Pieringer J., Sattelmayer T.

Combustion instabilities are a cause of concern in various technical combustion systems such as industrial- and household burners, gas turbines, or aircraft and rocket engines. The reason for the occurrence of combustion instabilities is the interaction of acoustics and flame dynamics, where initially small perturbations grow to oscillations of finite amplitude. The difficulty in predicting combustion instabilities lies in the necessary reduction of the complexity of the models so that the numerical cost is reduced to a reasonable level. Field methods solving an inhomogeneous wave equation in the time domain can be applied to three-dimensional combustor geometries and combine a relatively low degree of modelling with reasonable computational costs. The influence of the flame is described by a heat release model. It has been shown that this kind of approach can predict instable combustion modes and therefore can reproduce the principal physical mechanisms. Nevertheless, up to now, this time domain approach was restricted to the solution of the wave equation which excludes the incorporation of mean flow effects on acoustics. This limitation can be overcome by the solution of Acoustic Perturbation Equations (APEs), which describe the propagation of acoustic perturbations in inhomogeneous mean flows. The present study deals with the application of this method to a rocket engine. Classical approaches incorporate the nozzle by a nozzle admittance which reduces the influence of the nozzle to 1D-effects. Using APEs the convergent part of the rocket nozzle can be included into the computational domain which allows to include 3D-effects and reflection and refraction of acoustic waves in the nozzle. Additionally the use of the nozzle admittance boundary condition that in the general case depends on frequencies, mode shapes, and nozzle geometry can be avoided. For these reasons the description of the interaction of flame and acoustics in the model is improved.