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acoustic analogy acoustic source Aeroacoustics AIAA assumptions cells of mixture Chiu and Summerfield combustion heat release combustion roar combustor convective convective velocity critical review diffusion flame direct combustion noise directionality distributed reaction model Doak downstream ducted burners estimate experimental results explain observed farfield sound pressure firing rate flame front flame length Fluid Mechanics frequency range fuel mass fraction function gas turbine Gas-Fueled Burners hot products Hurle ideal gas interpret investigators irrotational jet noise laminar flame speed literature Mahan mixture flow velocity noise production nonhomogeneous wave equation nonpremixed nozzle obtained open turbulent premixed parameters peak frequency port diameter predict premixed flame products of combustion radiated power radiated sound power reaction zone report the results Shivashankara Smith and Kilham sound pressure level source activity source mechanism spectra stoichiometry Strouhal number correlation temperature thermoacoustic efficiency transverse modes turbulent flame turbulent mixing unburned mixture unsteady combustion velocity fluctuation wrinkled flame model