The basis of most jet engines is the same. Air is drawn in at the front and compressed. Fuel is then added and the resulting mixture is combusted. The combustion greatly increases the volume of the gases which are then exhausted out of the rear of the engine. The efficiency of the process, like any heat engine, is defined by the ratio of the compressed air's volume to the exhaust volume.
The advantage of the jet engine is its efficiency at high speeds (especially supersonic) and high altitudes. On slower aircraft, a propeller (powered by a gas turbine), commonly known as a turboprop is more common.
The earliest attempts at jet engines were hybrid designs, where the compression was supplied by an external power source. In this system (called a thermojet by Secondo Campini) the air is compressed by a fan driven by a conventional gasoline engine, mixed with fuel, and then burned for jet thrust. Three known examples of this sort of design were the Henri Coanda's Coanda-1910 aircraft, the much later Campini Caproni CC.2, and the Japanese Tsu-11 engine intended to power Ohka kamikaze planes towards the end of World War II. None were entirely successful, and the CC.2 ended up being slower than a traditional design with the same engine.
The key to the useful jet engine was the gas turbine, used to extract energy to drive the compressor from the engine itself. Work on such a "self-contained" design started in England in 1930 when Frank Whittle submitted patents for such an engine (granted in 1932) using a single turbine stage in the exhaust to drive a centrifugal compressor[?]. In 1935 Hans von Ohain started work on a similar design in Germany, seemingly unaware of Whittle's work.
Whittle had significant problems in getting anyone to fund research into the design, and the Air Ministry largely ignored it while they concentrated on more pressing issues. Using private funds he was able to get a test engine running in 1937, but this was very large and unsuitable for use in an aicraft. By 1939 work had progressed to the point where the engine was starting to look useful, and Whittle's Power Jets Ltd. started receiving Air Ministry money. In 1941 a flyable version of the engine called the W.1, developing 1000 lbs of thrust, was fitted to the Gloster E28/39[?] airframe[?], and flew in May 1941.
Ohain had fewer problems, which is notable considering the highly political nature of the German aircraft industry at the time. He approached Ernst Heinkel, one of the larger aircraft industrialists of the day, who immediately saw the promise of the design. Heinkel had recently purchased the Hirth engine company, and Ohain and his master machinist Max Hahn were set up there as a new division of the Hirth company. They had their first HeS-1 engine running by 1937. Unlike Whittle's design, Ohain used hydrogen as a fuel, which he credits for the early success. Their follow-on designs culminated in the HeS-3 of 1,100lbs, which was fitted to Heinkel's simple He 178[?] airframe and flew in August 1939, an impressively short time for development.
One problem with both of these early designs was that the compressor works by "throwing" air outward from the intake to the sides of the engine, where it is compressed by being "crushed" up against the side. This leads to a very large cross section for the engine, as well as having the air flowing the wrong way after compression - it has to be collected up and "bent" to flow to the rear of the engine where the turbine is located.
Anselm Franz of Junkers' engine division (Jumo for Junkers Motoren) addressed this problem with the introduction of the axial-flow compressor. Essentially this is a turbine in reverse. Air coming in the front of the engine is blown to the rear of the engine by a fan, where it is crushed against a set of non-rotating blades called stators. The process is nowhere near as powerful as the centrifugal compressor, so a number of these pairs of fans and stators are placed in series to get the needed compression. Even with all the added complexity, the resulting engine is much smaller. Jumo was assigned the next engine number, 4, and the result was the Jumo 004 engine. This would be the first jet engine to see service, when it powered the Me 262 in 1944.
By the end of the war the British designs were generally much better than their German counterparts. Their main advantage was Britain's long history of working with high-heat metals. Their engines were licensed widely in the US, whose own designs wouldn't come fully into their own until the 1960s. Their most famous design, the Nene, would also power the USSR's jet aircraft after a particularly stupid technology exchange.
