Jet engine

All jet engines are reaction engines that generate thrust by emitting a jet of fluid rearwards at relatively high speed. The forces on the inside of the engine needed to create this jet give a strong thrust on the engine which pushes the craft forwards.

Jet engines make their jet from propellant from tankage that is attached to the engine (as in a 'rocket') as well as in duct engines (those commonly used on aircraft) by ingesting an external fluid (very typically air) and expelling it at higher speed.

Propelling nozzle
Main article: Propelling nozzle
The propelling nozzle is the key component of all jet engines as it creates the exhaust jet. Propelling nozzles turn internal and pressure energy into high velocity kinetic energy.[25] The total pressure and temperature don't change through the nozzle but their static values drop as the gas speeds up.

The velocity of the air entering the nozzle is low, about Mach 0.4, a prerequisite for minimizing pressure losses in the duct leading to the nozzle. The temperature entering the nozzle may be as low as sea level ambient for a fan nozzle in the cold air at cruise altitudes. It may be as high as the 1000K exhaust gas temperature for a supersonic afterburning engine or 2200K with afterburner lit.[26] The pressure entering the nozzle may vary from 1.5 times the pressure outside the nozzle, for a single stage fan, to 30 times for the fastest manned aircraft at mach 3+.[27]

The velocity of the gas leaving a convergent nozzle may be subsonic or sonic (Mach 1) at low flight speeds or supersonic (Mach 3.0 at SR-71 cruise)[28] for a con-di nozzle at higher speeds where the nozzle pressure ratio is increased with the intake ram.[29] The nozzle thrust is highest if the static pressure of the gas reaches the ambient value as it leaves the nozzle. This only happens if the nozzle exit area is the correct value for the nozzle pressure ratio (npr). Since the npr changes with engine thrust setting and flight speed this is seldom the case. Also at supersonic speeds the divergent area is less than required to give complete internal expansion to ambient pressure as a trade-off with external body drag. Whitford[30] gives the F-16 as an example. Other underexpanded examples were the XB-70 and SR-71.

The nozzle size, together with the area of the turbine nozzles, determines the operating pressure of the compressor.[31]

Thrust
Main article: Thrust
Origin of engine thrust
The familiar explanation for jet thrust is a "black box" description which only looks at what goes into the engine, air and fuel, and what comes out, exhaust gas and an unbalanced force. This force, called thrust, is the sum of the momentum difference between entry and exit and any unbalanced pressure force between entry and exit, as explained in "Thrust calculation". As an example, an early turbojet, the Bristol Olympus Mk. 101, had a momentum thrust of 9300 lb. and a pressure thrust of 1800 lb. giving a total of 11,100 lb.[32] Looking inside the "black box" shows that the thrust results from all the unbalanced momentum and pressure forces created within the engine itself.[33] These forces, some forwards and some rearwards, are across all the internal parts, both stationary and rotating, such as ducts, compressors, etc., which are in the primary gas flow which flows through the engine from front to rear. The algebraic sum of all these forces is delivered to the airframe for propulsion.[34] "Flight" gives examples of these internal forces for two early jet engines, the Rolls-Royce Avon Ra.14[35] and the de Havilland Goblin[36]

Transferring thrust to the aircraft
The engine thrust acts along the engine centreline. The aircraft "holds" the engine on the outer casing of the engine at some distance from the engine centreline (at the engine mounts). This arrangement causes the engine casing to bend (known as backbone bending) and the round rotor casings to distort (ovalization). Distortion of the engine structure has to be controlled with suitable mount locations to maintain acceptable rotor and seal clearances and prevent rubbing. A well-publicized example of excessive structural deformation occurred with the original Pratt & Whitney JT9D engine installation in the Boeing 747 aircraft.[37] The engine mounting arrangement had to be revised with the addition of an extra thrust frame to reduce the casing deflections to an acceptable amount.[38][39]

Rotor thrust
The rotor thrust on a thrust bearing is not related to the engine thrust. It may even change direction at some RPM. The bearing load is determined by bearing life considerations. Although the aerodynamic loads on the compressor and turbine blades contribute to the rotor thrust they are small compared to cavity loads inside the rotor which result from the secondary air system pressures and sealing diameters on discs, etc. To keep the load within the bearing specification seal diameters are chosen accordingly as, many years ago, on the backface of the impeller[40] in the de Havilland Ghost engine. Sometimes an extra disc known as a balance piston has to be added inside the rotor. An early turbojet example with a balance piston[41] was the Rolls-Royce Avon.

