The Brayton cycle is a thermodynamic process used in gas turbine engines, commonly found in

jet aircraft. It involves four stages: isentropic compression, constant-pressure heat addition,
isentropic expansion, and constant-pressure heat rejection to produce thrust, as shown in Figure
1.

Brayton cycle

constant- constant-
isentropic isentropic
pressure heat pressure heat
compression expansion
addition rejection

Figure 1 Brayton cycle stages

Gas turbine engine components are meticulously designed to align with the thermodynamic
processes outlined in the Brayton cycle, ensuring efficient and continuous energy conversion.
Figure 2 illustrates the ideal Pressure–Volume (P–V) diagram of the Brayton cycle, which
effectively represents the key stages of the process. This diagram provides a clear visualization
of how pressure and volume interact throughout the cycle, aiding in the assessment and
optimization of engine performance parameters.

K r

H
C

Figure 2 Turbojet engine and its Brayton cycle ideal pressure-volume

diagram
For instance, in the Concorde aircraft, flying at 2,200 km/h, the pressure within the air intake
rises by a factor of nine, matching the pressure ratio achieved by the compressor itself. At even
greater velocities, the pressure increase generated solely by the air intake can exceed that
produced by the compressor, highlighting the important role of aerodynamic compression in
high-speed propulsion systems

The Brayton cycle begins with isentropic compression from point 1 to 2, as shown in the P–V
diagram. Atmospheric air is drawn into the engine and compressed adiabatically by the
compressor, increasing its pressure and temperature without heat transfer. This work, supplied by
the turbines via a shaft, prepares the air for combustion. The area under curve 1–2 represents the
required compression work. Also, higher pressure ratio (P2/P1) improves cycle efficiency by
increasing the average temperature during heat addition at constant pressure. At supersonic
speeds, the dynamic compression of incoming air significantly contributes to the overall pressure
within the engine system.

During the constant-pressure heat addition phase (2–3), compressed air enters the combustion
chamber, where it mixes with fuel and undergoes combustion. This isobaric process, shown in
Figure 2, raises the temperature of the air–fuel mixture without altering pressure. The heat input
transforms the fuel’s chemical energy into thermal energy, generating high-energy gases essential
for propulsion. Given the low fuel-to-air mass ratio (~1:50), the combustion products are
typically neglected in ideal Brayton cycle analysis for preliminary thermodynamic performance
evaluation.

Following combustion, the high-temperature, high-pressure gases undergo isentropic expansion

from point 3 to 4. This expansion occurs through the turbine and nozzle (or power turbine),
decreasing pressure and temperature while increasing volume and thermal efficiency represented

where the absolute temperatures 𝑇3 and 𝑇4 correspond to the thermodynamic

T4
by η Β=1−
T3
states at points 3 and 4, respectively, as illustrated in Figure 2. The work extracted from 3–3′,
denoted as 𝑊33, ideally equals the compressor work 𝑊12. The remaining energy, 𝑊3′4 which
represent useful work Wnet , is available for thrust or shaft power and it given by following
relation.

1
Wnet=ηΤ . cρ. T 3 (1− 1
)
k−
k
r

cp
Where ηT is the thermal (adiabatic) efficiencies of the turbine, K specific heat ratio = , cp and
cv
cv are specific heat capacity at constant pressure and volume respectively.

The Brayton cycle concludes with a constant-pressure heat rejection phase (4–1), where exhaust
gases are expelled to the atmosphere. This process converts unused thermal energy into kinetic
energy, propelling the aircraft according to Newton’s third law. In most aviation applications, the
cycle operates in an open mode, drawing atmospheric air at point 1 and discharging it at point 4.
This continuous cycle enables efficient propulsion by extracting mechanical energy and
converting residual heat into useful thrust.

At supersonic speeds, the dynamic compression of incoming air significantly contributes to the
overall pressure within the engine system. For instance, in the Concorde aircraft, flying at 2,200
km/h, the pressure within the air intake rises by a factor of nine, matching the pressure ratio
achieved by the compressor itself. At even greater velocities, the pressure increase generated
solely by the air intake can exceed that produced by the compressor, highlighting the important
role of aerodynamic compression in high-speed propulsion systems.

