SIMILARITY SOLUTIONS AND APPLICATIONS TO TURBULENT UPWARD FLAME SPREAD ON NONCHARRING MATERIALS

The primary achievement in this work has been the discovery that turbu lent upward flame spread on noncharring materials (for pyrolysis lengt hs less than 1.8 m) can be directly predicted by using measurable flam mability parameters. These parameters are: a characteristic length sca le which is proportional to a turbulent combustion and mixing related length scale parameter (q(net)('') (Delta H-c/Delta H-upsilon))(2), a pyrolysis or ignition time tau(p), and a parameter which determines th e transient pyrolysis history of a non-charring material: lambda = L/c Delta T-p = ratio of the latent heat to the sensible heat of the pyro lysis temperature of the material. In the length scale parameter, q(ne t)('') is the total net heat flux from the flames to the wall (i.e., t otal heat flux minus reradiation losses), Delta H-c is the heat of com bustion and Delta H-upsilon is an effective heat of gasification for t he material. The pyrolysis or ignition time depends (for thermally thi ck conditions) on the material thermal inertia, the pyrolysis temperat ure, and the total heat flux from the flames to the wall, q(fw)(''). T he present discovery was made possible by using both a numerical simul ation, developed earlier, and exact similarity solutions, which are de veloped in this work. The predictions of the analysis have been valida ted by comparison with upward flame spread experiments on PMMA. The pr esent results are directly applicable for pyrolysis lengths less than 1.8 m over which experiments in practical materials show that the tota l (radiative and convective) heat flux to the wall from the flames is a function of the height normalized by the flame height (Z/Z(f)) havin g a maximum value that is nearly constant for many materials; this pro file is approximated in the work by a uniform profile of constant heat flux over the flame length, without loss of generality or violation o f the physical situation. As the pyrolysis length increases (> similar to 1.8 m), radiation dominates and a different total wall heat flux d istribution applies. For this case a numerical simulation, such as FMR C's upward Flame Spread and Growth (FSG) code, can be used to predict upward flame spread rates while the present correlations can provide a n upper bound for the flame spread rate.