Training Combustion Engineering — Stoichiometry, Thermochemistry & Emissions Adiabatic Flame Temperature & Zeldovich NOx Kinetics
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Adiabatic Flame Temperature & Zeldovich NOx Kinetics

60 min Combustion Engineering — Stoichiometry, Thermochemistry & Emissions

Adiabatic Flame Temperature & Zeldovich NOx Kinetics

The adiabatic flame temperature $T_{ad}$ is the maximum temperature achievable when all combustion heat is absorbed by the product gases. It is the single most important parameter governing both thermal efficiency and thermal NOx formation, which follows an Arrhenius exponential in $T_{ad}$. Reducing $T_{ad}$ by just 100 K can cut NOx by 50–80%.

1. First-Law Energy Balance for Adiabatic Combustion

At constant pressure, with no heat loss ($Q = 0$) and no work ($W = 0$):

$$H_{reactants}(T_0) = H_{products}(T_{ad})$$

Expanding: $\sum_i n_i [\Delta h_{f,i}° + \bar{h}(T_0) - \bar{h}(298)] = \sum_j n_j [\Delta h_{f,j}° + \bar{h}(T_{ad}) - \bar{h}(298)]$

In practice, the lower heating value (LHV) of the fuel equals the sensible enthalpy rise of the products:

$$LHV = \sum_j n_j \int_{T_0}^{T_{ad}} c_{p,j}(T)\,dT$$

Approximate constant-$c_p$ solution: $T_{ad} \approx T_0 + LHV / (n_{prod} \bar{c}_p)$. Exact solutions require iteration using JANAF polynomial $c_p(T)$ tables or software (Cantera, CEA).

2. Effect of Excess Air on T_ad

At stoichiometric ($\phi = 1$): $T_{ad,CH_4} \approx 2227$ K, $T_{ad,C_8H_{18}} \approx 2277$ K, $T_{ad,H_2} \approx 2480$ K (all from 298 K preheat). Adding excess air dilutes the products and increases $n_{prod}$ while $LHV$ per unit fuel remains constant:

$$T_{ad}(\lambda) \approx T_0 + \frac{LHV}{\lambda \cdot n_{prod,st} \bar{c}_p} = T_0 + \frac{T_{ad,st} - T_0}{\lambda}$$

At $\lambda = 1.5$, $T_{ad}$ drops by roughly 400–600 K, dramatically reducing NOx.

3. Extended Zeldovich Mechanism — Thermal NOx

The dominant high-temperature NOx formation pathway:

$$\text{R1: } O + N_2 \to NO + N \quad k_1 = 1.8\times10^8 e^{-38370/T}$$

$$\text{R2: } N + O_2 \to NO + O \quad k_2 = 1.8\times10^4 T\,e^{-4680/T}$$

$$\text{R3: } N + OH \to NO + H \quad k_3 = 7.1\times10^{10}$$

The NO formation rate is dominated by R1 due to its high activation energy ($E_a/R = 38370$ K):

$$\frac{d[NO]}{dt} \approx 2k_1[O][N_2]$$

Since $[O]^{1/2} \propto [O_2]^{1/2}$ (partial equilibrium) and $[O] \propto e^{-27550/T}$ (O-atom equilibrium), the NOx formation rate is extremely sensitive to $T_{ad}$: a 100 K increase in $T_{ad}$ roughly doubles NOx.

4. Low-NOx Combustion Strategies

Based on kinetics, effective NOx reduction strategies:

  • Lean premixed combustion: premix fuel-air at $\phi \approx 0.55{-}0.75$ to lower $T_{ad}$ below 1800 K, suppressing thermal NOx
  • Flue gas recirculation (FGR): dilute reactants with 15–30% recirculated flue gas; reduces O₂ concentration and $T_{ad}$
  • Staged combustion: rich primary zone ($\phi > 1$) followed by lean secondary zone; NOx formed in rich zone is reduced by fuel-N chemistry
  • Selective catalytic reduction (SCR): post-combustion injection of NH₃ or urea with a $V_2O_5$/$TiO_2$ catalyst; $4NO + 4NH_3 + O_2 \to 4N_2 + 6H_2O$, 85–95% NOx removal
Worked Example — Approximate T_ad for Methane at φ=0.8

$LHV_{CH_4} = 802.3$ kJ/mol. At $\phi = 0.8$, $\lambda = 1.25$. Products (per mol CH₄): 1 CO₂, 2 H₂O, 0.5 O₂, 9.4 N₂. Total moles = 12.9. Mean $c_p \approx 35$ J/mol·K. $\Delta T = 802300 / (12.9 \times 35) = 802300 / 451.5 = 1777$ K. $T_{ad} \approx 298 + 1777 = 2075$ K. (Exact CEA value: ≈ 2050 K — close agreement. ✓)

Adiabatic Flame Temperature & NOx Estimator
T_ad =?K
T_stoichiometric =?K
NOx index (rel.) =?(1.0 = stoich)

Practice Problems

1. Calculate the adiabatic flame temperature for stoichiometric hydrogen combustion ($H_2 + \frac{1}{2}O_2 + 1.88N_2 \to H_2O + 1.88N_2$) using $LHV_{H_2} = 241.8$ kJ/mol and assuming constant $c_p = 38$ J/mol·K for the product mixture.
2. Using the approximation $d[NO]/dt \propto e^{-38370/T}$, compute the relative NOx formation rate at $T = 1900$ K vs $T = 2100$ K. Express as a ratio and comment on the sensitivity to temperature.
3. A gas turbine combustor operates at $\phi = 0.30$ (very lean) to meet 25 ppm NOx. Explain why operation must avoid local rich zones ($\phi > 1$) and how fuel-air premixing quality affects NOx emissions even at a globally lean equivalence ratio.
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