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

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

doi:10.3390/en14082316

Michał Głogowski, Piotr Piersa + Show 4 more

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https://doi.org/10.3390/en14082316

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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.

Highlights

In this paper Carnote cycle was modified using the popular Vibe function [1], which was replaced in the theoretical cycle by two isochoric and isothermal transformations.We know from the theory of thermal machines [2] that the Carnot cycle achieves the highest efficiency at a given temperature difference, while the Otto cycle achieves the highest efficiency for a given compression ratio
No 1 and dark green Figure 2 is that kinematic modifications are only sought for theoretical cycles do not take into account the influence of time, and yet they should isochoric andreal isothermal transformations heat supplied, which is equivalent to correlate with cycles subject to time
The conclusion to use the Fourier series to decompose the kinematics of the complementary system into its terms has a specific purpose

Summary

Introduction

In this paper Carnote cycle was modified using the popular Vibe function [1], which was replaced in the theoretical cycle by two isochoric and isothermal transformations.We know from the theory of thermal machines [2] that the Carnot cycle achieves the highest efficiency at a given temperature difference, while the Otto cycle achieves the highest efficiency for a given compression ratio. Before we go in to that, it is necessary to present the already existing solutions that have reached the stage of technical implementation In this regard, we can find a large amount of scientific information, which is why it was decided to choose those that contain a compendium of knowledge on the development of spark ignition engines or those that have very unusual solutions or have been published recently. In the combination of both circuits, it was decided to look for the best solution, but before we get to that, it is necessary to present the already existing solutions that have reached the stage of technical implementation In this regard, we can find a large amount of scientific information, which is why it was decided to choose that which contained a compendium of knowledge on the development of spark ignition engines or that has very unusual solutions or has been published recently. We found, among others, the aspect related to the timing system control, which currently seems to be the most common in engines, [3,4,5,6,7,8,9]

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