A theoretical and numerical evaluation of the steady-state burning rate of vertically oriented PMMA slabs
Résumé
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 (Grx < 4.3 × 107), the predicted normalised burning rate, m″px/μ∞, is a power-law function of Grx 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 Grx < 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 Grx = 2.5 × 109 model results show that the surface mass flux of pyrolyzate increases with x, in agreement with experimental data in literature.
Mots clés
Chemical reactions
Fluid dynamics
Fluid mechanics
Numerical methods
Burning rates
Condensed phase processes
Laminar boundary layer
Laminar boundary layers
Mass transfer number
Methyl methacrylates
Model predictions
Numerical evaluations
Numerical modelling
One-dimensional heat
Phase changes
Poly-methyl-methacrylate
Soot production
Steady state burning rate
Steady states
Sub-models
Vertical fire
Navier Stokes equations