Compact Green's Function for a Generic Rijke Burner

• Main Authors: P. R. Murray, M. S. Howe
• Format: Article
• Language: English
• Published: SAGE Publishing 2011-09-01
• Series: International Journal of Spray and Combustion Dynamics
• Online Access: https://doi.org/10.1260/1756-8277.3.3.191

A theoretical examination is made of the thermo-acoustic properties of a Rijke burner of large aspect ratio rectangular cross-section. Such a generic device has been proposed by Kok et al . (2009 paper presented at the 16th International Congress on Sound & Vibration ) to make canonical studies of combustion instabilities. An aeroacoustic Green's function is derived which permits the sound pressure produced by arbitrary thermal and vortex sources within the burner to be calculated by convolution. The Green's function corresponds to the potential flow sound field produced by an impulsive point source; its calculation taking account of flame-holder geometry is facilitated by use of the Schwarz-Christoffel transformation. The transformation is performed numerically to accommodate complex burner geometry and validated by comparison with an alternative procedure involving the direct numerical integration of Laplace's equation.