TY - GEN

T1 - Energetically consistent computation of combustor stability with a model consisting of a helmholtz-fem-domain and a low-order network

AU - Heilmann, Gerrit

AU - Hirsch, Christoph

AU - Sattelmayer, Thomas

N1 - Publisher Copyright:
Copyright © 2020 ASME

PY - 2020

Y1 - 2020

N2 - An efficient approach for the detection of the acoustic damping of gas turbine combustors is the combination of spatially resolved FEM approaches based on the Helmholtz equation with low-order networks for all elements leading to acoustic damping. A fundamental problem of such hybrid approaches is that the flow is considered in the networks, but not in the spatially resolved FEM area. Without special treatment of the coupling plane and the boundary conditions this leads to serious errors in the calculation of the damping rate. The purpose of the paper is the derivation of the required correction procedures, which allow the energetically consistent formulation of such hybrid models and lead to correct damping rates. The time averaged equation of acoustic energy flux for non-uniform fluid flows is expressed in terms of reflection coefficients and compared to the equivalent formulation for vanishing mean flows. An existing transformation for boundary conditions to obtain equal energy flux at the interface between network and Helmholtz domain is analyzed in detail. The findings are then used to derive an energetically consistent transformation of transfer matrices to couple two FEM domains via a network model. The relevance of energetically consistent transfer matrices for stability analysis is demonstrated with a generic test case. The central partition is acoustically characterized via a low order model considering mean flow. The resulting acoustic two-port is transformed to obtain an energetically consistent transfer matrix for a subsequent FEM discretized eigenvalue analysis of the remaining geometry. The eigenvalues of energetically consistent calculations are finally compared to eigenvalues of energetically inconsistent setups.

AB - An efficient approach for the detection of the acoustic damping of gas turbine combustors is the combination of spatially resolved FEM approaches based on the Helmholtz equation with low-order networks for all elements leading to acoustic damping. A fundamental problem of such hybrid approaches is that the flow is considered in the networks, but not in the spatially resolved FEM area. Without special treatment of the coupling plane and the boundary conditions this leads to serious errors in the calculation of the damping rate. The purpose of the paper is the derivation of the required correction procedures, which allow the energetically consistent formulation of such hybrid models and lead to correct damping rates. The time averaged equation of acoustic energy flux for non-uniform fluid flows is expressed in terms of reflection coefficients and compared to the equivalent formulation for vanishing mean flows. An existing transformation for boundary conditions to obtain equal energy flux at the interface between network and Helmholtz domain is analyzed in detail. The findings are then used to derive an energetically consistent transformation of transfer matrices to couple two FEM domains via a network model. The relevance of energetically consistent transfer matrices for stability analysis is demonstrated with a generic test case. The central partition is acoustically characterized via a low order model considering mean flow. The resulting acoustic two-port is transformed to obtain an energetically consistent transfer matrix for a subsequent FEM discretized eigenvalue analysis of the remaining geometry. The eigenvalues of energetically consistent calculations are finally compared to eigenvalues of energetically inconsistent setups.

UR - http://www.scopus.com/inward/record.url?scp=85099775057&partnerID=8YFLogxK

U2 - 10.1115/GT2020-14610

DO - 10.1115/GT2020-14610

M3 - Conference contribution

AN - SCOPUS:85099775057

T3 - Proceedings of the ASME Turbo Expo

BT - Combustion, Fuels, and Emissions

PB - American Society of Mechanical Engineers (ASME)

T2 - ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition, GT 2020

Y2 - 21 September 2020 through 25 September 2020

ER -