Bubble size and system pressure effects on the phase distribution for two-phase turbulent bubbly flows

Abstract

The coupled Eulerian± Lagrangian approach was used to study the eOE ects of bubble size and high-pressure transport behaviour on the phase distribution mechanisms in vertically upward air± water two-phase bubbly¯ows. The approach solves the conservation equations of liquid phase in Eulerian space and equations of motion in conjunction with the random walk method for dispersed air bubbles in Lagrangian space. Numerical calculations were performed under conditions of three bubble diameters (2.8, 4.0 and 5.0 mm) and two diOE erent pressure levels (0.1 and 7.17 MPa) to explore the¯ow and void fraction development phenomena. Simulation results indicate the tendency of higher slip ratios and the movement of the void fraction peak towards the¯ow core for larger gas bubbles. In the pressure range 0.1± 7.17 MPa, predictions reveal that the eOE ect of high-pressure transport behaviour on the phase distribution is insigni® cant. NOTATIONC vm virtual mass coe cientˆ0:5 C "1 ; C "2 ; C · constants for k± " model C ·b bubble induced viscosity constantˆ1:2 d b equivalent bubble diameter D pipe diameter f M turbulent kinetic energy ratio F B buoyancy force F D interfacial drag force F L interfacial lift force F V virtual mass force F W interfacial wall force g gravitational acceleration G L turbulent kinetic energy production k L turbulent kinetic energy of the liquid phase K relative¯uctuating-mean velocity ratio m b mass of bubble M G volumetric momentum transfer rate of the gas phase M L volumetric momentum transfer rate of the liquid phase M D L momentum transfer due to the drag force M L L momentum transfer due to the lift force M V L momentum transfer due to the virtual mass eOE ect M W L momentum transfer due to the wall force · P pressure r radial location Re L Reynolds number S k L turbulence redistribution term t time ¢t time step T t L stress tensor · U G time-averaged velocity of the gas phase · U L time-averaged velocity of the liquid phase V b volume of a bubble V G bubble velocity x axial location x bubble location ¬ G volumetric fractions for the gas phasê 1 ¡ ¬ L ¬ L volumetric fraction of the liquid phase " L turbulent energy dissipation rate · L viscosity · t B bubble-induced turbulent viscosity · t L turbulent viscosity » G density of the gas phase » L density of the liquid phase ¼ standard deviation ¼ k eOE ective Prandtl number for the turbulent kinetic energy The MS was

Hydrodynamic focusing investigation in a micro-flow cytometer

“…The macroscopic flow properties can be determined through a crucial variable, namely, the volume fraction. To describe the focusing flowfield, the present analysis deals with the full Navier-Stokes problem for resolving high shear-rate and recirculating flows (Drew and Lahey, 1982;Park et al,1998;Lahey and Drew, 2001;Kuo et al, 2001;Ishii, 1975). The governing equations are stated as follows.…”