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The power expenditure to produce thrust consists of two parts, thrust power from the rate of change of momentum and aircraft speed, and the power represented by the wake kinetic energy.<ref name=":1">{{Cite report |last=Rubert |first=Kennedy F. |date=1945-02-01 |title=An analysis of jet-propulsion systems making direct use of the working substance of a thermodynamic cycle |url=https://ntrs.nasa.gov/citations/19930093532 |language=en}}</ref>
Entropy, identified as 's', is introduced here because, although its mathematical meaning is acknowledged as difficult,<ref>{{Cite journal |last=Smith |first=Trevor I. |last2=Christensen |first2=Warren M. |last3=Mountcastle |first3=Donald B. |last4=Thompson |first4=John R. |date=2015-09-23 |title=Identifying student difficulties with entropy, heat engines, and the Carnot cycle |url=https://link.aps.org/doi/10.1103/PhysRevSTPER.11.020116 |journal=Physical Review Special Topics - Physics Education Research |volume=11 |issue=2 |
The mathematical meaning of entropy, as applicable to the gas turbine jet engine, may be circumvented to allow use of the term in connection with the T~s diagram:
Quoting [[Frank Whittle]]:<ref>"Gas Turbine Aero-thermodynamics", Sir Frank Whittle, {{ISBN|0-08-026718-1}}, p. 2</ref> "Entropy is a concept which many students have a difficulty in assimilating. It is a somewhat intangible quantity...". Entropy is generated when energy is converted into an unusable form analogous to the loss of energy in a waterfall where the original potential energy is converted to unusable energy of turbulence.
Cumpsty says<ref>{{Cite book |last=Cumpsty |first=N. A. |url=http://archive.org/details/jetpropulsionsim0000cump |title=Jet propulsion
Denton compares it with aircraft drag, which is intuitive, "For an aircraft the ultimate measure of lost performance is the drag of its components....entropy creation reflects loss of efficiency in jet engines".<ref>Entropy Generation In Turbomachinery Flows"'Denton, SAE 902011, p. 2251</ref> He uses an analogy which imagines any inefficiency mechanism, such as the creation of whirls in the airflow, as producing smoke. Once created it cannot be destroyed and the concentration at the exit of the engine includes contributions from all loss-producing sources in the engine. The loss of efficiency is proportional to the concentration of the smoke at the exit.<ref>"Loss mechanisms in Turbomachines" Denton, ASME 93-GT-435, p. 4</ref>
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File:Schematic diagram of a heat engine02.jpg|This depiction of a jet engine as a [[heat engine]] shows that significant energy is wasted in the production of work, the energy balance being W=QH - Qa.<ref>{{Cite book |last=rayner joel |url=http://archive.org/details/heatengines0000rayn |title=heat engines |date=1960 |others=Internet Archive}}</ref> There is heat transfer QH from continuous combustion at TH to the airflow in the combustor, and simultaneous kinetic energy production W and energy dissipation with heat transfer Qa on leaving the engine to the surrounding atmosphere at Ta.
File:Joule-T-s-diagram.jpg|The T~s diagram (absolute temperature, T, and entropy, s,) is a graphic representation of two heat transfers, represented by areas of the diagram, and an area (blue-lined) representing mechanical work but in heat units. Heat transfer to the engine Qzu is area between line 2-3 and x-axis. Heat transferred to atmosphere Qab is area between line 1-4 and x-axis and the difference between the areas is the thermal energy converted to kinetic energy Wi.<ref>{{Cite journal |last=Kurzke |first=Joachim |last2=Halliwell |first2=Ian |date=2018 |title=Propulsion and Power |url=https://link.springer.com/book/10.1007/978-3-319-75979-1 |journal=SpringerLink |language=en |doi=10.1007/978-3-319-75979-1}}</ref> For a real engine, with flow losses (entropy-producing processes), the area of Wi (useful output) shrinks within the heat added area since less heat is converted to work and more is rejected in the exhaust.
