可压缩粘性流中力和力矩的分配律和广义Kutta-Joukowski定理

本文引进了动力学涡量概念,推导出可压缩粘性流中的力和力矩的一般表达式。作用在任意运动物体(系)上的力和力矩可以分别表示成流场中动力学涡量的一阶矩和二阶矩随时间的变化率。 利用 Navier-Stokes 方程求出动力学涡量的变化率,进一步把力和力矩表示成一些显式积分。它们分别对应于产生空气动力的一些特定的物理过程,称之为力和力矩的分配律。同时,流场中任何运动的动力学涡量均产生一个空气动力贡献量。相应的计算公式即为广义Kutta-Joukowski 定理。

THE DISTRIBUTION LAW OF AERODYNAMIC FORCE AND MOMENT AND THE GENERALIZED KUTTA-JOUKOWSKI THEOREM

A concept of 'kinetic vorticity' has been introduced and the general formulas of aerodynamic force and moment are developed-through a rigorous analysis of the compressible viscous flow equations. The force and moment exerted on the solid body are expressed as the rate of change of the first-and second-order kinetic vorticity moments, respectively. A distribution law of aerodynamic force and moment is further developed from the genera) formulas cooperating with the Navier-Stokes equation. Each of the explicit integrations in the expression of the distribution law corresponds to one of the special physical processes. A generalized Kutta-Joukowski theorem is developed. It can be used to calculate the contribution to aerodynamic force and moment from any moving kinetic vorticity in the flow field.