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Modelling Flame inhibition. Serafim Kalliadasis 1 , Alice Lazarovici 2 , John Merkin 2 , Steve Scott 3 1 Department of Chemical Engineering, 2 Department of Applied Mathematics, 3 School of Chemistry, University of Leeds, Leeds, LS2 9JT, UK. Introduction.
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Modelling Flame inhibition Serafim Kalliadasis1, Alice Lazarovici2, John Merkin2, Steve Scott3 1Department of Chemical Engineering, 2Department of Applied Mathematics, 3School of Chemistry, University of Leeds, Leeds, LS2 9JT, UK
Introduction • the Montreal Protocol has banned the use of halon-based chemical fire extinguishers • no obvious replacement has been identified • water mists with dissolved ionic salts are more effective at quenching flames • salt coatings of vessel walls provide thermoneutral radical removal
Model • (1) A+X 2X rate=kb(T)ax • (2) 2X P rate=ktx2 • (3) W V+rS rate=kw(T)w • (4) S+X S+P rate=kisx • A - fuel, X - radical • W- water,V-vapour • S - salt, P -products • (1) - temperature-dependent, branched-chain reaction, produces X • (2) - recombination of radical (exothermic) • (3) - evaporation of water mist droplets (endothermic), produces S which catalyses radical removal (4) • r - stoichiometric coefficient (concentration of salt in water mist)
Feedback • There are four types of feedback in the system
Governing equations • The non-dimensionalized governing equations are • a - dimensionless water density, • b - inverse exothermicity parameter, • g - dimensionless coefficient for water evaporation
Pure water mist (r=0) • In the presence of pure water mist with no dissolved salt (r=0), the model is that of a second order exothermic reaction subject to an endothermic step. Depending on the initial concentration of A and W, the relative exo- and endothermicities of the steps and the reaction rate • a flame front solution for which the temperature jumps sharply from its initial value to some final, high temperature in the rear of the flame • a flame pulse for which the temperature jumps in the flame front, but then falls back to its initial low value in the rear of the wave • quenching of the flame for which the flame fails to develop and propagate from the initial stimulus
Flame front • Flame front
Flame Pulse • Flame pulse
Flame failure • Flame propagation failure
Transition from front to pulse • Transition from front to pulse • Analysis on the equation provided the condition to be satisfied by a, b, g to have a pulse or a front flame • transition from pulse flame to front flame occurs at ab = g. • In terms of the physical parameters, this represents the relation • which is the condition for the exothermic processes to release exactly enough enthalpy to vaporise the water present • Transition from flame to quenching • determined numerically
Flame speed • Flame speed with varying water mist density
Salt dissolved in the water () • Salt dissolved into the water changes the flame propagation speed and lowers the quenching point • Flame speed by water mist density Critical water mist density for salt concentrations for salt solutions