Discrete logarithm: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
en>Averykhoo
m (superfluously?) specifying integral constraint
 
Line 1: Line 1:
{{for|the [[Hong Kong]] based ferry company|TurboJET}}
The one who wrote this article is known as LidaKayaking is what she enjoys performingHer husband and her reside in West VirginiaReleasing output is her day job currently and her pay hasbeen definitely fulfilling.<br><br>Also visit my homepage :: [http://www.linkedin.com/pub/jordan-kurland/a/618/581 Jordan Kurland]
{{Refimprove|date=April 2008}}
[[File:Jet engine.svg|thumb|300px|Diagram of a typical gas turbine jet engine]]
{|{{Infobox aircraft begin
|name=
|image=
|caption=
}}{{Seriesbox aircraft propulsion}}
|}
 
The '''turbojet''' is a kind of general-purpose [[airbreathing jet engine]]. Two engineers, [[Hans von Ohain]] in [[Germany]] and [[Frank Whittle]] in the [[United Kingdom]], developed the concept independently into practical engines during the late 1930s.
 
Turbojets consist of an air inlet, an [[air compressor]], a combustion chamber, a gas [[turbine]] (that drives the air compressor) and a [[nozzle]]. The air is compressed into the chamber, heated and expanded by the fuel combustion and then allowed to expand out through the turbine into the nozzle where it is accelerated to high speed to provide propulsion.<ref>{{cite web | title = Turbojet Engine | publisher = NASA Glenn Research Center | url = http://www.grc.nasa.gov/WWW/K-12/airplane/aturbj.html | accessdate =2009-05-06 }}</ref>
 
Compared to [[turbofan]]s, turbojets are quite inefficient if flown below about Mach 2{{citation needed|date=October 2010}} and are very [[Jet engine#Noise|noisy]]. Turbojet efficiency only comes into play at supersonic Mach numbers and high altitudes where small frontal area is optimal, and large fan blades are inefficient. Few aircraft cruise in this expensive regime, so most modern aircraft use turbofans instead for fuel economy and low altitude performance. However, turbojets are still common in medium range [[cruise missile]]s, due to their high exhaust speed, small frontal area, and relative simplicity.
 
== History ==
[[File:Albert Fono's Patents for jet engines 1928.jpg|thumb|left|[[Albert Fonó]]'s German patent for jet Engines (January 1928). The third illustration is a turbojet]]
[[File:Ohain USAF He 178 page61.jpg|thumb|left|[[Heinkel He 178]], the world's first aircraft to fly purely on turbojet power, using an [[Heinkel HeS 3|HeS 3]] engine]]
 
The first patent for using a gas turbine to power an aircraft was filed in 1921 by Frenchman [[Maxime Guillaume]].<ref name="Guillaume" >Maxime Guillaume,"Propulseur par réaction sur l'air," French patent {{cite patent|FR|534801}} (filed: 3 May 1921; issued: 13 January 1922)</ref>  His engine was to be an axial-flow turbojet, but was never constructed, as it would have required considerable advances over the state of the art in compressors.
 
Practical axial compressors were made possible by ideas from [[Alan Arnold Griffith|A.A.Griffith]] in a seminal paper in 1926 ("An Aerodynamic Theory of Turbine Design").
 
The first turbojet to run was the [[Power Jets WU]] which ran on 12th April 1937.
 
On 27 August 1939 the [[Heinkel He 178]] became the world's first aircraft to fly under turbojet power with test-pilot [[Erich Warsitz]] at the controls,<ref>Warsitz, Lutz: [http://www.pen-and-sword.co.uk/?product_id=1762 ''THE FIRST JET PILOT - The Story of German Test Pilot Erich Warsitz'' (p. 125), Pen and Sword Books Ltd., England, 2009, ISBN 978-1-84415-818-8]</ref> thus becoming the first practical jet plane. The first two operational turbojet aircraft, the [[Messerschmitt Me 262]] and then the [[Gloster Meteor]] entered service towards the end of [[World War II]] in 1944.
 
