Abstract

Nonlinear Gas Oscillation and Streaming Motion in a Closed Tube with Varying Cross Section

T.Yano (Department of Mechanical Science, Hokkaido University, Sapporo, Japan)

e-mail: yano@mech-me.eng.hokudai.ac.jp

The nonlinear resonant gas oscillation and acoustic streaming motion in a closed tube with varying cross section filled with an ideal gas are numerically studied. The resonant gas oscillation is excited by a piston at one end of the tube, which oscillates harmonically at the fundamental resonant frequency of linear quasi-one-dimensional wave motion. The system of Navier-Stokes equations for axisymmetric flow is directly solved by a high-resolution upwind TVD finite-difference scheme. In the case that the wave motion is excited at M=0.001 (M is the piton Mach number), the almost steady oscillation state is shock free and the pressure profile, except for maximum amplitude, agrees with that of the linear quasi-one-dimensional wave motion. In particular, pressure profiles in the tube with the same cross-sectional variation but with different mean radii are almost the same except for amplitude. On the other hand, the resulting streaming motion is strongly affected by the mean radius of the tube. We shall demonstrate that the number of streaming vortices increases in a relatively wide tube.

Section : 7