黏性可压缩气体动力学和气动声学的统一理论基础初探(Ⅱ)边界上的纵场源

A unified theory for gas dynamics and aeroacoustics in viscous compressible flows.PartⅡ.Sources on solid boundary

本项工作试图将经典气体动力学的基本理论扩展到黏性可压缩流动,其中气动声学自然是其中的一个特殊分支.作为(1I)无界流动(Maoetal,2022)文章的延续,本文研究由纵横过程的运动学和黏性动力学耦合导致的固体边界上的纵场源.我们发现在这种情况下,两个独立的热力学变量的最简单选择是无量纲压力和温度.将连续性方程及其法向导数应用于固体表面,可以得到纵场边界动力学的双层次结构.我们的研究表明,边界胀量流忠实地代表了涡声和熵声的边界产生;同时,边界上纵横场的相互生成机制并不是“对称”地发生在同一层次上,而是沿着曲折的路线出现.在第一层次,压力梯度单向地产生涡量;而在第二层次,涡量单向地产生胀量.

This work attempts to extend the fundamental theory for classic gas dynamics to viscous compressible flow,of which aeroacoustics will naturally be a special branch.As a continuation of Part I.Unbounded fluid(Mao et al.,2022),this paper studies the source of longitudinal field at solid boundary,caused by the on-wall kinematic and viscous dynamic coupling of longitudinal and transverse processes.We find that at this situation the easiest choice for the two independent thermodynamic variables is the dimensionless pressure P and temperature T.The two-level structure of boundary dynamics of longitudinal field is obtained by applying the continuity equation and its normal derivative to the surface.We show that the boundary dilatation flux represents faithfully the boundary production of vortex sound and entropy sound,and the mutual generation mechanism of the longitudinal and transverse fields on the boundary does not occur symmetrically"at the samc level,but appears along a zigzag route.At the first level,it is the pressure gradient that generates vorticity unidirectionally;while at the second level,it is the vorticity that generates dilatation unidirectionally.