Finite Amplitude Standing Wave in an Axi-Symmetric Closed Duct with Cross-Sectional Area Change

When an air-column in an axi-symmetric closed tube with constant cross-section is driven by a piston vibrating at resonant frequency at one end, finite amplitude standing wave is induced in the tube. The increase of oscillation amplitude in the tube brings about the nonlinear phenomena of wave motion, such as mean pressure distribution along the tube axis, acoustic streaming, and thermoacoustic effect. The large amplitude pressure fluctuation and the thermoacoustic effect generated by finite amplitude standing wave induced in the closed tube are principal physical phenomena in the engineering applications of the finite amplitude wave motion to acoustic compressor and thermoacoustic refrigerator. In order to develop these practical systems, it is essential to realize large amplitude oscillation in the tube. However, the increase of oscillation amplitude is limited by the acoustic saturation caused by nonlinear wave distortion which steepens wave front to shock wave. In order to avoid the acoustic saturation, axi-symmetric tubes with cross-sectional area contraction toward the closed end are used. Basic characteristics of wave motion in the tubes with area change have been discussed with linear acoustic theory. Finite amplitude wave motions generated in different shape tubes have been analyzed numerically and compared with experimental results. Fundamental knowledge and estimation for the development of the acoustic compressor have been given from the results obtained