Analytical models for thermoacoustic interactions in axially varying flows

Abstract

Thermoacoustic instabilities are a major problem in boilers, low NO_x gas-turbine combustors, and rocket engine combustors. They occur due to positive feedback between the unsteady heat release of the combustion and the acoustic waves, which leads to self-sustained oscillations. These oscillations increase the overall noise emissions of the engine, lead the system to operate in off-design conditions, and result in premature component failure or permanent structural damage. The ability to accurately model the acoustic propagation and acoustic energy balance for given operating conditions can help identify the regions susceptible to instability during the preliminary design phase. This identification can be achieved using computationally efficient low-order acoustic network models where the equations for the mean flow and the acoustics can be solved sequentially.

Lower order models for the acoustics which employ analytical solutions have the benefit of being grid-independent (or, for the case of semi-analytical solutions, grid convergent) and are computationally fast. They also provide more physical insight into the acoustic behaviour across the various mean flow and boundary conditions and thus allow for swift parametric sweeps.

The primary objective of the present thesis is to develop simplified analytical frameworks for estimating the one-dimensional and two-dimensional acoustic fields established in axial and annular nozzles, respectively. These nozzles can (i) feature varying cross-sectional area, (ii) feature varying axial mean temperature, and (iii) sustain subcritical/supercritical mean flow, which does not have to be isentropic. These acoustic field predictions are achieved using asymptotic methods, and the resulting model estimates are validated using numerical simulations. The applicability of some of the developed models for stability analysis is shown by comparing the obtained modal solutions to in-house developed low order network model solvers based on modal expansions.

The analytical models thus developed can be of great interest to both thermoacoustic and acoustic communities.