Abstract
A multi-scale Euler–Lagrange method was developed and applied to numerically assess cavitation-induced erosion based on the collapse dynamics of Lagrangian bubbles. This approach linked macroscopic and microscopic scales and captured large vapour volumes on an Eulerian frame, while small vapour volumes were treated as spherical Lagrangian bubbles. Interactions between vapour bubbles and the liquid phase were considered via a two-way coupling scheme. A verification and sensitivity study of the developed procedure to transform vapour volumes between Eulerian and Lagrangian frames was performed. First, the developed method was validated for bubble dynamics, using analytical and experimental data. Second, the cavitating flow through an axisymmetric nozzle was simulated using a measurement-based distribution of cavitation nuclei. Details of single bubble collapses were used to assess cavitation erosion. Based on well-recognised fundamental experiments and theoretical considerations from the literature, model assumptions were derived to account for the effects of a bubble’s stand-off distance on the bubble’s motion and its radiated pressure during an asymmetric near-wall bubble collapse. Computed maximum collapse radii of bubbles correlated well with diameters of measured erosion pits. Considering a nonlinear dependence of erosion on impact pressure, calculated erosion potentials compared well to measured erosion depths.
Highlights
The various approaches for cavitation modelling differ mainly in the treatment of the vapour phase
Large vapour structures are treated in the Eulerian frame, while small vapour volumes are considered as spherical Lagrangian bubbles, whose motions and associated bubble dynamics are calculated on a local coordinate system
We numerically simulated cavitating flow using a multi-scale Euler–Euler/Euler– Lagrange approach to assess cavitation erosion based on Lagrangian bubble collapses
Summary
The various approaches for cavitation modelling differ mainly in the treatment of the vapour phase. Krumenacker, Fortes-Patella & Archer (2014) developed a numerical method that determines the cavitation intensity as an indicator for erosion risk when cloud-like cavitation areas collapse In their method, the flow is simulated using an Euler–Euler approach and a Reynolds-averaged Navier–Stokes (RANS) method coupled with a solver to compute the acoustic energy of single bubbles from a bubble dynamics equation. The computation of transport and dynamics of spherical single bubbles provided greater insight into bubble behaviour Depending on their absolute size and spatial resolution relative to the numerical grid, our multi-scale approach switched between an Eulerian and a Lagrangian treatment of vapour structures. Our multi-scale approach links the macroscopic Eulerian treatment of large vapour structures to the microscopic Lagrangian treatment of single cavitation bubbles and uses the bubble collapses to assess cavitation-induced erosion. The cavitating flow through an axisymmetric nozzle was simulated, and numerically evaluated cavitation-induced erosion was compared to measured erosion depths
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