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Theoretical analysis and quantitative methodology are proposed to predict the behavior of flame expansion in pool fire extinguishment with an impinging steam jet. The theoretical analysis contains the following three standpoints: (1) a fuel vapor-rich core exists in the base of the pool fire while oxygen is lacking. The existence of a fuel vapor-rich core is the prerequisite for flame expansion phenomenon. (2) The root cause responsible for the flame expansion is the fuel vapor convection by the impinging steam jet. An expanded fire ball is formed due to the burning of the convected fuel vapor, resulting in flame expansion phenomenon. (3) The flame expansion phenomenon could be divided to three typical stages: the flame height-decreasing stage, the fire-expanding stage, and the burn-out stage. The flame height-decreasing stage is the stage in which the steam jet impacts the flame and reaches the fuel vapor-rich core. The fire-expanding stage is the stage in which the fuel vapor is convected and burnt as a fire ball after the steam impacts the fuel vapor-rich core. The fire is then suppressed in the burn-out stage. Three quantitative features of the flame expansion phenomenon, the expansion ratio of the flame width ϕl, the expansion ratio of the flame volume ϕv, and the expansion ratio of the flame radiation ϕr, are defined to characterize the level of the expansion. A series of extinguishment tests using medium-size pool fires with an impinging steam jet were conducted to validate the theoretical analysis. The experimental results reveal that the theoretical analysis describes the flame expansion phenomenon quite well. Based on the experimental data, the height of the fuel vapor-rich core was calculated for each test case, and it was found that the height of the fuel vapor-rich core was about 0.2 times the visible flame height. The durations of the three stages and the flame shapes calculated using the proposed theoretical analysis compare favorably with the experimental measurements. The calculation shows that the expansion ratio of the flame width is about 2.0 in each test case of the medium size pool fire; the expansion ratio of the flame volume approximately matches the calculated value, and the calculated values of the expansion ratio of the flame radiation are close to the experimental values.

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