Modelling of Turbulent Flows with Strong Dispersed Phase-Continuous Fluid Interactions

Abstract

Dispersed gas-liquid flows are common in nature and industrial applications. They can be found in systems such as gas-stirred metallurgical ladles, subsea gas releases and pneumatic oil barriers. Basic conservation equations for two-way coupled gas-liquid turbulent flows are firstly derived based on a double-step averaging procedure. Favre averaging on the prior volume-averaged equations is performed. From the doubleaveraged momentum equation and mechanical energy equations, the double-averaged transport equation for turbulent kinetic energy of the carrier fluid is rigorously derived. The shear work performed on the liquid turbulence by the coupled drag force and virtual mass force is modelled as the product of the forces and the relative velocity between bubbles and fluid. For analogous terms in the dissipation transport equation, a similar heuristic is used as for the single phase model.

In light of the derivation, we obtain a model to account for the extra turbulent agitation introduced by bubbles into the fluid. This model remedies some deficiencies of the standard k-epsilon turbulence model. The standard turbulence model also does not account for turbulence damping in the vicinity of free surface, which may lead to an underestimation of the surface outward flow. And the turbulence modifications due to the density variation created by the non-uniform distribution of the bubbles should also be incorporated. Thus an enhanced turbulence model is proposed and implemented to account for the above effects. This allows improved representation of the physics of bubble plumes, as well as the transport phenomena at, and close to, the free surface.

There are three applications presented in this thesis: a gas-stirred ladle, a subsea gas release and a bubble plume as pneumatic oil barrier. To model such flows numerically, bubbles can be tracked with discrete phase model (DPM), using a parcel-based Lagrangian approach. Capturing the free surface formed by the surfacing bubble plumes can be handled by volume of fluid (VOF) model. Thus the model framework is an Eulerian-Lagrangian-Interface Capturing approach combining the DPM and VOF models, and closed by the formulated enhanced turbulence model.

The integral kinetic energy budgets in dispersed flows are another focus of this thesis. The analysis of a set of data from two-way coupled direct numerical simulations (DNS) for turbulent particle suspension in a channel flow reveals the role of particles in the kinetic energy transport, conversion and dissipation. The particles, gaining energy from mean flow earlier, will thereafter release energy to the turbulence. The particles are concluded to play an intermediary role in the energy transport from the mean flow to turbulence, accompanied by irreversible energy dissipation.