Abstract
Starting from the flammability diagram, a thermal theory is proposed to scale various critical concentrations in combustion. By an analogy between ignition and suppression, the flammability limits are extrapolated to minimum extinguishing concentrations. Thus the suppressibility of a fuel will be evaluated from its flammability, while the suppression capability of an agent will be evaluated using the cup-burner (CB) value. By setting up the thermal balance at extinguishing, the synergistic effect can also be explained by an adjustable flame temperature factor. This thermal mechanism will guide the future work on selecting new combinations of binary agents.
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Abbreviations
- CAFT:
-
Critical adiabatic flame temperature (K)
- \( C_{O} \) :
-
The oxygen coefficient in a reaction, dimensionless
- \( C_{st} \) :
-
The stoichiometric number for a reaction, dimensionless
- \( H_{O} \) :
-
The heating potential of oxygen based on air, dimensionless
- \( H_{F} \) :
-
The heating potential of fuel based on air, dimensionless
- LFL:
-
Lower flammability limit (volume ratio), % or dimensionless
- LOC:
-
Limiting oxygen concentration
- MEC:
-
Minimum extinguishing concentration
- MIC:
-
Minimum inerting concentration
- NP/IP:
-
Nitrogen point/inertion point
- OI:
-
Oxygen index
- \( Q_{D} \) :
-
The quenching potential of diluent based on air, dimensionless
- \( Q_{F} \) :
-
The quenching potential of fuel based on air, dimensionless
- \( T_{a} \) :
-
Ambient temperature (K)
- UFL:
-
Upper flammability limit (volume ratio), % or dimensionless
- \( x_{L} \) :
-
Lower flammability limit (volume ratio), % or dimensionless
- \( x_{st} \) :
-
Stoichiometric fuel/air volume concentration, % or dimensionless
- \( x_{U} \) :
-
Upper flammability limit (volume ratio), % or dimensionless
- α:
-
Quenching potential of a thermal agent, known and retrieved from NIST chemistry webbook
- β:
-
Contribution of flame temperature change from ignition (diffusion flame) to extinction (premixed flame)
- γ:
-
Contribution of wall and other heat transfer effects on extinction for a cup-burner test
- a:
-
Ambient
- d:
-
Diluent
- i:
-
Component of a mixture
- m:
-
Sum of a mixture
- st:
-
Stoichiometric
- AF:
-
Adiabatic flame
- L:
-
Lower flammable limit
- U:
-
Upper flammable limit
- D:
-
Diluent-based potential to air potential
- F:
-
Fuel-based potential to air potential
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Appendices
Appendix A: Development of the suppression index for a diluent
First, we establish the volume balance for LFL in (17)
Here \( x_{a} \) is the concentration of excess air not reacting at ignition (or at the lower flammability limit). So we have
Now we assume the suppression is similar to the above ignition process, but using a new thermal agent to replace the excess air. This new agent has a quenching potential of R times that of air. So the volume concentration of the new agent is scaled-down by R.
Now we have the extinction concentration defined as
Rearrange the terms, we have
For nitrogen, the CB value is \( x_{E} = 0.32 \). Plugging the flammability data of Heptane, \( x_{L} = 0.012 \), \( C_{st} = 53.4 \), we have \( R = 1.194 \) for Nitrogen. This is more than its quenching potential \( \alpha = 0.992 \). The difference is the contribution of cup-burner test configuration (use \( \gamma \) to represent in this work), i.e., the flow effect, the wall cooling effect, the raised flame temperature effect, etc. Cup-burner test does not control the energy loss terms, while the flammability test does control such terms.
In order to compare all fire suppressing agents, R is scaled by the molecular weight. Then we have a new suppression index defined as
Since this index is normalized by mass, it shows the mass-averaged agent effectiveness. As expected, most agents are working by mass, with some exceptions due to synergistic effects.
Appendix B
See Table 2.
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Ma, T., Wang, Q. & Larrañaga, M.D. From Ignition to Suppression, a Thermal View of Flammability Limits. Fire Technol 50, 525–543 (2014). https://doi.org/10.1007/s10694-013-0338-5
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DOI: https://doi.org/10.1007/s10694-013-0338-5