M.Sc Thesis

M.Sc StudentAviad Gofer
SubjectTransport and Compressibility Phenomena in a Two-Phase
Bubbly Flow
DepartmentDepartment of Aerospace Engineering
Supervisor Professor Emeritus Gany Alon
Full Thesis text - in Hebrew Full thesis text - Hebrew Version


This work deals with two main subjects in the field of water-air two-phase flows. The first one focuses on shock wave phenomena in two-phase bubbly flows. Bubbly flows are characterized by relatively high density and high compressibility. One of the resulting features is a very low speed of sound in such medium, within the range of 20-60m/sec (depending on the air volume faction and pressure).

A physical-mathematical model has been developed, based on conservation equations and bubble dynamic equation for a homogenous two-phase water-air bubble mixture. Shock relations as a function of Mach number were developed revealing pressure ratios similar to those in air-only medium (somewhat higher ratios for adiabatic process in the gas bubbles and lower ratios for isothermal process). Bubble radius and hence air volume fraction are found to be smaller after the shock wave.

Shock wave in bubbly flow was found to be much thicker than in air. The higher inertia of the mixture due to its high density results in a few mm to a few cm thick shock wave compared to an order of 10-10m in air flow.

The wave structure is highly dependent on upstream mixture Mach number and Reynolds number (bases on bubble initial radius). A characteristic feature related to the two-phase shock wave structure is the appearance of oscillations of the main properties (pressure, Mach number, gas volume fraction, bubble radius, etc) within the shock until converging into a new equilibrium downstream of the shock wave.

Characteristic cycle time of the oscillations under typical conditions was found to be about 0.2ms, in a close agreement to experiments reported in the literature.

The second subject included in the thesis is the injection of an air layer into the water boundary layer under a flat plate.

This problem was solved using a CFD program - Fluent, with a flat plate length of 0.5m and water flow velocity of 5m/sec. Initial conditions before air injection were defined from a steady state solution of a turbulent water boundary layer on a flat plate. The injection of an 0.5mm thick air layer from the plate's leading edge into the water boundary layer at a speed of 5m/sec, was found to cause overall drag reduction of more than 98%.   

Though future research should deal with larger plates and longer air injection durations, the study indicates directions for drag reduction in marine vessels.