Airbreathing

Commonly aircraft are propelled by airbreathing jet engines. Most airbreathing jet engines that are in use are turbofan jet engines, which give good efficiency at speeds just below the speed of sound.

Rocket

The rocket engine uses the same basic physical principles of thrust as a form of reaction engine,^[25] but is distinct from the jet engine in that it does not require atmospheric air to provide oxygen; the rocket carries all components of the reaction mass. However some definitions treat it as a form of jet propulsion.^[26]

Because rockets do not breathe air, this allows them to operate at arbitrary altitudes and in space.^[27]

This type of engine is used for launching satellites, space exploration and crewed access, and permitted landing on the Moon in 1969.

Rocket engines are used for high altitude flights, or anywhere where very high accelerations are needed since rocket engines themselves have a very high thrust-to-weight ratio.

However, the high exhaust speed and the heavier, oxidizer-rich propellant results in far more propellant use than turbofans. Even so, at extremely high speeds they become energy-efficient.

An approximate equation for the net thrust of a rocket engine is:

${\displaystyle F_{N}={\dot {m}}\,g_{0}\,I_{\text{sp,vac}}-A_{e}\,p\;}$

Where ${\displaystyle F_{N}}$ is the net thrust, ${\displaystyle I_{\text{sp,vac}}}$ is the specific impulse, ${\displaystyle g_{0}}$ is a standard gravity, ${\displaystyle {\dot {m}}}$ is the propellant flow in kg/s, ${\displaystyle A_{e}}$ is the cross-sectional area at the exit of the exhaust nozzle, and ${\displaystyle p}$ is the atmospheric pressure.

Hybrid

Combined-cycle engines simultaneously use two or more different principles of jet propulsion.

Water jet

A water jet, or pump-jet, is a marine propulsion system that uses a jet of water. The mechanical arrangement may be a ducted propeller with nozzle, or a centrifugal compressor and nozzle. The pump-jet must be driven by a separate engine such as a Diesel or gas turbine.

Propelling nozzle

A propelling nozzle produces a high velocity exhaust jet. Propelling nozzles turn internal and pressure energy into high velocity kinetic energy.^[29] 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.^[30] 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+.^[31]

Convergent nozzles are only able to accelerate the gas up to local sonic (Mach 1) conditions. To reach high flight speeds, even greater exhaust velocities are required, and so a convergent-divergent nozzle is needed on high-speed aircraft.^[32]

The engine 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^[33] 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.^[34]

Thrust

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 generates thrust. 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^[35]) 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.^[36] 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,^[37] known as ${\displaystyle \eta _{th}}$. is dependent on the Thermodynamic cycle parameters, maximum pressure and temperature, and on component efficiencies, ${\displaystyle \eta _{compressor}}$, ${\displaystyle \eta _{combustion}}$ and ${\displaystyle \eta _{turbine}}$ 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,^[38] 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 ${\displaystyle \eta _{p}}$ 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 ${\displaystyle \eta _{th}}$ by increasing the Overall pressure ratio.

The overall efficiency of the engine at flight speed is defined as ${\displaystyle \eta _{o}=\eta _{p}\eta _{th}}$.^[39]

The ${\displaystyle \eta _{o}}$ 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 ${\displaystyle \eta _{th}}$ 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,^[40][41] 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.^[42]

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.^[43] These may be included in a transmission, or transfer, efficiency ${\displaystyle \eta _{T}}$. However, these losses are more than made up^[44] by the improvement in propulsive efficiency.^[45] 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,^[46] for example, between gas generator and transfer machinery giving ${\displaystyle \eta _{o}=\eta _{p}\eta _{th}\eta _{T}}$.

The energy efficiency (${\displaystyle \eta _{o}}$) of jet engines installed in vehicles has two main components:

• propulsive efficiency (${\displaystyle \eta _{p}}$): 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 (${\displaystyle \eta _{th}}$): how efficiently the engine can accelerate the jet

Even though overall energy efficiency ${\displaystyle \eta _{o}}$ is:

${\displaystyle \eta _{o}=\eta _{p}\eta _{th}}$

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.^{[lower-alpha 1]} For an airbreathing engine an exhaust velocity equal to the vehicle velocity, or a ${\displaystyle \eta _{p}}$ equal to one, gives zero thrust with no net momentum change.^[47] The formula for air-breathing engines moving at speed ${\displaystyle v}$ with an exhaust velocity ${\displaystyle v_{e}}$, and neglecting fuel flow, is:^[48]

${\displaystyle \eta _{p}={\frac {2}{1+{\frac {v_{e}}{v}}}}}$

And for a rocket:^[49]

${\displaystyle \eta _{p}={\frac {2\,({\frac {v}{v_{e}}})}{1+({\frac {v}{v_{e}}})^{2}}}}$

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.^[50] 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.

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.^[51]

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 air-breathing 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 the Concorde, the actual power generated by the engine for the same amount of fuel was higher for the Concorde at Mach 2 than the CF6. Thus, the Concorde's engines were more efficient in terms of energy per mile.

