Combustible systems generally consist of two types of chemically interacting components during combustion: an oxidizing agent (oxygen, fluorine, chlorine, their compounds) and fuel (hydrogen, hydrocarbons, nitrogen and hydrogen compounds, aluminum, etc.). The chemical properties of the components, their phase state, and their physical structure are essential when choosing the methods for supplying the components and organizing the processes in the combustion chambers, but they relatively weakly affect the basic laws of combustion processes. In the theory of combustion, the problems of burning homogeneous, premixed, gaseous components are studied in most detail. The concepts and methods of the theory of combustion are used in other areas of science and technology when considering exothermic processes with high heat generation. The separation of the issues of flame stability into diffusion-thermal and hydrodynamic problems, which is often encountered in theoretical works, is conditional and is caused by the desire to reduce the mathematical difficulties that arise when solving the problem in the general formulation. In fact, flame instability is determined by the influence of both transport processes in the flame (diffusion-thermal processes), depending on its structure, and hydrodynamic processes, i.e., the effects of gas flow. The determination of the concentration limits of flame propagation, ignition, and extinction, spontaneous instability of the flame front, the transition of combustion to detonation, and the excitation of oscillations during combustion are practical problems of the theory of combustion. Acoustic combustion instability can be considered as a self-oscillating process in which the feedback providing the energy necessary for maintaining undamped wave motions from a nonperiodic heat source (combustion process) is realized through the action of sound (acoustic) waves on combustion; in this case, the parameters of the wave motions, amplitude, waveform, and frequency, are determined by the internal properties of the system itself. This chapter provides a sequence of parametric estimates of acoustic instability during combustion in cylindrical chambers.
Part of the book: Direct Numerical Simulations