BASIC CYCLE FOR TURBO-JET ENGINE

The basic cycle of a turbo-jet engine in T-s diagram is shown in Fig. 17.7. The various processes are as follows:

Process 1−2: Isentropic diffusion of atmospheric air from velocity c₁ to c₂ = 0 with diffuser efficiency of 100%. 1−2′ is the actual diffusion with diffuser efficiency η_d from p₁ to p₂.

Process 2′−3: Isentropic compression of air in the compressor from p₂ to p₄. Process 2′–3′ is the actual compression with compressor efficiency η_c.

Process 3−4: Ideal heat addition at pressure p₄. Process 3′-4 is the actual heat addition at pressure p₄.

Process 4−5: Isentropic expansion of gas in the turbine from p₄ to p₃. Process 4−5′ is the actual expansion in the turbine with turbine efficiency η_t.

Process 5′−6: Isentropic expansion of gas in the nozzle from p₃ to p₁. Process 5′−6′ is the actual expansion of gas in the nozzle with nozzle efficiency η_n.

Consider 1kg of working fluid flowing through the system.

Diffuser:

The energy equation between states 1 and 2 is as follows:

In an ideal diffuser, c₂ = 0, q_1–2 = 0 and w_1–2 = 0

where c_pa = specific heat of air at constant pressure

Figure 17.7 T-s diagram for turbo-jet

Compressor:

Energy equation between state 2′ and 3:

Compressed work, 

Assuming c₃ ≃ c_2′, and q_2′–3 = 0, we have

w_c = h₃ − h_2′ = c_pa (T₃ − T_2′)

Actual compressor work, w_ca = h_3′ − h_2′

Combustion chamber:

Ideal heat supplied, q = q₃′ − ₄ = h₄ − h₃′

where c_pg = specific heat of gas at constant pressure

Turbine:

Energy equation between states 4 and 5:

If q_4-5 = 0, then

Turbine work, 

If c₄ ≃ c₅, then

now w_ta = w_ca

If c_pa = c_pg = c_p, then

 

T_5′ = T₄ − (T₄ − T₅)η_t

Jet nozzle:

Energy equation between states 5′ and 6:

Ideal case: 

Actual case: 

If c_5′ ≃ 0 as compared to c_6′, then

Thermal efficiency, 

1 Thrust

Let c_a = forward velocity of aircraft through air, m/s

= velocity of approach, assuming surrounding air velocity to be zero.

c_j = velocity of jet of gases relative to the aircraft, m/s

, mass rate of flow of products leaving the nozzle per 1kg of air.

Absolute velocity of gases leaving the aircraft = c_j − c_a

Absolute velocity of air entering the aircraft = 0

∴ Change of momentum = ṁ (c_j − c_a)

2 Thrust Power

It is defined as the rate at which work must be developed by the engine if the aircraft is to be kept moving at a constant velocity c_a against friction force or drag.

Thrust power, T.P. = forward thrust × speed of aircraft

3 Propulsive Power

The energy required to change the momentum of the mass flow of gases represents the propulsive power. It is expressed as the difference between the rate of kinetic energies of the entering air and exit gases.

4 Propulsive Efficiency

It is defined as the ratio of thrust power to propulsive power.

5 Thermal Efficiency

It is defined as the ratio of propulsive work to the energy released by the combustion of fuel.

6 Overall Efficiency

Overall efficiency, 

for η₀ to be maximum, 

 

c_j − 2c_a = 0

Therefore, for maximum overall efficiency, the aircraft velocity is one-half of the jet velocity.

7 Jet Efficiency

Jet efficiency is defined as follows:

8 Ram Air Efficiency

In Fig. 17.2(b), process 1-2′ is the ramming process during which the total energy or stagnation enthalpy remains unchanged, if the process is assumed adiabatic, while pressure of air increases. Process 1-2 is the ideal ramming action.