each fluid time step with a finite element code; 3. Fluid-structure data exchange : A module is integra-ted in order to perform the task of load transfer from the fluid to the structure and to exchange the structure motion to the fluid; 4. Aeroelastic sensitivity : Gradientbased (sometimes referred to as first-order) methods will be used.