Waves Transmission and Generation in Turbine Stages in a Combustion-Noise Framework

A non-negligible part of the noise emitted from aero-engines is due to combustion. The relative importance of this source is even expected to increase with the next generations of engines where both fan and jet noise are reduced with such technologies as chevrons, micro-jets or highly-swept and leaned composite blades. In his PhD. dissertation, Candel showed that the noise due to combustion in aero-engines could have two different origins: (a) the well-known direct combustion noise, which is directly generated by the unsteady combustion, and transmitted and reflected through the upstream (compressor) and downstream (turbine) turbo-machinery stages; and (b) an additional source of noise, the indirect combustion noise. The latter comes from the conversion of entropy spots generated by the combustion into acoustic waves when they accelerate in the downstream turbine stages. Candel showed that this source could be important and explain the observed excess noise. More recently, Leyko et al. developed scaling laws from a simplified one-dimensional (1-D) model of combustor, which showed that the indirect combustion noise could even be ten times as important as the direct one. For both direct and indirect noise sources, the downstream turbo-machinery is involved in the transmission and generation of the combustion noise. Thus, the acoustic behavior of the turbine blade rows must be known to evaluate the noise due to combustion at the engine outlet. More specifically, the transfer functions of the turbo-machinery stages for the waves involved in the combustion process (acoustic, entropy and vortical) must be calculated. Several analytical and semi-analytical approaches have been proposed for 2-D flows to deal with the propagation of acoustic waves and vortices through turbo-machinery stages. Muir 5 delt with the case of the actuator disk theory which assumed a 2-D configuration with an infinitely thin blade row, and used classical conservation laws to establish relations between upstream and downstream flow. Kaji and Okazaki 7 proposed the semi-disk actuator theory assuming in a first step that the spacing between the blades was infinitely thin but the chord-length was finite. A second step 7 proposed a model with a finite chord-length and a finite spacing between blades. For both cases, the equations were solved numerically. Many other models are available for such 2-D problems. Recently Posson and Roger proposed a three-dimensional rectilinear cascade model both for generation and transmission losses based on Glegg’s response, which also accounted for cascade effects and finite chord, but neglected flow deviation (flat plates