Efficient retrieval of the thermo-acoustic flame transfer function from a linearized CFD simulation of a turbulent flame

The stability of thermo-acoustic pressure oscillations in a lean premixed methane-fired generic gas turbine combustor is investigated. A key element in predicting the acoustically unstable operating conditions of the combustor is the flame transfer function. This function represents the dynamic relationship between a fluctuation in the combustor inlet conditions and the flame's acoustic response. A transient numerical experiment involving spectral analysis in computational fluid dynamics (CFD) is usually conducted to predict the flame transfer function. An important drawback of this spectral method application to numerical simulations is the required computational effort. A much faster and more accurate method to calculate the transfer function is derived in this paper by using a most important basic assumption: the fluctuations must be small enough for the system to behave linear. This alternative method, which is called the linear coefficient method, uses a linear representation of the unsteady equations describing the CFD problem. This linearization is applied around a steady-state solution of the problem, where it can consequently describe the dynamics of the system. Finally, the flame transfer function can be calculated from this linear representation. The advantage of this approach is that one only needs a steady-state solution and linearization of the unsteady equations for calculating a dynamic transfer function, i.e. no time-consuming transient simulations are necessary anymore. Nevertheless, as a consequence of the large number of degrees of freedom in a CFD problem, an extra order reduction step needs to be performed prior to calculating the transfer function from the linear representation. Still, the linear coefficient method shows a significant gain in both speed and accuracy when calculating the transfer function from the linear representation as compared to a spectral analysis-based calculation. Hence, this method gives a major improvement to the application of the flame transfer function as a thermo-acoustic design tool.