Journal of Mechanical Science and Technology

, Volume 33, Issue 11, pp 5547–5559 | Cite as

Numerical investigation on combustion instability modeling in a lean premixed gas turbine combustor combining finite element analysis with local flame transfer function

  • Yeongmin Pyo
  • Daesik KimEmail author
  • Seong-Ku Kim
  • Dong Jin Cha


The present work suggests a numerical approach using an FEM (finite element method) code for the eigenvalue calculation of the thermoacoustic combustion instabilities coupling with the local flame transfer function in a generic lean premixed combustor. The URANS (unsteady Reynolds average Navier-Stokes) simulation shows a good agreement in capturing steady and unsteady flame geometries with the measurement in the literature. Also, global and local parameters of flame responses to acoustic velocity fluctuations undergo quantitatively similar changes in prediction and in the experiment. The numerically determined flame transfer function and gas properties are incorporated in an in-house Helmholtz solver to compute eigenvalues of the target combustor. In the solver, the Helmholtz equation is discretized with a Galerkin FEM on a multi-dimensional hybrid unstructured mesh. The nonlinearity related with the heat release source term is treated with an iterative methodology, and the large scale eigenvalue calculation is performed using the shift-invert approach available in the ARPACK (ARnoldi PACKage) library. The predictive capabilities of the current modeling approach are validated against the measured mode frequency and instability growth rate. In addition, the prediction results show the effect of spatially-distributed heat release on the thermoacoustic model accuracy.


Combustion instability Thermoacoustics Helmholtz equation Flame response model Local flame transfer function 



Speed ot sound






Flame length


Gain of transfer function




Heat release rate


Reflection coefficient




Axial position

Greek symbolds


Specific heat ratio




Time delay of transfer function




Angular frequency



Value of global FTF


Average value






Total value






ith slot or imaginary part of complex number


Mean value


ean value


Fourier transformation


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The first and second authors appreciate the support of the Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education (NRF-2018R1D1A3B07044440), and the Korea Aerospace R&D Program in Parts and Materials, funded by the Ministry of Trade, Industry and Energy (10067074).


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Copyright information

© KSME & Springer 2019

Authors and Affiliations

  • Yeongmin Pyo
    • 1
  • Daesik Kim
    • 1
    Email author
  • Seong-Ku Kim
    • 2
  • Dong Jin Cha
    • 3
  1. 1.School of Mechanical and Automotive EngineeringGangneung-Wonju National UniversityGangwonKorea
  2. 2.Combustion Chamber TeamKorea Aerospace Research InstituteDaejeonKorea
  3. 3.Department of Building and Plant EngineeringHanbat National UniversityDaejeonKorea

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