摘要
This paper presents a deep reflection on the advective wave equations for velocity vector and dilatation discovered in the past decade.We show that these equations can form the theoretical basis of modern gas dynamics,because they dominate not only various complex viscous and heat-conducting gas flows but also their associated longitudinal waves,including aero-generated sound.Current aeroacoustics theory has been developing in a manner quite independently of gas dynamics;it is based on the advective wave equations for thermodynamic variables,say the exact Phillips equation of relative disturbance pressure as a representative one.However,these equations do not cover the fluid flow that generates and propagates sound waves.In using them,one has to assume simplified base-flow models,which we argue is the main theoretical obstacle to identifying sound source and achieving effective noise control.Instead,we show that the Phillips equation and alike is nothing but the first integral of the dilatation equation that also governs the longitudinal part of the flow field.Therefore,we conclude that modern aeroacoustics should merge back into the general unsteady gas dynamics as a special branch of it,with dilatation of multiple sources being a new additional and sharper sound variable.
本文是对过去十年发现的速度矢量和胀量的运流波动方程的反思和深化.结果表明,矢量速度方程和胀量方程不仅能刻画黏性传热流体的各种复杂流动本身,而且能刻画包括气动噪声在内的各种纵波在复杂流场中的非线性形成与演化,因此它们可以构成现代气体动力学的理论基础.现代气动声学理论的建立是基于热力学变量的运流波动方程(例如Phillips方程),其发展完全独立于气体动力学.然而,基于热力学变量的方程不能预测产生并传播声波的各种复杂流动本身,使得人们不得不代之以过度简化的模型,因而导致了声源识别的不确定性和噪声难以控制.我们证明,Phillips方程和同类基于热力学变量的方程只不过是胀量方程的一次积分,后者主管了流动的纵场部分.因此,现代气动声学作为气体动力学的一个分支应该重新融合到气体动力学的统一理论框架之中,同时具有多种物理源的胀量也应该视为新的且更普适的声学变量.
作者
Feng Mao
Linlin Kang
Luoqin Liu
Jiezhi Wu
毛峰;康林林;刘罗勤;吴介之(State Key Laboratory for Turbulence and Complex Systems,College of Engineering,Peking University,Beijing,100871,China;Shenzhen Tenfong Technology Co.,LTD,Shenzhen,518055,China;School of Engineering,Westlake University,Hangzhou,310024,China;Department of Modern Mechanics,University of Science and Technology of China,Hefei,230026,China;Physics of Fluids Group,University of Twente,7500 AE,Enschede,The Netherlands)
基金
supported by the National Natural Science Foundation of China(Grant Nos.12102365,91752202 and 11472016)
Luoqin Liu was supported by the Hundred Talents Program of the Chinese Academy of Sciences(CAS).
