A parametric study of sound generation by premixed laminar flame annihilation

A numerical and theoretical study of sound generation by planar, axisymmetric and spherically symmetric premixed laminar flame annihilation is presented in this paper. The compressible Navier–Stokes, energy, and progress variable equations are solved using Direct Numerical Simulation with one-step chemistry. A theory is developed to relate the pressure amplitude to the flame’s propagation velocity and consumption speed, which were identified as key parameters in the generation of sound in our previous study (Talei et al., 2011[38]). The results show that by obtaining the propagation velocity of the flame from the simulations, the sound generation can be predicted accurately for unity Lewis number. Use of Markstein’s linear theory relating flame speed and curvature is also investigated as a more practical way of applying this theory. It is shown that this leads to under-prediction of the radiated sound in the spherical and axisymmetric configurations, but it is able to capture the qualitative trends. The effects of laminar flame speed, temperature ratio and Zel’dovich number are then investigated. These are interpreted in terms of a scaling argument put forward in our previous study, and also in terms of the flame’s propagation velocity and consumption speed. Finally, cases involving non-unity Lewis number are investigated. As the flames approach annihilation, either flame acceleration or deceleration is observed depending on the Lewis number, and this is shown to affect the radiated sound significantly. For Lewis numbers greater than unity, the annihilation of the flame results in a local increase in consumption speed at annihilation, leading to more sound production compared with that of unity Lewis number. Lewis numbers less than unity exhibit the opposite behaviour.