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

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.