Mass Fire Model: An Experimental Study of the Heat Transfer to Liquid Fuel Burning from a Sand-Filled Pan Burner

Abstract

The heat transfer and mass transfer phenomena to a burning array of fuel elements are considered for the various phases of the burning episode which are obtained by burning a fixed amount of liquid fuel in a 152 cm sand-wick pan burner. Quantitative experimental measurements include burning rate, wick temperature distribution, and flame radiation heat flux distributions to the fuel surface as a function of time after ignition. The radiation heat flux is measured with four radiometers which view the flame from beneath the fuel bed with a prescribed view-angle. The total heat flux from the fire plume to the fuel surface is determined from the burning rate and wick temperature histories. A comparison of the aforementioned results is given for non-luminous and luminous flames using methanol and acetone respectively. A comparison of the total heat flux data and the radiation heat flux data indicates that radiation contributes between 20 and 40 percent of the thermal load to the fuel surface for the methanol flame. For the acetone flame, approximately 40-60 percent of the total heat flux is radiation during the two steady burning rate periods. However, during the falling burning rate period the amount of radiation ranged from 50-100 percent. The radiation from the acetone flame was strongly dependent on fire plume size and shape and whether or not there was an absorbing layer of fuel vapor above the sand wick. Using the data in conjunction with Spalding's theory it is shown that the convective heat transfer coefficient h must increase with an increase in burning rate for the methanol flame. Thus, the increase in turbulence caused by the stronger inflow velocities at the higher burning rates more than compensates for the insulating effect of the buoyant fuel vapor. The flame heights exhibited in these transient sand-wick burns were correlated with the Froude number, i.e., H/d = K Frⁿ During the initial steady burning rate period the values for K and n are in agreement with those found in the literature. However, for the falling burning rate period there is a marked change in n and K. K is approximately 5 × 10¹¹ and 3 × 10⁶ and n is approximately 4 and 3 for acetone and methanol respectively. It is shown that the measured values of H/d for the 152 cm diameter sand-wick during the second steady burning rate period approach those measured in fires of practical interest.