An energy conservative method to predict the erosive aggressiveness of collapsing cavitating structures and cavitating flows from numerical simulations Schenke, Sören; van Terwisga, Tom J.C. a b s t r a c tA new technique is proposed in this study to assess the erosive aggressiveness of cavitating flows from numerical flow simulations. The technique is based on the cavitation intensity approach by Leclercq et al. (2017), predicting the instantaneous surface impact power of collapsing cavities from the potential energy hypothesis (see Hammitt, 1963;Vogel and Lauterborn, 1988). The cavitation intensity approach by Leclercq et al. (2017) is further developed and the amount of accumulated surface energy caused by the near wall collapse of idealized cavity types is verified against analytical predictions. Furthermore, two different impact power functions are introduced to compute a weighted time average of the impact power distribution caused by the cavity collapses in cavitating flows. The extreme events are emphasized to an extent specified by a single model parameter. Thus, the impact power functions provide a physical measure of the cavitating flow aggressiveness. This approach is applied to four idealized cavities, as well as to the cavitating flow around a NACA0015 hydrofoil. Areas subjected to aggressive cavity collapse events are identified and the results are compared against experimental paint test results by Van Rijsbergen et al. (2012) and the numerical erosion risk assessment by Li et al. (2014). The model is implemented as a runtime post-processing tool in the open source CFD environment OpenFOAM (2018), employing the inviscid Euler equations and mass transfer source terms to model the cavitating flow.

This study presents a novel physical model to convert the potential energy contained in vaporous cavitation into local surface impact power and an acoustic pressure signature caused by the violent collapse of these cavities in a liquid. The model builds on an analytical representation of the solid angle projection approach by Leclercq et al. ["Numerical cavitation intensity on a hydrofoil for 3D homogeneous unsteady viscous flows," Int. J. Fluid Mach. Syst. 10, 254-263 (2017)]. It is applied as a runtime post-processing tool in numerical simulations of cavitating flows. In the present study, the model is inspected in light of the time accurate energy balance during the cavity collapse. Analytical considerations show that the potential cavity energy is first converted into kinetic energy in the surrounding liquid [D. Obreschkow et al., "Cavitation bubble dynamics inside liquid drops in microgravity," Phys. Rev. Lett. 97, 094502 (2006)] and focused in space before the conversion into shock wave energy takes place. To this end, the physical model is complemented by an energy conservative transport function that can focus the potential cavity energy into the collapse center before it is converted into acoustic power. The formulation of the energy focusing equation is based on a Eulerian representation of the flow. The improved model is shown to provide physical results for the acoustic wall pressure obtained from the numerical simulation of a close-wall vapor bubble cloud collapse.

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Despite significant progress in understanding and foretelling pressure-driven bubble dynamics, models that faithfully predict the emitted acoustic waves and the associated shock formation of oscillating or collapsing bubbles have received comparably little attention. We propose a numerical framework using a Lagrangian wave tracking approach to model the acoustic emissions of pressure-driven bubbles based on the Kirkwood–Bethe hypothesis and under the assumption of spherical symmetry. This modeling approach is agnostic to the equation of the state of the liquid and enables the accurate prediction of pressure and velocity in the vicinity of pressure-driven bubbles, including the formation and attenuation of shock fronts. We validate and test this new numerical framework by comparison with solutions of the full Navier–Stokes equations and by considering a laser-induced cavitation bubble as well as pressure-driven microbubbles in excitation regimes relevant to sonoluminescence and medical ultrasound, including different equations of state for the liquid. A detailed analysis of the bubble-induced flow field as a function of the radial coordinate r demonstrates that the flow velocity u is dominated by acoustic contributions during a strong bubble collapse and, hence, decays predominantly with [Formula: see text], contrary to the frequently postulated decay with [Formula: see text] in an incompressible fluid.

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