Linearised Theory for LPP Combustion Dynamics

Gas turbines which are operated under lean, premixed, pre–vaporised (LPP) conditions are notoriously susceptible to self–excited oscillations. In the combustion chamber the unsteady heat released by combustion processes interacts with pressure fluctuations. The challenge is to develop a tool which can determine the frequency and stability characteristics of self–excited oscillations in realistic gas–turbine geometries. To this end, the flow through the gas turbine is described as far as possible by taking advantage of linearised theory and analytical models of the behaviour in the combustion chamber. First, a steady, mean flow solution for an idealised axi–symmetric combustor geometry is calculated using the inviscid Euler equations for continuity, momentum and energy with a specified distributed mean heat release. Superimposed on this is a linearised, three–dimensional perturbed flow in which the time and circumferential variation are described by a complex frequency and mode number respectively. Within this numerical model of the combustor a ‘flame model’ is used to describe the change in the rate of combustion due to inlet flow perturbations. The flame model may be given by an analytical expression—for example using a simple time lag with an expression proportional to the mean heat release in order to describe the unsteady heat release. An alternative approach would be to use a localised and detailed unsteady CFD calculation to determine the flow downstream of a generic premix duct geometry. If the flow is perturbed at the inlet a relationship between these fluctuations and the unsteady heat release may be obtained. In order to capture the response of the system to a wide frequency range an appropriately chosen broad–band forcing function may be used to perturb the flow. System identification techniques allow the transfer function to be extracted and a suitable flame model for the linearised Euler calculations may be constructed. Sample calculations of each aspect of the research will be presented to demonstrate the capabilities of each technique and the viability of combining the approaches towards the goal of aiding the design of gas–turbine combustors. Calculations using the linearised Euler methodology with analytical expressions for the flame model will demonstrate the capability of the approach to identify the frequencies of oscillation, mode shapes and zones of stability of particular combustor geometries.