基于非定常曲面涡格法的气动灵敏度和线性化分析

Linearization and Analytical Sensitivity of Unsteady Vortex-Lattice Aerodynamics

非定常曲面涡格法可以准确考虑曲面气动构型和非定常尾涡对气动载荷的影响,是分析大柔性机翼气动弹性动稳定性的重要手段。基于小扰动假定对气动载荷的状态空间方程线性化处理,基于链式法则对气动载荷的解析灵敏度推导,是构造线性化气动弹性方程的基础,并可用于提高动稳定性分析效率。此外,线性化的状态空间方程和解析灵敏度还可应用于气动弹性控制及优化设计。通过数值仿真发现,气动载荷对涡格节点在竖直方向的位移分量最为敏感。与有限差分法相比,使用解析灵敏度可以保障计算精度并大幅提高计算效率。

The unsteady vortex-lattice method(UVLM)provides a high-efficient,medium-fidelity way to capture large deformations and free wake effects of flexible wings.It has been favored in research on the stability analysis of flexible wings.It is possible to construct linearized aeroelastic equations and improve the efficiency of dynamic stability analysis,by applying linearized governing equations based on the assumption of small disturbances and analytical aerodynamic sensitivities based on the chain rule.The linearized governing equations and analytical sensitivities of UVLM can also be applied to aeroelastic control and optimization design.Numerical simulations show that aerodynamic loads are more sensitive to the normal component of node displacement.Analytical sensitivities are validated to be accurate and more efficient than finite difference methods.