There are a number of different types of jet engines:
Whittle's and von Ohain's designs are now classified as turbojets, mostly to distinguish them from some of the types outlined below. Generally turbojets are arranged around a central shaft running the length of the engine, with the compressor and turbine connected to the shaft at either end. In the middle is a combustion area, typically in the form of a number of individual "flame cans" which are used to stabilize the combustion.
Like all heat engines, the effeciency of a jet engine is strong dependant on the temperature of the exhaust gas, higher temperature means more energy from the fuel. Due to the physics of gasses, where temperature are pressure are inversely related, a simplification is to compare the pressure of gas taken in to when it is burned, the so-called compression ratio. Early jet engines had compression ratios as low as 5 to 1, compared to a normal otto cycle engine at anywhere from 6 to 1 to 9 to 1. The limiting factor is the temperature at the front of the turbine; increasing the compression ratio means that there is considerably more fuel/air mixture (the charge) burning in the flame cans, and a higher temperature. This is primarily a problem when taking off, as the aircraft climbs the ambient pressure drops and the compressor can be run at higher ratios.
German engines had serious problems in this regard, their early engines averaged only 10 hours of operation before failing, often with chunks of metal flying out the back of the engine when the turbine overheated. British engines tended to fair much better due to better metals. For a time some US jet engines included the ability to inject water onto the engine to cool the exhaust in these cases. This was particularly notable because of the huge amounts of smoke that would pour out of the engine when it was turned on (typically for takeoff).
Today this problem is no longer a concern. Better materials have increased the critical temperature, and automatic throttle controls have made it basically impossible to overheat the engine. However the real solution was to bleed off some of the air from the compressor, run it down the shaft, and blow it through the middle of hollow turbine blades. This made the blades quite expensive to build, which is why jet engines never became as universal as it was first believed. However the quality of these bleed systems has continued to improve to the point where the latest Rolls-Royce Trent[?] designs operate at a compression ratio of 44:1, considerably better than piston engines.
The compressor uses up about 60 to 65% of all of the power generated by a jet engine. This explains why they aren't used in cars: you would be burning the fuel needed for a race while sitting still at a red light. Every bit of efficiency in running the compressor is needed, so one common design technique is to use more than one turbine to drive the compressors at various speeds. Most such designs use two stages, are are known as "two spool" engines, and a few have used three stages.
Given that 60% of the engine's power is being used up for driving the compressor, one option for better efficiency is to do less compression - that is, make a smaller engine. This seems self-defeating, but it's not the case. If you instead use some of that energy not to compress the air, but simply push it, you can get thrust without compression. This leads to....
By adding another turbine stage to the engine, all of the jet exhaust can be used for rotary force rather than jet thrust. Coupling this second (or third) turbine to a propeller makes for a very efficient engine due to the inherent efficiency of a propeller at low speeds. This is called a turboprop, and can be found on many smaller commuter planes, cargo planes, and helicopters (where it is often known as a turboshaft, largely for academic reasons). Propellers lose efficiency as aircraft speed increases, which is why they are not used on higher-speed aircraft.
Similar engines are "hidden" in many places. Connected to a generator they make excellent light-weight and very reliable power sources. In fact almost all large aircraft include another much smaller engine to provide power while parked at the airport, called an APU, and you can often see small pop-up doors near the tail to feed them air.
Larger versions of the same design are found in many industrial applications, peak-demand power generation stations, as well as military ships.
If the propeller is better at low speeds, and the turbojet is better at high speeds, you might imagine that at some speed range in the middle a mixture of the two is best. Such an engine is the turbofan (originally termed bypass turbojet by the inventors at Rolls Royce). Turbofans essentially increase the size of the first-stage compressor to the point where they act as a ducted propeller (or fan) blowing air past the "core" of the engine.
In fact the speed range where this type of engine is best turns out to be everything from about 250mph to 650mph, which is why the turbofan is by far the most used type of engine for aviation use.
The bypass ratio (the ratio of bypassed air to combustor air) is an important parameter for turbofans. Early turbofans (and most modern jet fighter engines) are low-bypass turbofans with bypass ratios less than 1. However, the "large mouthed" engines you have seen on almost all modern civilian jet aircraft are high-bypass turbofans which generally have bypass ratios of 3 or more.
