Brake Horsepower Calculation with E20 Fuel Blend

Question

Calculate the change in brake horsepower (BHP) generated by a 250 cc single-cylinder engine if a mix of 20% ethanol (E20) is added to the fuel. Assume standardized values for unknowns, such as fuel density, lower heating value (LHV), and brake thermal efficiency (BTE). Compare the BHP generated using pure gasoline and the E20 blend.

Solution

1. Key Assumptions and Standardized Values:

• Displacement: 250 cc single-cylinder engine.
• Fuel blend: 80% gasoline and 20% ethanol by volume (E20).
• Compression ratio: \( r = 9:1 \) (assumed).
• Brake Thermal Efficiency (BTE): 30% for gasoline, 32% for E20 blend.
• Lower Heating Value (LHV):
  • Gasoline: 44 MJ/kg
  • Ethanol: 26.8 MJ/kg
• Fuel density:
  • Gasoline: 0.74 kg/L
  • Ethanol: 0.789 kg/L

2. Brake Horsepower Formula

The brake horsepower \( \text{BHP} \) is proportional to the brake thermal efficiency \( \eta_b \), the mass flow rate of fuel \( \dot{m_f} \), and the lower heating value \( LHV \) of the fuel:

\[ \text{BHP} \propto \eta_b \cdot \dot{m_f} \cdot LHV \]

For simplicity, we focus on the relative difference in BHP between pure gasoline and the E20 blend.

3. Energy Content of the E20 Blend

The lower heating value (LHV) of the E20 blend is calculated by taking a weighted average of gasoline and ethanol:

\[ LHV_{\text{E20}} = 0.80 \times 44 + 0.20 \times 26.8 = 40.16 \, \text{MJ/kg} \]

The energy content of the E20 blend is about 91.27% of the energy content of pure gasoline.

4. Change in Brake Thermal Efficiency (BTE)

Ethanol has a higher octane rating than gasoline, which improves combustion efficiency. We assume that the BTE increases from 30% for gasoline to 32% for the E20 blend:

\[ \eta_b(\text{E20}) = 0.32, \quad \eta_b(\text{Gasoline}) = 0.30 \]

This represents a 6.67% increase in thermal efficiency.

5. Calculating the Change in Brake Horsepower

The change in BHP when using E20 compared to gasoline is proportional to both the energy content of the fuel and the brake thermal efficiency:

\[ \frac{\text{BHP}_{\text{E20}}}{\text{BHP}_{\text{Gasoline}}} = \frac{\eta_b(\text{E20}) \cdot LHV_{\text{E20}}}{\eta_b(\text{Gasoline}) \cdot LHV_{\text{Gasoline}}} \]

Substituting the values:

\[ \frac{\text{BHP}_{\text{E20}}}{\text{BHP}_{\text{Gasoline}}} = \frac{0.32 \cdot 40.16}{0.30 \cdot 44} = \frac{12.8512}{13.2} \approx 0.973 \]

Therefore, the BHP with the E20 blend is approximately 97.3% of the BHP generated with pure gasoline.

6. Conclusion

The BHP generated by a 250 cc single-cylinder engine using an E20 blend is approximately 97.3% of the BHP generated using pure gasoline. This corresponds to a **2.7% decrease in BHP** due to the lower energy content of ethanol, despite a slight improvement in thermal efficiency.