Analytical Equations for Thermoacoustic Instability Sources and Acoustic Radiation from Reacting Turbulence

• Published in: International journal of aerospace engineering Vol. 2020; no. 2020; pp. 1 - 12
• Main Author: Miller, S. A. E.
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Publishing Corporation 08-10-2020; Hindawi; Hindawi Limited
• Subjects: Acoustic noise; Acoustics; Aerodynamics; Aerospace engineering; Combustion; Computational fluid dynamics; Noise; Point sources; Propagation; Reacting flow; Sound waves; Source studies; Stability; Stability analysis; Thermoacoustics; Turbulence; Velocity
• ISSN: 1687-5966; 1687-5974
• DOI: 10.1155/2020/8890360

We seek to ascertain and understand source terms that drive thermoacoustic instability and acoustic radiation. We present a new theory based on the decomposition of the Navier-Stokes equations coupled with the mass fraction equations. A series of solutions are presented via the method of the vector Green’s function. We identify both combustion-combustion and combustion-aerodynamic interaction source terms. Both classical combustion noise theory and classical Rayleigh criterion are recovered from the presently developed more general theory. An analytical spectral prediction method is presented, and the two-point source terms are consistent with Lord Rayleigh’s instability model. Particular correlations correspond to the source terms of Lighthill, which represent the noise from turbulence and additional terms for the noise from reacting flow.