基于N-S方程和离散共轭方法的气动设计方法研究

Aerodynamic design method based on N-S equations and discrete adjoint approach

对于基于梯度信息的优化设计方法,很重要的一点是快速准确获得目标函数对设计变量的梯度。本文采用离散共轭方法计算目标函数关于设计变量的梯度,流动控制方程为N-S方程。对于离散共轭方程和流动控制方程均采用LU-SGS方法求解。算例表明,对于亚声速和跨声速两种情况,该方法都能快速准确地获得升力和阻力关于设计变量的梯度。本文采用该方法进行了翼型优化设计,成功地减弱了激波,降低了总阻力。算例证明了本文方法可靠性好、收敛快,特别适合工程实际。

One of the most important things in design optimization that based on gradient is to acquire the gradient quickly and accurately. A discrete adjoint approach is developed in this paper to get the gradient, and the flow governing equations are NS equations. Both the adjoint equations and the flow governing equations are solved by LU-SGS method. Examples show that this method acquire gradient quickly and accurately in both subsonic and transonic case. An airfoil is optimized using this method. Shockwave of the airfoil is weakened and the total drag is reduced. The test results show that the present method is reliable and efficient and is especially applicable in engineering.