Thrust calculation
The net thrust (FN) of a turbojet is given by:[42]

{\displaystyle F_{N}=({\dot {m}}{air}+{\dot {m}}{fuel})v_{e}-{\dot {m}}{air}v} F{N}=({\dot {m}}{air}+{\dot {m}}{fuel})v_{e}-{\dot {m}}_{air}v
where:
ṁ air = the mass rate of air flow through the engine
ṁ fuel = the mass rate of fuel flow entering the engine
ve = the velocity of the jet (the exhaust plume) and is assumed to be less than sonic velocity
v = the velocity of the air intake = the true airspeed of the aircraft
(ṁ air + ṁ fuel)ve = the nozzle gross thrust (FG)
ṁ air v = the ram drag of the intake air
The above equation applies only for air-breathing jet engines. It does not apply to rocket engines. Most types of jet engine have an air intake, which provides the bulk of the fluid exiting the exhaust. Conventional rocket engines, however, do not have an intake, the oxidizer and fuel both being carried within the vehicle. Therefore, rocket engines do not have ram drag and the gross thrust of the rocket engine nozzle is the net thrust of the engine. Consequently, the thrust characteristics of a rocket motor are different from that of an air breathing jet engine, and thrust is independent of velocity.

If the velocity of the jet from a jet engine is equal to sonic velocity, the jet engine's nozzle is said to be choked. If the nozzle is choked, the pressure at the nozzle exit plane is greater than atmospheric pressure, and extra terms must be added to the above equation to account for the pressure thrust.[42]

The rate of flow of fuel entering the engine is very small compared with the rate of flow of air.[42] If the contribution of fuel to the nozzle gross thrust is ignored, the net thrust is:

{\displaystyle F_{N}={\dot {m}}{air}(v{e}-v)} F_{N}={\dot {m}}{air}(v{e}-v)
The velocity of the jet (ve) must exceed the true airspeed of the aircraft (v) if there is to be a net forward thrust on the aircraft. The velocity (ve) can be calculated thermodynamically based on adiabatic expansion.[43]

Thrust augmentation
Thrust augmentation has taken many forms, most commonly to supplement inadequate take-off thrust. Some early jet aircraft needed rocket assistance to take off from high altitude airfields or when the day temperature was high. A more recent aircraft, the Tupolev Tu-22 supersonic bomber, was fitted with four SPRD-63 boosters for take-off.[44] Possibly the most extreme requirement needing rocket assistance, and which was short-lived, was zero-length launching. Almost as extreme, but very common, is catapult assistance from aircraft carriers. Rocket assistance has also been used during flight. The SEPR 841 booster engine was used on the Dassault Mirage for high altitude interception.[45]

Early aft-fan arrangements which added bypass airflow to a turbojet were known as thrust augmentors.[46] The aft-fan fitted to the General Electric CJ805-3 turbojet augmented the take-off thrust from 11,650lb to 16,100lb.

Water, or other coolant,[47] injection into the compressor or combustion chamber and fuel injection into the jetpipe (afterburning/reheat) became standard ways to increase thrust, known as 'wet' thrust to differentiate with the no-augmentation 'dry' thrust.

