The Diagrammatical Understanding of Thermoacoustic Theory

Abstract

In thermoacoustic theory, which represents thermodynamical and fluid mechanical phenomena of oscillating fluid in flow channels, remarkable advances have been made in the last several years. Then it is found that the theory and its numerical calculations are useful for the understanding and analysis of the phenomena which occur in the working space not only of regenerative refrigerator (e.g. Stirling, G-M and pulse tube refrigerator) but also of the resonance tube refrigerator and the Stirling engine. This paper describes the easier understanding of the basic idea of the thermoacoustic theory and the physical images of the appeared quantities in the theory by means of graphical representation with keeping the accuracy of the discussion. This theory consists of two steps. The first step is to derive the quasi-local formulas of energy transfer and conversion for oscillating fluid by considering the heat transfer between the fluid and the wall of the flow channel in a cross sectional area. The second step is to derive the formulas of spatial variation for the axial direction based on the quasi-local formulas. In this paper, only the first step is treated and the derivation process of the formulas by visual thermodynamical diagrams is shown. The quasi-local formulas, which are derived from the complex equations in the original treatment, are diagrammatically derived from the combination of components of the corresponding complex values. The thermoacoustic theory provides us with a new classification for heat transfer and work losses in a regenerative refrigerator by expressing the phenomena observed from oscillating (i.e. Lagrangian view point), then it is expected that their intrinsical and physical meaning are well understood and to be effectively used for the design and improvement of actual devices and instruments.