Karlovitz Number
Computes the Karlovitz number of a turbulent premixed flame, Ka = (u'/S_L)^1.5 · (ℓ_t/δ_L)^−0.5, comparing the chemical time of the flame front with the turnover time of the smallest eddies (Kolmogorov scale). Ka below 1 means the laminar flame structure survives the turbulence (wrinkled and corrugated regimes); between 1 and 100 eddies penetrate the preheat zone and thicken the flame; above 100 the reaction zone itself is broken. Together with the Damköhler number it forms the axes of the Borghi diagram, used to pick combustion models in CFD. Peters' form is adopted; integral scale and flame thickness must share the same unit. Enter the velocity fluctuation, the laminar flame speed, the integral length scale and the laminar flame thickness.
Result
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Karlovitz Number: locating a flame on the Borghi diagram
Before picking a combustion model for a simulation, someone has to decide whether the flame still behaves as a thin sheet wrinkled by the flow or whether turbulence has already worked its way inside it. Getting that wrong is expensive: a flamelet model used in a regime where eddies have torn into the reaction zone predicts a stability the burner does not have, under-predicts CO and misses blow-off. The Karlovitz number is the vertical axis of the Borghi diagram, and it settles the question with a single figure.
The tool uses Peters' form, Ka = (u'/S_L)^1.5 · (ℓ_t/δ_L)^−0.5, picked because it needs only four quantities that any measurement or LES already provides. Here u' is the turbulent velocity fluctuation, roughly 0.5 to 10 m/s in industrial burners; S_L is the laminar flame speed, 0.4 m/s for stoichiometric methane-air and above 2 m/s for hydrogen; ℓ_t is the integral length scale, typically the order of the nozzle diameter; δ_L is the laminar flame thickness, near 0.5 mm at 1 atm. Below Ka = 1 the laminar structure survives; from 1 to 100 the smallest eddies thicken the preheat zone; above 100 the reaction layer itself breaks up.
The expression assumes homogeneous isotropic turbulence with a fully developed Kolmogorov cascade. At low turbulent Reynolds number, close to a wall or inside a recirculation bubble, the value it returns is a rough estimate at best. It carries no information about Lewis number, curvature-induced stretch or heat loss, which happen to be exactly the effects that govern extinction around Ka = 1. Units deserve the same attention: ℓ_t and δ_L must share one unit, since mixing millimetres with metres divides Ka by 31.6, the square root of a thousand.
Frequently asked questions
What does the Ka = 3.536 shown on page load mean?
Can I enter the integral scale in millimetres and the thickness in metres?
Which entries does the calculator reject, and what shows up then?
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