Otto cycle:
The Otto cycle or inertial combustion engine uses a spark to ignite a compressed air-fuel
mixture, typically gasoline or aviation gasoline, within the engine cylinder. This spark-induced
combustion rapidly releases heat energy, sharply increasing gas pressure and driving the piston
outward. The resulting expansion generates the force necessary to rotate the crankshaft, thus
converting the chemical energy of the fuel into mechanical energy, which powers the engine’s
rotary motion.

At Stage 1 of the Otto cycle, the piston is positioned at the top of its cylinder, with minimal gas
volume and near-atmospheric pressure. As the intake valve opens, the piston moves downward,
expanding the chamber volume. This draws a fresh air–fuel mixture into the cylinder at nearly
constant pressure. The intake stroke continues until the piston reaches the bottom of its travel,
after which the intake valve closes, preparing the mixture for the subsequent compression phase.

Stage 2 begins with the closing of the intake valve. The piston moves upward from Bottom Dead
Center (BDC) to Top Dead Center (TDC) (Figure 4 (b)) which represents swept volume as it
increases the engine can take in more air-fuel mixture to produce more power, compressing the
air-fuel mixture adiabatically. Gas volume decreases, pressure rises, and isentropic compression
occurs, preparing the mixture for combustion.

Stage 3 initiates combustion at constant volume when the spark ignites the compressed fuel-air
mixture near Top Dead Center (TDC). This rapid combustion significantly elevates the mixture’s
temperature and pressure without altering cylinder volume. Transitioning to Stage 4, known as
the power stroke, these high-pressure gases expand adiabatically, driving the piston downward
toward crankshaft converting thermal energy into mechanical work as shown in Figure 4 (a)
ideally there are no heat leak but in actual application it calculated by following relation.

At Stage 5, the exhaust valve opens, initiating constant-volume heat rejection, and residual heat
in the exhaust gas is expelled to the surroundings, rapidly reducing the pressure back toward
atmospheric levels. The cycle concludes with Stage 6, the exhaust stroke, as the piston ascends
once again from BDC to TDC, expelling exhaust gases at constant pressure through the open
exhaust valve. At the completion of Stage 6, cylinder conditions revert to those of Stage 1, and
the entire Otto cycle repeats to maintain continuous engine operation.

(a) (b)
Figure 4 (a) The Four-stroke Cycle. (b) TDC and BDC (Swept volume)

The turboshaft engine, in which the output power drives a helicopter rotor,
is of great importance and is virtually universally used because of its low
weight and high power. In the helicopter application, free turbine
configurations are always used. Ideally, the helicopter rotor should operate
at constant speed by changing the pitch, and the power is varied by
changing the gas-generator speed. In practice, during transient operation,
there will be· a slight change in the rotor speed and this must be minimized
by careful attention to the engine transient response and control system.
A typical free power-turbine engine has two independent counter-rotating turbines. One turbine
drives the compressor, while the other
drives the propeller through a reduction gearbox. The compressor in the basic engine consists of
three axial flow compressor stages
combined with a single centrifugal compressor stage. The axial and centrifugal stages are
assembled on the same shaft and operate as
a single unit

The turboshaft engine, in which the output power drives a helicopter rotor,
is of great importance and is virtually universally used because of its low
weight and high power. In the helicopter application, free turbine
configurations are always used. Ideally, the helicopter rotor should operate
at constant speed by changing the pitch, and the power is varied by
changing the gas-generator speed. In practice, during transient operation,
there will be· a slight change in the rotor speed and this must be minimized
by careful attention to the engine transient response and control system.
A typical free power-turbine engine has two independent counter-rotating turbines. One turbine
drives the compressor, while the other
drives the propeller through a reduction gearbox. The compressor in the basic engine consists of
three axial flow compressor stages
combined with a single centrifugal compressor stage. The axial and centrifugal stages are
assembled on the same shaft and operate as
a single unit
Inlet air enters the engine via a circular plenum near the rear of the engine and flows forward
through the successive compressor
stages. The flow is directed outward by the centrifugal compressor stage through radial diffusers
before entering the combustion
chamber, where the flow direction is actually reversed. The gases produced by combustion are
once again reversed to expand forward
through each turbine stage. After leaving the turbines, the gases are collected in a peripheral
exhaust scroll and are discharged to the
atmosphere through two exhaust ports near the front of the engine.

Reference