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

Michał Głogowski, Przemysław Kubiak, Szymon Szufa, Piotr Piersa, Łukasz Adrian and Mateusz Krukowski
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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

Energies, 2021, vol. 14, issue 8, 1-23

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.

Keywords: Carnot; Otto; Atkinson; theoretical thermodynamic cycle; Fourier series; ACC engine; Vibe function (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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