With 3% excess air, determine the following:
a. Theoretical Air-Fuel Ratio
b. Actual Air-Fuel Ratio
c. Higher Heating Value
d. Lower Heating Value
The Correct Answer and Explanation is:
To determine the requested combustion parameters with 3% excess air, we need to start by identifying the fuel type. However, since the fuel is not specified, we’ll use methane (CH₄) as a common example fuel for explanation. If you have a different fuel in mind, let me know and I’ll tailor the calculations accordingly.
a. Theoretical Air-Fuel Ratio (AFR)
Theoretical AFR is the amount of air required to completely combust a unit mass of fuel without any excess.
Balanced combustion equation for methane: CH4+2(O2+3.76 N2)→CO2+2 H2O+7.52 N2\text{CH}_4 + 2(\text{O}_2 + 3.76\ \text{N}_2) \rightarrow \text{CO}_2 + 2\ \text{H}_2\text{O} + 7.52\ \text{N}_2
- 2 moles of O₂ are required per mole of CH₄.
- Air contains 21% O₂ by volume → 1 mole O₂ needs 10021≈4.76\frac{100}{21} ≈ 4.76 moles of air.
Thus, Theoretical AFR (molar basis): AFRtheoretical=2×4.76=9.52 moles of air per mole of CH4\text{AFR}_{\text{theoretical}} = 2 \times 4.76 = 9.52\ \text{moles of air per mole of CH}_4
b. Actual Air-Fuel Ratio (with 3% excess air)
AFRactual=AFRtheoretical×(1+excess air)\text{AFR}_{\text{actual}} = \text{AFR}_{\text{theoretical}} \times (1 + \text{excess air}) AFRactual=9.52×(1+0.03)=9.8056\text{AFR}_{\text{actual}} = 9.52 \times (1 + 0.03) = 9.8056
c. Higher Heating Value (HHV)
For methane: HHV≈55.5 MJ/kg\text{HHV} ≈ 55.5\ \text{MJ/kg}
HHV includes the latent heat of water vapor formed during combustion.
d. Lower Heating Value (LHV)
LHV excludes the latent heat of vaporization of water: LHV≈50.0 MJ/kg\text{LHV} ≈ 50.0\ \text{MJ/kg}
Explanation (300 words)
Air-Fuel Ratio (AFR) is a crucial concept in combustion, determining how much air is required to burn a specific amount of fuel. The theoretical AFR is the minimum air needed for complete combustion without leaving any unburned fuel. For methane (CH₄), complete combustion requires 2 moles of oxygen per mole of methane. Since air is only about 21% oxygen, we multiply the oxygen demand by roughly 4.76 to account for nitrogen and other components, giving a theoretical AFR of 9.52 (molar basis).
However, in real-world applications, combustion is rarely perfect. To ensure complete combustion and minimize pollutants like carbon monoxide or unburned hydrocarbons, excess air is supplied. This means the actual AFR is higher than the theoretical value. With 3% excess air, the actual AFR becomes 9.8056, just slightly higher, ensuring full combustion while avoiding too much dilution of combustion gases, which could reduce efficiency.
The Higher Heating Value (HHV) and Lower Heating Value (LHV) are measures of the energy content in fuels. HHV includes the total energy released when the water produced during combustion is condensed, recovering latent heat. LHV assumes this water remains as vapor, which is typical in many combustion systems where water vapor is not condensed. For methane, HHV is approximately 55.5 MJ/kg, while LHV is around 50.0 MJ/kg.
Understanding these concepts is vital in designing efficient combustion systems, ensuring fuel economy, minimizing emissions, and maintaining safe operating conditions in engines, boilers, and industrial furnaces.
