Spectrally resolved calculation of thermal radiation penetration into liquid n-heptane in pool fires

The radiative heat transfer in a volatile hydrocarbon pool fire was investigated by obtaining the transmittance of infrared radiation through fuel (n-heptane) layers of different depths. The incident radiation spectrum was assumed to be either the same as a spectrum obtained experimentally for a 2 meter pool fire, or to be a Planck distribution corresponding to the approximate flame temperature. The transmittances were calculated by integrating either the single-ray Lambert-Beer formula, the two-flux method or the analytical plane-parallel monochromatic/gray solution of the radiative transfer equation over wavelength, using the liquid spectral absorption coefficients found in literature. The obtained results are validated against earlier measurements, and the possibility of calculating them with significantly less computation time by using a k-distribution method was investigated. The results managed to replicate the measured heat flux values in the liquid with a fractional error of only about 5% being attainable even with a 3-point quadrature method. The use of the k-distribution, more known and used in gas phase thermal radiation calculations, significantly speeds up the calculations. It was found out that in the calculation of total transmitted fractions of radiation, the flame spectrum can be approximated with a Planck distribution of an appropriate temperature.