Introduction

The turbojet is the name used for a gas turbine engine designed to produce thrust by discharging gases at high speed out of the rear of the engine (i.e., the “jet”), which is done through a suitably shaped propelling nozzle. The turbojet engine, a cutaway example shown in the photograph below, is used on many types of aircraft, particularly those designed to fly at higher flight speeds, including supersonic flight. Unfortunately, turbojets have relatively poor propulsive efficiency at lower airspeeds, limiting their usefulness to high-speed aircraft. Nevertheless, the turbojet has been, and still is, a common form of propulsion for various aircraft.

Basic Design of a Turbojet

The basic design of a turbojet engine is shown in the schematic below. The gas turbine has an air inlet, a compressor stage (driven by the high-pressure turbine), a combustion chamber, and high-pressure and low-pressure turbines. The compressed air that passes through the compressor stage mixes with the fuel in the combustion chamber, where it is ignited, and then hot gases flow to drive the main turbine stages. The exhaust is expanded in the propelling nozzle. It is accelerated to a relatively high jet velocity to provide the propulsive thrust by increasing the time change in momentum of the net flow, i.e., the momentum of the air and hot gases that are a combustion product.

Operational Principle

The operational principle of a turbojet engine is straightforward to understand, which can be appreciated from the figure below. The thermodynamic operation of a turbojet is based on the Brayton cycle.

There are five primary stages:

1. Air intake stage. The intake stage in front of the compressor slows the air down, slightly increasing its static pressure. By design, the speed of the airflow into the compressor of a turbojet engine needs to be subsonic, regardless of the aircraft’s airspeed. In the case of supersonic flight, a diverging duct with doors and/or baffles can be used to reduce the incoming flow to subsonic conditions.

2. Compressor stage. The flow is then directed onto vanes and then the spinning compressor blades, where progressively larger increases in pressure are produced. Older turbojet engines had fixed vanes (stators) in front of the moving blades. However, modern engines have stators with variable pitch to direct the oncoming air onto the compressor blades at the appropriate angles based on the engine’s operating state and flight speed. Notice that the compressor is driven through a forward-facing shaft by the high-pressure turbine in the hot stage.

3. Combustion stage. Fuel-burning occurs in the combustor, where the fuel mixture burns to produce a gas flow at a much higher temperature. This process is a continuous, almost constant pressure process, which is different from the combustion process in a piston engine. As the fuel burns, the pressure increases quickly in the confined region on top of a piston. This flow then passes into the gas generator turbine.

4. Gas generator turbine stage. This stage rotates relatively faster than the compressor stage, significantly adding a lot of kinetic energy to the airflow. Notice that the process of compressing the air increases both its pressure and its temperature. Additional air from the compressor is bled into the region downstream of the combustion chambers through a bypass circuit to reduce the temperature of the hot gases so that turbine blades in the power stage can safely tolerate these gases without burning or melting. The hot-stage high-pressure and low-pressure turbine blades are made of special steel alloys that can sustain extremely high temperatures. Nevertheless, the turbine vanes and blades need internal cooling passages to keep the material temperatures at acceptable levels.

5. Exhaust stage through a nozzle. After the turbine, the gases expand through the exhaust nozzle producing a high-velocity jet, which is the thrust source. One problem with this high-speed flow from a turbojet engine is that it creates significant noise. Therefore, as shown in the figure below, most turbojet engines use noise suppression devices such as corrugated or lobe-type suppressors. Such devices alter the turbulent mixing in the jet to change its frequency content in favor of higher frequencies, which are more quickly absorbed by the atmosphere. So the resulting jet flow then sounds quieter to an external observer.

Basis of Thrust Production

The thrust produced by a turbojet engine can be examined using conservation principles of fluid dynamics applied to a control volume surrounding the engine, as shown in the figure below. The basic principle of operation is that air comes in and is then compressed to a level to support combustion, the energy being used to drive the compressor, and the exhaust gases exiting at high speed to produce the thrust.

