A statistical model for cavitation inception at the sub-grid scale

Bubbles incept via a cavitation process seen in applications from underwater propulsion to medicine.

Resolving all relevant flow features without additional modeling is computationally demanding due to a broad range of space and time scales.

Sub-grid scale models reduce these costs via a degree of modeling appropriate for the flow and suspended-phase physics under dilute assumptions.

The stochastic bubble variables are coupled to the suspending phase via ensemble averaging.

A population balance equation (PBE) models the evolution of the bubble distribution as it depends on the bubble dynamics and what drives them.

A quadrature method of moments scheme approximates the moments arising in the coupled ensemble-averaged flow equations.

Previous works used PBE-based models that use bubble radius and velocity as the relevant statistical variables.

Cavitation inception requires a more general representation of the bubble features to represent their dynamics faithfully.

We present a stochastic PBE-based model that represents inception by introducing additional variables that account for heat and mass transfer at the bubble interface.

Model verification and validation are achieved via comparison to Monte Carlo simulation and experimental results.