From Ignition to Suppression, a Thermal View of Flammability Limits

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.

Appendices

Appendix A: Development of the suppression index for a diluent

First, we establish the volume balance for LFL in (17)

$$ C_{st} \cdot x_{L} + x_{a} = 1 $$

(16)

Here $x_{a}$ is the concentration of excess air not reacting at ignition (or at the lower flammability limit). So we have

$$ x_{a} = 1 - C_{st} \cdot x_{L} $$

(17)

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.

$$ x_{i} = \frac{{x_{a} }}{R} $$

(18)

Now we have the extinction concentration defined as

$$ x_{E} = \frac{{x_{i} }}{{C_{st} \cdot x_{L} + x_{i} }} = \frac{{1 - C_{st} \cdot x_{L} }}{{R \cdot C_{st} \cdot x_{L} + 1 - C_{st} \cdot x_{L} }} $$

(19)

Rearrange the terms, we have

$$ R = \frac{{1 - x_{E} }}{{x_{E} }} \cdot \left( {\frac{{1 - C_{st} \cdot x_{L} }}{{C_{st} \cdot x_{L} }}} \right) $$

(20)

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

$$ SI = \frac{{\frac{{1 - x_{E} }}{{x_{E} }} \cdot \left( {\frac{{1 - C_{st} \cdot x_{L} }}{{C_{st} \cdot x_{L} }}} \right)}}{MW} $$

(21)

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.