The mass flow of air into the intake to the engine will be

(1)  

where is the inlet area, and the mass flow rate of fuel is . Therefore, using conservation of momentum, the thrust produced is

(2)  

where is the exit area and is the exit or “jet” velocity, which is usually given the symbol . The pressure (second) term in Eq. 2 is relatively small compared to the change in momentum of the flow, and so in practice, it may be neglected, i.e.,

(3)  

Notice that the thrust decreases when increases because depends on both the compression and the combustion, so the difference decreases. However, increases with increasing and so the value of thrust depends weakly on at low Mach numbers but more so at higher Mach numbers.

For a turbojet engine at subsonic Mach numbers, it is found that stays relatively constant with . Thrust increases with Mach number at higher flight Mach numbers but lapses with altitude, as shown in the figure below. A jet engine’s “Uninstalled Thrust” is typically determined during static tests on a test stand. The engine is calibrated to relate parameters such as engine speed, pressure ratio, and exhaust gas temperature to thrust. These parameters are also available to the pilot on the cockpit instrument panel. Together with information in the airplane flight manual, it can be used to calculate the anticipated aircraft performance.

The overall thrust characteristics of a turbojet depend significantly on the flight Mach number and the operational altitude at which the engine operates. Again, remember that when speaking of “altitude,” it is generally density altitude, i.e., the altitude corresponding to the local ambient density when measured according to the ISA. In particular, the maximum thrust is influenced by ambient temperature, with thrust decreasing as temperature increases. This means that on hot days, an airplane may require a longer runway for takeoff compared to cooler days. Engine manufacturers provide a rated thrust value that is guaranteed for use in the airplane flight manual. This rated thrust is often “flat-rated,” meaning it is a single value based on the highest ambient temperature and is determined through analysis of static engine test data, and possibly flight test data.

One approximation for the thrust produced by a turbojet engine is that it increases linearly with flight Mach number according to

(4)  

where is the lowest Mach number for which the thrust is known and is a constant. The thrust will also decrease with altitude according to

(5)  

where is the thrust produced at MSL conditions and the density ratio is the density at altitude relative to the density at MSL. The density of the air can be estimated using the ISA equations based on the local ambient pressure (i.e., pressure altitude) and outside air temperature.

Worked Example #1 – Estimating the Thrust Produced by a Turbojet

Consider a turbojet-powered airplane flying at a pressure altitude of 30,000 ft at ISA standard conditions. The true airspeed of the airplane is 500 kts. The engine has an inlet area, , of 0.7 m. The velocity at the exit, , is 463 m/s. All velocities are measured relative to the engine. Estimate the thrust of the turbojet and the equivalent power it produces. Neglect the mass of fuel into the engine and all pressure difference effects.

The thrust, , of the engine can be expressed as

   

where

   

At 30,000 ISA standard conditions, kg/m. The flight velocity is 500 kts, which is equivalent to 257.2 m/s. Hence, the mass flow into the engine is

   

In this case, we are told to neglect the pressure difference effects, so the thrust, , from the engine is equal to the time rate of change of the momentum of the flow as it goes through the engine, i.e.,

   

Inserting the numerical values gives

   

The equivalent power produced by the engine, , is given by

   

Thrust Specific Fuel Consumption (TSFC)

The output from a turbojet is the thrust, so the specific fuel consumption is based on thrust production. Recall that for engines that primarily produce shaft power (e.g., a piston engine or a turboshaft engine); the specific fuel consumption is based on shaft or brake power. The thrust specific fuel consumption or TSFC is a measure of the weight of fuel consumed per unit thrust produced per unit time, i.e.,

(6)  

Normally, the TSFC is measured in terms of units of lb lb hr in the USC system or units of kg kN hr in the SI system. Again, note the anomaly of the SI system where mass units are used instead of weight. Further caution should be exercised, however, because other units may be used for TSFC in publications. Published values of TSFC for different turbojet engines are often quoted at the maximum rated thrust at sea-level on a standard day.

