Spectral characteristics of the heat release rate in confined turbulent flames

The broad-band direct combustion noise is an important problem for industrial and domestic burners. The power spectral density (PSD) of this noise is related to the local spectral density of fluctuating heat release rate (HRR) ( $\psi _{\dot {q}}$ ), which is challenging to measure but is readily available from large eddy simulations (LES) results. The behaviour of $\psi _{\dot {q}}$ for a wide range of thermochemical and turbulence conditions is investigated. Three burners are studied, namely a dual-swirl burner, a bluff-body burner and a jet in cross-flow burner, operating at atmospheric conditions with $\textrm {CH}_4$ –air and $\textrm {H}_2$ –air mixtures. In contrast to the classical $f^{-5/2}$ scaling, the far-field sound pressure level and volume-integrated HRR ( $\psi _{\dot {Q}}$ ) spectra reveal a universal $f^{-5}$ scaling for high frequencies. This differing spectral decay rate for $\psi _{\dot {Q}}$ compared to the classical scaling is due to multi-regime combustion, related to either partial premixing or the local turbulence intensity. The dependence of $\psi _{\dot {q}}$ on the chosen spatial locations, flame configuration and its relation to velocity spectra are studied. A simple model for $\psi _{\dot {q}}$ involving the velocity spectra is found that compares well with LES results. The characteristic frequency involved in this model is related to the time scale of the coherent structures of the flow.