On the whistling of corrugated pipes: effect of pipe length and flow profile

Whistling behaviour of two geometrically periodic systems, namely corrugated pipes and multiple side branch systems, is investigated both experimentally and numerically. Tests are performed on corrugated pipes with various lengths and cavity geometries. Experiments show that the peak-whistling Strouhal number, where the maximum amplitude in pressure fluctuations is registered, is independent of the pipe length. Experimentally, a decrease of the peak-whistling Strouhal number by a factor of two is observed with increasing confinement ratio, i.e. the ratio of pipe diameter to cavity width. A numerical methodology that combines incompressible flow simulations with vortex sound theory is proposed to estimate the acoustic source power in periodic systems. The methodology successfully predicts the Strouhal number ranges of acoustic energy production/absorption and the nonlinear saturation mechanism responsible for the stabilization of the limit cycle oscillation. The methodology predicts peak-whistling Strouhal numbers in agreement with experiments and explains the dependence of the peak-whistling Strouhal number on the confinement ratio. Combined with an energy balance, the proposed methodology is used to estimate the acoustic fluctuation amplitudes.