Numerical study of nonlinear sustained oscillations in a cylindrical open-ended tube

The study of nonlinear sustained oscillations in ducts requires taking into account a variety of relevant physical phenomena, which may occur at different scales, and which therefore are described by different fluid dynamics regimes. In the present work the joint effect of these phenomena is investigated by means of numerical simulation, using a full-wave finite volume method (FiVoNAGI) over a 2D spatial domain assuming axial symmetry, which includes nonlinear propagation and thermoviscous attenuation over a wide range of scales. Excitation at one end of a straight cylindrical tube, open at the other end, is provided by a nonlinear feedback mechanism. First, a transitory state is observed, which is finally followed by a sustained-oscillation state with a self-regulated resonance frequency. For sufficiently large values of the excitation amplitude, shock waves are formed, and their development can be analyzed in terms of progressive waves. The results obtained reproduce qualitatively some well-known featur...