Effects of Polydispersity in Bubbly Flows

Citation

Ando, Keita (2010) Effects of Polydispersity in Bubbly Flows. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/SW8K-Y135. https://resolver.caltech.edu/CaltechTHESIS:05272010-133830557

Abstract

This thesis concerns the dynamics of bubbly flows with a distribution of equilibrium bubble sizes. The main goal is to formulate the physical and numerical models of continuum bubbly flows that enable us to efficiently compute the average mixture dynamics. Numerical simulations are conducted to quantify the effects of bubble size distributions on the averaged dynamics for several model flows.

First, the ensemble-averaged conservation laws for polydisperse bubbly flows are derived. One-way-coupled flow computations are conducted to illustrate that the different-sized bubbles can oscillate with different frequencies. The resulting phase cancellations can be regarded as an apparent damping of the averaged dynamics of polydisperse flows. A high-order-accurate finite-volume method is then developed to compute the flow, paying special attention to issues of wave dispersion and stiffness.

Next, computations of one-dimensional shock propagation through bubbly liquids are performed. The numerical experiments reveal that the bubble size distribution has a profound impact on the averaged shock structure. If the distribution is sufficiently broad, the apparent damping due to the phase cancellations can dominate over the single-bubble-dynamic dissipation (due to thermal, viscous, and compressibility effects) and the averaged shock dynamics become insensitive to the individual bubble dynamics. One-dimensional cloud cavitation caused by fluid-structure interaction is also solved to investigate the collapse of cavitation clouds with both monodisperse and polydisperse nuclei. The phase cancellations among the cavitation bubbles with broad nuclei size distributions are found to eliminate violent cloud collapse in the averaged dynamics.

Finally, shock propagation through a bubbly liquid-filled, deformable tube is considered. The quasi-one-dimensional conservation law that takes into account structural deformation is formulated and steady shock relations are derived. The results are compared to water-hammer experiments; the present shock theory gives better agreement with the measured wave speeds than linear theory. This indicates that the gas-phase nonlinearity needs to be included to accurately predict the propagation speeds of finite-amplitude waves in a deformable tube filled with a bubbly liquid.

Thesis Files