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Zeldovich Thermal NOx Formation Rate Calculator

Thermal NOx is generated by the high-temperature oxidation of atmospheric nitrogen inside combustion chambers.

Peak temperature in the flame or post-flame zone (typically 1900 K to 2300 K).

Combustor operating pressure in atmospheres.

Oxygen mole fraction in post-flame zone (e.g. 0.03 for 3% O2).

Nitrogen mole fraction (typically ~0.73).

Combustor high-temperature residence time.

Calculated Result
1409.2 ppmvd

Thermal NOx Concentration

NO Formation Rate

70.460 ppm/ms

Flame Temperature

2100 K (1827 °C)

Forward Rate Constant k1

2.09e+3 cm³/(mol·s)

Arrhenius Sensitivity Factor

1.16e-8

Calculation Breakdown

  1. Zeldovich Rate Limiting ReactionO + N₂ ⇄ NO + N (Ea = 319 kJ/mol)
  2. Rate of Formationd[NO]/dt = 2·k1·[O]eq·[N₂] = 70.460 ppm/ms at 16 atm
  3. Cumulative Residence Time Integration[NO] = Rate · τ = 70.460 ppm/ms · 20 ms = 1409.2 ppmvd

What Is the Zeldovich Thermal NOx Formation Rate Calculator?

The Zeldovich mechanism describes thermal NO formation through three elementary reactions: O + N2 ⇄ NO + N, N + O2 ⇄ NO + O, and N + OH ⇄ NO + H.

The initial breaking of the strong N≡N triple bond requires 319 kJ/mol, causing the rate to soar above 1800 K.

How Does the Zeldovich Thermal NOx Formation Rate Calculator Work?

Thermal NO formation rate is proportional to P^0.5, [O2]^0.5, [N2], and exp(-Ea/RT).

Because of this exponential dependence, reducing peak flame temperature by only 50 K can cut thermal NOx in half.

Zeldovich Thermal NOx Formation Rate Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

\frac{d[NO]}{dt} = 2 k_1 [O]_{eq} [N_2], \quad k_1 = 1.8 \times 10^{11} \exp\left( -\frac{38370}{T} \right) \text{ cm}^3/(\text{mol}\cdot\text{s})

Rate-limiting O + N2 -> NO + N reaction with high activation energy (319 kJ/mol).

How to Use the Zeldovich Thermal NOx Formation Rate Calculator

  1. Input flame temperature, combustor pressure, O2/N2 fractions, and residence time.
  2. Inspect the formation rate in ppm/ms and total emitted NOx in ppmvd.

Step-by-Step Example Calculation

Gas Turbine Combustor Hot Section

Input Values:

flameTemperatureKelvin:2050
combustorPressureAtm:20
oxygenMoleFraction:0.035
nitrogenMoleFraction:0.73
residenceTimeMilliseconds:15
Worked Steps: Calculates thermal NO formation rate and total ppmvd concentration.

Understanding Your Result

Dry low NOx (DLN) lean-premixed combustors target flame temperatures below 1800 K to suppress thermal NOx below 9–15 ppm.

Factors That Affect the Result

  • Higher combustor pressure and longer residence time linearly or root-square increase emissions.
  • Steam or water injection cools flame temperatures to curb thermal NOx.

When Should You Use This Calculator?

  • Gas turbine combustor design, industrial burner emission modeling, and EPA compliance engineering.

Assumptions & Limitations

  • Focuses on thermal NOx; prompt NOx (Fenimore) and fuel-bound NOx are not included in this model.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Standard chemical kinetics formulation based on GRI-Mech and NIST rate data.

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