Brayton Cycle

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The Brayton cycle is the fundamental thermodynamic cycle for gas turbine engines used in aircraft propulsion. It describes how air is compressed, heated, expanded, and exhausted to produce work and thrust. Understanding the Brayton cycle is essential for analyzing engine performance, efficiency, and design.

1. Overview of the Brayton Cycle

The ideal Brayton cycle consists of four processes:

  1. Isentropic Compression in the compressor
  2. Constant Pressure Heat Addition in the combustor
  3. Isentropic Expansion in the turbine
  4. Constant Pressure Heat Rejection (in open-cycle engines, exhaust to atmosphere)

In aircraft engines, the cycle is open: air enters from the atmosphere and exhaust gases are expelled after expansion.

2. T-s Diagram of the Brayton Cycle

The Temperature–Entropy (T–s) diagram illustrates the cycle:

1–2: Isentropic compression (vertical line upward)
2–3: Constant pressure heat addition (horizontal right)
3–4: Isentropic expansion (vertical downward)
4–1: Constant pressure heat rejection (horizontal left)

The area within the loop represents net work output.

3. Pressure-Volume (p-V) Representation

Although less common for gases, a p-V diagram for Brayton cycle shows:

  • Compression: volume decreases, pressure increases
  • Heat addition: volume increases at constant pressure
  • Expansion: volume increases, pressure decreases
  • Heat rejection: volume decreases at constant pressure

For practical design, the T–s diagram is preferred because it directly shows temperature and entropy changes, which correlate with efficiency and work.

4. Ideal Brayton Cycle Analysis

For an ideal gas with constant specific heats:

  • Compressor work input:

w_c = c_p (T_2 - T_1)

  • Turbine work output:

w_t = c_p (T_3 - T_4)

  • Net work output:

w_{net} = w_t - w_c

  • Heat added in combustor:

q_{in} = c_p (T_3 - T_2)

  • Thermal efficiency:

\eta_{thermal} = \frac{w_{net}}{q_{in}}

5. Thermal Efficiency of the Ideal Brayton Cycle

Thermal efficiency depends on pressure ratio (r_c = \frac{p_2}{p_1}):

\eta_{thermal} = 1 - \frac{1}{r_c^{(\gamma - 1)/\gamma}}

Where:

  • \gamma = \frac{c_p}{c_v} (specific heat ratio)

Key insight:

  • Higher pressure ratios increase thermal efficiency.
  • However, increasing pressure ratio requires stronger, heavier, and more expensive compressors.

6. Real Brayton Cycle Considerations

Real engines deviate from the ideal cycle due to:

  • Compressor and turbine inefficiencies (isentropic efficiencies < 100%)

\eta_{c} = \frac{\text{Isentropic work}}{\text{Actual work}}

\eta_{t} = \frac{\text{Actual work}}{\text{Isentropic work}}

Pressure losses in the combustor

Non-ideal heat addition (variable specific heats)

These losses reduce overall efficiency and net work output.

7. Open vs. Closed Brayton Cycle

  • Closed cycle: Working fluid recirculates in a sealed system; used in some power plants.
  • Open cycle (air-breathing): Air enters from the atmosphere, fuel is burned, exhaust is expelled. All aircraft gas turbine engines operate on an open Brayton cycle.

8. Regeneration and Intercooling (Advanced Variations)

To improve efficiency:

  • Regeneration: Recovers heat from exhaust to preheat compressed air before combustion.
    • Reduces fuel required for same turbine inlet temperature.
  • Intercooling: Cools air between compression stages.
    • Reduces compressor work.
  • Reheating: Adds heat between turbine stages.
    • Increases work output.

These modifications aim to improve thermal efficiency, especially for stationary power-generation turbines. In aircraft, weight and complexity often limit their use.

9. Application in Aircraft Engines

In aircraft propulsion:

  • Compressor: Increases pressure and temperature of incoming air.
  • Combustor: Adds heat at nearly constant pressure (via fuel combustion).
  • Turbine: Extracts work to drive the compressor and other accessories.
  • Nozzle: Converts remaining thermal energy into jet velocity (thrust).

The Brayton cycle explains how these components interact thermodynamically.

10. Importance for Engine Design

  • Thermal efficiency sets limits on fuel economy.
  • Pressure ratio and turbine inlet temperature are key design drivers.
  • Cycle analysis guides decisions about materials, cooling, and performance targets.

Understanding the Brayton cycle allows engineers to optimize engines for maximum efficiency, thrust, and reliability across flight conditions.

The Brayton cycle is the core thermodynamic model for analyzing and designing jet engines, turboprops, and turbofans. Mastery of this cycle is essential for anyone studying aircraft propulsion.

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