Premixed flame propagation in a confining vessel with weak pressure rise

Abstract

The propagation of a premixed flame inside of a confining vessel filled with combustible fluid is determined using large-activation-energy asymptotics. The flame structure is analysed assuming that spatial and temporal variations in the transverse direction are weak compared to those in the direction normal to the flame surface. The analysis considers weak pressure rise from confinement and also allows for mixtures that are both near and removed from stoichiometry, non-unity reaction orders, temperature-dependent transport coefficients, and general Lewis numbers. The resulting equations for flame propagation speed are expressed in a coordinate-free form and describe the evolution of an arbitrary shaped flame in a general confining flow. These expressions are specifically applied to the case of a spherical flame propagating inside a spherical chamber. The radius at which the confining vessel influences the flame propagation is determined and the various mechanisms influencing flame behaviour are discussed. The results give rise to a simplified asymptotic relationship that provides an improved equation that may be used to more accurately extrapolate unstretched laminar flame speeds from experimental measurements.

On the accuracy of laminar flame speeds measured from outwardly propagating spherical flames: Methane/air at normal temperature and pressure

“…The accuracy and performance of the nonlinear model were discussed in [22,[45][46][47]. This paper summarizes the experimental data for CH 4 /air at NTP from previous studies [13][14][15][16][17][18][19][20][21][22][23][24][25][26] which measured S 0 u using the OPF method.…”

“…These sources include mixture preparation [5,9,27,28], ignition [29][30][31][32], buoyancy [33,34], instability [35][36][37], confinement [38][39][40][41], radiation [9,10,[41][42][43][44], nonlinear stretch behavior [22,[45][46][47][48][49], and extrapolation [50,51]. The references cited above provide information or details about the effects of each source on S 0 u measured using the OPF method.…”

“…(3)) can be used in extrapolation of unstretched laminar flame speed. It has been found that for mixtures with Lewis number appreciably different from unity (large absolute value of Markstein length), nonlinear stretch behavior occurs [22,[45][46][47][48][49] and the nonlinear model in Eq. (3) helps to get more accurate extrapolation results than the linear model.…”

“…Specifically, a variety of experimental data sets for CH 4 /air reported in the literature [13][14][15][16][17][18][19][20][21][22][23][24][25][26] is collected to show the differences in S 0 u measurement using the OPF method. Moreover, effects of mixture preparation [5,9,27,28], ignition [29][30][31][32], buoyancy [33,34], instability [35][36][37], confinement [38][39][40][41], radiation [9,10,[41][42][43][44], nonlinear stretch behavior [22,[45][46][47][48][49], and extrapolation [50,51] on the discrepancies in S 0 u measurement are examined based on 1-D simulation of propagating planar and spherical flames. It should be noted that Egolfopoulos et al [5] have recently reviewed possible sources of uncertainty in S 0 u measurement using the OPF method.…”

Experimental assessment of various methods of determination of laminar flame speed in experiments with expanding spherical flames with positive Markstein lengths

“…(6) was theoretically supported by Kelley et al [65] who extended (''mixtures that are both near and removed from stoichiometry, non-unity reaction orders, temperature-dependent transport coefficients, and general Lewis numbers'') the earlier analyses by Matalon and Bechtold [57] and Ronney and Sivashinsky [58]. Eq.…”