Jet engine performance: Difference between revisions

Revision as of 22:01, 17 November 2023

Revision as of 01:39, 19 November 2023

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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 |pages=020116 |doi=10.1103/PhysRevSTPER.11.020116}}</ref> its common representation on a Temperature~entropy (T~s) diagram for a jet engine cycle is graphical and intuitive since its influence is shown as areas of the diagram. The T~s diagram was invented to help engineers responsible for the operation of steam engines to understand the efficiency of their engines. It supplemented the already-existing p~v diagram which only gave half the heat engine efficiency story in only showing the cylinder work done with no reference to the heat supplied and wasted in doing so. The need for an additional diagram, as opposed to understanding difficult theories, recognized the value of graphically representing heat transfers to and from an engine.<ref>Transactions The Manchester Association of Engineers 1904, The Temperature-Entropy Diagram, Mr. G. James Wells, p. 237</ref> It would show areas representative of heat converted to work compared to heat supplied (thermal efficiency).<ref>{{Cite book |last= |url=http://archive.org/details/reportcommittee05unkngoog |title=Report of the committee appointed on the 31st March, 1896, to consider and report to the Council upon the subject of the definition of a standard or standards of thermal efficiency for steam-engines .. |date=1898 |publisher=London, the Institution}}</ref>

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 in tointo 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 : a simple guide to the aerodynamic and thermodynamic design and performance of jet engines |date=1997 |publisher=Cambridge; New York: Cambridge University Press |via=Internet Archive |isbn=978-0-521-59330-4}}</ref> "... a rise in entropy is a loss in the capability of turning thermal energy into work".

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Thrust is generated inside a jet engine by internal components as they energize a gas stream.<ref>{{Cite web |date=2023-10-24 |title=Jet engine {{!}} Engineering, Design, & Functionality {{!}} Britannica |url=https://www.britannica.com/technology/jet-engine |access-date=2023-11-16 |website=Britannica |language=en}}</ref>

Fuel energy released in the combustor is accounted for in two main categories: acceleration of the mass flow through the engine and residual heat.<ref>{{Cite book |url=http://archive.org/details/sim_journal-of-aircraft_september-october-1966_3_5 |title=Journal of Aircraft September-October 1966: Vol 3 Iss 5 |date= |publisher=American Institute of Aeronautics and Astronautics |via=Internet Archive |language=English}}</ref>

Acceleration of the flow through the engine causes simultaneous production of kinetic energy accompanying the thrust-producing backward momentum. The kinetic energy is left behind the engine without contributing to the thrust power<ref>'Jet Propulsion For Airplanes', Buckingham, NACA report 159, p. 85</ref> and is known as residual velocity loss. The thrust force from a stationary engine becomes thrust power when an aircraft is moving under its influence.

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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. <ref>{{Cite report |last=Weber |first=Richard J. |last2=Mackay |first2=John S. |date=1958-09-01 |title=An Analysis of Ramjet Engines Using Supersonic Combustion |url=https://ntrs.nasa.gov/citations/19930085282 |language=en}}</ref>

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 inefficiencesinefficiencies 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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