IDEAS home Printed from https://ideas.repec.org/a/gam/jeners/v14y2021i8p2316-d539525.html
   My bibliography  Save this article

The Use of the Fourier Series to Analyze the Shaping of Thermodynamic Processes in Heat Engines

Author

Listed:
  • Michał Głogowski

    (Faculty of Process and Environmental Engineering, Lodz University of Technology, Wolczanska 213, 90-924 Lodz, Poland)

  • Przemysław Kubiak

    (Institute of Vehicles, Warsaw University of Technology, str. Narbutta 84, 02-524 Warsaw, Poland)

  • Szymon Szufa

    (Faculty of Process and Environmental Engineering, Lodz University of Technology, Wolczanska 213, 90-924 Lodz, Poland)

  • Piotr Piersa

    (Faculty of Process and Environmental Engineering, Lodz University of Technology, Wolczanska 213, 90-924 Lodz, Poland)

  • Łukasz Adrian

    (Eko-Look, Lokajskiego 1A, 98-200 Sieradz, Poland)

  • Mateusz Krukowski

    (Institute of Mathematics, Lodz University of Technology, Wolczanska Str. 215, 90-924 Lodz, Poland)

Abstract

The article presents the application of the Fourier series to theoretical considerations on the method of maximum temperature control in thermodynamic cycles of internal combustion engines equipped with an additional independent kinematic system. The analysis assumes that the processes are zero-dimensional and the gases consumed in the engine cycles are perfect, simplifying the considerations for temperature control as a function of the two variables, pressure and volume, of which the volume as a geometric quantity can be completely controlled. In view of this fact, a predetermined temperature curve was assumed, ultimately reducing the considerations of specific volume changes, that is to say a kinematic system that could implement these changes. Moreover, in the analysis of volume changes, a cycle not used so far in the description of internal combustion engines was used. In the next step, the cycle was modified using the popular Vibe function, which was replaced in the theoretical cycle by two isochoric and isothermal transformations. Heat exchange was completely omitted in the considerations, in that it is of secondary importance, ultimately bringing the temperature function to the function of one variable, the angle of rotation of the crankshaft. Then, the kinematics was divided into the kinematics of the crank-piston system and the additional system, which was approximated with five words from the Fourier series, which in the technique correspond, for example, to the system of oscillators. At the end of the article we have explained one of the ways of actual technical implementation using a single nonlinear oscillator, the so-called ACC system equivalent to a few words from the mentioned Fourier series.

