Combustion instabilities in the aviation, aerospace and power generation industries have been a matter of concern for engineers since the 1950s, but with the increase in computer processing speed and the development of CFD it is now possible to attempt to predict frequencies and stability of a combustion system by numerical means, or by combining numerical, analytical and experimental approaches.
Currently available analytical methods for the prediction of the frequency and stability of thermoacoustic oscillations make use of one-dimensional models where the frequency of oscillation is assumed to be low enough that only plane waves propagate in the burner, with higher order modes decaying quickly. While accurate and well-suited for longitudinal oscillations, these methods are unable to predict the frequency of instabilities where the unsteady heat release couples with the higher frequency transverse acoustic modes. Therefore a method is needed for applications where high frequency transverse oscillations are important.
A method in which the linearised Euler equations are employed to calculate the propagation of acoustic waves is then suitable for solving this thermoacoustic problem. When a flame model that appropriately represents the frequency-dependent dynamics of the flame front is included, this method can predict the frequency of the oscillation resulting from the coupling between acoustics and combustion in an arbitrarily complex geometry.
In this paper, a linearised Euler solver called INSTANT is introduced and validated against a well known theoretical model for the calculation of thermoacoustic oscillations in a one dimensional cylindrical duct with rigid walls and a radially uniform mean flow. The frequencies of oscillation and the modeshapes for this stable configuration match the theoretical ones well.
An example calculation of transverse acoustic resonant mode is then presented. The ability of the code to predict the production of an entropy mode as a result of the interaction between an acoustic wave and a heat source region and its ability to predict frequencies of oscillation and modeshapes in a one dimensional configuration give confidence it can serve as a predictive tool for high frequency, transverse thermoacoustic oscillations in the more complex geometries of practical combustion systems once a suitable model for the frequency dependent flame response is included. The development of such a flame model is left for future work.
Photoacoustic 3-D imaging of polycrystalline microstructure improved with transverse acoustic waves
