Time domain phenomenological formulation for the sound generation in corrugated pipes

The study deals with a possibility to formulate the complex fluid–structure interaction problem of noise generation due to the unsteady flow in corrugated pipes by phenomenological formulation. Although the details of fluid dynamics are not accessible this way, the computational framework is much less demanding and the key features are still present. The van der Pol-like equations serve as a model of self-sustained sources coupled to the acoustic resonances of the tube. The effects of the sound field convection are discussed. A closer case-study investigation using linear stability analysis and a semi-analytical solution is presented. Numerical analysis investigating the flow velocity sweeps and fitting the model to the experimental data follows. The proposed system exhibits the key features known from experiments such as mode-locking and hysteresis and is capable of capturing the experimental data correctly.