Capturing the gas-phase action of triphenyl phosphate in PMMA flames: A PLIF-calibrated reaction rate model and experimental verification

Predicting flame spread over polymer materials containing flame retardants remains a challenge for fire safety engineering, as conventional modeling approaches either rely on detailed chemical kinetics that are computationally prohibitive or introduce empirical fitting parameters that limit predictive capability. This study addresses this gap by developing a numerically efficient framework for horizontal flame spread over polymethyl methacrylate (PMMA) doped with triphenyl phosphate (TPP), a phosphorus-based flame retardant. The proposed model introduces a physically grounded submodel that reduces the gas-phase reaction rate constant in direct proportion to the experimentally measured decrease in hydroxyl radical concentration at the flame front, as determined by planar laser-induced fluorescence. Importantly, this submodel contains no adjustable parameters, distinguishing it from earlier empirical inhibition schemes. The solid-phase pyrolysis is described by a two-step mechanism, while the gas-phase oxidation is represented by a single global reaction. The model is implemented in the open-source platform OpenFOAM. Validation against comprehensive experimental data for neat PMMA and PMMA containing 10 wt% and 20 wt% TPP demonstrates strong predictive performance. The model captures the reduction in flame spread rate by 31% and 39%, and the decrease in mass burning rate by 20% and 44%, respectively, for the two additive concentrations. Thermal structures and heat feedback at the flame front are also well reproduced. However, the simplified gas-phase chemistry shows limitations in predicting detailed species concentrations downstream of the reaction zone, highlighting the trade-off between computational efficiency and chemical resolution. The key contribution of this work is a calibration-free approach that eliminates the need for empirical tuning or extensive kinetic mechanisms, offering a practical and computationally affordable tool for rapid fire hazard assessment and preliminary screening of phosphorus-based flame retardants. This framework extends beyond previous efforts by demonstrating that a single experimentally derived inhibition coefficient can be physically interpreted and directly applied, bridging the gap between detailed diagnostics and engineering-scale modeling.