Multi-phase Flow: Fountain Waterfall

This project presents a numerical simulation of a fountain waterfall using ANSYS Fluent, with multiphase flow as the central theme. The system involves two fluids — water as the primary working fluid and air as the secondary phase — and the heart of the study is capturing how these two phases interact as the fountain fills and spills. To do this, the Eulerian multiphase model is used, treating water and air as interpenetrating phases each with its own set of governing equations. Water enters the fountain at 1 m/s, and gravity is included at −9.81 m/s² along the y-axis, since the rise and fall of the water under gravity is exactly what the simulation sets out to reproduce.

The three-dimensional geometry was created in Design Modeler and consists of a fountain with a single inlet set within a surrounding cylindrical ground domain. The base of the cylinder is treated as the ground, while the remaining surfaces are pressure outlets. Meshing was performed in ANSYS Meshing using an unstructured grid with no element quality below 0.64, ensuring a reliable representation of the flow.

The simulation uses a pressure-based, transient solver, appropriate for following the time-dependent filling and spilling of the fountain. Only the fluid behaviour is examined here — heat transfer is not modelled — and gravity acts along the y-axis as noted. Turbulence is represented with the standard k-ω model including shear-flow corrections. Within the multiphase setup, air is defined as the primary phase and water as the secondary phase using an explicit formulation, which sharply resolves the evolving water–air interface. At the inlet, water enters at 1 m/s with a volume fraction of unity; at the outlets, the backflow volume fraction is set to air, so that any returning flow is treated as air rather than water. Phase-coupled pressure–velocity coupling is used together with the PRESTO! pressure scheme and first-order upwind discretisation for momentum, specific dissipation rate and volume fraction.

The solution yields two- and three-dimensional fields of velocity and of the water and air volume fractions, together with an animation of the fountain filling. Starting from an inlet velocity of 1 m/s, the fountain takes about 1.8 s to fill, after which it begins to spill over and the simulation ends. The results reveal a clear relationship between the inlet velocity and diameter and both the time required to fill the fountain and the resulting wetted area. As a study in multiphase flow modelling, the project demonstrates how the Eulerian model can track the coupled motion of water and air under gravity — resolving the free-surface filling and overflow behaviour that defines the operation of a fountain.