In this paper the mathematical model of self - oscillation in Rijke's tube is found. We introduce the characteristic of the pressure of the heat supply. Using the energy equation in the form of the first law of thermodynamics to flow defined mechanisms of thermoacoustic instability in this problem. Using the pressure characteristic of the supply of heat and the classical Lyapunov’s theory of stability defines the conditions for self-excitation of oscillation. It was found that when the increasing combustion delay the harmonic self-oscillations of the "singing" flame are converted to the relaxation oscillations.
| Published in | American Journal of Mechanical and Industrial Engineering (Volume 2, Issue 1) |
| DOI | 10.11648/j.ajmie.20170201.18 |
| Page(s) | 48-53 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Rijke’s Tube, "Singing" Flame, Self-Oscillations, Combustion Delay Time, Instability, Head Characteristics of Heat Supply
| [1] | Larinov V. M., Zaripov R. G. Self-Oscillations of the Gas in Combustion-Involving Plants [in Russian]. Kazan: Izd. Kazansk. Gos. Tekhn. Univ. 2003. 327 pp. |
| [2] | Shklyar F. R., Malkin V. M., Kashtanova S. P., Kalugin Ya. P., and Sovetkin V. L. Blast Furnace Stoves [in Russian]. Moscow: Metallurgiya. 1982. 176 pp. |
| [3] | Zuker D., Glas P., and Beneke G. “Pressure pulsations in air heaters // Chern. Metally. – 1980. – No. 22. P. 20–26. |
| [4] | Belyaev N. M., Belik N. P., and Pol’shin A. V. Thermoacoustic Oscillations of Gas-Liquid Flows in Complex Pipeline Power Plants [in Russian]. Kiev-Donetsk: Vysshaya Shkola, 1985. 160 pp. |
| [5] | Larinov V. M., Zaripov R. G. Self-Oscillations of the Gas in Combustion-Involving Plants [in Russian]. Kazan: Izd. Kazansk. Gos. Tekhn. Univ. 2003. 327 pp. |
| [6] | V. V. Gotsulenko. Special modes of the Rijke’s phenomenon// Journal of Engineering Physics and Thermophysics. – 2007. – Vol. 78, No. 2. P. 375–379. |
| [7] | Gotsulenko V. V On the problem of control of relaxation oscillations of a "singing" flame // Journal of Engineering Physics and Thermophysics. – 2007. – Vol. 80, No. 3. P. 563–569. |
| [8] | Basok B. I. Gotsulenko V. V. Self-oscillations in a Rijke’s tube with receiver positioning at its input // Thermophysics and Aeromechanics. – 2014. – Vol. 21, No. 4. – P. 487–496. |
| [9] | Basok B. I. Gotsulenko V.V. Calculating the Parameters of Self – Oscillations in the Vertical Combustion Chamber of the Blast – Furnace Air Heater during Unstable Combustion // Thermal Engineering. – 2015, Vol. 62, No. 1. – P. 58–63. |
| [10] | Demidovich B. P. Lectures on the mathematical theory of stability [in Russian]. Moscow: Nauka, 1967. 472 pp. |
APA Style
Boris Basok, Vladimir Gotsulenko. (2017). Mathematical Modeling of Self-Oscillations in a Rijke’s Tube with Variable Heat Flow Power. American Journal of Mechanical and Industrial Engineering, 2(1), 48-53. https://doi.org/10.11648/j.ajmie.20170201.18
ACS Style
Boris Basok; Vladimir Gotsulenko. Mathematical Modeling of Self-Oscillations in a Rijke’s Tube with Variable Heat Flow Power. Am. J. Mech. Ind. Eng. 2017, 2(1), 48-53. doi: 10.11648/j.ajmie.20170201.18
AMA Style
Boris Basok, Vladimir Gotsulenko. Mathematical Modeling of Self-Oscillations in a Rijke’s Tube with Variable Heat Flow Power. Am J Mech Ind Eng. 2017;2(1):48-53. doi: 10.11648/j.ajmie.20170201.18
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Download@article{10.11648/j.ajmie.20170201.18,
author = {Boris Basok and Vladimir Gotsulenko},
title = {Mathematical Modeling of Self-Oscillations in a Rijke’s Tube with Variable Heat Flow Power},
journal = {American Journal of Mechanical and Industrial Engineering},
volume = {2},
number = {1},
pages = {48-53},
doi = {10.11648/j.ajmie.20170201.18},
url = {https://doi.org/10.11648/j.ajmie.20170201.18},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmie.20170201.18},
abstract = {In this paper the mathematical model of self - oscillation in Rijke's tube is found. We introduce the characteristic of the pressure of the heat supply. Using the energy equation in the form of the first law of thermodynamics to flow defined mechanisms of thermoacoustic instability in this problem. Using the pressure characteristic of the supply of heat and the classical Lyapunov’s theory of stability defines the conditions for self-excitation of oscillation. It was found that when the increasing combustion delay the harmonic self-oscillations of the "singing" flame are converted to the relaxation oscillations.},
year = {2017}
}
TY - JOUR T1 - Mathematical Modeling of Self-Oscillations in a Rijke’s Tube with Variable Heat Flow Power AU - Boris Basok AU - Vladimir Gotsulenko Y1 - 2017/01/12 PY - 2017 N1 - https://doi.org/10.11648/j.ajmie.20170201.18 DO - 10.11648/j.ajmie.20170201.18 T2 - American Journal of Mechanical and Industrial Engineering JF - American Journal of Mechanical and Industrial Engineering JO - American Journal of Mechanical and Industrial Engineering SP - 48 EP - 53 PB - Science Publishing Group SN - 2575-6060 UR - https://doi.org/10.11648/j.ajmie.20170201.18 AB - In this paper the mathematical model of self - oscillation in Rijke's tube is found. We introduce the characteristic of the pressure of the heat supply. Using the energy equation in the form of the first law of thermodynamics to flow defined mechanisms of thermoacoustic instability in this problem. Using the pressure characteristic of the supply of heat and the classical Lyapunov’s theory of stability defines the conditions for self-excitation of oscillation. It was found that when the increasing combustion delay the harmonic self-oscillations of the "singing" flame are converted to the relaxation oscillations. VL - 2 IS - 1 ER -
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