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.

Physics-informed neural networks (PINN) can be used to predict flow fields with a minimum of simulated or measured training data. As most technical flows are turbulent, PINNs based on the Reynolds-averaged Navier–Stokes (RANS) equations incorporating a turbulence model are needed. Several studies demonstrated the capability of PINNs to solve the Naver–Stokes equations for laminar flows. However, little work has been published concerning the application of PINNs to solve the RANS equations for turbulent flows. This study applied a RANS-based PINN approach to a backward-facing step flow at a Reynolds number of 5100. The standard k-$\omega$ model, the mixing length model, an equation-free ${\nu }_t$ and an equation-free pseudo-Reynolds stress model were applied. The results compared favorably to DNS data when provided with three vertical lines of labeled training data. For five lines of training data, all models predicted the separated shear layer and the associated vortex more accurately.

Thermodynamic characteristics and their effects on single cavitation bubble dynamics are important to elucidate the physical behaviors of cavitation phenomena. In this study, experimental and numerical methods were utilized to explore the thermodynamic effects on single cavitation bubble dynamics under various ambient temperature conditions. A series of experiments was performed to generate a single cavitation bubble at ambient temperatures between 20 and 80 °C using a laser-induced method and a high-speed camera to observe the dynamic behaviors of bubbles. By increasing the ambient temperature, a nonspherical bubble shape with a jet flow at the bubble rebound stage was observed. Next, the numerical simulation results in terms of the bubble radius and bubble shape were validated with the corresponding experimental data. Generally, the results exhibited reasonable agreement, particularly at the later collapse and rebound stages. Critical hydrodynamic and thermodynamic mechanisms over multiple oscillation stages at different ambient temperatures were analyzed. The bubble behaviors and their intensities were numerically quantified with respect to the bubble radius, collapsing time, internal pressure, internal temperature, and phase transition rate parameters. The results showed that the maximum bubble radius, first minimum bubble radius, and collapsing time increased with an increase in the ambient temperature. Nevertheless, the peak values of the internal pressure and internal temperature decreased with an increase in the ambient temperature. Generally, the bubble collapsed less violently at high temperatures than at low temperatures.