# Premixed Verses Non-Premixed Flames

To understand the differences between flames propagating through a gaseous fuel and flames propagating through a combustible dust cloud, it is useful to compare the two basic categories of flame propagation. These two categories are Premixed propagation and Non-Premixed propagation. Gaseous flames occur in both categories, depending on how the fuel and oxidizer are mixed. As the mixing process is a prerequisite for having a dust explosion (e.g., see the dust explosion pentagon) dust flames generally propagate in a non-premixed mode, although under certain conditions the flame can resemble a premixed one.

This post demonstrates the two basic categories of flames for gas-only fuel systems, and explores the important parameters of each. The reader interested in a more in-depth coverage of this topic and the mathematical expressions that can be used in computer simulation models, is encouraged to review Chapter 2 and Chapter 3 in the turbulent and multiphase combustion textbook by Kuo [1].

A premixed flame results when the fuel and oxidizer are mixed prior to the passage of the reaction zone. An example premixed flame is shown in the photo above for a gas stove where natural gas (70-90% methane, 30%-10% other gases) and oxygen are mixed prior to being ignited inside the burner. The properties of a laminar premixed flame were explored in a previous post and the properties of turbulent premixed flames will be outlined in a future post.

A non-premixed flame occurs when the fuel and oxidizer are not mixed prior to reacting. An example of this is the diffusion flame from a lighter as shown above. Lighter fuel is typically compressed butane which is liquid inside the lighter canister, but rapidly expands to gas once released from the lighter nozzle. The concentration of the butane near the nozzle is too high for combustion, and the flame cannot form until it mixes with the surrounding air. Diffusion flames are typically much cooler than premixed flames as the mixing step limits the overall combustion.

A common way to characterize non-premixed flames is to look at the relative importance of the mixing and reaction processes. This type of comparison is frequently done in reactive systems by using dimensionless ratios. In the case of non-premixed flames, the Damkohler number ($\text{Da}$) is used to compare the timescale of mixing to the timescale of chemical reaction.

$\text{Da} = \frac{t_{mix}}{t_{ch}}$

$t_{mix}: \text{[Time Scale for Mixing (s)]}$

$t_{ch}: \text{[Time Scale for Chemical Reaction (s)]}$

When the Damkohler number is very large ($\text{Da} \gg 1$), the reaction occurs in a very thin region between the fuel and oxidizer and the flame speed is limited by the diffusion rate (e.g., the diffusion flame above). This is the basis for the Flame-Sheet model  for diffusion flames (e.g., See Kuo [1] Chapter 3.2). When the Damkohler number is very small ($\text{Da} \ll 1$), a premixed flame occurs as mixing is fast relative to reaction. If the timescale of mixing and reaction are similar ($\text{Da} \approx 1$) a Partially-Premixed flame occurs where both the mixing and reaction processes are important to consider.

[1] K. Kuo, Fundamentals of turbulent and multiphase combustion, John Wiley & Sons, Inc., 2012.
[Bibtex]
@BOOK{Kuo2012,
title={Fundamentals of Turbulent and Multiphase Combustion},
author={Kuo, K.},
publisher={John Wiley \& Sons, Inc.},
}