摘要
反命题作为一种可变(未知)边界问题近年来得到了广泛的研究。本文给出了亚声速平面叶栅反命题计算的势函数变域变分有限元解法。变域变分通过把可变边界结合在变分泛函中,使其与求解流场的控制方程结合起来,从而使可变边界求解和流场分析可以完全耦合进行。本文针对亚声速平面叶栅的反命题,根据泛函的驻值必要条件,介绍了变域变分有限元方法的求解过程,最后给出了两个数值算例。这两个算例均采用四节点矩形单元的插值基函数,第一个算例用于检验程序的可靠性,第二个算例设计了一个给定叶面马赫数分布的叶型,并与试验结果进行对照。
Inverse problem, as a kind of free (unknow) boundary problem, attracts extensive research. The Variabledomain variational FEM is used to design 2 D subsonic cascades. The free boundary condition is incorporated into the functionals of variational principles by variable domain variational calculus, which makes it possible to calculate both the flow field and unknown boundary (airfoil shape) simultaneously. Based on the functional stationary condition, the variable domain variational FEM for shape design of cascades was introduced. Two numerical examples were given to validate the present method. The first shows that the method is reliable. Blades with prescribed distributions of Mach number was calculated in the second sample problem and compared with the result of examination.
出处
《力学季刊》
CSCD
北大核心
2004年第4期439-443,共5页
Chinese Quarterly of Mechanics
基金
国家自然科学基金(50136030)
关键词
叶栅
变域变分有限元
反问题
cascades
variable domain variational FEM
inverse problem