Coolant injection (pre-compressor cooling) has been used, together with afterburning, to increase thrust at supersonic speeds. The 'Skyburner' McDonnell Douglas F-4 Phantom II set a world speed record using water injection in front of the engine.[48]

At high Mach numbers afterburners supply progressively more of the engine thrust as the thrust from the turbomachine drops off towards zero at which speed the engine pressure ratio (epr) has fallen to 1.0 and all the engine thrust comes from the afterburner. The afterburner also has to make up for the pressure loss across the turbomachine which is a drag item at higher speeds where the epr will be less than 1.0.[49][50]

Thrust augmentation of existing afterburning engine installations for special short-duration tasks has been the subject of studies for launching small payloads into low earth orbits using aircraft such as McDonnell Douglas F-4 Phantom II, McDonnell Douglas F-15 Eagle, Dassault Rafale and Mikoyan MiG-31,[51] and also for carrying experimental packages to high altitudes using a Lockheed SR-71.[52] In the first case an increase in the existing maximum speed capability is required for orbital launches. In the second case an increase in thrust within the existing speed capability is required. Compressor inlet cooling is used in the first case. A compressor map shows that the airflow reduces with increasing compressor inlet temperature although the compressor is still running at maximum RPM (but reduced aerodynamic speed). Compressor inlet cooling increases the aerodynamic speed and flow and thrust. In the second case a small increase in the maximum mechanical speed and turbine temperature were allowed, together with nitrous oxide injection into the afterburner and simultaneous increase in afterburner fuel flow.

Energy efficiency relating to aircraft jet engines
This overview highlights where energy losses occur in complete jet aircraft powerplants or engine installations.

A jet engine at rest, as on a test stand, sucks in fuel and tries to thrust itself forward. How well it does this is judged by how much fuel it uses and what force is required to restrain it. This is a measure of its efficiency. If something deteriorates inside the engine (known as performance deterioration[53]) it will be less efficient and this will show when the fuel produces less thrust. If a change is made to an internal part which allows the air/combustion gases to flow more smoothly the engine will be more efficient and use less fuel. A standard definition is used to assess how different things change engine efficiency and also to allow comparisons to be made between different engines. This definition is called specific fuel consumption, or how much fuel is needed to produce one unit of thrust. For example, it will be known for a particular engine design that if some bumps in a bypass duct are smoothed out the air will flow more smoothly giving a pressure loss reduction of x% and y% less fuel will be needed to get the take-off thrust, for example. This understanding comes under the engineering discipline Jet engine performance. How efficiency is affected by forward speed and by supplying energy to aircraft systems is mentioned later.

The efficiency of the engine is controlled primarily by the operating conditions inside the engine which are the pressure produced by the compressor and the temperature of the combustion gases at the first set of rotating turbine blades. The pressure is the highest air pressure in the engine. The turbine rotor temperature is not the highest in the engine but is the highest at which energy transfer takes place ( higher temperatures occur in the combustor). The above pressure and temperature are shown on a Thermodynamic cycle diagram.

The efficiency is further modified by how smoothly the air and the combustion gases flow through the engine, how well the flow is aligned (known as incidence angle) with the moving and stationary passages in the compressors and turbines.[54] Non-optimum angles, as well as non-optimum passage and blade shapes can cause thickening and separation of Boundary layers and formation of Shock waves. It is important to slow the flow (lower speed means less pressure losses or Pressure drop) when it travels through ducts connecting the different parts. How well the individual components contribute to turning fuel into thrust is quantified by measures like efficiencies for the compressors, turbines and combustor and pressure losses for the ducts. These are shown as lines on a Thermodynamic cycle diagram.

The engine efficiency, or thermal efficiency,[55] known as {\displaystyle \eta _{th}} \eta _{{th}}. is dependent on the Thermodynamic cycle parameters, maximum pressure and temperature, and on component efficiencies, {\displaystyle \eta _{compressor}} {\displaystyle \eta _{compressor}}, {\displaystyle \eta _{combustion}} {\displaystyle \eta _{combustion}} and {\displaystyle \eta _{turbine}} {\displaystyle \eta _{turbine}} and duct pressure losses.

