Zeldovich Number
Computes the Zeldovich number of a flame, β = E_a·(T_b − T_u) ÷ (R·T_b²), the activation energy made dimensionless by the temperature rise across the flame front. It measures how sensitive the reaction rate is to a small temperature change: a high β (typically 8 to 12 for hydrocarbons) means the reaction is concentrated in a very thin layer near the flame temperature, which justifies the large-activation-energy assumption of asymptotic flame theory and the extinction and cellular-instability criteria. The universal gas constant R = 8.314 J/(mol·K) is adopted, with activation energy in J/mol and temperatures in kelvin. Enter the activation energy, the burned gas temperature and the unburned gas temperature.
Result
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Zeldovich Number: how temperature-sensitive a flame is
Anyone calibrating one-step global chemistry for a flame simulation finds out early that matching the laminar flame speed is not enough. Pick an activation energy that is too low and the simulated flame shrugs off stretch and heat loss that would kill the real one: it never blows out, and the extinction criterion behind the design turns optimistic. The Zeldovich number puts that activation energy on the dimensionless scale asymptotic flame theory actually works in, and shows at a glance whether the fit is plausible.
The formula is β = E_a·(T_b − T_u) ÷ (R·T_b²), with R fixed at 8.314 J/(mol·K), activation energy in joules per mole and both temperatures in kelvin — T_b enters squared, so slipping in degrees Celsius wrecks the answer. Global-mechanism activation energies for hydrocarbons run from 125 to 210 kJ/mol, meaning 125,000 to 210,000 in the box; T_b is the adiabatic flame temperature, 1,800 to 2,400 K; T_u is the reactant temperature, almost always 300 K. Expect β between 8 and 12. The larger it grows, the thinner the reaction zone, whose thickness scales as δ_L divided by β.
The scaling assumes a single Arrhenius reaction, which no real fuel obeys — E_a here is an effective parameter tuned to reproduce flame speed or extinction, never the barrier of an elementary step. It also assumes the reaction hugs T_b, an assumption that falls apart with strong dissociation, heavy preheat or low-temperature chemistry. Use an equilibrium adiabatic temperature rather than the ideal one: 200 K of error in T_b feeds a squared denominator. Activation energy typed in kJ/mol returns a β a thousand times too small, which at least fails loudly.
Frequently asked questions
Where do I get the activation energy to type in?
Why does the page reject a T_b at or below T_u?
Is the β = 7.885 from the default values high or low?
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.