Numerical simulations of two-phase flow: Eulerian and Lagrangian predictions

© 2016 Dr. Shuang J. ZhuTwo-phase flow is common in many environmental systems including rain, snow, sandstorms, avalanches, sediment transport debris flow and countless other natural phenomena. It is also of extreme importance in many industrial and engineering applications, such as fluidised bed, droplet spray process, drug aerosol delivery, dense gas dispersion, particle deposition and pollution control. The study of dynamics of two-phase flow using high resolution numerical simulations has gained considerable momentum with the recent development in computational fluid dynamics (CFD) methodologies. In particular, the use of direct numerical simulations (DNS) resolves the entire range of spatial and temporal scales of the fluid motion, which provides new insights into the structure and dynamics of the two-phase flow. Current two-phase flow simulations modelling can be broadly classified based on the treatment of the dispersed phase. Two types of approaches are prevalent, Eulerian approach (commonly known as the "two-fluid" model) and Lagrangian approach (also known as the "trajectory" model). In the present thesis, investigations are carried out into three different two-phase flow problems using both approaches, namely gravity currents, particle-driven currents and enhanced targeted drug delivery in a vascular tree. The elliptical finite release Boussinesq gravity currents on a uniform slope was performed using a de-aliased pseudo-spectral code. The study comprises a series of simulations of elliptical gravity currents on a range of slope angles. The shape parameters are varied to study the effects of the initial cross-sectional aspect ratio and the mean height to lock radius ratio on the dynamics of the gravity currents. Both the slope angle and the initial shape of the release are shown to significantly influence the spatial mass distribution and dynamics of the gravity currents. The temporal evolution of the front velocity reveals that the current undergoes a second acceleration phase immediately after the first acceleration phase. Numerical simulations of circular finite release particle-driven currents on a uniform slope were carried out using a fast Eulerian approach. The currents with different particle settling velocities released along a range of slope angles at Reynolds number Re=5000 are considered. The mass in the particle-driven currents is found to decrease as the settling velocity of the particle increases. However, the general shapes of the particle-driven current remains the same as the corresponding gravity current with no particle case using the same release condition. The particle-driven current is also observed to undergo a second acceleration phase. The final sedimentation pattern shows a strong dependence on the sloping boundary. The sedimentation is seen to be enhanced by increasing the particle settling velocity. The global energy budget of the flow reveals that the energy budget is dominated by a rapid conversion of potential energy into convective motion during the initial stage of the release. However, the kinetic energy starts to decay after reaching a maximum value as a result of the growing influence of dissipation, which is dominated by microscopic dissipation as a result of particle settling. The possibility of targeting desired locations in an idealised but complex three-dimensional vascular tree using the concept of "controlled particle release and targeting" was numerically investigated. The shear-thinning non-Newtonian behaviour of blood was accounted for by the Carreau-Yasuda model. The one-way coupled Lagrangian approach was used to record individual drug particle trajectories. The current one-way coupled Lagrangian particle tracking model is shown to be able to capture the important particle transport features in the three-dimensional vascular tree model under realistic hemodynamic conditions. The present results do confirm the hypothesis and warrant further research into this area