The engine needs compressed air for itself just to run successfully. This air comes from its own compressor and is called secondary air. It does not contribute to making thrust so makes the engine less efficient. It is used to preserve the mechanical integrity of the engine, to stop parts overheating and to prevent oil escaping from bearings for example. Only some of this air taken from the compressors returns to the turbine flow to contribute to thrust production. Any reduction in the amount needed improves the engine efficiency. Again, it will be known for a particular engine design that a reduced requirement for cooling flow of x% will reduce the specific fuel consumption by y%. In other words, less fuel will be required to give take-off thrust, for example. The engine is more efficient.

All of the above considerations are basic to the engine running on its own and, at the same time, doing nothing useful, i.e. it is not moving an aircraft or supplying energy for the aircraft's electrical, hydraulic and air systems. In the aircraft the engine gives away some of its thrust-producing potential, or fuel, to power these systems. These requirements, which cause installation losses,[56] reduce its efficiency. It is using some fuel that does not contribute to the engine's thrust.

Finally, when the aircraft is flying the propelling jet itself contains wasted kinetic energy after it has left the engine. This is quantified by the term propulsive, or Froude, efficiency {\displaystyle \eta _{p}} \eta _{p} and may be reduced by redesigning the engine to give it bypass flow and a lower speed for the propelling jet, for example as a turboprop or turbofan engine. At the same time forward speed increases the {\displaystyle \eta _{th}} \eta _{{th}} by increasing the Overall pressure ratio.

The overall efficiency of the engine at flight speed is defined as {\displaystyle \eta _{o}=\eta _{p}\eta _{th}} {\displaystyle \eta _{o}=\eta _{p}\eta _{th}}.[57]

The {\displaystyle \eta _{o}} {\displaystyle \eta _{o}} at flight speed depends on how well the intake compresses the air before it is handed over to the engine compressors. The intake compression ratio, which can be as high as 32:1 at Mach 3, adds to that of the engine compressor to give the Overall pressure ratio and {\displaystyle \eta _{th}} \eta _{{th}} for the Thermodynamic cycle. How well it does this is defined by its pressure recovery or measure of the losses in the intake. Mach 3 manned flight has provided an interesting illustration of how these losses can increase dramatically in an instant. The North American XB-70 Valkyrie and Lockheed SR-71 Blackbird at Mach 3 each had pressure recoveries of about 0.8,[58][59] due to relatively low losses during the compression process, i.e. through systems of multiple shocks. During an 'unstart' the efficient shock system would be replaced by a very inefficient single shock beyond the inlet and an intake pressure recovery of about 0.3 and a correspondingly low pressure ratio.

The propelling nozzle at speeds above about Mach 2 usually has extra internal thrust losses because the exit area is not big enough as a trade-off with external afterbody drag.[60]

Although a bypass engine improves propulsive efficiency it incurs losses of its own inside the engine itself. Machinery has to be added to transfer energy from the gas generator to a bypass airflow. The low loss from the propelling nozzle of a turbojet is added to with extra losses due to inefficiencies in the added turbine and fan.[61] These may be included in a transmission, or transfer, efficiency {\displaystyle \eta _{T}} {\displaystyle \eta _{T}}. However, these losses are more than made up[62] by the improvement in propulsive efficiency.[63] There are also extra pressure losses in the bypass duct and an extra propelling nozzle.

With the advent of turbofans with their loss-making machinery what goes on inside the engine has been separated by Bennett,[64] for example, between gas generator and transfer machinery giving {\displaystyle \eta _{o}=\eta _{p}\eta _{th}\eta _{T}} {\displaystyle \eta _{o}=\eta _{p}\eta _{th}\eta _{T}}.

