对于给定压力分布的黏性气动反问题,考虑到壁面微小扰动造成的压力变化主要由势流作用引起,因此可以简化用以获得目标函数对设计变量敏感性导数的共轭方程。将黏性流场插值到粗网格中作为彻体力模型方程的解,则其相应的共轭方程将以简单的源项取代原方程中复杂的黏性项。由于在粗网格中求解,网格数减少,同时收敛速度加快,简化的共轭方程计算时间可以减少到黏性方程的十分之一。典型的算例结果表明,对于附着的边界层流动简化方法计算得到的敏感性导数具有较高的精度,能够有效完成反问题设计且减少总的计算耗时。
For the viscous aerodynamic inverse design with specified pressure distribution, in view of the fact that the pressure variation caused by wall perturbation is dominantly owing to its potential effect, an approximate adjoint equation is proposed to calculate the object function gradient with respect to the design variables. A viscous flow field of fine mesh is interpolated into the coarse mesh and the new mesh is treated as the solution of the viscous body force model. In this case, a simple source term replaces a complex viscous term in the original adjoint equations. The time cost by the approximate adjoint equations can be decreased to one tenth of the viscous equations because of the drastically reduced grid points of the coarse mesh and much faster convergence. The results of typical cases indicate that the sensitivity derivative gained by the approximate method has good accuracy and the inverse design can be completed efficiently with reduced total computational time.
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