On a general theory for compressing process and aeroacoustics： linear analysis

• Published in: Acta mechanica Sinica Vol. 26; no. 3; pp. 355 - 364
• Main Authors: Mao, F., Shi, Y. P., Wu, J. Z.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.06.2010
• Subjects: Classical and Continuum Physics; Compressing; Computational Intelligence; Diagnosis; Engineering; Engineering Fluid Dynamics; Entropy; Formulations; Mathematical analysis; Noise control; Nonlinearity; Research Paper; Shearing; Theoretical and Applied Mechanics; 压缩过程; 和声学; 因子分析法; 完全非线性; 流体运动; 相互耦合; 线性分析; 非线性理论; Transversal (shearing) process; Acoustic mode; Aeroacoustics; Entropy mode; Longitudinal (compressing) process
• ISSN: 0567-7718; 1614-3116
• DOI: 10.1007/s10409-010-0335-6

Of the three mutually coupled fundamental processes （shearing, compressing, and thermal） in a general fluid motion, only the general formulation for the compress- ing process and a subprocess of it, the subject of aeroacous- tics, as well as their physical coupling with shearing and thermal processes, have so far not reached a consensus. This situation has caused difficulties for various in-depth complex multiprocess flow diagnosis, optimal configuration design, and flow/noise control. As the first step toward the desired formulation in fully nonlinear regime, this paper employs the operator factorization method to revisit the analytic linear theories of the fundamental processes and their decomposi- tion, especially the further splitting of compressing process into acoustic and entropy modes, developed in 1940s-1980s. The flow treated here is small disturbances of a compressible, viscous, and heat-conducting polytropic gas in an unbounded domain with arbitrary source of mass, external body force, and heat addition. Previous results are thereby revised and extended to a complete and unified theory. The theory pro- vides a necessary basis and valuable guidance for developing corresponding nonlinear theory by clarifying certain basic issues, such as the proper choice of characteristic variables of compressing process and the feature of their governing equations.