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Brayton Cycles

This article will give you a comprehensive overview of the Brayton Cycle, by itself, with regeneration and a reheater, and present different equations for considering Brayton Cycles.
The Brayton cycle has been significant in gas turbine engines, commonly used in aircraft propulsion, power generation, and industrial applications.
Named after its creator, George Brayton, this cycle defines the operation of gas turbines that rely on the continuous airflow through the engine.

This process involves four key stages.

The Brayton cycle is efficient and has a high power output, making it essential and valuable in aviation, power plants, and various industries.

Check out our different Brayton Cycle calculators to run these calcs:
  1. Brayton Cycle
  2. Brayton Cycle with Regeneration
  3. Brayton Cycle with Reheater

Definitions

Here are some important definitions to keep in mind for Brayton cycles!

  1. Isobaric: the process takes place under constant pressure.
  2. Adiabatic: no heat is transferred, and change in internal energy is only the result of work.
  3. Isothermal: the process takes place under constant temperature.
  4. Internal Energy: the total kinetic energy in a system due to the motion of molecules and the potential energy in atoms.
  1. Isentropic: an ideal thermodynamic process that is both adiabatic (no heat transfer) and reversible, there is constant entropy.
  2. Compression: a reduction in volume.
  3. Addition: i.e. an isobaric addition, where heat may increase and be added under constant pressure.
  4. Rejection: with respect to thermodynamics, a rejection usually involves the release of heat to the surroundings during a process.

Equations Commonly Used For Brayton Cycles

The following are the variables for the equations

  1. T = the temperature. i.e. T(1) is the temperature at state 1.
  1. Q = the heat energy. i.e. Q(A) is the heat from the fuel source.
  1. V = the volume. i.e. V(1) is the volume at state 1.
  2. W = the work completed. i.e. W(C) is the work done by the compressor.
  1. r(p) is the pressure ratio
  1. r(BW) is the back wash ratio
  1. η = the efficiency of the cycle
  2. k = the adiabatic index

Brayton Cycle

Figure 1: Temperature vs Entropy Graph for a Brayton Cycle

Figure 2: Diagram of a Brayton Cycle

The typical backwash ratio lies between the range of 50% To 15% and is defined as the ratio of the power of work done in the cycle to work done by the turbine.
1-2 SC Isentropic Compression
3-4 SE Isentropic Expansion
2-3 PA Isobaric Addition
4-1 PR Isobaric Rejection

WP=mCPΔTW_P=mC_P{\Delta}T
This is the equation for the work of the power of the Brayton cycle.

WT=mCPΔTW_T=mC_P{\Delta}T
This is the equation for the work of the turbine of the Brayton cycle.

QA=mCPΔTQ_A=mC_P{\Delta}T
This is the equation for the heat energy at the input of the Brayton cycle.

T2T1=T3T4\frac{T_2}{T_1}=\frac{T_3}{T_4}
In a Brayton Cycle, the temperature ratio from state 2 to state one is the same as that from state 3 to state 4.

rBW=WCWTr_{BW}=\frac{W_C}{W_T}
The back-wash ratio for the Brayton Cycle is the ratio of the compressor work (wc) to the turbine work (wt).

η=1−1rpk−1k\eta=1-\frac{1}{r_p\frac{k-1}{k}}
The efficiency of the Brayton cycle is defined as the net work over the heat in the system, where k is the specific heat ratio.
Maximum Net Work

Px=P1P2P_x=\sqrt{P_1P_2}
If the pressure drops are equal across both turbines at the first and second stages, one can define P(x) with the above equation.

T2=T1T3T_2=\sqrt{T_1T_3}
For a Brayton Cycle, one can calculate the temperature at the second state if the temperature at the first and third states are known.

rp=(TmaxTmin)k2k−2r_p=(\frac{T_{max}}{T_{min}})^{\frac{k}{2k-2}}
This is the equation for r(p), the pressure ratio, which can alter the work output of the cycle.
Combustor Efficiency

rB=rpk−1k(T1T3)r_B=r_p^{\frac{k-1}{k}}(\frac{T_1}{T_3})

ec=QairQfuele_c=\frac{Q_{air}}{Q_{fuel}}
The combustion efficiency is defined as the heat the fuel releases into the air to the heat input by the fuel.

Use this calculator to solve these equations!

