A Green’s function approach to the rapid prediction of thermoacoustic instabilities in combustors

Abstract

The prediction of thermoacoustic instabilities is fundamental for combustion systems such as domestic burners and industrial gas turbine engines. High-amplitude pressure oscillations cause thermal and mechanical stress to the equipment, leading to premature wear or even critical damage. In this paper we present a new approach to produce nonlinear (i.e. amplitude-dependent) stability maps of a combustion system as a function of various parameters. Our approach is based on the tailored Green's function of the combustion system, which we calculate analytically. To this end, we assume that the combustor is one-dimensional, and we describe its boundary conditions through reflection coefficients. The heat release is modelled by a generalised nτ law. This includes a direct-feedback term in addition to the usual time-lag term; moreover, its parameters (time lag, coupling coefficients) depend on the oscillation amplitude. The model provides new insight into the physical mechanism of the feedback between heat release rate and acoustic perturbations. It predicts the key nonlinear features of the thermoacoustic feedback, such as limit cycles, bistability and hysteresis. It also explains the frequency shift in the acoustic modes.

Advances by the Marie Curie project TANGO in thermoacoustics

“…The procedure described in section 4.2 was applied by Bigongiari et al 30 to find an analytical description for the heat release rate in a specific laboratory test rig developed by Komarek and Polifke 15 at TU Munich. The rig is called the 'BRS test rig' and is shown schematically in Figure 13.…”

“…A hybrid approach, combining the accuracy of numerical CFD simulations with the fast prediction speed of a Green's function approach, was taken by Bigongiari et al 30 They applied this to the BRS test rig described in section 4.3 and shown in Figure 13.…”

“…Analytical expressions for the Green's function amplitudes g n and frequencies ! n for the test rig in Figure 21 can be found in Bigongiari et al 30 The flame is modelled by an FDF similar to the one in section 4.3…”

Thermodynamics-Acoustics Coupling Studies on Self-Excited Combustion Oscillations Maximum Growth Rate

“…Thus predicting eigen-frequencies and mode-shapes and the growth rate of combustion-driven acoustic disturbances is needed [14]. Determining the modeshapes and eigen-frequencies [15] is not a difficult task by solving linearized Euler [16] or Helmholtz solvers in 1D network [17,18] or complex 2D [19] and 3D models [20]. However, estimating the growth rate [21] in real time is quite challenging [22], since it requires more accurate online evaluation of 1) boundaries conditions, 2) the flame response (flame transfer/describing function for example) and 3) intrinsic acoustic dissipation [23] due to acoustics-vorticity interaction and wall friction.…”

“…Noiray and Denisov [25] proposed a Fokker-Planckbased method to identify the growth rate from the experimentally measured pressure data. It is indeed important to the stability map [18] the combustor is operated so that a small change in operating condition does not trigger thermoacoustic instability [26].…”