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A statistics-based model for cavitating polydisperse bubble clouds and their two-way-flow coupling

Phase-averaged bubbly flow models require statistical moments of the evolving bubble dynamics distributions. Under step forcing, these moments reach a statistical equilibrium in finite time. However, actual flows entail time-dependent pressure forcing and equilibrium is generally not reached. In such cases, the statistics of the evolving bubble population must be represented and evolved. Since phase-averaged models compute these moments point-wise, a low-cost algorithm for this evolution is of particular significance for large-scale simulations. We present a population-balance-based method for this purpose. The bubble dynamic coordinates are treated via a quadrature moment method and conditioned on the equilibrium bubble size. Statistics in the equilibrium bubble size coordinate are computed using a fixed quadrature rule and averaged over the period of bubble oscillation. Results show that two quadrature points in each of the bubble dynamic coordinates are sufficient to quantitatively reproduce key statistics. Further, averaging is shown to remove oscillatory behaviors that do not contribute to the moments. Together, this results in a method capable of tracking the bubble population statistics with significantly less computational expense than Monte Carlo approaches. The generality introduced by including statistics in the bubble dynamics coordinates is explored via acoustically excited bubble screen problems.