A Simplified Model for Linear and Nonlinear Processes in Thermoacoustic Prime Movers. Part I. Model and linear theory

A simplified quasi-one-dimensional model of thermoacoustic devices is formulated by averaging the conservation equations over the cross section. Heat transfer and drag effects are introduced by means of suitable coefficients. While the primary motivation for this work is the development of a model approximately valid in the nonlinear regime, the focus of this paper is the proper formulation of the transfer coefficients and the analysis of the linear problem. The accuracy of the model is demonstrated by comparison with existing more precise theories and data. Examples of devices with variable cross section demonstrate the flexibility of the approach.