A Correlation for the Flame Height in "Group" Fires

Abstract

A correlation of flame heights is presented for recent experiments of merging group fires produced from arrays of gaseous burners. The correlation is based on two considerations: a) the air entrainment up to the flame height is proportional to the stoichiometric requirements for combustion of the fuel and b)the air entrained is equal to the side area of the plume multiplied by an entrainment velocity proportional to the square root of the vertical distance from the source. This correlation is applicable for an array of merging fires as recent results verify. Justification for merging of the investigated group fires is given together with comparison with older work.

Experimental study on flame merging behaviors from two pool fires along the longitudinal centerline of model tunnel with natural ventilation

“…(12) and ( 14 ), the radial flame length ( r f ) from a single fire in tunnel can be expressed as Figure 12 presents the comparison of Eq. (15) and the data of single 13 cm and single 16 cm pools in both current and previous studies [24,26,43,44] . It can be seen that most data points are predicted well by the correlation although some scatters are located at the outside of ± 20% error lines.…”

“…However, most of them [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] were conducted in open space to investigate the effects of fuel type, fire shape, size, number, spacing and array pattern on the mass loss rate (MLR), flame height, flame merging, heat feedback, fire whirl, etc.. For example, Weng et al [2] , Kamikawa et al [3] and Fukuda et al [4] studied the effects of fire spacing and heat release rate (HRR) http …”

A Review of Fire Interactions and Mass Fires

“…In their experiments, flame merging was likely to occur when closer than 0.29 to 0.34 times the merged flame length. Delichatsios [104] also found that flames began to merge at spacing less than 0.33 times the actual flame length for gaseous burners. The discrepancy in these constants may be due to different definitions of flame interaction (tilting versus change in flame height) and flame merging (using completely merged flame height versus actual flame height), different fuels, and possibly uncertainty of measuring flame dimensions.…”

“…Correlations exist for the critical parameters for both flame interaction [99][100][101] and merging [24,[102][103][104]. These correlations take many forms-some define a critical ratio between the fire spacing and fire diameter [24,100] or flame height [99,101,104], some define a critical ratio between the flame height and fire diameter [24], and some define a critical dimensionless heat release rate [102,103]. Upon close examination, however, it becomes clear that fire spacing, fire diameter, flame height, and dimensionless heat release rate have interdependencies and, thus, these different correlations are not necessarily contradictory.…”

“…For example, for the interaction of relatively tall flames compared to the actual burner diameter (L f /D > 1, or high values of Q * ), Putnam and Speich [102] and Sugawa and Takahashi [100] showed that the dimensionless flame height correlates well with the dimensionless heat release rate to the two-fifths power (L f /D ∼ Q * 2/5 ). Delichatsios [104] successfully correlated the dimensionless flame height to the dimensionless heat release rate to the two thirds power (L f /D ∼ Q * 2/3 ) for Q * between 0.1 and 1. On the other hand, Weng et al [120] and Kamikawa et al [113] showed that the data for merged flame height is better correlated with the exponent "a" varying with the number of burners.…”