Multiscale Computational Methodology Applied to Hydroacoustic Resonance in Cavitating Pipe Flow

The present work is a contribution to the physical analysis and numerical simulation of the pressure surges in hydraulic machinery and connected conduit systems. Localized hydrodynamic instabilities including cavitation are prone to interact with the entire conduit through the propagation of acoustic plane waves. At resonance, the superimposition of the acoustic waves leads to the formation of large amplitudes standing waves along the entire conduit. The resulting fluctuation of velocity and pressure in the source region may have a significant role on the hydrodynamic instability. A computational methodology based on two fields is proposed to simulate this interaction in the time domain: a 1D hydroacoustic model (HA model) is selected to analyze the entire acoustic field including the source region, a 3D incompressible hydrodynamic model (HD model) is used to describe the flow in the source region. The acoustic perturbation due to the instability is precisely evaluated with the HD model and injected in the HA model through discrete sources. To describe the complete interaction between the fields, two methods are proposed: the acoustic feedback is either fully modeled (two way coupled simulation) or accounted for using interaction parameters (one way concurrent simulation). In the first method, the boundary conditions of the HD model are adjusted dynamically using the solution field of the HA model and all components of the sources are evaluated in the HD model. In the second method, the acoustics and hydrodynamics components of the sources are considered as independent. The components due to the hydrodynamic field are evaluated in the HD model with steady boundary conditions and injected in HA model through discrete sources. The components of the sources due to the acoustic fluctuations are accounted for with specific parameters of the HA model; those interaction parameters, i.e. cavity compliance and mass flow gain factor, are evaluated with the help of the HD model. A reference case study has been setup; video analysis and dynamic pressure measurement have been performed to validate the simulations. The case study consists in a straight pipe connecting two constant pressure tanks. A bluff body is placed at 3/4 of the pipe length, the resulting flow instability is characterized by the alternate shedding of vortices at a frequency proportional to the flow velocity. The hydroacoustic resonator is the pipe itself. Measurements have been performed for resonant and non-resonant conditions in cavitating and cavitation free flow regime. In cavitation free flow regime, the hydrodynamic source is identified as a pure momentum source associated with the drag force on the bluff body. The flow conditions leading to resonance can be evaluated with the two way coupled simulation. At resonance, the distribution, frequency and amplitude of pressure fluctuation predicted in the simulation is in good agreement with the measurement. For the selected case study, the acoustic feedback is very weak and has no significant effect on the momentum source. In cavitating flow regime, two hydrodynamic sources have been identified, the momentum source and the mass source. The momentum source is associated with the drag force on the bluff body, the mass source is associated with the volume fluctuation of the fl vapor phase in the wake of the bluff body. The strength of the mass source is orders of magnitude larger and the momentum source can therefore be neglected. One way concurrent simulations using dynamic update of the interaction parameters have been performed. Fair agreement is obtained between the simulations and the measurements. The amplification of the fluctuation observed experimentally below incipient cavitation is reproduced. At intermediate cavitation index, the pressure fluctuation amplitude and the spectral energy distribution is in fair agreement with the experiment. The modifications of the pipe eigenmodes and eigenfrequencies due to cavitation is satisfactorily reproduced with the cavity compliance.