Nonlinear diffusion-wave equation for a gas in a regenerator subject to temperature gradient

• Published in: AIP conference proceedings Vol. 1685; no. 1
• Main Author: Sugimoto, N
• Format: Conference Proceeding
• Language: English
• Published: Melville American Institute of Physics 28.10.2015
• Subjects: Boundary conditions; Diffusion layers; Diffusion rate; Ideal gas; Temperature gradients; Thermoacoustics; Thickness; Wave equations; Wave propagation
• ISSN: 0094-243X; 1551-7616
• DOI: 10.1063/1.4934426

This paper derives an approximate equation for propagation of nonlinear thermoacoustic waves in a gas-filled, circular pore subject to temperature gradient. The pore radius is assumed to be much smaller than a thickness of thermoviscous diffusion layer, and the narrow-tube approximation is used in the sense that a typical axial length associated with temperature gradient is much longer than the radius. Introducing three small parameters, one being the ratio of the pore radius to the thickness of thermoviscous diffusion layer, another the ratio of a typical speed of thermoacoustic waves to an adiabatic sound speed and the other the ratio of a typical magnitude of pressure disturbance to a uniform pressure in a quiescent state, a system of fluid dynamical equations for an ideal gas is reduced asymptotically to a nonlinear diffusion-wave equation by using boundary conditions on a pore wall. Discussion on a temporal mean of an excess pressure due to periodic oscillations is included.