Development and implementation of a hybrid volume of fluid/level set method to study two-phase flows

Simulation of two-phase flows is a complicated problem due to the nature of interfacial behavior. Knowledge of the shape of the interface is required to determine the flow field. Thus computations need to recreate the interface for each time step. In this work, a new method is described that combines the best features of two previously utilized techniques, the Volume of Fluid and Level Set methods.;Since this is a new algorithm, the method is tested against a model problem of a drop within a tube. There is previous research on this problem both experimental and computational, which the results are compared with to display the accuracy of the simulation. The two main areas studied are buoyancy-driven motion of the drop and deformation of the drop within pressure-driven flow.;For buoyancy-driven flow, the change in density between the fluids causes the drop to rise until reaching a steady velocity. The stress on the drop causes it to change shape until equilibrium is reached. To verify the technique, simulations for small drops and low Reynolds numbers are compared with velocities from the analytical results for spheres. Computations done for deformable drops also compare well with previous experiments for drop velocity and shape. The effect of Capillary and Reynolds numbers are investigated in a parameter study. Increases in both numbers lead to increased deformation. This deformation elongates and narrows the drops and thus increases the migration velocity. It is also found that initial shape effects the steady state result of the simulation. Along with the other parameters, the viscosity ratio is varied and deformation is increased for both increases and decreases in the ratio. A power law fluid is utilized as the suspending fluid to test the effect of non-Newtonian fluids on the system. The power law shortens the drops and introduces a recirculation wake behind the drop for the higher power law index. This effect is seen to a lesser degree at smaller Reynolds number with smaller deformation. The power law also produces recirculation in front of larger sized drops due to the small gap between the drop and the wall.;In the case of pressure-driven flow, the deformation occurs by an entrant cavity in the back of the drop. Testing of the code is done again by comparison to previous results. A parameter study on Reynolds and Capillary numbers is carried out. For a certain Reynolds number, deformation increases with increasing Capillary numbers until a critical value is reached above which the drop breaks up and no steady shape can be found. The deformation increases with increasing Reynolds number, and thus the critical Capillary number decreases as the Reynolds number is increased. In two different studies, the critical Capillary number passes through a maximum value at small Reynolds numbers before falling below literature results at higher Reynolds numbers. The addition of a small amount of inertia appears to stabilize the drop while higher values produce larger deformations and the drop breaks up at a lower Capillary number. The effect of viscosity ratio is also tested and the drop deformation increases with increasing viscosity ratio, a trend observed in earlier experiments. Last, the suspending fluid is modeled as a power law non-Newtonian fluid. The power law fluid produces drops with tapered heads and flattened backs. This shape is similar to the larger size ratios in buoyancy-driven motion and to previous experiments with viscoelastic fluids.