This study describes the development and validation of Computational Fluid Dynamics (CFD) methodology for the simulation of dispersed two-phase flows. A two-fluid (Euler-Euler) methodology previously developed at Imperial College is adapted to high phase fractions. It employs averaged mass and momentum conservation equations to describe the time-dependent motion of both phases and, due to the averaging process, requires additional models for the inter-phase momentum transfer and turbulence for closure. The continuous phase turbulence is represented using a two-equation k − ε−turbulence model which contains additional terms to account for the effects of the dispersed on the continuous phase turbulence. The Reynolds stresses of the dispersed phase are calculated by relating them to those of the continuous phase through a turbulence response function. The inter-phase momentum transfer is determined from the instantaneous forces acting on the dispersed phase, comprising drag, lift and virtual mass. These forces are phase fraction dependent and in this work revised modelling is put forward in order to capture the phase fraction dependency of drag and lift. Furthermore, a correlation for the effect of the phase fraction on the turbulence response function is proposed. The revised modelling is based on an extensive survey of the existing literature. The conservation equations are discretised using the finite-volume method and solved in a solution procedure, which is loosely based on the PISO algorithm, adapted to the solution of the two-fluid model. Special techniques are employed to ensure the stability of the procedure when the phase fraction is high or changing rapidely. Finally, assessment of the methodology is made with reference to experimental data for gas-liquid bubbly flow in a sudden enlargement of a circular pipe and in a plane mixing layer. Additionally, Direct Numerical Simulations (DNS) are performed using an interface-capturing methodology in order to gain insight into the dynamics of free rising bubbles, with a view towards use in the longer term as an aid in the development of inter-phase momentum transfer models for the two-fluid methodology. The direct numerical simulation employs the mass and momentum conservation equations in their unaveraged form and the topology of the interface between the two phases is determined as part of the solution. A novel solution procedure, similar to that used for the two-fluid model, is used for the interface-capturing methodology, which allows calculation of air bubbles in water. Two situations are investigated: bubbles rising in a stagnant liquid and in a shear flow. Again, experimental data are used to verify the computational results.

Computational fluid dynamics of dispersed two-phase flows at high phase fractions

Particle drag coefficients in turbulent fluids

Numerical simulation of the dynamic flow behavior in a bubble column : A study of closures for turbulence and interface forces

Gas—liquid flow in bubble columns and loop reactors: Part I. Detailed modelling and numerical simulation

Modelling of dispersed bubble and droplet flow at high phase fractions

This article outlines a computational procedure for the prediction of dispersed two-phase, solid-liquid and gas-liquid, turbulent flows in baffled, impeller-stirred vessles common in the chemical industries. A two-flow Eulerian model is employed, based on the main assumption of interpenetrating coexisting continua. Mean momentum and mass conservation equations are solved for each phase and turbulent closure is effected by extending the single phase k- epsilon turbulence model to two-phase flows. The resulting set of highly coupled equations is solved by a two-phase implicit algorithm, PISO-2P, which allows calculation for a wide range of phase fraction, particle size and phase density ratios. Predictions are presented for solid-liquid and gas-liquid (bubbly) flows. Comparisons are made with experimental data for the mean phase velocities and volume fraction, mean slip velocity and turbulence quantities. (from Authors)

S. Politis

Papers

Multidimensional modeling of turbulent two‐phase flows in stirred vessels