二维机翼非定常气动力学反命题的变分理论

非定常流动的反命题迄今在世界文献中尚属空白。本文首次对它进行探讨，就二维振荡机翼的非定常气动力学反命的适当提法及其数学模型作了较深的研究，利用变域变分工具成功地建立了相应的变分原理及广义变分原理，为非定常机翼设计及有限元解的应用提供完整周密的理论基础。

Formulation of Inverse Problem of 2-D Unsteady Flow Around Oscillating Airfoils by Variational Principles

The overwhelming majority of the existing fluid mechanics literature is dedicated to the direct problem. though the inverse problem is directly oriented to and more useful for aerodynamic design. Only in the last decade,witb the rapid development of computational fluid dynamics, more and more interest of scientists and:engineers has been attached to the inverse problem of steady aerodynamics1,2,11].As far as the auther is aware, up to now, there has never appeared any paper that deals with the inverse problem of unsteady flow.It is the purpose of the present paper to carry out, for the first time,a detailed theoretical investigation on the unsteady inverse problem,special attention is paid to finding proper ways of problem-posing and mathematical formulation. First of all, in contrast to the steady flow case, in the unsteady inverse problem the pressure distribution along the airfoil contour can not be specified over the whole oscillation period in order to keep the airfoil geometry unchanged with time, while allowing the airfoil to move as a rigid body. Second, the unsteady inverse problem accommodates several different types, depending on different ways of specifying pressure distribution. In the present paper our attention is concentrated on one type (designated by lA) of the unsteady inverseproblem: Given is the time-averaged pressure over the airfoil contour,while the corresponding airfoil shape is to be sought. For this IA problem, a family of variational principles with variable domain is established on the basis of the previous papers3, 4] dealing with the direct problem of unsteady flow. Thus, this paper has laid down a new solid theoretical foundation for unsteady airfoil design as well as for finite element applications.