A theoretical and numerical evaluation of the steady-state burning rate of vertically oriented PMMA slabs

Abstract

The steady state burning rate of vertically oriented slabs of poly-methyl-methacrylate (PMMA) is numerically investigated. Model predictions are compared with measurements and results of the laminar boundary layer (LBL) theory. The numerical model provides a solution of the Favre-averaged Navier–Stokes equations coupled with sub-models for turbulence, combustion, soot production and radiation. The modelling of condensed phase processes is based on the one-dimensional heat transfer equation and pyrolysis is treated as a phase change using the latent heat approach. Results show that the pyrolysing region can be divided into three regions. In the laminar part of the flow (Gr x < 4.3 × 107), the predicted normalised burning rate, ṁ″ p x/μ∞, is a power-law function of Gr x with an exponent close to that of the LBL theory, surface re-radiation being the primary source of discrepancies. From the LBL theory for free flow, it is demonstrated that the local burning rate is inversely proportional to the shear velocity gradient. This is globally confirmed by numerical model results. At Gr x = 4.3 × 107 the change in slope of the burning rate observed experimentally, which indicates the end of the laminar flow region, is reproduced numerically. From Gr x = 2.5 × 109 model results show that the surface mass flux of pyrolyzate increases with x, in agreement with experimental data in literature.