Gas turbine combustors are often susceptible to self excited oscillations, which lead to unacceptable levels of pressure, velocity and heat release fluctuations. Although instabilities can occur in systems with locally constant equivalence ratio, it is very important to take into account the influence of equivalence ratio fluctuations, which are generated in the fuel air mixer in the unstable case. These fluctuations are convected into the flame and lead to an additional mechanism for the generation of heat release fluctuations. Moreover, entropy waves are produced in the flame, which travel through the combustor and generate additional pressure waves during the acceleration of the flow at the combustor exit.
To date, available theories use the physically unrealistic assumption that the equivalence ratio waves as well as the entropy waves are convected downstream without any spatial dispersion due to the combustor aerodynamics. An analytical approach is presented, which allows to take the spatial dispersion into consideration. For that purpose, the response of the burner and the combustor to an equivalence ratio impulse or an entropy impulse is calculated using the Laplace transformation and a more general transfer function for harmonic waves is derived. The obtained expression has three parameters, which represent the influence of the burner or the combustor aerodynamics, respectively. This equation can be used in numerical codes, which represent the combustion system through a network of acoustic multiports, if the equivalence ratio and the entropy are added to the vector of variables considered. The parameters required for the dynamic combustor model can be deduced from a detailed CFD analysis of the combustor flow in case of the application of the theory to a particular combustor design.
As an example, a simple model combustor is used to demonstrate the application of the theory. It is highlighted how the spatial dispersion of the equivalence ratio and entropy fluctuations can be included in the stability analysis. The calculated examples reveal that the influence of both variables on the generation of instabilities is highly overpredicted if the spatial dispersion is not taken into account. Furthermore, it can be deduced from the study, that burner and combustor designs with a wide range of convective time scales have advantages with respect to the stability of the combustor.