Lambda (λ)
Lambda (λ) represents the air-fuel ratio in combustion engines relative to the stoichiometric ideal. Calculated as \( \lambda = \frac{\text{Actual Air-Fuel Ratio}}{\text{Stoichiometric Ratio}} \), this dimensionless value is critical for engine management and emissions control.
Stoichiometric Principle
The optimal λ value is 1.0 (14.7:1 air-fuel mass ratio for gasoline), where all fuel completely burns with available oxygen. This balance maximizes catalytic converter (CAT) efficiency while minimizing emissions.
Petrol vs. Diesel Optimization
Fundamental differences in combustion create distinct lambda requirements:
| Engine Type | Optimal λ | Operating Principle | Key Constraints |
| ————- | —————– | ———————————– | ——————————— |
| Petrol | 1.0 (precisely) | Stoichiometric combustion | Three-way catalyst efficiency |
| Diesel | 1.4 - 4.0 | Always lean (excess air) | Soot formation limits |
Petrol Engines:
- Require precise λ=1.0 for three-way catalysts to simultaneously reduce NOx, CO, and HC
- Temporary rich operation (λ≈0.8-0.9) only during high load for knock protection
- Lean operation (λ>1) limited to specific low-load conditions
Diesel Engines:
- Minimum λ≈1.4 at full load (prevents visible smoke)
- Idle λ≈4.0 (maximizes air for complete combustion)
- Require complex aftertreatment (DPF+SCR) due to oxygen-rich exhaust
Measurement & Control
Modern engines use wideband oxygen sensors for real-time λ monitoring. The engine control-unit adjust fuel delivery up to 100 times/second to maintain target lambda based on:
- Engine temperature
- Load demands
- Emissions requirements
- Aftertreatment status
Application Examples
* Petrol cold start: λ≈0.9 (rich for catalyst heating) * Diesel regeneration: λ<1.5 temporarily (raises exhaust temperature) * Hybrid engines: λ>1.0 during electric-assist phases
Lambda management remains critical for meeting Euro 7/ULEV standards, with petrol-diesel differences driving distinct emission control strategies.
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