A Helmholtz-type numerical simulation of thermo-acoustic instabilities in a 3-D Rijke tube

Cengiz, Kenan
Özyörük, Yusuf
A thermo-acoustic instability prediction tool has been developed both for 2-D and 3-D ducts. The tool works in frequency domain, making use of linearized Euler equations with quiescent flow. In this work, a 3-D horizontal Rijke tube simulation is performed. Nonetheless, implementation of open boundary condition at the duct ends somewhat requires close attention. A reverse idea has been developed to determine the open-air boundary condition. Numerical tests showed that the method works well in 2-D cases, involving solution of a linear system with dense matrices. However, the pertinent complex-valued matrix turns out to be highly ill-conditioned in the 3-D case. This work proposes use of Singular Value Decomposition(SVD) to remedy this problem. QR decomposition is to be examined as well, as a performance and accuracy comparison. Results obtained for the Rijke tube problem validates the tool, at least, for linear stability requirements.


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Citation Formats
K. Cengiz and Y. Özyörük, “A Helmholtz-type numerical simulation of thermo-acoustic instabilities in a 3-D Rijke tube,” San Jose, CA, Amerika Birleşik Devletleri, 2013, Accessed: 00, 2021. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84883670098&origin=inward.