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

Cengiz K., ÖZYÖRÜK Y.

49th AIAA/ASME/SAE/ASEE Joint PropulsionConference, San Jose, CA, United States Of America, 14 - 17 July 2013 identifier

  • Publication Type: Conference Paper / Full Text
  • Volume:
  • Doi Number: 10.2514/6.2013-4060
  • City: San Jose, CA
  • Country: United States Of America
  • Middle East Technical University Affiliated: Yes


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.