A Dynamic Model of Resonant Interactions in Combustion Systems

In continuous combustion processes, often there is a two-way coupling present between the heat release and pressure oscillations which leads to a form of resonance referred to as thermoacoustic instability. If allowed to persist in a practical device, this instability can endanger the structural integrity of the system as large amplitude pressure oscillations lead to vibrations, local hot spots, and other undesirable behavior. An active feedback controller offers help in this regard, since it could be employed to detect the onset of these growing oscillations and appropriately modulate the input sources. In order to provide clear guidelines for the design of such control, an analytical framework for studying the instability as well as the details of the interactions between the key process variables must be provided. In this paper, we present the preliminary results obtained from our efforts to develop such a systematic framework. These pertain to the development of a feedback model of a premixed combustor which is derived using the conservation equations of one-dimensional flow dynamics and a fundamentally based flame dynamics model. We show that this feedback model sheds light not only on the thermoacoustic instability behavior, but also provides a way of quantifying the relation between the instability and the physical parameters, and in addition, illustrates that this behavior is dependent on various modes of the system which are coupled with each other. A simple numerical example is used to illustrate the accuracy of the proposed model and is compared with experimental results reported in the literature.