Chapter 5. Turbofan engine

Nowadays, the usage of turbojet engines is drastically reduced due to a low efficiency. To increase the efficiency, the additional bypass duct has been introduced (Fig. 5.1). The bypass air going through a fan directly to the separated nozzle. The ratio between bypass and core mass flow is called bypass ratio. Sometimes, the bypass air mix with core gases in the mixing section situated between turbine and nozzle. Such scheme usually is used with afterburner (Chapter6) or in the turbofan engines with low bypass ratio. Here, the turbofan engine with separated nozzle is considered (Fig. 5.1).

Fig. 5.1. Scheme of turbofan engine.

1. The calculation of inlet section is identical to the turbojet engine.

2 (fan). The total pressure after fan is

where  is a pressure ratio of fan. The total temperature after fan is

where  is an efficiency of fan.

2-4. The calculation of core (gas generator) is identical to the turbojet engines until a section after turbine of high-pressure compressor (HPC). 5. The pressure ratio of fan’s turbine can be found as

where the coefficient  is

Here  is a total temperature after compressor’s turbine,  is an efficiency of fan’s turbine and  is a mechanical efficiency of fan’s turbine.

The total pressure after turbine is

and the total temperature is

5 (int). The calculation of internal (core) exhaust is similar to the turbojet engine (Chapter 3). Below, the algorithm to calculate the core exhaust with converging nozzle is presented.     

If the pressure is fully discharged in the nozzle the normalized gas speed from the nozzle can be calculated as

The normalized isentropic gas speed from nozzle   can be find from

and the total pressure at the nozzle exit of internal duct 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

The equivalent gas speed from the nozzle exit is

6 (int). The specific thrust of core is

5 (ext). The calculation of external (bypass) exhaust is similar to the internal exhaust.

The total pressure at the entrance of external nozzle is

where  is the pressure losses in the external duct.

If the pressure is fully discharged in the nozzle the normalized gas speed from the nozzle can be calculated as

The normalized isentropic gas speed from nozzle  can be find from

and the total pressure at the nozzle exit of external duct 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

The equivalent gas speed from the nozzle exit is

6 (ext). The specific thrust of bypass duct is

6. The total specific thrust is

and the specific fuel consumption is

The total thrust is

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