1. 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

2. 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

3. Model (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) (1) A+X  2Xrate=k b (T)ax (2) 2X  Prate=k t x 2 (3) W  V+rSrate=k w (T)w (4) S+X  S+Prate=k i sx A - fuel, X - radical W- water,V-vapour S - salt, P -products

4. Feedback There are four types of feedback in the system

5. Governing equations The non-dimensionalized governing equations are   - dimensionless water density,   - inverse exothermicity parameter,   - dimensionless coefficient for water evaporation

6. Pure water mist (  In the presence of pure water mist with no dissolved salt (  ), 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

7. Flame front

8. Flame Pulse Flame pulse

9. Flame failure Flame propagation failure

10. Transition from front to pulse Analysis on the equation provided the condition to be satisfied by  to have a pulse or a front flame transition from pulse flame to front flame occurs at  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 Transition from front to pulse

11. Flame speed Flame speed with varying water mist density

12. 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