Turbofans (especially high bypass engines) have another nice feature, they are fairly quiet. The noise of a jet engine is strongly related to the temperature of the air coming out the back. In the turbofan this hot air is mixed with the cold air bypassing the engine, so the result is a much lower temperature. You might think that jet aircraft are actually quite noisy, but if you stop to consider that the engines are delivering several tens of thousands of horsepower, you can see that a conventional engine of the same power would be much louder.
The reason propeller engines lose efficiency at high speed is the same reason that airplanes find it difficult to fly at supersonic speeds: an effect known as wave drag significantly increases drag just below the speed of sound, and led to the concept of the sound barrier.
In the case of a propeller this effect can happen any time the prop is spun fast enough that the tips of the prop start travelling near the speed of sound, even if the plane is sitting still. This can be controlled to a large degree by adding more blades to the prop, using up more power at a lower speed. This is why most WWII fighters started with two-blade props and were using five-blade designs by the end of the war as their engines increased in power, they couldn't just spin the prop faster. However this solution does not help as the plane itself accelerates; at some point the forward speed of the plane combined with the rotational speed of the propeller will once again result in wave drag problems.
The solution to decreasing wave drag was discovered by German researchers in WWII: it was to sweep the wing backwards at a strong angle. Today almost all aircraft designed to fly much above 450km use a swept-wing. In the 1970s NASA started researching propellers with similar sweep, although since the inside of the prop is turning slower than the outside, the blade became progressively more swept toward the outside, leading to a curved shape.
Although in reality such designs remained turboprops, the name propfan was picked to make them sound more interesting. However the ducting of the normal turbofan has the side effect of containing the sonic boom of the fan inside the engine where it is largely muted. Such is not the case on a propfan. Propfans were at one time thought to be the next logical step in engine development for subsonic aircraft, but their very high noise levels made them unattractive, and work on them has since stopped.
Propfans are also known as ultra high by-pass (UHB) engines.
At the other end of the scale from the increasing complexity of the fans is the ramjet. When air enters a jet engine its speed decreases and its pressure increases, called the ram compression effect. At high speeds this process can be fairly effective, and can provide enough compression to run an engine all on its own. Typically the speed needed to make this process work effectively is above 600mph, and doesn't outperform traditional designs until supersonic.
Ramjets are built to utilize this compression effect through a careful inlet design. Beyond that the engine is largely nothing more than a well-designed tube. A ramjet thus contains no (major) moving parts and is particularly useful in cases where you need small and simple engine for high speed use. On the downside they need to be flying at high speed to start with, making them less than useful for general tasks. As you might expect they have found use almost exclusively in missiles, where they are boosted to operating speeds by a rocket motor, or by being attached to another aircraft (typically a fighter). Today ramjets have been generally replaced by small turbofans, or rockets.
When the air inside a ramjet exceeds the speed of sound (meaning an aircraft speed of around Mach 5+) combustion fails to occur properly. This is overcome in a scramjet (supersonic combusting ramjet): the inlet is much wider (typically the entire underside of the craft) so the compression is less and the air remains at supersonic speeds. But conventional fuels are unusable at these speeds, so reactive chemicals or gases are used and the design of the jet is much more complex. Like a ramjet the scramjet must already be moving extremely fast before it will start working, but theoretically, speeds in excess of Mach 20 are possible.
Rocket engines need to carry both their fuel and air, which makes them carry around much more weight than a jet for the same amount of fuel burned. The turborocket is an attempt to reduce the amount of air (or to be exact, oxidizer) that needs to be carried by extracting some from the air the rocket flies through. Typical designs use a compressor similar to that of a traditional jet engine, but mix that along with additional oxidizer from the tanks. The compressor is turned off when reaching altitudes where there is no longer enough air to make this practical. Note that there are several other systems for extracting oxider from the air as well, designs known as LACE[?].