What is the equivalence ratio φ?

The equivalence ratio φ is the actual fuel-air ratio divided by the stoichiometric fuel-air ratio. φ = 1 is stoichiometric, φ 1 is rich with excess fuel. Automotive engines are often controlled near φ ≈ 1 for three-way catalyst performance.

How is adiabatic flame temperature calculated?

Adiabatic flame temperature can be approximated by dividing the heat of combustion by the total heat capacity of the products: ΔT = ΔH_rxn / Σ(n_i × Cp_i). Here ΔH_rxn is the reaction enthalpy, n_i is the mole amount of each product, and Cp_i is its heat capacity.

Why does CO form when φ > 1?

In a rich mixture (φ > 1), the oxygen supply is insufficient, so carbon in the fuel cannot be fully oxidized to CO₂ and can remain as carbon monoxide (CO). CO is toxic and is a key indicator of incomplete combustion.

Why is adiabatic flame temperature highest near φ = 1?

For φ 1, the fuel does not burn completely and the released heat decreases. The best balance occurs near φ ≈ 1, where the flame temperature is highest.

What is excess air ratio?

Excess air ratio describes how much air is supplied beyond the theoretical requirement. For φ = 0.8, excess air is 25% because 1/φ − 1 = 0.25. Industrial burners commonly use 10-30% excess air to balance complete combustion with NOx reduction.

How is hydrogen fuel different from other fuels?

Hydrogen (H2) has a very high heating value of about 120 MJ/kg, and its combustion product is only water (H2O), so direct CO2 emissions are zero. However, high temperatures can promote NOx formation from atmospheric N2 and O2. Its adiabatic flame temperature is around 2500 K, higher than methane.

How accurate is this simulator compared with Cantera or measurements?

This tool is an equilibrium and stoichiometric approximation. Unlike detailed reaction mechanisms such as Cantera, it does not account for dissociation or thermal NOx, so high-temperature accuracy above about 2000 K is typically within roughly ±10-15%. Use it for concept learning and early design estimates.

Combustion Calculator — Equivalence Ratio, Adiabatic Flame Temperature

Parameters

Fuel type

T_in

Stoichiometric mixture (φ = 1.00)

Results

AFR

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T_ad (K)

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CO2 (kg/kg)

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Excess air (%)

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Product Mole Fraction vs Equivalence Ratio φ

Flame Visualization — Combustion State vs Equivalence Ratio

Move the φ slider to see the flame color and height change. Blue flame (lean) → orange/yellow (stoich) → red/smoky (rich).

Adiabatic Flame Temperature T_ad vs φ (4 Fuel Comparison)

Theory & Key Formulas

$$\phi = \frac{(F/A)_{\rm actual}}{(F/A)_{\rm stoich}}$$

Equivalence ratio $\phi$: the actual fuel/air ratio relative to the stoichiometric ratio. $\phi<1$ is lean, $\phi>1$ is rich.

$$T_{ad} = T_u + \frac{\Delta H_c \cdot Y_f}{c_p}$$

Adiabatic flame temperature (K): $\Delta H_c$ is the heating value (J/kg), $Y_f$ is the fuel mass fraction, and $c_p$ is the constant-pressure specific heat.

$$\dot{m}_{air} = \frac{\dot{m}_{fuel}}{\phi \cdot (F/A)_{stoich}}$$

Required air mass flow rate (kg/s): obtained from $\phi$ and the stoichiometric ratio.

About the Combustion Calculator

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The term "equivalence ratio φ" sounds difficult, but what does it mean in simple terms?

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Roughly speaking, it's the "richness of the fuel-air mixture." φ=1 is exactly the theoretical amount of air needed for complete combustion. Move the slider left to 0.7, and you get a "lean mixture" with too much air. Move it right to 1.5, and you get a "rich mixture" with excess fuel. A blue flame on a gas stove indicates a lean mixture, while an orange flame signals a rich mixture or incomplete combustion.

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When I opened the "Flame Animation" tab and changed φ, the flame color changed! It's bluish when lean and turns red when rich. Is this the same as a real flame?

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Good observation. That's exactly how real flames behave. A lean mixture (φ<1) has plenty of oxygen and tends to burn completely, producing a blue flame—this is the ideal state. Conversely, try increasing φ to around 1.2 or higher. The flame turns red, and a smoky haze appears at the top of the screen. This represents soot and carbon monoxide generated by incomplete combustion.

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In the "Product Composition" tab graph, CO suddenly increases after φ=1. Why does CO appear at this point?

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Because oxygen becomes insufficient. Taking methane as an example, complete combustion of CH4 requires 2 moles of O2. At φ=1, the oxygen is just enough. When φ>1, the supplied O2 is insufficient, so some carbon doesn't fully oxidize to CO2 and stops at CO (carbon monoxide). The CO curve in the graph starts to rise sharply at φ=1—that's exactly the "critical point of oxygen deficiency."

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Looking at the "T_ad vs φ Curve" tab, the peak adiabatic flame temperature is around φ≈1.0 to 1.1. Why is that?

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On the lean side (φ<1), excess air gets in the way, and the combustion heat is used to warm up the extra air. On the rich side (φ>1), the fuel doesn't burn completely, so the heat release decreases. The balance between these two occurs near φ≈1. In practice, for gas turbines and industrial furnaces, this peak temperature point is compared with the material's heat resistance limit to determine the operating point.

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When I switch to hydrogen (H2), the T_ad curve becomes higher than for other fuels. CO2 is also zero. Is hydrogen fuel the best?

