摘要
将基于控制理论的形状优化设计方法应用于粘性可压流动条件下的透平叶栅三维气动反设计,详细推导了三维N-S方程伴随系统的偏微分方程组及其各类边界条件。讨论了伴随系统的解的适定性条件,并由此给出应用N-S方程进行气动优化的目标函数的选取限制．研究了伴随方程的数值求解技术,给出敏感性导数的最终计算式,结合拟牛顿算法发展了三维透平叶栅粘性反问题的气动设计方法。
The optimal shape design based on control theory is applied to 3D turbine blades aerodynamic design for compressible viscous flow. The adjoint partial differential equation （P.D.E.） of the N-S equation and its all manner of boundary conditions are deduced in detail. Due to the characteristic analysis of the adjoint P.D.E., the restrictions of cost function are discussed in the case of given surface temperature and adiabatic conditions on blade walls. Numerical techniques are discussed here to solve the adjoint linear P.D.E., and the final expression of sensitivity gradient is formulated via adjoint variables. In conjunction with quasi-Newton algorithm, the aerodynamic design method for viscous inverse problem of 3D turbine blades is developed.
出处
《工程热物理学报》
EI
CAS
CSCD
北大核心
2007年第4期580-582,共3页
Journal of Engineering Thermophysics
关键词
反问题
控制理论
敏感性导数
N-S方程
伴随方程
inverse problem
control theory
sensitivity gradient
N-S equation
adjoint equation
