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Article

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

1
Faculty of Process and Environmental Engineering, Lodz University of Technology, Wolczanska 213, 90-924 Lodz, Poland
2
Institute of Vehicles, Warsaw University of Technology, str. Narbutta 84, 02-524 Warsaw, Poland
3
Eko-Look, Lokajskiego 1A, 98-200 Sieradz, Poland
4
Institute of Mathematics, Lodz University of Technology, Wolczanska Str. 215, 90-924 Lodz, Poland
*
Authors to whom correspondence should be addressed.
Academic Editors: Georgios Mavropoulos, E.C. Andritsakis and Roussos G. Papagiannakis
Energies 2021, 14(8), 2316; https://doi.org/10.3390/en14082316
Received: 26 February 2021 / Revised: 12 April 2021 / Accepted: 14 April 2021 / Published: 20 April 2021
(This article belongs to the Special Issue Internal Combustion Engine Performance)
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. View Full-Text
Keywords: Carnot; Otto; Atkinson; theoretical thermodynamic cycle; Fourier series; ACC engine; Vibe function Carnot; Otto; Atkinson; theoretical thermodynamic cycle; Fourier series; ACC engine; Vibe function
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MDPI and ACS Style

Głogowski, M.; Kubiak, P.; Szufa, S.; Piersa, P.; Adrian, Ł.; Krukowski, M. The Use of the Fourier Series to Analyze the Shaping of Thermodynamic Processes in Heat Engines. Energies 2021, 14, 2316. https://doi.org/10.3390/en14082316

AMA Style

Głogowski M, Kubiak P, Szufa S, Piersa P, Adrian Ł, Krukowski M. The Use of the Fourier Series to Analyze the Shaping of Thermodynamic Processes in Heat Engines. Energies. 2021; 14(8):2316. https://doi.org/10.3390/en14082316

Chicago/Turabian Style

Głogowski, Michał, Przemysław Kubiak, Szymon Szufa, Piotr Piersa, Łukasz Adrian, and Mateusz Krukowski. 2021. "The Use of the Fourier Series to Analyze the Shaping of Thermodynamic Processes in Heat Engines" Energies 14, no. 8: 2316. https://doi.org/10.3390/en14082316

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