File:Ts Real Brayton Cycle 2.png|The black-line diagram represent a jet engine cycle with maximum pressure p2 and temperature T3. When component inefficiencies are incorporated for a real engine the blue-lined area is the result which shows that entropy is increased in each process, including the combustion pressure loss from p3 tp p3', by the loss-making characteristics of air flow, such as friction, through each.<ref name=":2">{{Cite book |last=Mattingly |first=Jack D. |url=https://arc.aiaa.org/doi/book/10.2514/4.103711 |title=Elements of Propulsion: Gas Turbines and Rockets, Second Edition |last2=Boyer |first2=Keith M. |date=2016-01-20 |publisher=American Institute of Aeronautics and Astronautics, Inc. |isbn=978-1-62410-371-1 |___location=Reston, VA |language=en |doi=10.2514/4.103711}}</ref> Afterburning adds area to the cycle beyond line 3-4. The diagram also applies to a turbofan core cycle and an additional, smaller diagram<ref name=":2" /> is required for the bypass compression, bypass duct pressure loss and fan nozzle expansion.<ref>{{Cite journal |last=Lewis |first=John Hiram |date= |title=Propulsive efficiency from an energy utilization standpoint |url=https://arc.aiaa.org/doi/10.2514/3.44525 |journal=Journal of Aircraft |language=en |volume=13 |issue=4 |pages=299–302 |doi=10.2514/3.44525 |issn=0021-8669}}</ref>
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Thrust is easily controlled by regulating airflow and since all of the airflow is pumped by the fan N1 is used for setting thrust by [[General Electric Aviation]].<ref>Jet Engines And Propulsion Systems For Engineers, edited by Thaddeus Fowler, GE Aircraft Engines 1989, pp. 11–19</ref>
The EGT is a cockpit indicator for fuel flow since the fuel burned in the combustor determines the turbine entry temperature, which cannot be reliably measured, and EGT is a suitable alternative. Any deterioration from the engine as-new condition will require more fuel, resulting in higher temperature gas, to produce the thrust. At the take-off EPR, for example, the fuel flow and hence EGT rise with time in service as the engine deteriorates from its as-new condition. It progressively uses more fuel, until parts have to be replaced to restore the original lower operating temperature and reduce the cost of buying fuel.<ref>Performance of the Jet Transport Airplane, Young 2018, {{ISBN|{{Format ISBN|9781118534779}}}}, Fig 8.19</ref>
===Cockpit performance indicators may be misleading===
Although EPR is directly related to thrust over the flight envelope American Airlines experience with their first jet engines, [[Pratt & Whitney JT3C]], was marred by instrumentation problems so the cockpit reading was questioned and other parameters, FF and N1, were used by flight personnel in desperation.<ref>"American Airlines Experience with Turbojet/Turbofan Engines", Whatley, ASME 62-GTP-16</ref>
EPR is based on pressure measurements with the sampling tubes vulnerable to getting blocked. [[Air Florida Flight 90]] crashed on take-off in snow and icing conditions. The required take-off thrust was 14,500 lb which would normally be set by advancing the thrust levers to give an EPR reading of 2.04. Due to EPR probe icing the value set, ie 2.04, was erroneous and actually equivalent to 1.70 which gave an actual thrust of only 10,750 lb. The slower acceleration took 15 seconds longer than normal to reach lift off speed and contributed to the crash.<ref>{{cite web|title=Special Report: Air Florida Flight 90 |url=http://www.airdisaster.com/special/special-af90.shtml |website=AirDisaster.Com |access-date=May 30, 2015
EGT readings can also be misleading. The temperature of the gas leaving the turbine increases with engine use as parts become worn but the [[Strategic Air Command]] approved J57 and TF33 engines for flight without knowing they had bent and broken turbine parts. They were misled by low-reading EGT which indicated, when taken at face value, that the engines were in acceptable condition. It was found that the EGT probes were not positioned correctly to sample a representative gas temperature for the true condition of the engine.<ref>Who needs engine monitoring?, Aircraft Engine Diagnostics, NASA CP2190, 1981, p. 214</ref>
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The effects of heat transfer and friction in a combustor, both engine and afterburner, cause a loss of stagnation pressure and an increase in entropy. The loss in pressure is shown on a T~s diagram where it can be seen to reduce the area of the work part of the diagram. The pressure loss through a combustor has two contributions. One due to bringing the air from the compressor into the combustion area including through all the cooling holes (friction pressure loss), that is with air flowing but no combustion taking place. The addition of heat to the flowing gas adds another type of pressure loss (momentum pressure loss).