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In terms of zero CO2 emissions, it's certainly clean. But there are drawbacks. The high adiabatic flame temperature (over about 2500K) means that N2 and O2 in the air readily react to produce large amounts of NOx (nitrogen oxides), which cause air pollution. So NOx countermeasures are needed, such as lean combustion at low φ or mixing in steam to lower the temperature. It's not "the best"—there are trade-offs.

Physical Model and Equations

Stoichiometric complete combustion reaction for methane (CH₄)

$$\mathrm{CH_4 + 2\left(O_2 + 3.76\,N_2\right) \rightarrow CO_2 + 2\,H_2O + 7.52\,N_2}$$

Introducing the equivalence ratio φ makes the actual oxygen amount in the reactants $1/\phi$ times the stoichiometric amount:

$$\mathrm{CH_4 + \frac{2}{\phi}\left(O_2 + 3.76\,N_2\right) \rightarrow \sum_i n_i\,\text{Product}_i}$$

For φ < 1 (lean), residual O2 remains in the products; for φ > 1 (rich), CO and unburned H2 can appear.

Adiabatic flame temperature enthalpy balance

$$\sum_{\text{reactants}} n_i \left[\Delta H_{f,i}^\circ + \int_{T_\text{ref}}^{T_\text{in}} C_{p,i}(T)\,dT\right] = \sum_{\text{products}} n_j \left[\Delta H_{f,j}^\circ + \int_{T_\text{ref}}^{T_\text{ad}} C_{p,j}(T)\,dT\right]$$

$n_i, n_j$: moles of reactants and products | $\Delta H_f^\circ$: standard enthalpy of formation
$C_p(T)$: temperature-dependent constant-pressure heat capacity | $T_\text{ad}$: adiabatic flame temperature (unknown)
This tool calculates with a constant heat-capacity approximation ($C_p = \text{const}$): $$\Delta T \approx \frac{\Delta H_\text{rxn}}{\sum_j n_j C_{p,j}}$$

Frequently Asked Questions

In automobiles, the O2 sensor (λ sensor) in the exhaust gas measures the residual oxygen in the exhaust and calculates φ (more precisely, λ = 1/φ) in real time. In combustion research, the mass flow rates of fuel and air are accurately measured to obtain $\phi = (m_f/m_a)/(m_f/m_a)_\text{stoich}$.

This is because an ideal condition with zero heat loss to the outside is assumed. In actual combustors, heat dissipation to the walls, thermal radiation, and incomplete mixing cause the actual flame temperature to be lower than T_ad. T_ad is the theoretical maximum temperature and is used as a reference value for safety margins in material heat resistance design.

In actual combustors, due to non-uniform mixing of fuel and air, CO is generated somewhere even at the stoichiometric air-fuel ratio (φ=1). Adding 10–30% excess air prevents incomplete combustion. However, too much excess air increases exhaust gas losses and also increases NOx (since NOx is generated even in lean mixtures at high-temperature regions), so a balance is important.

CO2 emissions depend on the carbon content of the fuel. Looking at the simulator's "CO2 (kg/kg)", methane (CH4) is the smallest and octane is the largest. Propane (C3H8), the main component of LPG, produces less CO2 than gasoline and is used as a clean fuel in urban areas. However, it is also necessary to compare CO2 per unit of heating value (carbon intensity).

This tool uses a stoichiometric equilibrium approximation and treats specific heat as constant. In actual combustion, dissociation reactions such as CO⇌CO2, NO/NO2 formation, and the temperature dependence of Cp are neglected, so there is an error of about ±10–15% in the high-temperature range above 2000 K. It is sufficient for educational purposes and trend understanding, but for design values, detailed reaction calculations such as Cantera are recommended.

EGR (Exhaust Gas Recirculation) is a technology that reduces NOx by lowering the combustion temperature by mixing a portion of the exhaust gas into the intake air. This tool does not have a direct function to set the EGR rate, but the effect of EGR can be partially simulated by lowering the effective equivalence ratio (reducing φ) or increasing the inlet temperature T_in.

What is Combustion Calculator?

Combustion Calculator is a fundamental topic in engineering and applied physics. This interactive simulator lets you explore the key behaviors and relationships by directly manipulating parameters and observing real-time results.

By combining numerical computation with visual feedback, the simulator bridges the gap between abstract theory and physical intuition — making it an effective learning tool for students and a rapid-verification tool for practicing engineers.

Real-World Applications

Engineering Design: The concepts behind Combustion Calculator are applied across mechanical, structural, electrical, and fluid engineering disciplines. This tool provides a quick way to estimate design parameters and sensitivity before committing to full CAE analysis.

Education & Research: Widely used in engineering curricula to connect theory with numerical computation. Also serves as a first-pass validation tool in research settings.

CAE Workflow Integration: Before running finite element (FEM) or computational fluid dynamics (CFD) simulations, engineers use simplified models like this to establish physical scale, identify dominant parameters, and define realistic boundary conditions.

Common Misconceptions and Points of Caution

Model assumptions: The mathematical model used here relies on simplifying assumptions such as linearity, homogeneity, and isotropy. Always verify that your real system satisfies these assumptions before applying results directly to design decisions.

Units and scale: Many calculation errors arise from unit conversion mistakes or order-of-magnitude errors. Pay close attention to the units shown next to each parameter input.

Validating results: Always sanity-check simulator output against physical intuition or hand calculations. If a result seems unexpected, review your input parameters or verify with an independent method.

🎬 Watch it in motion