Air Standard Cycles

Air standard cycles are idealized thermodynamic cycles used to model internal combustion engines. These cycles assume air as the working fluid and apply simplifying assumptions to facilitate analysis. The most common air standard cycles include:

Otto Cycle (Spark Ignition Engines)
Diesel Cycle (Compression Ignition Engines)
Dual Cycle (Combination of Otto and Diesel)
Brayton Cycle (Gas Turbines)

Assumptions in Air Standard Analysis

Working fluid is air, modeled as an ideal gas.
All processes are internally reversible.
Combustion is replaced by heat addition from an external source.
Heat rejection simulates exhaust.
Specific heats are constant.

1. Otto Cycle

The Otto cycle consists of four processes:

1–2: Isentropic compression
2–3: Constant volume heat addition
3–4: Isentropic expansion
4–1: Constant volume heat rejection

Efficiency:

\[ \eta_{\text{Otto}} = 1 - \frac{1}{r^{\gamma - 1}} \] where \( r = \frac{V_1}{V_2} \) is the compression ratio and \( \gamma = \frac{C_p}{C_v} \) is the specific heat ratio.

2. Diesel Cycle

The Diesel cycle consists of:

1–2: Isentropic compression
2–3: Constant pressure heat addition
3–4: Isentropic expansion
4–1: Constant volume heat rejection

Efficiency:

\[ \eta_{\text{Diesel}} = 1 - \frac{1}{r^{\gamma - 1}} \cdot \left( \frac{\rho^\gamma - 1}{\gamma (\rho - 1)} \right) \] where \( \rho = \frac{V_3}{V_2} \) is the cutoff ratio.

3. Dual Cycle

The Dual cycle combines features of both Otto and Diesel cycles:

1–2: Isentropic compression
2–3: Constant volume heat addition
3–4: Constant pressure heat addition
4–5: Isentropic expansion
5–1: Constant volume heat rejection

Efficiency:

\[ \eta_{\text{Dual}} = 1 - \frac{1}{r^{\gamma - 1}} \cdot \left( \frac{\alpha \rho^\gamma - 1}{(\alpha - 1) + \gamma \alpha (\rho - 1)} \right) \] where \( \alpha = \frac{T_3}{T_2} \), and \( \rho = \frac{V_4}{V_3} \).

4. Brayton Cycle

The Brayton cycle is used for gas turbines and consists of:

1–2: Isentropic compression
2–3: Constant pressure heat addition
3–4: Isentropic expansion
4–1: Constant pressure heat rejection

Efficiency:

\[ \eta_{\text{Brayton}} = 1 - \frac{1}{r_p^{(\gamma - 1)/\gamma}} \] where \( r_p = \frac{p_2}{p_1} \) is the pressure ratio.

Comparison of Cycles

Otto cycle has higher efficiency than Diesel for same compression ratio.
Diesel cycle allows higher compression ratios due to delayed ignition.
Dual cycle offers a compromise between Otto and Diesel.
Brayton cycle is suitable for continuous flow systems like turbines.

Conclusion

Air standard cycles provide a simplified framework to analyze engine performance. While real engines deviate due to irreversibilities and complex combustion, these models offer valuable insights into thermodynamic efficiency and design trade-offs.