High Reynolds number, low Mach number gas flows in pipe systems with closed side branches exhibit spectacular low frequency self-sustained pulsations driven by periodic vortex shedding at specific values of the Strouhal number. A detailed study is presented of the behaviour of the flow in a system with two opposite closed side branches of equal length in a cross configuration. For junctions with both sharp and rounded edges the acoustic flow velocity amplitude is comparable to the main flow velocity. A two-dimensional potential flow model based on the vortex blob method, used to simulate the flow in the junction, describes accurately the flow visualization and laser Doppler data obtained in pipes with square cross-sections and with sharp edged junctions. The numerical simulation is used to calculate the acoustical power generated by the vortical flow at a given amplitude of the acoustic velocity field and Strouhal number. In reality, for a pulsation with constant amplitude, this power is balanced by the viscothermal losses and acoustic radiation, which is the basis for the indirect measurement of the source power. It is shown that, for the acoustic amplitude observed, radiation losses due to the generation of non-resonating harmonics by wavesteepening has to be taken into account in the energy balance. This finding is confirmed by the appearance of shock waves in the geometry with rounded edges.
Kriesels, P. C., Peters, M. C. A. M., Hirschberg, A., Wijnands, A. P. J., Iafrati, A., Riccardi, G., ... Bruggeman, J. C. (1995). High amplitude vortex-induced pulsations in a gas transport system. Journal of Sound and Vibration, 184(2), 343-368. https://doi.org/10.1006/jsvi.1995.0321