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

Abstract

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. The goal of Part I is to 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. Detailed computations of forced and oscillating bubbles including heat and mass diffusion show that the assumptions of polytropic behavior, constant vapor pressure, and an liquid viscosity do not accurately account for diffusive damping and thus do not accurately capture bubble dynamics. While the full bubble computations are readily performed for single bubbles, they are too expensive to implement into continuum models of complex bubbly flows where the radial diffusion equations would have to be solved at each grid point. Therefore reduced-order models that accurately capture diffusive effects are needed. We first develop a full bubble computation, where the full set of radial conservation equations are solved in the bubble interior and surrounding liquid. This provides insight as to which equations, or terms in equations, may be able to be neglected while still accurately capturing the bubble dynamics. Motivated by results of the full computations, we use constant heat and mass transfer coefficients to model the transfer at the bubble wall. In the resulting reduced-order model the heat and mass diffusion equations are each replaced by a single ordinary differential equation. The model is therefore efficient enough to implement into continuum computations. 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. An approximate analytical expression is developed to predict the critical back pressure for choked flow. The results agree with previous barotropic models for those flows where bubble dynamics are not important, but show that in many instances the neglect of bubble dynamics cannot be justified. Finally the computations show reasonable agreement with an experiment that measures the spatial variation of pressure, velocity and void fraction for steady shock free flows, and good agreement with an experiment that measures the throat pressure and shock position for flows with bubbly shocks. 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.