Modeling heat and mass transfer in bubbly cavitating flows and shock waves in cavitating nozzles

Two problems are considered in this thesis: the modeling of heat and mass diffusion effects on the dynamics of spherical bubbles, and the computation of unsteady, bubbly cavitating flows in nozzles. In Part I we develop a reduced-order model that is able to accurately and efficiently capture the effect of heat and mass transfer on the dynamics of bubbles. We first employ a full bubble computation, where the full set of radial conservation equations are solved in the bubble interior and surrounding liquid. This enables us to determine which equations, or terms in equations, are able to be neglected while still accurately capturing the bubble dynamics. Motivated by results of the full computations, we develop a reduced-order model that uses constant heat and mass transfer coefficients to approximate the transfer at the bubble wall. In the resulting model equations, each of the partial differential equations for heat and mass diffusion are replaced by a single ordinary differential equation. Comparisons of the reduced-order model to the full computations over a wide range of parameters indicate agreement that is superior to existing models.; In Part II we investigate the effects of unsteady bubble dynamics on cavitating flow through a converging-diverging nozzle. A continuum model that couples the Rayleigh-Plesset equation with the continuity and momentum equations is used to formulate unsteady, quasi-one-dimensional partial differential equations. Flow regimes studied include those where steady state solutions exist, and those where steady state solutions diverge at the so-called flashing instability. These latter flows consist of unsteady bubbly shock waves traveling downstream in the diverging section of the nozzle. In the model, damping of the bubble radial motion is restricted to a simple "effective" viscosity to account for diffusive effects. However, many features of the nozzle flow are shown to be independent of the specific damping mechanism. This is confirmed by the implementation of the more sophisticated diffusive modeling developed in Part I.