A turbojet engine is used primarily to propel [[aircraft]], but has been used for other vehicles, such as cars. Air is drawn into the rotating compressor via the intake and is compressed to a higher pressure before entering the combustion chamber. [[Fuel]] is mixed with the compressed air and ignited by a flame in the eddy of a [[flame holder]]. This [[combustion]] process significantly raises the temperature of the gas. Hot combustion products leaving the combustor expand through the [[turbine]] where [[Power (physics)|power]] is extracted to drive the compressor. Although this expansion process reduces the turbine exit gas temperature and pressure, both parameters are usually still well above ambient conditions. The gas stream exiting the turbine expands to ambient pressure via the propelling nozzle, producing a high velocity jet in the exhaust plume. If the momentum of the exhaust stream exceeds the momentum of the intake stream, the impulse is positive, thus, there is a net forward [[thrust]] upon the airframe.
 
Early generation jet engines were pure turbojets, designed initially to use a [[centrifugal compressor]] (as in the [[Heinkel HeS 3]]), and very shortly afterwards began to use [[Axial compressor]]s (as in the [[Junkers Jumo 004]]) for a smaller diameter to the overall engine housing. They were used because they were able to achieve very high altitudes and speeds, much higher than [[Propeller (aircraft)|propeller]] engines, because of a better compression ratio and because of their high exhaust speed. However, they were not very fuel efficient. Modern jet engines are mainly [[turbofan]]s, where a proportion of the air entering the intake bypasses the combustor; this proportion depends on the engine's [[bypass ratio]]. This makes turbofans much more efficient than turbojets at high subsonic/transonic and low supersonic speeds.
 
One of the most recent uses of turbojet engines was the [[Olympus 593]] on [[Concorde]]. Concorde used turbojet engines because the smaller cross-section and high exhaust speed is ideal for operation at Mach 2. Concorde's engine burnt less fuel to produce a given thrust for a mile at Mach 2.0 than a modern high-bypass turbofan such as [[General Electric CF6]] at its Mach 0.86 optimum speed. Concorde's airframe, however, was far less efficient than that of any subsonic airliner, resulting in a higher overall fuel burn than comparable subsonic aircraft.
 
Turbojet engines had a significant impact on [[commercial aviation]]. Aside from being faster than [[piston engines]], turbojets had greater reliability, with some models demonstrating dispatch reliability rating in excess of 99.9%. Pre-jet commercial aircraft were designed with as many as 4 engines in part because of concerns over in-flight failures. Overseas flight paths were plotted to keep planes within an hour of a landing field, lengthening flights. Turbojets' reliability allowed for three and two-engine designs, and more direct long-distance flights.<ref>{{Citation | last = Larson | first = George C. | title = Old Faithful | journal = "Air & Space" | volume = 25 | issue = 1 |date=April–May 2010 | page = 80 | url = http://www.airspacemag.com }}</ref>
 
Although [[ramjet]] engines are simpler in design as they have virtually no moving parts, they are incapable of operating at low flight speeds, and thus cannot be the only source of propulsion for an aircraft.
 
== Early designs ==
[[File:Air starter GE J79-11A by BMW.JPG|thumb|Cutaway of an [[air start system]] of a [[General Electric J79]] turbojet. The small turbine and epicyclic gearing are clearly visible]]
 
Early German engines had serious problems controlling the turbine inlet temperature. A lack of suitable alloys due to war shortages meant the turbine rotor and stator blades would sometimes disintegrate on first operation and never lasted long. Their early engines averaged 10–25 hours of operation before failing, often with chunks of metal flying out the back of the engine when the turbine overheated. British engines such as the [[Rolls-Royce Welland]] tended to fare better, being [[type certificate]]d for initially 80 hours, later extended to 150 hours between overhauls, as a result of an extended 500 hour run being achieved in tests.<ref>{{cite magazine|url=http://www.flightglobal.com/pdfarchive/view/1945/1945%20-%202113.html |title=Rolls-Royce Derwent &#124; 1945 |work=Flight |publisher=Flightglobal.com |date=1945-10-25 |accessdate=2013-12-14|page=448}}</ref> A few of the original fighters still exist with their original engines, but many have been re-engined with more modern engines with greater fuel efficiency and a longer [[Time between overhaul|TBO]] (such as the [[Messerschmitt 262#Reproductions|reproduction Me-262]] powered by [[General Electric J85]]s).
 
[[File:J85 ge 17a turbojet engine.jpg|thumb|left|J85-GE-17A turbojet engine from General Electric (1970)]]
 
The [[United States]] had the best materials because of their reliance on [[Turbocharger|turbo/supercharging]] in high altitude bombers of [[World War II]]. For a time some US jet engines included the ability to inject water into the engine to cool the compressed flow before combustion, usually during takeoff. The water would tend to prevent complete combustion and as a result the engine ran cooler again, but the planes would take off leaving a huge plume of smoke.
 
