Cavitation Modelling

The model is based on the Eulerian-Lagrangian approach. Liquid flow is modelled as continuous phase and cavitation bubbles as the dispersed one. Many of the fundamental physical processes assumed to take place in cavitating flows are incorporated into the model. These include bubble formation through nucleation, momentum exchange between the bubbly and the carrier liquid phase, bubble growth and collapse due to non-linear bubble dynamics, bubble turbulent dispersion and bubble turbulent/hydrodynamic break-up. The effect of bubble-to-bubble interaction on momentum exchange and during bubble growth/collapse is also considered. A novel approach accounting for bubble motion in Eulerian grids with cell size comparable to that of the cavitating bubbles has also been developed.

The dispersed phase is modelled on a Lagrangian frame of reference, in an analogous approach to the modelling of spray droplets. Following the assumption that cavitation film structures are comprised of spherical bubbles, a Monte-Carlo stochastic approximation has been used. The inception of cavitation is associated with the artificial creation of small bubble nuclei. The deciding parameters for their creation in any Eulerian grid flow cell, are local static pressure, which has to be below vapour pressure, the volume of the cell itself and the existence of other bubble nuclei. Bubble sizes are sampled from a PDF. The total volume of the nuclei is a prescribed fraction of the total volume of liquid which is below vapour pressure, undergoing ‘tension’.

Bubble velocities are calculated according to Newton’s second law. The forces arising from the bubbles’ interaction with the continuous phase are assessed, and the new velocity for each bubble is calculated. These are drag, added mass, pressure gradient, buoyancy and shear lift force.

Due to liquid turbulence, there is a dispersion effect on the motion of bubbles. Due to the varying pressure field, bubble nuclei grow and collapse, as a result of the force imbalance on their surface. The classical or the compressible bubble dynamics Rayleigh-Plesset equation is used to calculate the time dependent bubble radius. To improve this approach the effects of local turbulence, relative velocity and surrounding bubbles have all been included. The local pressure experienced by the bubble is lower than that calculated by the continuous phase solver at the bubble location. This difference depends on the levels of local continuous phase turbulence and on the magnitude of the relative velocity between the bubble and the surrounding liquid.

Due to their motion within the liquid, bubbles deform as a consequence of the shear forces exerted upon them. The origin of these shear forces is local turbulence and the relative velocity of the bubble to that of the liquid flowing around the bubble; both mechanisms are taken into account in the current model. According to the magnitude of the local turbulent kinetic energy dissipation, break-up can occur and in this case the resulting size of the daughter bubbles is generated by the PDF proposed. Regarding relative velocity induced break-up, a simple criterion based on the Weber number of each bubble is used.

As the approach is Eulerian-Lagrangian, there are two time levels; one for the continuous phase and one for the dispersed phase. Since the complex physics governing cavitation bubbles occur in small timescales, a much smaller time-step is used for their calculation part during the simulation and time sub-cycles are performed within each Eulerian time-step. For this reason any contribution from the dispersed phase to the continuous one is time-averaged within the sub-cycles.

Examples and validation cases of the spray model can be found in the following links.

    Cavitation Sample Cases

    Cavitation Validation Cases

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