In addition to stagnation pressure loss the other measure of combustion performance is incomplete combustion. Combustion efficiency had always been close to 100 % at high thrust levels meaning only small amounts of HC and CO are present, but big improvements had to be made near idle operation. In the 1990's reduction of nitrogen oxides (NOx) became the focus due to its contribution to smog and acid rain for example. Combustor technology for reducing NOx is the Rich burn, Quick mix, Lean burn (RQL)<ref>https://www.researchgate.net/publication/271367881_The_Pratt_Whitney_TALON_X_Low_Emissions_Combustor_Revolutionary_Results_with_Evolutionary_Technology</ref> introduced by Pratt & Whitney with the TALON (Technology for Advanced Low NOx) PW4098 combustor.<ref>{{Cite journal |last=Liu |first=Yize |last2=Sun |first2=Xiaoxiao |last3=Sethi |first3=Vishal |last4=Nalianda |first4=Devaiah |last5=Li |first5=Yi-Guang |last6=Wang |first6=Lu |date=2017 |title=Review of modern low emissions combustion technologies for aero gas turbine engines |journal=Progress in Aerospace Sciences |volume=94 |page=15
Engine combustor configurations are reverse-flow separate, straight-through separate, can-annular (all 3 historic because the annular flow chamber gives more area and more even flow to the turbine), and modern annular and reverse-flow annular. Fuel preparation for combustion is either done by converting it into small drops (atomization) or heating it with air in tubes immersed in flame (vaporization).
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File:Royal Military Museum Brussels 2007 224.JPG|[[de Havilland Goblin]] with sixteen straight-through combustion chambers. Each consists of a flame tube enclosed in a pressure-tight outer casing. They are connected by tubes which balance the pressure and propagate the flame during start from the two tubes with igniters one of which is shown on a top tube.<ref>"Series II Goblin", Flight magazine,21st February,1946</ref>
File:Combustor on Rolls-Royce Nene turbojet (2).jpg|[[Rolls-Royce Nene]] with nine combustion chambers. The cutaway is one of 2 chambers fitted with a flame igniter which places the igniter in a cooler ___location than directly in the hot gas stream. During a start atomized fuel from the small self-contained unit (orange-coloured solenoid shown) is ignited by its ignition plug and the flaming jet of fuel is projected into the main fuel spray from the burner. Combustion is propagated to all the chambers through interconnecting tubes.<ref>https://archive.org/details/in.ernet.dli.2015.19428/page/n71/mode/2up,"Gas Turbines and Jet Propulsion" 4th edition, Smith, Fig. 73 and 77</ref>
File:Westinghouse J46-WE-8 axial flow jet engine - Hiller Aviation Museum - San Carlos, California - DSC03061.jpg|[[Westinghouse J46]] "walking stick" fuel vapouriser tubes in an annular combustor.<ref>"Westinghouse J46 Axial Turbojet Family. Development History And Technical Profiles", Paul J. Christiansen, {{ISBN|{{Format ISBN|978-0692764886}}}}, Figure 3 and 8</ref> Fuel vaporization was also used in the Sapphire, Viper, Pegasus, Olympus 593, and RB211 engines. Otherwise engines use some form of atomizing nozzle<ref>https://asmedigitalcollection.asme.org/gasturbinespower/article/132/11/116501/464800/GAS-TURBINE-COMBUSTION-Alternative-Fuels-and, p. 237</ref> which converts fuel pressure in the fuel tube to kinetic energy in the combustor producing a well-atomized spray.
File:Pratt & Whitney JT3.jpg|[[Pratt & Whitney J57]] with eight can-annular combustors, meaning the flame cans are separate but contained within the annular space between outer and inner casings. Each can was an annular combustion chamber in miniature with a central tube for cooling air and six burners arranged around it.<ref>"Two-spool Turbo Wasp", ''Flight magazine'', 27 November 1953.</ref>
File:Pratt & Whitney Canada PW500 (EBACE 2023).jpg|PW500 reverse flow annular combustor. The next-bigger series, the PW300, uses straight-through combustion but still with a centrifugal compressor supplying the air.
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=== Tip clearance changes with thrust changes ===
An engine is designed to run steady state at design points such as take-off, climb, and cruise with running clearances which minimize fuel use. Steady state means being at a constant rpm for long enough (several minutes) for all parts to have stopped moving relative to each other from transient thermal growths. During this time clearances between parts may close up to rubbing contact and wear to give larger clearances, and fuel consumption, at the important stabilized condition. This scenario inside the engine is prevented by internal compressor bore cooling<ref>"Jet Engines And Propulsion Systems For Engineers, GE Aircraft Engines 1989, pp. 8–10</ref> and external turbine casing cooling on big fan engines (active clearance control).
