Sound generation by laminar premixed flame annihilation

Abstract

This paper presents a numerical and theoretical investigation of the sound generated by premixed flame annihilation. Planar, axisymmetric and spherically symmetric flame annihilation events are considered. The compressible Navier–Stokes, energy and progress variable equations are first solved using simple chemistry simulations, resolving both the flame dynamics and the acoustics. These simulations show that the amplitude of the far-field sound produced by the annihilation events depends on the flame thickness, particularly for the axisymmetric and spherically symmetric flame annihilation events. The flame propagation velocity is also always observed to increase significantly prior to flame annihilation, which is in keeping with other reported experimental and numerical studies. A theory is then presented that relates the far-field sound to the flame annihilation event by using a previously reported and extended form of Lighthill's acoustic analogy. A comparison with the numerical results shows that this theory accurately represents the far-field sound produced by considering only the temporal heat release source term in Lighthill's acoustic analogy, as reported by others. Additional assumptions of an infinitely thin flame and constant flame speed are then invoked in an attempt to simplify the problem. In the planar annihilation, this theory results in good predictions of the overall pressure change. However, these assumptions lead to significant under-prediction of the amplitude of far-field sound produced for the axisymmetric and spherically symmetric annihilation events. Finally, dimensional reasoning supported by the simulations and theory is used to develop scalings of the far-field sound in terms of the flame parameters.