Chapter 3. Turbojet engine

In general, an aircraft turbojet engine has inlet, compressor, combustion chamber turbine and nozzle (Fig. 3.1). The coming air is preliminary compressed in the inlet (subsonic/supersonic) if the aircraft is on fly. After it, the air is highly compressed in the axial compressor. The compressed air mix with fuel and burns in the combustion chamber. The burned gases are expanded in the turbine that rotates the compressor. The rest of energy is going to the nozzle to generate a jet thrust. The detailed description of turbojet engine working principles can be found in the specialized literature [1, 2, 3].

Fig. 3.1. Scheme of turbojet engine.

The calculation of turbojet engine is processed by sections: from the section before engine inlet to the end at the nozzle exit.

At the given altitude, the pressure , temperature  and speed of sound  can be defined from standard atmospheric conditions. 

1. The pressure losses  in the supersonic or subsonic inlet are calculated based on the empirical curves [4]. The total pressure after inlet is

and the total temperature is

The flying speed can be found as

2. The total pressure after compressor is

where  is air pressure ratio in the compressor.

The total temperature is

where is the efficiency of compressor.

3. The total pressure after combustion chamber is

where  is the pressure losses in the combustion chamber. The relative fuel consumption can be found from the following equation [1, 2, 3]

where the enthalpies   and    can be found from the empirical curves [1]. The lower heating value of kerosene is .  The air-fuel ratio is

where  is the stochiometric coefficient for kerosene.

4. The pressure ratio in turbine can be found from the balance equation for compressor and turbine. The final relation can be written as

where  is an efficiency of turbine,  is a mechanical efficiency and  is an air fraction required for turbine cooling.

The total pressure after turbine is

and the total temperature is

5. The disposable pressure ratio at the nozzle is

If the pressure is fully discharged in the nozzle

the normalized gas speed from the nozzle is

where a normalized isentropic gas speed from nozzle can be find from

The total pressure at the nozzle exit is

If the pressure is not fully discharged in the nozzle

the normalized gas speed from nozzle is  and the pressure at the nozzle exit is

The normalized gas speed from nozzle is

and the total pressure at the nozzle exit is

The exit speed from nozzle is

6. The specific thrust is

where a coefficient  is calculated as

The specific fuel consumption is

The thrust is

where   is an air mass flow.

7. The effective efficiency of cycle is

where  is an effective work of cycle that can be found from

The flying efficiency is

The total efficiency is

The thermal efficiency of cycle can be found from