Evaluation of numerical procedures for instabilities and acoustic waves propagation

Abstract

The performance of gas turbine combustion chambers and rocket engines depends on the interaction between the flame, the acoustic field and the hydrodynamic field. The generation and diffusion of vorticity due to hydrodynamic perturbations modifies the flame front, resulting in oscillations in the rate of heat release. These oscillations excite the acoustic and hydrodynamic field, leading to a process of self-excitation that can resonate with the natural frequencies of the combustor and imply its destruction. The numerical simulation of these physical phenomena requires a code that has as low numerical dissipation and dispersion characteristics, besides having boundary conditions that avoid the contamination of the phenomena to be studied through reflection in these contours. Focusing on a numerical code that has these characteristics, the present project aims to implement and to study numerical methods of high spatial and temporal orders, as well as appropriate boundary conditions and filters for wave transport simulation. It is intended to work with a one-dimensional convection and diffusion equation, investigating in depth the behavior of discretizations and boundary conditions. The results of this investigation should be approximations and numerical procedures that will be implemented in an existing two-dimensional code. In this way the student will develop programming skills and numerical analysis that should strengthen his training, working in areas not covered by his undergraduate course. (AU)