Boundary Conditions for Acoustic Eigenmodes Computationin Gas turbine Combustion Chambers

Abstract

Understanding and predicting acoustic instabilities in gas turbine combustion chambers requires the knowledge of the acoustic behavior of all the elements feeding the combustion chamber (characterized by their impedance). Inlets and outlets of chambers are often represented as one-dimensional ducts and existing methods to evaluate impedances of choked and unchoked nozzles are described: 1) analytical formulas, 2) numerical methods using the linearized Euler equations and a finite dfference solver in Fourier space and 3) full space-time solver in which the response of the nozzle is studied by forcing its inlet (or outlet) and measuring its response in the time domain. These three methods are compared in reference cases (a straight duct and a subsonic distributor). Practical implications for gas turbines are then discussed. In such cases, if the diffusers and distributors connected to the chamber are not choked, it is shown that solving the acoustic problem becomes very difficult because compressor and turbine impedances are usually not known. This paper finally shows how these impedances control the acoustic oscillations of a combustion chamber by presenting an example of acoustic eigenmode calculations in a realistic gas turbine, using a Helmholtz solver and various impedances for the inlet and outlet of the combustor.