Today these problems are much better handled, but temperature still limits turbojet airspeeds in supersonic flight. At the very highest speeds, the compression of the intake air raises the temperatures throughout the engine to the point that the turbine blades would melt, forcing a reduction in fuel flow to lower temperatures, but giving a reduced thrust and thus limiting the top speed. [[Ramjet]]s and [[scramjet]]s do not have turbine blades; therefore they are able to fly faster, and [[rocket engine]]s run even hotter still.
 
At lower speeds, better materials have increased the critical temperature, and automatic fuel management controls have made it nearly impossible to overheat the engine.
 
== Design ==
{{stack|
[[File:Axial compressor.gif|thumb|An animation of an axial compressor. The stationary blades are the stators]]
[[File:Turboreacteur anime.gif|thumb|Turbojet animation]]
[[File:Turbojet operation- centrifugal flow.png|thumb|Schematic diagram showing the operation of a centrifugal flow turbojet engine. The compressor is driven via the turbine stage and throws the air outwards, requiring it to be redirected parallel to the axis of thrust]]
[[File:Turbojet operation- axial flow.png|thumb|Schematic diagram showing the operation of an axial flow turbojet engine. Here, the compressor is again driven by the turbine, but the air flow remains parallel to the axis of thrust]]
}}
 
=== Air intake ===
Preceding the compressor is the air intake (or inlet). It is designed to be as efficient as possible at recovering the ram pressure of the air stream tube approaching the intake. The air leaving the intake then enters the compressor. The stators (stationary blades) guide the airflow of the compressed gases.
 
=== Compressor ===
The compressor is driven by the turbineThe compressor rotates at a very high speed, adding [[energy]] to the airflow and at the same time squeezing (compressing) it into a smaller space.  Compressing the air increases its [[pressure]] and [[temperature]].
 
In most turbojet-powered aircraft, [[bleed air]] is extracted from the compressor section at various stages to perform a variety of jobs including air conditioning/pressurization, engine inlet anti-icing and turbine coolingBleeding air off decreases the overall efficiency of the engine, but the usefulness of the compressed air outweighs the loss in efficiency.
 
Several types of compressors are used in turbojets and [[gas turbines]] in general: axial, centrifugal, axial-centrifugal, double-centrifugal, etc.
 
Early turbojet compressors had overall pressure ratios as low as 5:1 (as do a lot of simple [[auxiliary power unit]]s and small propulsion turbojets today). Aerodynamic improvements, plus splitting the compression system into two separate units and/or incorporating variable compressor geometry, enabled later turbojets to have overall pressure ratios of 15:1 or more. For comparison, modern civil [[turbofan]] engines have overall pressure ratios of 44:1 or more.
 
After leaving the compressor section, the compressed air enters the combustion chamber.
 
=== Combustion chamber ===
The burning process in the [[combustor]] is significantly different from that in a [[piston engine]]. In a piston engine the burning gases are confined to a small volume and, as the fuel burns, the pressure increases dramatically. In a turbojet the air and fuel mixture passes unconfined through the [[combustion chamber]]. As the mixture burns its temperature increases dramatically, but the pressure actually decreases a few percent.
 
The fuel-air mixture must be brought almost to a stop so that a stable flame can be maintainedThis occurs just after the start of the combustion chamber. The [[aft]] part of this flame front is allowed to progress rearward. This ensures that all of the fuel is burned, as the flame becomes hotter when it leans out, and because of the shape of the combustion chamber the flow is accelerated rearwards. Some pressure drop is required, as it is the reason why the expanding gases travel out the rear of the engine rather than out the front. Less than 25% of the air is involved in combustion, in some engines as little as 12%, the rest acting as a reservoir to absorb the heating effects of the burning fuel.
 
Another difference between piston engines and jet engines is that the peak flame temperature in a piston engine is experienced only momentarily in a small portion of the full cycle. The combustor in a jet engine is exposed to the peak flame [[temperature]] continuously and operates at a pressure high enough that a [[Stoichiometry#Stoichiometry of combustion|stoichiometric]] fuel-air ratio would melt the can and everything downstream. Instead, jet engines run a very lean mixture, so lean that it would not normally support combustion. A central core of the flow (primary airflow) is mixed with enough fuel to burn readily. The cans are carefully shaped to maintain a layer of fresh unburned air between the metal surfaces and the central core. This unburned air (secondary airflow) mixes into the burned gases to bring the temperature down to something a turbine can tolerate.
 
