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Eulerian-Lagrangian method for simulation of cloud cavitation
We present a coupled Eulerian-Lagrangian method to simulate cloud cavitation
in a compressible liquid. The method is designed to capture the strong,
volumetric oscillations of each bubble and the bubble-scattered acoustics. The
dynamics of the bubbly mixture is formulated using volume-averaged equations of
motion. The continuous phase is discretized on an Eulerian grid and integrated
using a high-order, finite-volume weighted essentially non-oscillatory (WENO)
scheme, while the gas phase is modeled as spherical, Lagrangian point-bubbles
at the sub-grid scale, each of whose radial evolution is tracked by solving the
Keller-Miksis equation. The volume of bubbles is mapped onto the Eulerian grid
as the void fraction by using a regularization (smearing) kernel. In the most
general case, where the bubble distribution is arbitrary, three-dimensional
Cartesian grids are used for spatial discretization. In order to reduce the
computational cost for problems possessing translational or rotational
homogeneities, we spatially average the governing equations along the direction
of symmetry and discretize the continuous phase on two-dimensional or
axi-symmetric grids, respectively. We specify a regularization kernel that maps
the three-dimensional distribution of bubbles onto the field of an averaged
two-dimensional or axi-symmetric void fraction. A closure is developed to model
the pressure fluctuations at the sub-grid scale as synthetic noise. For the
examples considered here, modeling the sub-grid pressure fluctuations as white
noise agrees a priori with computed distributions from three-dimensional
simulations, and suffices, a posteriori, to accurately reproduce the statistics
of the bubble dynamics. The numerical method and its verification are described
by considering test cases of the dynamics of a single bubble and cloud
cavitaiton induced by ultrasound fields.Comment: 28 pages, 16 figure
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