Prediction of thermoacoustic instabilities in combustors using linearized Navier-Stokes equations in frequency domain

The paper presents a numerical methodology for the prediction of the thermoacoustic instabilities with the effects of the mean-flow as well as the viscosity. As an academic standard test case, the configuration within the flame sheet located in the middle of the duct is investigated. First, the ducted flame numerical reference case is solved by the inhomogeneous Helmholtz equations in combination of the n - τ flame model assuming that the flow is at rest. Then, we derive the linearized Navier-Stokes equations (LNSE) in frequency domain in combination of the flame model. The unsteady effect of the flame is modeled by the n - τ flame model in harmonic form, which is essentially a 1D formulation relating the rate of heat release and the acoustic velocity at the reference point.Funding Details: FP7-PEOPLE-ITN-2012, EC, European CommissionQC 20161128