=== Turbine ===
Hot gases leaving the combustor are allowed to expand through the turbine. Turbines are usually made up of metals such as [[inconel]] or [[Nimonic]]<ref>[http://www.flightglobal.com/pdfarchive/view/1960/1960%20-%201525.html 1960 &#124; Flight &#124; Archive]</ref> to resist the high temperature, and frequently have built-in cooling channels.
 
In the first stage the turbine is largely an impulse turbine (similar to a [[pelton wheel]]) and rotates because of the impact of the hot gas stream. Later stages are convergent ducts that accelerate the gas rearward and gain energy from that process. Pressure drops, and energy is transferred into the shaft. The turbine's [[Angular momentum|rotational energy]] is used primarily to drive the compressor. Some shaft power is extracted to drive accessories, like fuel, oil, and hydraulic pumps. Because of its significantly higher entry temperature, the turbine pressure ratio is much lower than that of the compressor. In a turbojet almost two-thirds of all the power generated by burning fuel is used by the compressor to compress the air for the engine.{{Citation needed|date=November 2009}}
 
=== Nozzle ===
{{main|propelling nozzle}}
 
After the turbine, the gases are allowed to expand through the exhaust nozzle to atmospheric pressure, producing a high velocity jet in the exhaust plume. In a convergent nozzle, the ducting narrows progressively to a throat. The nozzle pressure ratio on a turbojet is usually high enough for the expanding gases to reach Mach 1.0 and choke the throat. Normally, the flow will go supersonic in the exhaust plume outside the engine.
 
If, however, a convergent-divergent [[de Laval nozzle]] is fitted, the divergent (increasing flow area) section allows the gases to reach supersonic velocity within the nozzle itself. This is slightly more efficient on thrust than using a convergent nozzle. There is, however, the added weight and complexity since the convergent-divergent nozzle must be fully variable in its shape to cope with changes in gas flow caused by engine throttling.
 
===Thrust Augmentation===
Thrust can be increased by injecting additional fluids. It is then called ''wet thrust''.
 
Early and nonafterburning engines use water injection to temporarily increase thrust. Water is injected at the compressor air inlet or the diffuser to cool the compressing air which permits an increase in pressure for a higher burning. A 10-30% additional thrust can be gained. Examples being the Pratt & Whitney J-57 and derivatives still in use today.
 
==== Afterburner ====
{{main|afterburner}}
 
An afterburner or "reheat jetpipe" is a device added to the rear of the jet engine. It provides a means of spraying fuel directly into the hot exhaust, where it ignites and boosts available thrust significantly; a drawback is its very high fuel consumption rate. Afterburners are used almost exclusively on [[supersonic aircraft]] – most of these are military aircraft. The two supersonic civilian transports, [[Concorde]] and the [[TU-144]], also used afterburners but these two have now been retired from service. [[Scaled Composites White Knight]], a carrier aircraft for the experimental [[Scaled Composites SpaceShipOne|SpaceShipOne]] [[suborbital]] spacecraft, also uses an afterburner.
 
== Net thrust ==
The net [[thrust]] <math>F_N\;</math> of a turbojet is given by:<ref name="JP3.1" >{{Cite book | last=Cumpsty  |first=Nicholas | year=2003 | title=Jet Propulsion | edition=2nd | publisher=Cambridge University Press | isbn=0-521-54144-1 | ref=Cumpsty, Jet Propulsion | chapter=3.1 }}</ref><ref>{{cite web | title = Turbojet Thrust | publisher = NASA Glenn Research Center | url = http://www.grc.nasa.gov/WWW/K-12/airplane/turbth.html | accessdate =2009-05-06 }}</ref>
 
<math>F_N =( \dot{m}_{air}  + \dot{m}_f) V_{j} - \dot{m}_{air} V</math>
 
where:
 
