For the tip-leakage cavitating flow, the existence of both interface and microbubbles at scales separated by orders of magnitude makes it difficult to be comprehensively reproduced by numerical modeling. This work aims to develop a multiscale model that directly resolves the large-scale cavities and models small discrete bubbles. The volume of fluid (VOF) method and the Schnerr–Sauer cavitation model are first adopted to represent the phase field of water and vapor from a macroscale point of view. A discrete bubble model (DBM) based on the Lagrangian formulation is then developed to simulate the microscale cavitation bubbles that are smoothed in the macroscale model due to the limited mesh resolution. The transition between DBM and VOF is also implemented to achieve the multiscale simulation. For modeling of the turbulence, the scale adaptive simulation approach is used. The tip-leakage cavitating flows induced by the NACA0009 hydrofoil under the conditions with different gaps according to the reported experiment are simulated. Results show that, using the proposed multiscale model, better agreements can be obtained compared with the macroscale model, and specific phenomena can be well revealed including the bubble nucleation, growth and collapse, the interaction between discrete bubbles and large-scale cavities.

For understanding tip-leakage cavitating flow features, the present work aims to implement a multiscale model to comprehensively reproduce the complicated phase structure. The volume of fluid (VOF) interface capturing method is applied to simulate macroscale cavities, while a discrete bubble model using the Lagrangian formulation is newly developed to take the microscale bubbles into account. The Schnerr–Sauer cavitation model is incorporated into the VOF model to calculate the mass transfer rate between phases from the macroscale point of view. For microscale bubbles, the simplified Rayleigh–Plesset equation is adopted to simulate the bubble growing and collapsing stages. An algorithm for coupling the approaches simulating macroscale cavities and microscale bubbles is also implemented to achieve multiscale simulation. Unsteady flow features are simulated using the large eddy simulation approach. The results show that an anti-diffusive compression scheme for the spatial discretization of volume fraction equation is relatively accurate for simulating the tip-leakage cavitating flow. Applying the multiscale model, the tip-leakage cavitating flow features with multiple time and space scales including the formation of glass cavity tube and the transport of bubble clouds can be revealed. Suitable model parameters including the coefficient of saturated pressure, and the bubble evaporation and condensation coefficients are studied.

Numerical simulations of multiphase flows with both interfaces and discrete particles are challenging because they possess a wide range of length and time scales. Meanwhile, the volume of fluid (VOF) method is suitable for resolving the interface, while the discrete particle model (DPM) under the Lagrangian frame better simulates unresolvable particles; a multiscale VOF–DPM combined model is urgently needed for multiscale multiphase flows. The present work implements a VOF–DPM solver that includes a two-way transition algorithm to model the transformation between discrete and continuous phases for bubbles or droplets using OpenFOAM. The interface-capturing scheme in the solver is based on the interIsoFoam solver, which supports the geometric reconstruction of the interface and adaptive mesh refinement. A connected component labeling approach is used for particle detection and VOF-to-DPM transition for discrete bubbles or droplets produced by interface breakup. Conversely, a DPM-to-VOF transition algorithm for particles touching the interface is incorporated to achieve a two-way transition. In addition, phase change modeling between continuous phases and bubble dynamic modeling for cavitating flow cases are also implemented in the solver. Test simulations are performed for validation, including the gas–liquid two-phase dam break and cavitating flow in a convergent–divergent test section. The results demonstrate that the solver is reasonably accurate and can adequately represent the complex phase structure, including the interface and discrete particles.