Heat release rate correlation and combustion noise in premixed flames

Abstract

The sound emission from open turbulent flames is dictated by the two-point spatial correlation of the rate of change of the fluctuating heat release rate. This correlation in premixed flames can be represented well using Gaussian-type functions and unstrained laminar flame thermal thickness can be used to scale the correlation length scale, which is about a quarter of the planar laminar flame thermal thickness. This correlation and its length scale are observed to be less influenced by the fuel type or stoichiometry or turbulence Reynolds and Damkohler numbers. The time scale for fluctuating heat release rate is deduced to be about τ c /34 on an average, where τ c is the planar laminar flame time scale, using direct numerical simulation (DNS) data. These results and the spatial distribution of mean reaction rate obtained from Reynolds-averaged Navier-Stokes (RANS) calculations of open turbulent premixed flames employing the standard k-ε model and an algebraic reaction rate closure, involving a recently developed scalar dissipation rate model, are used to obtain the far-field sound pressure level from open flames. The calculated values agree well with measured values for flames of different stoichiometry and fuel types, having a range of turbulence intensities and heat output. Detailed analyses of RANS results clearly suggest that the noise level from turbulent premixed flames having an extensive and uniform spatial distribution of heat release rate is low.

Spatial correlation of heat release rate and sound emission from turbulent premixed flames

“…The prime objectives of this study are three folds, viz., (i) to assess 62 the isotropy of the two-point spatial correlation function, Ω 1 , assumed in 63 an earlier study [6], using DNS data [21] and is about two orders of magnitude larger than other sources [24,25]. This 83 leads to a linear wave equation of the reduced form:…”

“…Both of the values are slightly larger than the values reported in an earlier study because correlation between the far-field acoustic power and burner geometry or 16 operating flow conditions. It has been recently noted [5,6] that the two-point 17 spatial correlation of the rate of change of fluctuating heat release rate, 18 and hence the associated correlation volume v cor and its length scale, is 19 crucial to predicting combustion noise. In previous studies, different length 20 scales have been suggested to estimate v cor empirically, ranging from the 21 laminar flame thickness δ L [12], turbulence integral length scale Λ [13] to the 22 turbulent flame-brush thickness [14,15] or a combination of them.…”

“…27 Recently, it has become feasible to obtain high-fidelity information on the 28 correlation of fluctuating heat release rate because of the advancement in 29 computing technologies and techniques, and laser metrology. Swaminathan 30 et al [5,6] have attempted to analyse and model this two-point correlation 31 using DNS [16][17][18] and laser diagnostics [19] data of turbulent premixed 32 flames. They found that the two-point correlations of heat release rate, 33 Ω, and the rate of change of fluctuating heat release rate, Ω 1 , can be 34 well represented by Gaussian-type functions commonly used in classical 35 turbulence, and that the length scale of the correlation volume, v cor , is 36 0.5δ L .…”

“…This model was then shown to give a good agreement with recent 37 experimental measurements [20] of the far-field overall sound pressure level The construction of Ω 1 requires the rate of change of fluctuating heat 40 release rate, which was calculated in Refs. [5,6] indirectly by using a balance equation for a progress variable and taking the instantaneous reaction rate 42 to be a function of the progress variable. In this way the time derivative 43 is obtained using the spatial derivative of the progress variable field at one 44 single time step from the DNS data [16][17][18].…”

“…Following the common practice in the analysis of turbulent premixed 115 flames [5,6], one can use a progress variable, c, which varies from zero in 116 reactants to unity in products and define it using the fuel mass fraction [28].…”