zbMATH — the first resource for mathematics

On a general theory for compressing process and aeroacoustics: linear analysis. (English) Zbl 1269.76108
Summary: Of the three mutually coupled fundamental processes (shearing, compressing, and thermal) in a general fluid motion, only the general formulation for the compressing process and a subprocess of it, the subject of aeroacoustics, 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 decomposition, 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 provides 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.

76Q05 Hydro- and aero-acoustics
Full Text: DOI
[1] Wu J.Z., Ma H.Y., Zhou M.D.: Vorticity and Vortex Dynamics. Springer, Berlin (2006)
[2] Rayleigh L.: The Theory of Sound. Dover, New York (1929) · JFM 55.1221.04
[3] Doak P.E.: Analysis of internally generated sound in continuous materials: 2. A critical review of the conceptual adequacy and physical scope of existing theories of aerodynamic noise, with special reference to supersonic jet noise. J. Sound Vib. 25, 263–335 (1972) · Zbl 0245.76069 · doi:10.1016/0022-460X(72)90435-X
[4] Lagerstrom, P.A., Cole, J.D., Trilling, L.: Problems in the Theory of Viscous Compressible Fluids. Technical report, California Institute of Technology, Pasadena, California (1949)
[5] Wu T.Y.T.: Small perturbations in the unsteady flow of a compressible, viscous and heat-conducting fluid. J. Math. Phys. 35, 1327 (1956) · Zbl 0072.20202
[6] Chu B.T., Kovasznay L.S.G.: Non-linear interactions in a viscous heat-conducting compressible gas. J Fluid Mech. 3, 494–514 (1958) · doi:10.1017/S0022112058000148
[7] Pierce A.D.: Acoustics: an Introduction to Its Physical Principles and Applications, 2nd edn. Acoustical Society of America, New York (1989)
[8] Lighthill M.J.: On sound generated aerodynamically. I. General theory. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 211(1107), 564–587 (1952) · Zbl 0049.25905 · doi:10.1098/rspa.1952.0060
[9] Wang M., Freund J.B., Lele S.K.: Computational prediction of flow-generated sound. Annu. Rev. Fluid Mech. 38(1), 483–512 (2006) · Zbl 1100.76058 · doi:10.1146/annurev.fluid.38.050304.092036
[10] Doak P.E.: Fluctuating total enthalpy as the basic generalized acoustic field. Theor. Comput. Fluid Dyn. 10(1–4), 115–133 (1998) · Zbl 0910.76075 · doi:10.1007/s001620050054
[11] Yates, J.E.: Application of the Bernoulli enthalpy concept to the study of vortex noise and jet impingement noise. Technical report, Aeronautical Research Associates of Princeton, Inc., NJ (1978)
[12] Enflo B.O., Hedberg C.M.: Theory of Nonlinear Acoustics in Fluids, 1st edn. Springer, Berlin (2002) · Zbl 1049.76001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.