Computational modeling and analysis of viscoelastic multiphase flows

Interface-resolved direct numerical simulations of multiphase viscoelastic fluid flows have been performed by using a high fidelity finite-difference/front-tracking method to explore some of the most complex dynamics of these intricate flow regimes. Surfactant contamination is also considered. The flow equations are solved fully coupled with the viscoelastic model equations and the equations governing interfacial and bulk surfactant concentrations. The latter coupling is accomplished by a nonlinear equation of state that relates the surface tension to the surfactant concentration. Simulations are first performed to study the phenomenon of negative wakes generated behind a pair of bubbles rising in an otherwise quiescent viscoelastic fluid under buoyancy. It is found that, in addition to the formation of long tails that tilt towards each other, the lateral symmetry is also broken in the two-bubble system. The rise velocity of the parallel bubbles remains slightly smaller than that of the single bubble due to bubble-bubble interactions. Symmetry observed in the case of parallel bubble pairs is broken when bubbles are initialized by an initial offset in vertical direction. Next, lateral migration of a deformable bubble in a viscoelastic pressure driven channel flow is studied. It is found that the forces induced by fluid inertia push a bubble towards wall while elasticity and deformability pull it towards channel center. This interplay between fluid inertia, elasticity, and bubble deformability determines the orientation of bubble migration in the channel and its final equilibrium position. It is shown that secondary flow velocity induced by a bubble migrating towards wall is an order of magnitude higher than the one induced by a solid particle under similar flow conditions. This behavior is attributed to the slip condition on the bubble surface. Then, a novel mechanism of achieving an elasto-inertial turbulent (EIT) state by injecting bubbles into a pressure-driven viscoelastic channel flow under the conditions for which a single-phase flow remains laminar is demonstrated even for the Reynolds number as low as Re = 10 and a Weissenberg number as low as Wi = 1. It is found that curved streamlines across the bubble interfaces provide the necessary condition to trigger an elastic instability that leads to a fully chaotic motion even at very low Reynolds and Weissenberg numbers for which the single-phase flow remains completely laminar. The energy spectra shows a scaling of −2 for this multiphase EIT regime. It is also found that bubbles move towards the channel centerline and form a string-shaped alignment pattern in the core region at lower values of Re = 10 and Wi = 1. Unlike solid particles, increasing shear-thinning effect tends to break up alignment of bubbles. Finally, interface-resolved direct numerical simulations are performed to investigate drag reduction by polymer additives in a bubbly turbulent channel flow in the presence of surfactant contamination for a fixed Reynolds number of Re = 5600. Simulations are carried out for the high-drag-reduction (HDR) and maximum-drag-reduction (MDR) regimes. It is shown that, once flow is made viscoelastic by polymer additives, an HDR regime is achieved with a drag reduction of 49%. It is found that Reynolds stress is reduced in this HDR regime but still remains higher than polymer stress. Injection of contaminated bubbles reduces Reynolds stress even further and drag is not increased. Reynolds stress in single-phase flow of maximum MDR regime reduces below the value of polymer stress with a drag reduction of 68% and flow is dominated by elastic effects. Injection of bubbles in this MDR regime produces non-monotonic effect. A small concentration of contaminated bubbles increases Reynolds stress, turbulence production by mean flow and turbulent kinetic energy whereas a higher concentration of bubbles in the MDR regime reduces all these quantities. However, these effects remain restricted to core region of the channel and do not increase drag. It is found that turbulent kinetic energy spectrum shows a scaling of −2 in both of these multiphase HDR and MDR regimes and this scaling is not affected by a change in bubble concentration.