Suggested Citation

  • Michał Głogowski & Przemysław Kubiak & Szymon Szufa & Piotr Piersa & Łukasz Adrian & Mateusz Krukowski, 2021. "The Use of the Fourier Series to Analyze the Shaping of Thermodynamic Processes in Heat Engines," Energies, MDPI, vol. 14(8), pages 1-23, April.
    • Handle: RePEc:gam:jeners:v:14:y:2021:i:8:p:2316-:d:539525
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1996-1073/14/8/2316/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1996-1073/14/8/2316/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Maciej Dzikuć & Arkadiusz Piwowar & Szymon Szufa & Janusz Adamczyk & Maria Dzikuć, 2021. "Potential and Scenarios of Variants of Thermo-Modernization of Single-Family Houses: An Example of the Lubuskie Voivodeship," Energies, MDPI, vol. 14(1), pages 1-11, January.
    2. Szwaja, Stanislaw & Jamrozik, Arkadiusz & Tutak, Wojciech, 2013. "A two-stage combustion system for burning lean gasoline mixtures in a stationary spark ignited engine," Applied Energy, Elsevier, vol. 105(C), pages 271-281.
    3. Maciej Dzikuć & Piotr Kuryło & Rafał Dudziak & Szymon Szufa & Maria Dzikuć & Karolina Godzisz, 2020. "Selected Aspects of Combustion Optimization of Coal in Power Plants," Energies, MDPI, vol. 13(9), pages 1-15, May.
    4. You Zhou & Wei Hong & Ye Yang & Xiaoping Li & Fangxi Xie & Yan Su, 2019. "Experimental Investigation of Diluents Components on Performance and Emissions of a High Compression Ratio Methanol SI Engine," Energies, MDPI, vol. 12(17), pages 1-18, September.
    5. Xuewei Pan & Yinghua Zhao & Diming Lou & Liang Fang, 2020. "Study of the Miller Cycle on a Turbocharged DI Gasoline Engine Regarding Fuel Economy Improvement at Part Load," Energies, MDPI, vol. 13(6), pages 1-26, March.
    6. Hüseyin Emre Doğan & Osman Akın Kutlar & Majid Javadzadehkalkhoran & Abdurrahman Demirci, 2019. "Investigation of Burn Duration and NO Emission in Lean Mixture with CNG and Gasoline," Energies, MDPI, vol. 12(23), pages 1-18, November.
    7. Zhao, Jinxing, 2017. "Research and application of over-expansion cycle (Atkinson and Miller) engines – A review," Applied Energy, Elsevier, vol. 185(P1), pages 300-319.
    8. Zhen, Xudong & Wang, Yang & Xu, Shuaiqing & Zhu, Yongsheng & Tao, Chengjun & Xu, Tao & Song, Mingzhi, 2012. "The engine knock analysis – An overview," Applied Energy, Elsevier, vol. 92(C), pages 628-636.
    9. Hunicz, Jacek & Mikulski, Maciej, 2018. "Investigation of the thermal effects of fuel injection into retained residuals in HCCI engine," Applied Energy, Elsevier, vol. 228(C), pages 1966-1984.
    10. Łukasz Adrian & Szymon Szufa & Piotr Piersa & Piotr Kuryło & Filip Mikołajczyk & Krystian Kurowski & Sławomir Pochwała & Andrzej Obraniak & Jacek Stelmach & Grzegorz Wielgosiński & Justyna Czerwińska , 2021. "Analysis and Evaluation of Heat Pipe Efficiency to Reduce Low Emission with the Use of Working Agents R134A, R404A and R407C, R410A," Energies, MDPI, vol. 14(7), pages 1-29, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Łukasz Adrian & Szymon Szufa & Piotr Piersa & Filip Mikołajczyk, 2021. "Numerical Model of Heat Pipes as an Optimization Method of Heat Exchangers," Energies, MDPI, vol. 14(22), pages 1-38, November.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wang, Shuofeng & Ji, Changwei & Zhang, Bo & Liu, Xiaolong, 2014. "Lean burn performance of a hydrogen-blended gasoline engine at the wide open throttle condition," Applied Energy, Elsevier, vol. 136(C), pages 43-50.
    2. Li, Yangtao & Khajepour, Amir & Devaud, Cécile & Liu, Kaimin, 2017. "Power and fuel economy optimizations of gasoline engines using hydraulic variable valve actuation system," Applied Energy, Elsevier, vol. 206(C), pages 577-593.
    3. Pramit Verma & Justyna Chodkowska‐Miszczuk & Agata Lewandowska & Łukasz Wiśniewski, 2023. "Local resilience for low‐carbon transition in Poland: Frameworks, conditions and opportunities for Central European countries," Sustainable Development, John Wiley & Sons, Ltd., vol. 31(3), pages 1278-1295, June.
