时变系统流场动量定理的积分形式及其在流体动力系数分析中的应用  

The Integral Form Fluid Momentum Theorem on Tim e-Varying Systems and Its Application to Aerodynamic Force Coefficient Analysis

作　　者：林献武[1] 兰维瑶[1] 李智斌[2] 李赫[1] 符松 

机构地区：[1]厦门大学航空航天学院,福建厦门361005 [2]北京控制工程研究所,北京100190 [3]应用数学和力学

出　　处：《应用数学和力学》2016年第6期551-566,共16页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11072028;61273199);福建省自然科学基金(2016J01030);中央高校基本科研业务费专项资金(20720150177)~~

摘　　要：为解决飞艇的非定常流体动力系数的计算问题,利用准平衡假设在涡量流体动力学理论的基础上构建了一种流体动力系数计算方法.首先提出了时变系统的概念及其与流场空间区域的对应关系,在此基础上建立了时变系统的输运方程和流场动量定理积分形式为后面的讨论做准备.其次,将动量定理应用于一个由无穷远固定边界和物面所包含的流体系统,将流体动力表征为流场扰动动量总和变化率的函数.进而提出准平衡假设的概念,将有粘流中流场扰动速度、第一涡量矩和扰动动量表示为运动体速度和角速度的函数.最后,采用CFD技术,数值确定了这种关系并代入流体动力表达式,得到有粘流中流体动力系数的计算方法.研究结果还表明,由于考虑了系统的时变性,在得到的流体动力表达式中将多出一个稳态流体动力项.这个稳态流体动力项,在无粘流的情况下刚好等于零,与d’Alembert(达朗伯)佯谬的结论一致,在有粘流的情况下不等于零,与实际情况一致.To tackle the calculation problem on steady and unsteady hydrodynamic force coefficients of a moving body in viscous incompressible flow,a method for calculating hydrodynamic force coefficients in viscous flowwas proposed based on the quasi-equilibrium hypothesis and the vorticity aerodynamics. Firstly,the concept of time-varying flowsystems was defined,and its relationship with the space volume was clarified. Then,the momentum transport equation and the fluid momentum theorem for time-varying flowsystems were developed respectively,so as to provide a basis for the further discussion. Secondly,the fluid momentum theorem was applied to a flowsystem enclosed in the boundary composed of the body surface and the outer fixed surface with an infinite radius,and the fluid dynamic force was related to the change of the total fluid momentum. Thirdly,the quasi-equilibrium hypothesis was proposed and the total fluid momentum was expressed as a function of the body velocity and angular velocity. At last,this function was determined with the C FD technology and the method for calculating the fluid dynamic force coefficients in viscous flowwas established. The study also showthat the variation of the flowsystem should be considered during the derivation of the fluid momentum,and consequently an additional steady fluid dynamic force would come forth. This additional steady force can be proved to be zero for the body in linear uniform motion in the ideal flow,which is in accordance with d＇Alembert＇s paradox and Lamb＇s result. However,in the case of viscous flow,this additional steady force is not necessarily to be zero,which is in accordance with the experimental results.

关 键 词：流场动量定理 时变系统 输运方程 非定常流体动力 飞艇 

分 类 号：O357.41[理学—流体力学]