## Nonlinear effects on sound propagation through high subsonic Mach number flows in variable area ducts, Volume 3138Andrew John Callegari, United States. National Aeronautics and Space Administration. Scientific and Technical Information Office, Langley Research Center National Aeronautics and Space Administration, Scientific and Technical Information Office, 1979 - Technology & Engineering - 81 pages |

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acoustic field acoustic power transmitted acoustic quantities acoustic source acoustic streaming effect acoustic velocity amplitudes analytic function anechoic boundary Appendix Area Duct Carrying area variation asymptotic matching basic flow basic steady flow boundary conditions boundary value problem choked flow coefficients Crocco Crocco-Tsien derived determined dimensionless eigenvalue Figure flow Mach number Fourier series fundamental harmonic given by Eq hence higher harmonics hypergeometric functions inner equations inner region inner solution leading order linear theory linearized acoustic theory matching principle MQ(x nonlinear acoustic nonlinear effect numerical results ordinary differential equation outer expansion outer region outer solution parameter periodic function perturbation quantities perturbation Riemann invariants perturbation velocity quasi-one dimensional model second of Eqs shocks will occur singular behavior singular point sonic flow source frequency source strength Subsonic Mach Number superharmonics throat Mach number throat region upstream propagating sound Variable Area Duct yields