Eulerian-Lagrangian Computations on Phase Distribution of Two-Phase Bubbly Flows

Kuo, T. C.; Pan, Chin; Chieng, Ching-Chang; Yang, An-Shik

doi:10.1002/(sici)1097-0363(19970330)24:6<579::aid-fld510>3.0.co;2-e

Cited by 17 publications

(8 citation statements)

References 14 publications

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“…This agrees with the published literature where the model constants vary between 0.01 and 1 for C k (Boisson and Malin, 1996; Kuo et a! l., 1997) and between 1 and 1.92 for C ε (Bhanu and Mazumdar, 1997; Kuo et al, 1997).…”

Section: Modeling Of Turbulencementioning

confidence: 99%

Simulation of buoyancy driven bubbly flow: Established simplifications and open questions

2004

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Section: Modeling Of Turbulencementioning

confidence: 99%

Simulation of buoyancy driven bubbly flow: Established simplifications and open questions

2004

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“…The models reproduced the general trends seen experimentally, including uniform velocity and void fraction in the core, wall peaking for upflow and a wall layer without bubbles for downflow. Subsequent investigators have solved the model equations numerically, see, for example, Lopez De Bertodano, , Kuo, Pan & Chieng (1997) and Guet, Ooms & Oliemans (2005). Extensions of the two-fluid model to handle non-uniform bubble size distributions can be found in Celik & Gel (2002) and Politano, Carrica & Converti (2003), for example.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of nearly spherical bubbles in a turbulent channel upflow

Tryggvason

2013

J. Fluid Mech.

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The dynamics of bubbles in upflow, in a vertical channel, is examined using direct numerical simulations (DNS), where both the flow and the bubbles are fully resolved. Two cases are simulated. In one case all the bubbles are of the same size and sufficiently small so they remain nearly spherical. In the second case, some of the small bubbles are coalesced into one large bubble. In both cases lift forces drive small bubbles to the wall, removing bubbles from the channel interior until the two-phase mixture is in hydrostatic equilibrium, and forming a bubble-rich wall layer. The same evolution has been seen in earlier DNS of bubbly upflows, but here the friction Reynolds number is higher (Re + = 250). In addition to showing that the overall structure persists at higher Reynolds numbers, we show that the bubbles in the wall layer form clusters. The mechanism responsible for the clustering is explained and how bubbles move into and out of the wall layer is examined. The dynamics of the bubbles in the channel core is also compared with results obtained in fully periodic domains and found to be similar. The presence of the large bubble disrupts the wall layer slightly, but does not change the overall picture much, for the parameters examined here.

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“…Simulations have demonstrated that the computed results were in excellent agreement with the measured data in terms of the void fraction and the liquid/gas velocity pro® les in both developing and fully developed regions. Detailed¯ow conditions for code validation can be found in references [16], [21] and [24]. Figure 1 illustrates the physical model of the present case.…”

Section: Resultsmentioning

confidence: 99%

“…The detailed formulations for the interfacial drag, lift and wall forces can be found in reference [16]. The last term on the right-hand side of equation (3), M etc: L , involves eOE ects of the Basset and collision forces.…”

Section: Momentum Equationmentioning

confidence: 99%

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

Kuo

Yang

Chieng

2001

Proceedings of the Institution of Mechanical Engineers, Part C:

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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

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Eulerian-Lagrangian Computations on Phase Distribution of Two-Phase Bubbly Flows

Cited by 17 publications

References 14 publications

Simulation of buoyancy driven bubbly flow: Established simplifications and open questions

Simulation of buoyancy driven bubbly flow: Established simplifications and open questions

Dynamics of nearly spherical bubbles in a turbulent channel upflow

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

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