To use the non premixed combustion model of the Fluent the Damköhler number >>1. For nonpremixed methane/air.
The Damköhler number is defined to be the characteristic mixing time (which is how long it takes for the fluid to mix and its value is approximately equal to the turbulent integral timescale) divided by the characteristic chemical time (which is how long it takes for the chemical reactions to occur).
Since you're just trying to check whether Da >> 1, you can approximate the characteristic mixing time by the turbulent integral timescale. Depending on how your boundary conditions define turbulence, this can be computed many different ways. The classic definition is to divide the turbulent kinetic energy (k) by the turbulent dissipation (epsilon). You can also estimate it by dividing the integral length scale by the velocity fluctuations (the velocity fluctuations are by definition the Turbulent Intensity multiplied by the Mean Velocity).
The characteristic chemical time is a bit more tricky to get. It can be defined to be the laminar flame thickness divided by the laminar flame speed, but these values are very dependent on your conditions, e.g. pressure and temperature. You can obtain the values from a search through the academic literature. I did a google search for "laminar flame thickness methane" and the first hit looked like it might be useful: www.combustion.org.uk/ECM_2007/ecm2007_papers/6-7.pdf
In the end, you're only needing an approximation, so don't be too rigorous with your calculations: just get numbers that are reasonable.
www.combustion.org.uk/ECM_2007/ecm2007_papers/6-7.pdf
The Damköhler numbers (Da) are dimensionless numbers used in chemical engineering to relate the chemical reaction timescale (reaction rate) to the transport phenomena rate occurring in a system. It is named after German chemist Gerhard Damköhler. The Karlovitz number (Ka) is related to the Damköhler number by Da = 1/Ka.
In its most commonly used form, the Damköhler number relates the reaction timescale to the convection time scale, volumetric flow rate, through the reactor for continuous (plug flow or stirred tank) or semibatch chemical processes:
The value of Da provides a quick estimate of the degree of conversion that can be achieved. As a rule of thumb, when Da is less than 0.1 a conversion of less than 10% is achieved, and when Da is greater than 10 a conversion of more than 90% is expected.
https://en.wikipedia.org/wiki/Damk%C3%B6hler_numbers
Da = integral time scale(not length scale) / reaction time
Ka = Kolmogrove time scale / reaction time..
the equation is well explained in the turbulent literature.
Thank you.
If you have any question for calculating please mail me
the best formula for Dn is
Dn = k ((ca0)*n-1)tau
power n is order of reaction
ex. first order n=1, Dn =k tau
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