š„ Brayton Cycle Calculator
Analyze gas turbine power plants. Evaluate thermal efficiency and work output with regeneration, reheating, and intercooling options.
š Configuration
Brayton Cycle Analysis:
ā¢ Compressor Work: W_c = Cp * (T_exit - T_in)
ā¢ Turbine Work: W_t = Cp * (T_in - T_exit)
ā¢ Net Power: P_net = į¹ * (W_t - W_c)
ā¢ Regenerator: heats compressor exit air with turbine exhaust.
ā¢ Intercooling/Reheating: utilizes multiple stages to reduce compressor input / increase turbine output.
Assumptions: Air standard ideal gas properties ($Cp = 1.005$ kJ/kgĀ·K, $k = 1.4$).
ā¢ Compressor Work: W_c = Cp * (T_exit - T_in)
ā¢ Turbine Work: W_t = Cp * (T_in - T_exit)
ā¢ Net Power: P_net = į¹ * (W_t - W_c)
ā¢ Regenerator: heats compressor exit air with turbine exhaust.
ā¢ Intercooling/Reheating: utilizes multiple stages to reduce compressor input / increase turbine output.
Assumptions: Air standard ideal gas properties ($Cp = 1.005$ kJ/kgĀ·K, $k = 1.4$).
š Results & Visualization
Configure inputs and click Analyze to view Brayton cycle performance.
š Calculation Methodology
Mathematical Model & Theory
The Brayton cycle is the air-standard model for gas turbine engines. The cycle includes stages of compression, heating, expansion, and regeneration:
$$\eta_{th} = \frac{W_{net}}{Q_{in}} = \frac{W_t - W_c}{Q_{in}}$$
$$\varepsilon_{regen} = \frac{T_{regen,exit} - T_{comp,exit}}{T_{turb,exit} - T_{comp,exit}}$$
Worked Engineering Example
Problem Statement:
An air-standard Brayton cycle operates at a pressure ratio $r_p = 8$. Compressor inlet is at 300 K and turbine inlet is at 1300 K. Find the ideal thermal efficiency.
Step-by-step Solution:
1. Apply cold air-standard efficiency formula ($\gamma = 1.4$):
$$\eta_{th} = 1 - \frac{1}{r_p^{(\gamma - 1)/\gamma}}$$ $$\eta_{th} = 1 - \frac{1}{8^{(1.4-1)/1.4}} = 1 - \frac{1}{8^{0.2857}} = 1 - 0.552 = 0.448 \quad (44.8\%)$$
Final Result:
Thermal efficiency is 44.8%.
An air-standard Brayton cycle operates at a pressure ratio $r_p = 8$. Compressor inlet is at 300 K and turbine inlet is at 1300 K. Find the ideal thermal efficiency.
Step-by-step Solution:
1. Apply cold air-standard efficiency formula ($\gamma = 1.4$):
$$\eta_{th} = 1 - \frac{1}{r_p^{(\gamma - 1)/\gamma}}$$ $$\eta_{th} = 1 - \frac{1}{8^{(1.4-1)/1.4}} = 1 - \frac{1}{8^{0.2857}} = 1 - 0.552 = 0.448 \quad (44.8\%)$$
Final Result:
Thermal efficiency is 44.8%.