Abstract
Nonlinear resonant gas oscillations in closed tubes with varying cross-sections filled with an ideal gas are numerically studied. The resonant gas oscillation concerned is excited by a piston at one end of the tube, which oscillates harmonically with a resonant frequency obtained by solving the quasi-1-D linear wave equation. The system of Navier–Stokes equations for axisymmetric flow is directly solved by a high-resolution upwind TVD finite-difference scheme. The numerical results may be summarized as follows: (i) If the variation of cross-section is small, a quasi-steady oscillation state includes shock waves, as in the tubes of uniform cross-section. (ii) When the variation of cross-section is relatively large, the gas oscillation evolves into a standing wave of large amplitude, but shock waves are not formed. (iii) The (nondimensional) maximum amplitude can attain the order of the cubic root of M, where M is the acoustic Mach number at the sound source. (iv) Such a large amplitude oscillation induces relatively fast acoustic streaming.
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