Dependence of propulsion efficiency (η) upon the vehicle speed/exhaust velocity ratio (v/ve) for air-breathing jet and rocket engines.
The energy efficiency ( {\displaystyle \eta _{o}} {\displaystyle \eta _{o}}) of jet engines installed in vehicles has two main components:

propulsive efficiency ( {\displaystyle \eta _{p}} \eta _{p}): how much of the energy of the jet ends up in the vehicle body rather than being carried away as kinetic energy of the jet.
cycle efficiency ( {\displaystyle \eta _{th}} \eta _{{th}}): how efficiently the engine can accelerate the jet
Even though overall energy efficiency {\displaystyle \eta _{o}} {\displaystyle \eta _{o}} is:

{\displaystyle \eta _{o}=\eta _{p}\eta _{th}} {\displaystyle \eta _{o}=\eta _{p}\eta _{th}}
for all jet engines the propulsive efficiency is highest as the exhaust jet velocity gets closer to the vehicle speed as this gives the smallest residual kinetic energy.[65] For an airbreathing engine an exhaust velocity equal to the vehicle velocity, or a {\displaystyle \eta {p}} \eta {p} equal to one, gives zero thrust with no net momentum change.[66] The formula for air-breathing engines moving at speed {\displaystyle v} v with an exhaust velocity {\displaystyle v{e}} v{e}, and neglecting fuel flow, is:[67]

{\displaystyle \eta {p}={\frac {2}{1+{\frac {v{e}}{v}}}}} \eta {p}={\frac {2}{1+{\frac {v{e}}{v}}}}
And for a rocket:[68]

{\displaystyle \eta {p}={\frac {2,({\frac {v}{v{e}}})}{1+({\frac {v}{v_{e}}})^{2}}}} \eta {p}={\frac {2,({\frac {v}{v{e}}})}{1+({\frac {v}{v_{e}}})^{2}}}
In addition to propulsive efficiency, another factor is cycle efficiency; a jet engine is a form of heat engine. Heat engine efficiency is determined by the ratio of temperatures reached in the engine to that exhausted at the nozzle. This has improved constantly over time as new materials have been introduced to allow higher maximum cycle temperatures. For example, composite materials, combining metals with ceramics, have been developed for HP turbine blades, which run at the maximum cycle temperature.[69] The efficiency is also limited by the overall pressure ratio that can be achieved. Cycle efficiency is highest in rocket engines (~60+%), as they can achieve extremely high combustion temperatures. Cycle efficiency in turbojet and similar is nearer to 30%, due to much lower peak cycle temperatures.

Typical combustion efficiency of an aircraft gas turbine over the operational range.

Typical combustion stability limits of an aircraft gas turbine.
The combustion efficiency of most aircraft gas turbine engines at sea level takeoff conditions is almost 100%. It decreases nonlinearly to 98% at altitude cruise conditions. Air-fuel ratio ranges from 50:1 to 130:1. For any type of combustion chamber there is a rich and weak limit to the air-fuel ratio, beyond which the flame is extinguished. The range of air-fuel ratio between the rich and weak limits is reduced with an increase of air velocity. If the increasing air mass flow reduces the fuel ratio below certain value, flame extinction occurs.[70]

Specific impulse as a function of speed for different jet types with kerosene fuel (hydrogen Isp would be about twice as high). Although efficiency plummets with speed, greater distances are covered. Efficiency per unit distance (per km or mile) is roughly independent of speed for jet engines as a group; however, airframes become inefficient at supersonic speeds.
Consumption of fuel or propellant
A closely related (but different) concept to energy efficiency is the rate of consumption of propellant mass. Propellant consumption in jet engines is measured by Specific Fuel Consumption, Specific impulse or Effective exhaust velocity. They all measure the same thing. Specific impulse and effective exhaust velocity are strictly proportional, whereas specific fuel consumption is inversely proportional to the others.

For airbreathing engines such as turbojets, energy efficiency and propellant (fuel) efficiency are much the same thing, since the propellant is a fuel and the source of energy. In rocketry, the propellant is also the exhaust, and this means that a high energy propellant gives better propellant efficiency but can in some cases actually give lower energy efficiency.

It can be seen in the table (just below) that the subsonic turbofans such as General Electric's CF6 turbofan use a lot less fuel to generate thrust for a second than did the Concorde's Rolls-Royce/Snecma Olympus 593 turbojet. However, since energy is force times distance and the distance per second was greater for Concorde, the actual power generated by the engine for the same amount of fuel was higher for Concorde at Mach 2 than the CF6. Thus, the Concorde's engines were more efficient in terms of energy per mile.