Brayton Cycle Calculator

Brayton Cycle With Regeneration

The regenerator enables the heat from the air entering the chamber to heat the compressor through a counter-flow heat exchanger, also known as a regenerator.
Figure 3: Diagram of a Brayton Cycle with a Regenerator


ηreg=T2′−T2T4−T5\eta_{reg}=\frac{T_2'-T_2}{T_4-T_5}
To allow heat transfer, the temperature of the air leaving the regenerator at state 5 must be less than the temperature at state 4. In the same way, the temperature at state 6 must be higher than the temperature at state 2.
Assumption

If not stated: T2=T5\text{If not stated:}\ T_2=T_5
The following is the effectiveness of a Brayton Cycle with regeneration.

ereg=(T4−T3)−(T2−T1)T3−T2′e_{reg}=\frac{(T_4-T_3)-(T_2-T_1)}{T_3-T_2'}

Use this calculator to solve these equations!

Brayton Cycle With Regeneration Calculator

Brayton Cycle With Regeneration

The reheating occurs by spraying additional fuel into the exhaust gases, with the intent of improving the efficiency of the cycle.
Figure 4: Diagram of a Brayton Cycle with a Reheater

The following is the effectiveness of a Brayton Cycle with a reheater.

ereg=T3−T2T7−T8e_{reg}=\frac{T_3-T_2}{T_7-T8}
Assumptions

if not stated:T2=T8\text{if\ not\ stated}: T_2=T_8

QA1=mCp(T4−T3)Q_{A1}=mC_p(T_4-T_3)
Q(A1) is the net heat transfer at the input of the turbine.

QA2=mCp(T6−T5)Q_{A2}=mC_p(T_6-T_5)
Q(A2) is the net heat transfer at the turbine's output.

WT1=mCp(T4−T5)W_{T1}=mC_p(T_4-T_5)
This is the equation of work at the input of the turbine.

WT2=mCp(T6−T7)W_{T2}=mC_p(T_6-T_7)
This is the equation of work at the output of the turbine.


Use this calculator to solve these equations!

Brayton Cycle With Reheater Calculator



Additional Resources

If you liked this, check out our other articles and resources!
  1. Check out our library of templates here.
  1. Diesel Cycle
  2. Duel Combustion Cycle
  3. Introduction to Thermodynamics
  4. Importance of Mechanical Engineering Calculation Templates
  5. Intro to Power Cycles

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References

  1. Clean Energy Systems. 2023. Reheat Combustors. [ONLINE] Available at: https://www.cleanenergysystems.com/reheat-combustors#:~:text=The%20Clean%20Energy%20Systems%20reheat,gas%20turbines%20and%20even%20beyond.. [Accessed 30 October 2023].
  2. Concordia University. 2007. Brayton cycle with regeneration. [ONLINE] Available at: https://users.encs.concordia.ca/~kadem/Brayton%20cycle%20with%20regeneration.pdf. [Accessed 30 October 2023].
  3. Engineering Software. 2023. Brayton Cycle (Power) Analysis. [ONLINE] Available at: https://www.engineering-4e.com/brayton-cycle-power-analysis. [Accessed 27 October 2023].
  4. LinkedIn. 2023. Important Thermodynamic Concepts. [ONLINE] Available at: https://www.linkedin.com/feed/update/urn:li:activity:7095576421120548864?utm_source=share&utm_medium=member_desktop. [Accessed 24 October 2023].
  5. Massachusetts Institute of Technology. 2006. 3.7 Brayton Cycle. [ONLINE] Available at: https://web.mit.edu/16.unified/www/SPRING/propulsion/notes/node27.html. [Accessed 27 October 2023].
  6. Microelectronics Heat Transfer Laboratory. 2023. Brayton Cycle. [ONLINE] Available at: http://www.mhtlab.uwaterloo.ca/courses/me354/lectures/pdffiles/web7.pdf. [Accessed 27 October 2023].
  7. Nuclear Power. 2023. Brayton Cycle with Reheat, Regeneration and Inter-cooling. [ONLINE] Available at: https://www.nuclear-power.com/nuclear-engineering/thermodynamics/thermodynamic-cycles/brayton-cycle-gas-turbine-engine/brayton-cycle-with-reheat-regeneration-and-intercooling/. [Accessed 27 October 2023].
  8. Purdue University. 2021. Notes on Thermodynamics, Fluid Mechanics, and Gas Dynamics. [ONLINE] Available at: https://engineering.purdue.edu/~wassgren/teaching/ME20000/NotesAndReading/Lec39_Reading_Wassgren.pdf. [Accessed 27 October 2023]
  9. Science Direct. 2011. Combustion Efficiency. [ONLINE] Available at: https://www.sciencedirect.com/topics/earth-and-planetary-sciences/combustion-efficiency. [Accessed 27 October 2023].
  10. Simon Fraser University. 2023. Brayton Cycle. [ONLINE] Available at: https://www.sfu.ca/~mbahrami/ENSC%20461/Notes/Brayton%20Cycle.pdf. [Accessed 27 October 2023].