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 a...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.展开更多
As a continuation of a recent linear analysis by Mao et al.(Acta Mech Sin,2010,26:355),in this paper we propose a general theoretical formulation for the compressing process in complex Newtonian fluid flows,which cove...As a continuation of a recent linear analysis by Mao et al.(Acta Mech Sin,2010,26:355),in this paper we propose a general theoretical formulation for the compressing process in complex Newtonian fluid flows,which covers gas dynamics,aeroacoustics,nonlinear thermoviscous acoustics,viscous shock layer,etc.,as its special branches.The principle on which our formulation is based is the maximally natural and dynamic Helmholtz decomposition of the Navier-Stokes equation,along with the kinematic Helmholtz decomposition of the velocity field.The central results are the new dilatation equation and velocity-potential equation,which are the counterparts of vorticity transport equation and vector stream-function equation for the shearing process,respectively.Various couplings of the compressing process with shearing and thermal processes,including its physical sources,are carefully identified.While the possible applications and influences of the new formulation are yet to be explored,our preliminary discussion on the pros and cons of previous formulations pertain to acoustic analogy and that on the process splitting and coupling in highly compressible turbulence indicates that at least the formulation can serve as a new frame of reference by which one may gain some additional insight and thereby develop new approaches to the multi-process complex flow problems.展开更多
基金supported by the National Basic Research Program of China(2009CB724100)
文摘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.
基金supported by the Ministry of Science and Technology of China's Turbulence Program (Grant No.2009CB724101)the National Basic Research Program of China (Grant No.2007CB714600)the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant No.10921202)
文摘As a continuation of a recent linear analysis by Mao et al.(Acta Mech Sin,2010,26:355),in this paper we propose a general theoretical formulation for the compressing process in complex Newtonian fluid flows,which covers gas dynamics,aeroacoustics,nonlinear thermoviscous acoustics,viscous shock layer,etc.,as its special branches.The principle on which our formulation is based is the maximally natural and dynamic Helmholtz decomposition of the Navier-Stokes equation,along with the kinematic Helmholtz decomposition of the velocity field.The central results are the new dilatation equation and velocity-potential equation,which are the counterparts of vorticity transport equation and vector stream-function equation for the shearing process,respectively.Various couplings of the compressing process with shearing and thermal processes,including its physical sources,are carefully identified.While the possible applications and influences of the new formulation are yet to be explored,our preliminary discussion on the pros and cons of previous formulations pertain to acoustic analogy and that on the process splitting and coupling in highly compressible turbulence indicates that at least the formulation can serve as a new frame of reference by which one may gain some additional insight and thereby develop new approaches to the multi-process complex flow problems.