A turbojet engine’s overall propulsive efficiency increases with increasing Mach number because of the larger increase in thrust and relatively small change in TSFC. This reason is why this engine type is more suitable for higher-speed aircraft. Representative variations of the TSFC of a turbojet engine is shown in the figure below. Notice that the TSFC of a turbojet engine generally gets slightly worse with increasing flight Mach number.

In performance analyses, one linear approximation that can be used for the TSFC in the subsonic regime is

(7)  

which is measured in units of weight of fuel per unit of thrust per hour. The value of is engine specific and also depends on the throttle setting of the engine. However, for most flight operations a turbojet engine will run at or near to wide-open throttle settings. Remember that the density of air is lower at higher flight altitudes, so the mass flow of air into the engine decreases.

In supersonic flight, the inlet to a turbojet engine must be designed so that the intake to the compressor occurs at subsonic speeds. This is done using a duct and/or doors or baffles in which the total pressure increases according to the thermodynamic relationship

(8)  

This duct gives a total pressure recovery at the end of the inlet diffuser before the compressor stage. Therefore, thrust from a turbojet engine tends to increase linearly with supersonic flight Mach number according to the approximate relationship

(9)  

These characteristics are obtained because as increases and increases and then increases and eventually becomes supersonic, which all combine to increase the thrust . Also, as shown in the figure above, the TSFC remains relatively constant or gets slightly worse with in the supersonic regime, but the overall propulsive efficiency still increases.

Afterburning

Military aircraft often require a large increase in engine thrust for a relatively short time, such as during takeoff, climb, acceleration into supersonic flight, or for some types of combat maneuvers. This thrust is achieved by using an afterburner, as shown schematically in the figure below.

An afterburner injects additional fuel into the engine exhaust and burns in an extended tailpipe. In the afterburner tube are fuel spray bars, flame holders, and an adjustable nozzle. An adjustable exhaust nozzle is necessary for an afterburning engine, and usually, two or three-position nozzles are used. Raw fuel is injected into the exhaust from the engine core by the fuel spray bars, and the flame holders stabilize the resulting combustion process as it develops down the tube and into the tailpipe. The engine’s core exhaust contains enough excess oxygen to allow for afterburner operation, so no additional inlets are needed. The resulting exhaust flame from an afterburner is usually rather spectacular partly because the flow speeds are supersonic, and the hot gases contain diamond-shaped shock waves, as shown in the photograph below.

While the engine thrust may increase nearly twice when the afterburner is lit, the net engine TSFC increases markedly, so corresponding fuel burn increases rather quickly. Because of the higher jet velocities out of the tailpipe, engine noise also increases dramatically. Afterburning is usually used by military fighter aircraft for takeoff and initial climb. In this case, the high noise levels produced using an afterburner are particularly noticeable to an observer on the ground.

Afterburning is also possible with a turbofan engine. Afterburning turbofans are usually found on military aircraft designed to reach transonic and low-supersonic cruise speed ranges. When performance requirements encompass these speed ranges and subsonic flight under various conditions, selecting a low bypass ratio turbofan engine usually becomes the best design compromise to meet the flight requirements. In all cases, however, matching an engine to an aircraft requires careful consideration of not only the requirements for the aircraft but also weight, cost, and installation issues.

Ramjets

Summary & Closure

The turbojet engine is a classic solution to jet propulsion and is ideally suited for high subsonic or supersonic flight. Today, turbojets are used more on military aircraft. For supersonic flight, the turbojet will be fitted with an afterburner, which may give the engine twice the thrust, but it can only be used for short periods because of the high fuel consumption. For the most part, the choice of a turbojet for an aircraft that cruises at less than Mach 0.5 is inappropriate, and a turboprop should be used here because they have much better specific fuel consumption. At higher airspeeds, it is better to use a turbofan than a turbojet because it has a better specific fuel consumption than the turbojet. A turbofan also has much lower noise because of the lower jet velocity. With increasingly stringent aircraft engine noise constraints, the pure turbojet may eventually be relegated to aeronautical history, even for military aircraft.