<ref>https://ntrs.nasa.gov/citations/20060051674 "Transient tip clearance" fig.1</ref><ref>https://patents.google.com/patent/US6126390A/en "Passive clearance control system for a gas turbine"</ref>
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=== Tip clearance with backbone bending and case out-of-roundness ===
The advent of the high bypass civil engines, JT9D and CF6, showed the importance of thrust take off locations on the engine cases. Also, large engines have relatively flexible cases inherent in large diameter flight-weight structures giving relatively large relative displacements between heavy stiff rotors and the flexible cases.
Case distortion with subsequent blade tip rubbing and performance loss appeared on the JT9D installation in the Boeing 747 as a result of thrust being taken from a single point on top of the engine exhaust case. Thrust from the rear mount plane was a Boeing requirement.<ref>"Jet Engine Force Frame", US patent 3,675,418</ref> Compared to the 15,000 lb thrust JT3D with its four structural cases the 40,000 lb thrust JT9D made economical use of supporting structure with only three structural cases making a compact lightweight design.<ref>https://nyaspubs.onlinelibrary.wiley.com/doi/abs/10.1111/j.1749-6632.1968.tb15216.x, "Development Of The High Bypass Turbofan", p. 588 'Advanced Structural Concepts'</ref> During flight testing the engines suffered violent surges and loss in performance<ref>"747 Creating The World's First Jumbo Jet And Other Adventures From A Life In Aviation", Sutter, {{ISBN|978 0 06 088241 9}}, p. 187</ref> which were traced to bending of the engine backbone by 0.043 in. at the combustor case and the turbine case going out-of-round which in turn caused blade tip rubs and increased tip clearance.<ref>Flight International,13 November 1969, p. 749</ref>
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Gas path deterioration and increasing EGT coexist. As the gas path deteriorates the EGT limit ultimately prevents the take-off thrust from being achieved and the engine has to be repaired.<ref>Aircraft Engine Diagnostics, NASA CP 2190, 1981, JT8D Engine Performance Retention, p. 64</ref>
The engine performance deteriorates with use as parts wear, meaning the engine has to use more fuel to get the required thrust. A new engine starts with a reserve of performance which is gradually eroded. The reserve is known as its temperature margin and is seen by a pilot as the EGT margin. For a new [[CFM International CFM56]]-3 the margin is 53 °C.<ref>https:smart cockpit.com, CFM Flight Operations Support, page 37</ref><ref>Performance of the Jet Transport Airplane, Young 2018, {{ISBN|{{Format ISBN|9781118534779}}}}, Fig 8.19</ref> Kraus<ref>https://reposit.haw-hamburg.de/handle/20.500.12738/5576,"Further investigation of engine performance loss, in particular exhaust gas temperature margin, in the CF6-80C2 jet engine and recommendations for test cell modifications to record additional criteria, Tables 2.1–2.4</ref> gives the effect on increased fuel consumption of typical component degradation during service.
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==Terminology and explanatory notes==
===Clarifying momentum, work, energy, power===
A basic explanation for the way burning fuel results in engine thrust uses terminology like momentum, work, energy, power and rate. Correct use of the terminology may be confirmed by using the idea of fundamental units which are mass '''M''', length '''L''' and time '''T''', together with the idea of a dimension, ie power, of the fundamental unit, say '''L'''<sup>1</sup> for distance, and in a derived unit, say speed which is distance over time, with dimensions '''L'''<sup>1</sup> '''T''' <sup>−1</sup>
Force dimensions are '''M'''<sup>1</sup> '''L'''<sup>1</sup> '''T'''<sup>−2</sup> , momentum has dimensions '''M'''<sup>1</sup>'''L'''<sup>1</sup> '''T'''<sup>−1</sup> and rate of change of momentum has dimensions '''M'''<sup>1</sup> '''L'''<sup>1</sup>'''T'''<sup>−2</sup>, ie the same as force. Work and energy are similar quantities with dimensions '''M'''<sup>1</sup> '''L'''<sup>2</sup>'''T'''<sup>−2</sup>. Power has dimensions '''M'''<sup>1</sup> '''L'''<sup>2</sup>'''T'''<sup>−3</sup>.<ref>https://archive.org/details/masslengthtime0000norm_v5r2/page/150/mode/2up, Mass, Length and Time, Norman Feather 1959, p. 150</ref>
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