Parametric Investigation of Thermoacoustic Instability (TAI) in a Rijke Tube: A Time-Delay Perspective
This paper presents a novel deployment of a recent mathematical paradigm for predicting the thermo-acoustic instability (TAI) of a Rijke tube in the relevant parametric space. This benchmark problem in combustion science has been studied for over 1½ centuries with phenomenal achievements both in the...
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Online Access: | https://doi.org/10.1260/1756-8277.7.1.39 |
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doaj-62b5bd366aa04acb81596e9a62a4ff2c2020-11-25T03:44:01ZengSAGE PublishingInternational Journal of Spray and Combustion Dynamics1756-82771756-82852015-03-01710.1260/1756-8277.7.1.3910.1260_1756-8277.7.1.39Parametric Investigation of Thermoacoustic Instability (TAI) in a Rijke Tube: A Time-Delay PerspectiveNejat Olgac0Rudy Cepeda-Gomez1Umut Zalluhoglu2Ayhan S. Kammer3 University of Connecticut, Mechanical Engineering Department, 191 Auditorium Rd., Unit 3139, Storrs, Connecticut, 06269-3139 Saint Thomas University, Mechatronic Engineering Department, Bucaramanga, Santander, Colombia University of Connecticut, Mechanical Engineering Department, 191 Auditorium Rd., Unit 3139, Storrs, Connecticut, 06269-3139 University of Connecticut, Mechanical Engineering Department, 191 Auditorium Rd., Unit 3139, Storrs, Connecticut, 06269-3139This paper presents a novel deployment of a recent mathematical paradigm for predicting the thermo-acoustic instability (TAI) of a Rijke tube in the relevant parametric space. This benchmark problem in combustion science has been studied for over 1½ centuries with phenomenal achievements both in theoretical and practical fronts. The new paradigm is called the Cluster Treatment of Characteristic Roots (CTCR), which is originally developed to assess the asymptotic stability of Linear Time Invariant (LTI) Time-delayed Systems (TDS). A notorious subcategory within LTI-TDS is called “Neutral TDS”, which matches the characteristics of the linearized dynamics of thermo-acoustic instability. The CTCR is shown to reveal a non-conservative and exhaustive linear stability map of the Rijke tube within the space of its geometric and operational parameters. We present a review of this paradigm as well as several case studies to demonstrate its capabilities and some encouraging comparison with the earlier literature. This paper is a concept document and it is prepared with the intent of providing a breeding ground for studies beyond its present coverage.https://doi.org/10.1260/1756-8277.7.1.39 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Nejat Olgac Rudy Cepeda-Gomez Umut Zalluhoglu Ayhan S. Kammer |
spellingShingle |
Nejat Olgac Rudy Cepeda-Gomez Umut Zalluhoglu Ayhan S. Kammer Parametric Investigation of Thermoacoustic Instability (TAI) in a Rijke Tube: A Time-Delay Perspective International Journal of Spray and Combustion Dynamics |
author_facet |
Nejat Olgac Rudy Cepeda-Gomez Umut Zalluhoglu Ayhan S. Kammer |
author_sort |
Nejat Olgac |
title |
Parametric Investigation of Thermoacoustic Instability (TAI) in a Rijke Tube: A Time-Delay Perspective |
title_short |
Parametric Investigation of Thermoacoustic Instability (TAI) in a Rijke Tube: A Time-Delay Perspective |
title_full |
Parametric Investigation of Thermoacoustic Instability (TAI) in a Rijke Tube: A Time-Delay Perspective |
title_fullStr |
Parametric Investigation of Thermoacoustic Instability (TAI) in a Rijke Tube: A Time-Delay Perspective |
title_full_unstemmed |
Parametric Investigation of Thermoacoustic Instability (TAI) in a Rijke Tube: A Time-Delay Perspective |
title_sort |
parametric investigation of thermoacoustic instability (tai) in a rijke tube: a time-delay perspective |
publisher |
SAGE Publishing |
series |
International Journal of Spray and Combustion Dynamics |
issn |
1756-8277 1756-8285 |
publishDate |
2015-03-01 |
description |
This paper presents a novel deployment of a recent mathematical paradigm for predicting the thermo-acoustic instability (TAI) of a Rijke tube in the relevant parametric space. This benchmark problem in combustion science has been studied for over 1½ centuries with phenomenal achievements both in theoretical and practical fronts. The new paradigm is called the Cluster Treatment of Characteristic Roots (CTCR), which is originally developed to assess the asymptotic stability of Linear Time Invariant (LTI) Time-delayed Systems (TDS). A notorious subcategory within LTI-TDS is called “Neutral TDS”, which matches the characteristics of the linearized dynamics of thermo-acoustic instability. The CTCR is shown to reveal a non-conservative and exhaustive linear stability map of the Rijke tube within the space of its geometric and operational parameters. We present a review of this paradigm as well as several case studies to demonstrate its capabilities and some encouraging comparison with the earlier literature. This paper is a concept document and it is prepared with the intent of providing a breeding ground for studies beyond its present coverage. |
url |
https://doi.org/10.1260/1756-8277.7.1.39 |
work_keys_str_mv |
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