Scaling flame height of fully turbulent pool fires based on the turbulent transport properties

Abstract

Previous studies on turbulent pool fires were almost entirely based on the air entrainment concept, while the characteristics of turbulent mixing between fuel gas and air following entrainment have not been elucidated. This paper presents scaling analysis on turbulent viscosity (νt) and diffusivity (Dt) by using literature data of 2-D velocity and mass fraction in large scale turbulent pool fires and strong He plume, thereby the flame height correlations are developed based on the turbulent mixing concept. It is found that the radial position of the maximum shear stress is close to that of the maximum radial gradient of axial velocity at the same level. The combustion reaction can affect the radial profile of turbulent viscosity. It is found that the turbulent viscosity (νt) increases first and then decreases with radial distance in turbulent pool fires, while decreases steadily with radius in the near-field He plume and far-field plume. The turbulent mass diffusivity (Dt) is proven to increase slightly with radius in the near-field He plume. The radial-mean turbulent Schmidt number is about 0.75 in the near field of strong He plume. The mean turbulent viscosities (νt=) within the mean flame height (H) are scaled by F1/3H2/3 for the fully turbulent pool fires, where F is the buoyancy flux. The classical two-fifths law of H*(H/d, d is the pool size) regarding the dimensionless heat release rate (Q˙*) is developed based on the turbulent transport properties. The coefficient of the power law is related to known ambient and fuel parameters, the turbulent Schmidt number and turbulent viscosity coefficient. The predicted coefficient agrees well with the empirical values from experimental data of flame height in literature.