Simple Turbojet Cycle

Alberto Mag-aso III

Turbojet Cycle Analysis

• Allows us to determine the various thermodynamic states needed to calculate the specific thrust

T-s Diagram of an Ideal Turbojet Cycle

Given Conditions

• The inlet atmospheric pressure Pa = P1 is given

• Inlet atmospheric temperature Ta is known

• flight speed of the aircraft Ca is given

• The compressor pressure ratio P02 / P01 is known

• The turbine inlet temperature T03 is given

• The pressure at exhaust nozzle outlet matches the ambient pressure (P5 = Pa)

• The isentropic efficiencies of each component are given

Assumptions

• The kinetic energies can be neglected• Potential energy changes are negligible• Accessory loads to the engine are negligible;

power produced by the turbine = power input of the compressor

Actual Turbojet Cycle

Schematic Diagram of a Turbojet Engine

Analysis

Process a-1(isentropic compression of an ideal gas in a diffuser)

(eq. 3.1)

When the fluid is a perfect gas, cpT can be subsituted for h

(eq. 3.2)

Where: Ta = atmospheric temperature

T01 = compressor inlet temperature

Ca = inlet velocity / flight speed of the aircraft

Analysis

Process a-1(isentropic compression of an ideal gas in a diffuser)

(eq. 3.3)

Where: T’01= the temperature which would have been reached

after an isentropic compression to p01

Analysis

Process 1-2 (isentropic compression of an ideal gas in a

compressor)

(eq. 3.4)

Where: p02 / p01 is the compressor pressure ratio

p02 = is the compressor outlet pressure

p01 = is the compressor inlet pressure

(eq. 3.5)

Analysis

Process 1-2 (isentropic compression of an ideal gas in a

compressor)

(eq. 3.5)

Where: T01 = compressor inlet temperature

T02 = compressor outlet temperature

Analysis

Process 1-2 (isentropic compression of an ideal gas in a

compressor)

(eq. 3.6)

Where: ήc = compressor efficiency

Analysis

Process 2-3 (constant pressure heat addition)

(eq. 3.7)

Where: Q = heat added

T03 = turbine inlet temperature

Analysis

Process 3-4 (isentropic expansion of an ideal gas in a turbine)(eq. 3.8)

Expanding this equation we have:

(eq. 3.9)

Where: cpa = specific heat of ambient air = 1.005 kJ/kg – K

cpg = specific heat of combustion gases = 1.148 kJ/kg – K

ήm = mechanical efficiency

Wt = turbine power output

Wc= compressor power input

Analysis

Process 3-4 (isentropic expansion of an ideal gas in a turbine)

(eq. 3.10)

And turbine efficiency is:

(eq. 3.11)

Analysis

Process 3-4 (isentropic expansion of an ideal gas in a turbine)

Where: p03 = turbine inlet pressure

T03 = turbine inlet temperature

p04 = turbine outlet pressure

T04 = turbine outlet temperature

ήt = turbine efficiency

Analysis

Process 4-5 (isentropic expansion of an ideal gas in a nozzle)

(eq. 3.11)

And

(eq.3.12)

Where: T04 = turbine outlet temperature

T5 = nozzle exit temperature

C5 = Cj = nozzle exit velocity / jet velocity

Analysis

Process 4-5 (isentropic expansion of an ideal gas in a nozzle)

(eq. 3.13)

Where: F = net thrust

Ca = inlet velocity / flight speed of the aircraft

Cj = nozzle exit velocity / jet velocity

m = mass flow of air

Analysis

Process 4-5 (isentropic expansion of an ideal gas in a nozzle)

(eq. 3.14)

Where: Fs = specific thrust

m = mass flow of air

F = net thrust

Optimization of the Turbojet Cycle

• When considering the design of a turbojet, the basic thermodynamic parameters at the disposal of the designer are the turbine inlet temperature and the compressor ratio

Variation of thrust and SFC with flight conditions for a given engine• At different flight conditions, both the thrust

and SFC will vary, due to the change in air mass flow with density and the variation of momentum drag with forward speed.