    4. Pochwała, Sławomir & Anweiler, Stanisław & Tańczuk, Mariusz & Klementowski, Igor & Przysiężniuk, Dawid & Adrian, Łukasz & McNamara, Greg & Stevanović, Žana, 2023. "Energy source impact on the economic and environmental effects of retrofitting a heritage building with a heat pump system," Energy, Elsevier, vol. 278(PB).
    5. Li, Yangtao & Khajepour, Amir & Devaud, Cécile, 2018. "Realization of variable Otto-Atkinson cycle using variable timing hydraulic actuated valve train for performance and efficiency improvements in unthrottled gasoline engines," Applied Energy, Elsevier, vol. 222(C), pages 199-215.
    6. Teodosio, Luigi & Pirrello, Dino & Berni, Fabio & De Bellis, Vincenzo & Lanzafame, Rosario & D'Adamo, Alessandro, 2018. "Impact of intake valve strategies on fuel consumption and knock tendency of a spark ignition engine," Applied Energy, Elsevier, vol. 216(C), pages 91-104.
    7. Zhou, Xianjie & Chen, Zheng & Zou, Peng & Liu, Jingping & Duan, Xiongbo & Qin, Tao & Zhang, Shiheng & Shen, Dazi, 2020. "Combustion and energy balance analysis of an unthrottled gasoline engine equipped with innovative variable valvetrain," Applied Energy, Elsevier, vol. 268(C).
    8. Yang, Zhuyong & Miganakallu, Niranjan & Miller, Tyler & Bonfochi Vinhaes, Vinicius & Worm, Jeremy & Naber, Jeffrey & Roth, David, 2020. "Investigation of high load operation of spark-ignited over-expanded Atkinson cycle engine," Applied Energy, Elsevier, vol. 262(C).
    9. Maciej Dzikuć & Rafał Miśko & Szymon Szufa, 2021. "Modernization of the Public Transport Bus Fleet in the Context of Low-Carbon Development in Poland," Energies, MDPI, vol. 14(11), pages 1-12, June.
    10. Maciej Dzikuć & Joanna Wyrobek & Łukasz Popławski, 2021. "Economic Determinants of Low-Carbon Development in the Visegrad Group Countries," Energies, MDPI, vol. 14(13), pages 1-12, June.
    11. Tehseen Johar & Chiu-Fan Hsieh, 2023. "Design Challenges in Hydrogen-Fueled Rotary Engine—A Review," Energies, MDPI, vol. 16(2), pages 1-22, January.
    12. Zhao, Zhenfeng & Cui, Huasheng, 2022. "Numerical investigation on combustion processes of an aircraft piston engine fueled with aviation kerosene and gasoline," Energy, Elsevier, vol. 239(PD).
    13. Zhen, Xudong & Wang, Yang, 2013. "Study of ignition in a high compression ratio SI (spark ignition) methanol engine using LES (large eddy simulation) with detailed chemical kinetics," Energy, Elsevier, vol. 59(C), pages 549-558.
    14. Osorio, Julian D. & Rivera-Alvarez, Alejandro, 2018. "Efficiency enhancement of spark-ignition engines using a Continuous Variable Valve Timing system for load control," Energy, Elsevier, vol. 161(C), pages 649-662.
    15. Aldona Standar & Agnieszka Kozera & Łukasz Satoła, 2021. "The Importance of Local Investments Co-Financed by the European Union in the Field of Renewable Energy Sources in Rural Areas of Poland," Energies, MDPI, vol. 14(2), pages 1-23, January.
    16. Amaral, Lucimar Venâncio & Santos, Nathália Duarte Souza Alvarenga & Roso, Vinícius Rückert & Sebastião, Rita de Cássia de Oliveira & Pujatti, Fabrício José Pacheco, 2021. "Effects of gasoline composition on engine performance, exhaust gases and operational costs," Renewable and Sustainable Energy Reviews, Elsevier, vol. 135(C).
    17. Mikulski, Maciej & Balakrishnan, Praveen Ramanujam & Hunicz, Jacek, 2019. "Natural gas-diesel reactivity controlled compression ignition with negative valve overlap and in-cylinder fuel reforming," Applied Energy, Elsevier, vol. 254(C).
    18. La Xiang & Enzhe Song & Yu Ding, 2018. "A Two-Zone Combustion Model for Knocking Prediction of Marine Natural Gas SI Engines," Energies, MDPI, vol. 11(3), pages 1-23, March.
    19. Shen, Kai & Xu, Zishun & Chen, Hong & Zhang, Zhendong, 2021. "Investigation on the EGR effect to further improve fuel economy and emissions effect of Miller cycle turbocharged engine," Energy, Elsevier, vol. 215(PB).
    20. José R. Serrano & Francisco J. Arnau & Jaime Martín & Ángel Auñón, 2020. "Development of a Variable Valve Actuation Control to Improve Diesel Oxidation Catalyst Efficiency and Emissions in a Light Duty Diesel Engine," Energies, MDPI, vol. 13(17), pages 1-26, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jeners:v:14:y:2021:i:8:p:2316-:d:539525. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.