Ideal Isobaric Gas System - Brayton Cycle

brayton

Process 1-2

Isentropic Compression

\( W = -m C_p \Delta T = - \Delta H_{12} \)

\( Q = 0 \)

Process 2-3

Isobaric Heat Transfer

\( W = 0 \)

\( Q = m C_p \Delta T = \Delta H_{23} \)

Process 3-4

Isentropic Expansion

\( W = -m C_p \Delta T = - \Delta H_{34} \)

\( Q = 0 \)

Process 4-1

Isobaric Heat Transfer

\( W = 0 \)

\( Q = m C_p \Delta T = \Delta H_{34} \)


Pressure Ratio

\( r_P = \frac{P_2}{P_1} = \frac{P_3}{P_4} \)


Thermal Efficiency

Kinetic energy is significant

\( \eta _{th} = \frac{W_{net} + \frac{1}{2} \dot{m} \Delta V^2}{Q_{in}} \)

Since the turbine only serves to drive the compressor:

\( W_{turb} + W_{comp} = 0 \)

\( W_{net} = 0 \)

\( \eta _{th} = \frac{\frac{1}{2} \dot{m} \Delta V^2}{Q_{in}} \)

Air Standard Efficiency

\( \eta _{th} = 1 - \frac{1}{r_P ^ {\frac{\gamma -1}{\gamma }}} \)