Investigation of a Solution Approach to Quadratic Eigenvalue Problem for Thermoacoustic Instabilities


Öztürkmen M. O. , ÖZYÖRÜK Y.

AIAA Science and Technology Forum and Exposition, AIAA SciTech Forum 2022, California, United States Of America, 3 - 07 January 2022 identifier

  • Publication Type: Conference Paper / Full Text
  • Doi Number: 10.2514/6.2022-1855
  • City: California
  • Country: United States Of America

Abstract

© 2022, American Institute of Aeronautics and Astronautics Inc.. All rights reserved.The interactions between the unsteady heat release and pressure fluctuations in a combustion chamber may lead to thermoacoustic instabilities. Linear stability characteristics of the chamber may be determined by solving the nonhomogeneous wave equation in frequency domain that takes these interactions into account. The discretization of the wave equation with frequency-dependent source terms due to heat release and impedance boundary conditions results in a nonlinear quadratic eigenvalue problem. While the solution of the standard linear quadratic eigenvalue problem can be obtained directly, the nonlinear one requires some linearization procedures to reduce it to the standard general eigenvalue problem. In this paper, three different linearization procedures are investigated. For validation of the considered approaches a canonical problem that contains impedance walls and uniformly distributed heat source is set up and solved analytically. An experimental experimental test case from literature is also considered to assess the utilized linearization methods in terms of convergence and CPU times. It is shown that among the employed linearization approaches, the Taylor series based one yields faster convergence.