Transonic Wing Aeroelastic Design Optimization

The unsteady aerodynamic models based on linear theory only need small amounts of calculations.Because of this,they have been widely applied to aeroelastic analysis and aeroelastic design optimization in subsonic and supersonic regime.But the linear theory can not consider the nonlinear effect in transonic flow.The aeroelastic analysis method directly based on CFD can effectively solve the transonic nonlinear aeroelastic problem,but it can not be applied to aeroelastic design optimization for its typically large computational cost,only can be used as a validation tool for aeroelastic check.The unsteady aerodynamic reduced-order modeling methods based on CFD offer significant improvements to the efficiency of transonic aeroelastic analysis.But the existing unsteady aerodynamic reduced-order modeling methods are based on the physical mode shapes and the unsteady aerodynamic reduced-order model can only be applied to the physical mode shapes used to construct the reduced-order model.When the physical mode shapes change with the structure,the new reduced-order model should be constructed to be applied to the new structure.In the process of reduced-order modeling,one run of the CFD solver is required.The large computational cost associated with repeated runs of the CFD solver impedes the application of existing reduced-order modeling methods to aeroelastic design optimization.A new unsteady aerodynamic reduced-order modeling method which is not based on the physical mode shapes is demonstrated.It can produce the aerodynamic responses corresponding to the mode excitations for a wing with arbitrary structure.Using the mode excitations and the corresponding aerodynamic responses to construct the unsteady aerodynamic reduced-order model based on the mode shapes for aeroelastic analysis,the aeroelastic characteristics of the wing can be predicted quickly and accurately.The computation method of the aerodynamic responses corresponding to the mode excitations can replace the CFD solver used in the process of existing reduced-order modeling based on the physical mode shapes and the computational cost is only a few seconds.Applying the new aeroelastic analysis method to aeroelastic design optimization,the computational efficiency can be improved more than 1000 times compared to that of the aeroelastic analysis method directly based on CFD and more than 40 times compared to that of the existing unsteady aerodynamic reduced-order modeling methods.The new aeroelastic analysis method suitable for arbitrary mode shapes is applied to the transonic aeroelastic design optimization.In optimization,active set method and differential evolution method are respectively adopted.The structural weight can be reduced 10% to 40% by active set method.Active set method is a kind of local optimization algorithm and differential evolution method is a kind of global optimization algorithm.The structure designed by the differential evolution method is 15.78% lighter than that designed by the active set method.