Thrust-to-weight ratio

The thrust-to-weight ratio of jet engines with similar configurations varies with scale, but is mostly a function of engine construction technology. For a given engine, the lighter the engine, the better the thrust-to-weight is, the less fuel is used to compensate for drag due to the lift needed to carry the engine weight, or to accelerate the mass of the engine.

As can be seen in the following table, rocket engines generally achieve much higher thrust-to-weight ratios than duct engines such as turbojet and turbofan engines. This is primarily because rockets almost universally use dense liquid or solid reaction mass which gives a much smaller volume and hence the pressurization system that supplies the nozzle is much smaller and lighter for the same performance. Duct engines have to deal with air which is two to three orders of magnitude less dense and this gives pressures over much larger areas, which in turn results in more engineering materials being needed to hold the engine together and for the air compressor.

Comparison of types

Propeller engines handle larger air mass flows, and give them smaller acceleration, than jet engines. Since the increase in air speed is small, at high flight speeds the thrust available to propeller-driven aeroplanes is small. However, at low speeds, these engines benefit from relatively high propulsive efficiency.

On the other hand, turbojets accelerate a much smaller mass flow of intake air and burned fuel, but they then reject it at very high speed. When a de Laval nozzle is used to accelerate a hot engine exhaust, the outlet velocity may be locally supersonic. Turbojets are particularly suitable for aircraft travelling at very high speeds.

Turbofans have a mixed exhaust consisting of the bypass air and the hot combustion product gas from the core engine. The amount of air that bypasses the core engine compared to the amount flowing into the engine determines what is called a turbofan's bypass ratio (BPR).

While a turbojet engine uses all of the engine's output to produce thrust in the form of a hot high-velocity exhaust gas jet, a turbofan's cool low-velocity bypass air yields between 30% and 70% of the total thrust produced by a turbofan system.^[79]

The net thrust (F_N) generated by a turbofan can also be expanded as:^[80]

${\displaystyle F_{N}={\dot {m}}_{e}v_{he}-{\dot {m}}_{o}v_{o}+BPR\,({\dot {m}}_{c}v_{f})}$

where:

Rocket engines have extremely high exhaust velocity and thus are best suited for high speeds (hypersonic) and great altitudes. At any given throttle, the thrust and efficiency of a rocket motor improves slightly with increasing altitude (because the back-pressure falls thus increasing net thrust at the nozzle exit plane), whereas with a turbojet (or turbofan) the falling density of the air entering the intake (and the hot gases leaving the nozzle) causes the net thrust to decrease with increasing altitude. Rocket engines are more efficient than even scramjets above roughly Mach 15.^[81]

Altitude and speed

With the exception of scramjets, jet engines, deprived of their inlet systems can only accept air at around half the speed of sound. The inlet system's job for transonic and supersonic aircraft is to slow the air and perform some of the compression.

The limit on maximum altitude for engines is set by flammability – at very high altitudes the air becomes too thin to burn, or after compression, too hot. For turbojet engines altitudes of about 40 km appear to be possible, whereas for ramjet engines 55 km may be achievable. Scramjets may theoretically manage 75 km.^[82] Rocket engines of course have no upper limit.

At more modest altitudes, flying faster compresses the air at the front of the engine, and this greatly heats the air. The upper limit is usually thought to be about Mach 5–8, as above about Mach 5.5, the atmospheric nitrogen tends to react due to the high temperatures at the inlet and this consumes significant energy. The exception to this is scramjets which may be able to achieve about Mach 15 or more,^{[citation needed]} as they avoid slowing the air, and rockets again have no particular speed limit.

Noise

The noise emitted by a jet engine has many sources. These include, in the case of gas turbine engines, the fan, compressor, combustor, turbine and propelling jet/s.^[83]

The propelling jet produces jet noise which is caused by the violent mixing action of the high speed jet with the surrounding air. In the subsonic case the noise is produced by eddies and in the supersonic case by Mach waves.^[84] The sound power radiated from a jet varies with the jet velocity raised to the eighth power for velocities up to 2,000 ft/sec and varies with the velocity cubed above 2,000 ft/sec.^[85] Thus, the lower speed exhaust jets emitted from engines such as high bypass turbofans are the quietest, whereas the fastest jets, such as rockets, turbojets, and ramjets, are the loudest. For commercial jet aircraft the jet noise has reduced from the turbojet through bypass engines to turbofans as a result of a progressive reduction in propelling jet velocities. For example, the JT8D, a bypass engine, has a jet velocity of 1450 ft/sec whereas the JT9D, a turbofan, has jet velocities of 885 ft/sec (cold) and 1190 ft/sec (hot).^[86]

The advent of the turbofan replaced the very distinctive jet noise with another sound known as "buzz saw" noise. The origin is the shockwaves originating at the supersonic fan blades at takeoff thrust.^[87]

Cooling

Adequate heat transfer away from the working parts of the jet engine is critical to maintaining strength of engine materials and ensuring long life for the engine.

After 2016, research is ongoing in the development of transpiration cooling techniques to jet engine components.^[88]