{| style="border: none"
|-
|<math>\dot{m}_{air}</math>
| is the rate of flow of air through the engine
|-
|<math>\dot{m}_f</math>
| is the rate of flow of fuel entering the engine
|-
|<math>V_j\;</math>
| is the speed of the jet (the exhaust plume) and is assumed to be less than [[sonic velocity]]
|-
|<math>V\;</math>
| is the [[true airspeed]] of the aircraft
|-
|<math>(\dot{m}_{air} + \dot{m}_f) V_j</math>
| represents the nozzle gross thrust
|-
|<math>\dot{m}_{air} V</math>
| represents the ram drag of the intake
|}
 
If the speed of the jet is equal to [[sonic velocity]] the nozzle is said to be [[Choked flow|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''.<ref name="Cumpsty, 6.3" >[[#Cumpsty, Jet Propulsion|Cumpsty, Jet Propulsion]], Section 6.3</ref>
 
The rate of flow of fuel entering the engine is very small compared with the rate of flow of air.<ref name=JP3.1/>  If the contribution of fuel to the nozzle gross thrust is ignored, the net thrust is:
 
<math>F_N = \dot{m}_{air} (V_{j} - V)</math>
 
The speed of the jet <math>V_j\;</math> must exceed the true airspeed of the aircraft <math>V\;</math>if there is to be a net forward thrust on the airframe. The speed <math>V_j\;</math> can be calculated thermodynamically based on [[adiabatic expansion]].<ref>[http://web.mit.edu/16.unified/www/SPRING/propulsion/notes/node85.html#SECTION06364000000000000000 MIT.EDU Unified: Thermodynamics and Propulsion Prof. Z. S. Spakovszky - Turbojet Engine]</ref>
 
A simple turbojet engine will produce thrust of approximately: 2.5 pounds force per horsepower (15&nbsp;mN/W).
 
== Cycle improvements ==
Thermodynamics of a typical air-breathing jet engine are modeled approximately by a [[Brayton Cycle]].
 
Increasing the overall pressure ratio of the compression system also raises the combustor entry temperature. Therefore, at fixed fuel and air flows, there is an increase in turbine inlet temperature. Although the temperature rise across the compression system will also cause the turbine temperature to increase, the nozzle temperature remains unaffected because the same amount of heat is being added to the system. There is, however, a rise in nozzle pressure, because overall pressure ratio increases faster than the turbine expansion ratio. Consequently, net thrust increases, while specific fuel consumption (fuel flow/net thrust) decreases.
 
Thus turbojets can be made more fuel efficient by raising overall pressure ratio and turbine inlet temperature in union. However, better turbine materials and/or improved vane/blade cooling are required to cope with increases in both turbine inlet temperature and compressor delivery temperature. Increasing the latter requires better compressor materials.
 
Minimizing heat losses and optimizing the inlet temperature ratio will increase the system's useful work and the thermal efficiency of the turbo jet engine.
 
== See also ==
* [[Air start system]]
* [[Brayton Cycle]]
* [[Exoskeletal engine]]
* [[Jet dragster]]
* [[Turbojet development at the RAE]]
* [[Turbine engine failure]]
* [[Variable Cycle Engine]]
 
== Notes ==
{{Reflist}}
 
== References ==
{{refbegin}}
* {{cite book | last = Springer  |first=Edwin H. | year = 2001 | title = Constructing A Turbocharger Turbojet Engine | publisher = Turbojet Technologies | ref = Springer, Turbocharger Turbojet }}
{{refend}}
 
== External links ==
{{Commons category|Turbojet engines}}
* [http://www.erichwarsitz.com Erich Warsitz, the world's first jet pilot]: includes rare videos (Heinkel He 178) and audio commentaries]
* [http://www.grc.nasa.gov/WWW/k-12/airplane/Animation/turbtyp/ettf.html NASA Turbojet Engine Description]: includes a software model]
 
{{Aircraft gas turbine engine components}}
{{Aviation lists}}
{{Use dmy dates|date=September 2010}}
 
[[Category:Jet engines]]
[[Category:Gas turbines]]
[[Category:Research and development in Nazi Germany]]
[[Category:British inventions]]
 
{{Link GA|fr}}
[[cs:Proudový motor]]
[[de:Strahltriebwerk#Einstrom-Strahltriebwerk (Turbojet)]]
[[vi:Động cơ turbin phản lực]]

Latest revision as of 19:34, 27 October 2014

The one who wrote this article is known as Lida. Kayaking is what she enjoys performing. Her husband and her reside in West Virginia. Releasing output is her day job currently and her pay hasbeen definitely fulfilling.

Also visit my homepage :: Jordan Kurland