The Markstein number and Markstein length are two related parameters used to describe the stability of flames in combustion systems.

The Markstein length is a measure of the flame's sensitivity to curvature and is defined as the characteristic length scale over which the flame curvature has a significant effect on flame propagation. It is given by the formula:

L_M = - D_T / (d ln(phi)/dx)

Where L_M is the Markstein length, D_T is the thermal diffusivity, phi is the fuel-to-air equivalence ratio, and x is the axial coordinate.

The Markstein number, on the other hand, is a dimensionless parameter that relates the flame speed to the flame's sensitivity to curvature. It is defined as:

Ma = L_M / delta

Where delta is the flame thickness.

In other words, the Markstein number represents the ratio of the Markstein length to the flame thickness. A positive Markstein number indicates that the flame is stable to curvature, while a negative Markstein number indicates that the flame is unstable to curvature.

In summary, the Markstein number and Markstein length are related parameters used to describe the stability of flames in combustion systems. The Markstein length is a measure of the flame's sensitivity to curvature, while the Markstein number is a dimensionless parameter that relates the flame speed to its sensitivity to curvature.

Thanks to Muhammad Islam for the previous answer. Just some extra thoughts from me....

I want to shed some extra context, esp. re. the Lewis number on this:

The Markstein number (Ma) and the Lewis number (Le) are two important non-dimensional parameters in combustion science, and they are related to the flame front curvature.

The Markstein number is a measure of the flame's sensitivity to stretch, which is caused by changes in the flame front curvature and unsteady straining motion. A positive Markstein number indicates that the flame speed decreases with an increase in flame stretch, while a negative Markstein number indicates that the flame speed increases with an increase in flame stretch.

The Lewis number is the ratio of thermal diffusivity to mass diffusivity. It characterizes the relative rates of diffusion of heat and species in a flame. A Lewis number greater than one implies that heat diffuses more quickly than species, leading to a leaner flame, while a Lewis number less than one implies that species diffuse more quickly than heat, leading to a richer flame.

The relationship between these two numbers and flame front curvature is complex and depends on the specific combustion system. The relationship between curvature and flame front local burning speed has been extensively studied, and experimentally verified in the following article:

Article On the Improvement of Two-Dimensional Curvature Computation ...

However, generally speaking, an increase in flame front curvature (either positive or negative) leads to an increase in flame stretch. This, in turn, affects the flame speed in a way that depends on the Markstein number. The Lewis number, by affecting the relative rates of heat and species diffusion, can influence the flame structure and thus the flame's sensitivity to stretch, which is quantified by the Markstein number.

In summary, the Markstein number, Lewis number, and flame front curvature are interconnected parameters that together determine the dynamics of a flame. Understanding their interplay is crucial for accurate modeling and control of combustion processes.

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Robin Chrystie

Can you please guide me How Can I Calculate Flame Speed in an Optical Engine Experiment?

I'm currently conducting an experiment in an optical engine and capturing images using a high-speed camera. The primary objective is to determine the flame speed under various experimental conditions using the change rate of flame area.

The process involves analyzing a series of high-speed camera images to track the evolution of the flame front over time. I'm looking for insights or methodologies that could help in accurately calculating the flame speed.

Thanks