How the Flame Temperature Calculator Works

The theoretical flame temperature refers to the maximum temperature that can be achieved when a fuel reacts with an oxidizer (usually oxygen) in an ideal, adiabatic combustion process. This calculator estimates the flame temperature for a mixture of gases, such as carbon monoxide (CO) and nitrogen (N2), based on the composition of the gas and excess air.

Inputs:

CO Percentage (%): Enter the percentage of carbon monoxide (CO) in the fuel mixture.

N2 Percentage (%): Enter the percentage of nitrogen (N2) in the fuel mixture. This value should be complementary to the CO percentage and typically adds up to 100% for a binary mixture.

Excess Air (%): Enter the percentage of excess air used for combustion. A typical value is often 100% or more, where 100% excess air represents the theoretical amount of oxygen needed for complete combustion, and higher values indicate additional oxygen to ensure complete reaction.

How to Calculate the Theoretical Flame Temperature:

The calculator uses the principles of combustion and heat balance to estimate the theoretical flame temperature. The general approach involves calculating the heat of reaction for the combustion of carbon monoxide (CO) with oxygen (O₂), considering the amount of excess air provided, and the specific heat capacities of the products (CO₂, O₂, and N₂).

The combustion reaction can be written as:

    CO + 1/2 O₂ → CO₂

The heat of reaction is calculated using the following equation:

    ΔH_reaction = ΔH_f°(CO₂) - ΔH_f°(CO)

Where:

ΔH_f°(CO₂) is the heat of formation of CO₂ (-94052 cal/gmol)
ΔH_f°(CO) is the heat of formation of CO (-26412 cal/gmol)

The total heat released is then calculated by multiplying the heat of reaction by the fraction of CO in the mixture. This heat will raise the temperature of the product stream. The product stream consists of CO₂, O₂, and N₂, and the heat capacity of the products is used to calculate the resulting temperature.

The final flame temperature is determined by balancing the heat liberated and the heat absorbed by the product gases using the equation:

    ΔH = Σ(Cp_i * m_i * ΔT)

Where:

Cp_i is the specific heat capacity of each species in the product stream
m_i is the molar amount of each species
ΔT is the temperature rise of the products from their initial temperature (usually 25°C)

The temperature rise is calculated as:

    ΔT = (ΔH_reaction × fraction of CO) / Σ(Cp_i * m_i)

The result is then displayed as the theoretical adiabatic flame temperature.

Why Use Our Theoretical Flame Temperature Calculator?

Our Theoretical Flame Temperature Calculator offers several benefits:

Accurate Results: Provides precise flame temperature estimates based on combustion chemistry principles.
Easy to Use: A simple interface that requires minimal input to generate accurate results.
Instant Calculations: Get the flame temperature in real-time with just a few clicks.

Examples of Flame Temperature Calculations

Here are some examples of how our calculator can be used to estimate the theoretical flame temperature:

Example 1: CO and N₂ with 150% Excess Air

For a mixture of 20% CO and 80% N₂ with 150% excess air, the flame temperature is calculated as follows:

1. The combustion reaction for CO is:
   CO + 1/2 O₂ → CO₂

2. Heat of reaction:
   ΔH_reaction = ΔH_f°(CO₂) - ΔH_f°(CO) = -94052 - (-26412) = 67640 cal/gmol

3. Total heat liberated from 1 mole of the gas mixture:
   Heat Liberated = 67640 × 0.2 = 13528 cal

4. Composition of the product stream:
   - CO₂ produced = 0.2 moles
   - O₂ required = 0.1 moles
   - O₂ with excess air = 0.25 moles
   - N₂ with excess air = 0.9405 moles
   - O₂ leaving = 0.15 moles
   - N₂ leaving = 1.7405 moles

5. Adiabatic temperature calculation:
   Total heat capacity = 16.73 cal/°C
   Temperature rise = 13528 / 16.73 = 808.8°C

6. Final flame temperature:
   Flame Temperature = 808.8 + 25 = 833.8°C

Example 2: CO and N₂ with 200% Excess Air

For a mixture of 25% CO and 75% N₂ with 200% excess air, the flame temperature is calculated as follows:

1. The combustion reaction for CO is:
   CO + 1/2 O₂ → CO₂

2. Heat of reaction:
   ΔH_reaction = ΔH_f°(CO₂) - ΔH_f°(CO) = -94052 - (-26412) = 67640 cal/gmol

3. Total heat liberated from 1 mole of the gas mixture:
   Heat Liberated = 67640 × 0.25 = 16910 cal

4. Composition of the product stream:
   - CO₂ produced = 0.25 moles
   - O₂ required = 0.125 moles
   - O₂ with excess air = 0.375 moles
   - N₂ with excess air = 1.4643 moles
   - O₂ leaving = 0.25 moles
   - N₂ leaving = 1.7143 moles

5. Adiabatic temperature calculation:
   Total heat capacity = 20.14 cal/°C
   Temperature rise = 16910 / 20.14 = 839.6°C

6. Final flame temperature:
   Flame Temperature = 839.6 + 25 = 864.6°C