Gas oscillations in an annular channel induced by a longitudinal temperature gradient

Abstract

Background and Objectives: When selecting the design and layout scheme of the thermoacoustic converter, special requirements include the placement of heat exchangers in the areas of heat input and output. The most promising in this regard are coaxial schemes with coaxial location (tube in tube) of the acoustic pathway channels. Such design features pose their own optimization problems. To solve them, it is necessary to reveal the peculiarities of changing the dynamical parameters of oscillating gas under acoustic wave conditions. Materials and Methods: In this paper we derive a second-order linear differential equation for pressure oscillations in the annular section channel in the presence of a constant longitudinal temperature gradient based on linearized equations of compressible medium mechanics, which does not depend on other dynamical parameters. The solutions are expressed in terms of two dimensionless parameters h/δµ ; h and δµ represent, respectively, half the distance between two concentric channels and a characteristic length using the dynamical viscosity of the gas and the angular frequency of acoustic oscillations. Results: The solution of the equation makes it possible to present expressions for the dynamical parameters of gas oscillations, such as velocity, density, temperature, as functions of the dynamical pressure. Conclusion: It has been shown that the derived equation is a more general case of the Rott equation obtained for a circular section channel under the same conditions. The dynamical parameter equations derived in this paper are applied to measurements of the acoustic power distribution in a thermoacoustic transducer and make it possible to simulate linear acoustic processes in coaxial channels of thermoacoustic devices.

Keywords

• wave equation
• annular channel
• temperature gradient
• axial velocity
• acoustic gas displacement